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Chapter 3

Simulation Calculations for Wind Power Transmission Capability

Kun Ding, and Dunwen Song

Abstract

This chapter introduces the technical specifications on integrated wind turbine generators and the method for modeling wind turbine generators, carries out the transient analysis of wind power generation, and analyzes the reactive power and voltage characteristics of wind farms. Finally, software for evaluating the transmission capability of wind power is introduced.

Keywords

Evaluation software; Model; Reactive power and voltage characteristics; Stability analysis; Technical specifications; Transient analysis; Transmission capability; Wind turbine generator

3.1. Technical Specifications on Integration Operation of Wind Turbine Generators (WTGs)

3.1.1. Requirements on Voltage and Power Factor of WTG Integration

According to the general requirements on wind turbine generator (WTG) integration, the voltage deviation of variable-speed WTGs at the generator end shall be controlled within −10%～+10%. With consideration to the voltage drop in the wind farm and certain security margin, the voltage deviation of the bus on HV side in the wind farm shall be controlled within −5%～+5%. For the WTGs of rated voltage of 0.69 kV, the reference voltage at the generator end is 0.69 kV and the normal operating range is 0.621～0.759 kV.

For the doubly fed wind turbine generators and direct-driven wind turbine generators, the adjustable range of the power factor is −0.95～+0.98. The WTG in the control mode of constant power factor can only run at the constant power factor instead of automatic reactive power regulation based on the generator-end voltage. In the control mode of constant voltage, automatic reactive power regulation based on the generator-end voltage is available for the WTGs.

3.1.2. Requirements for Grid Voltage

SD 325–1989 “Power technical guideline for voltage and reactive power of the power system,” describes the following requirements on the busbar voltage at various voltage levels: For the 330 kV bus, the maximum operating voltage must not exceed +110% of system rated voltage in normal operation mode, and the minimum operating voltage should not affect stable synchronization and voltage stabilization of the power system, the normal service of the auxiliary power, as well as regulation of the next voltage level. For the bus in the grid of 220 kV and above, the permissive voltage deviation is 0～10% of system rated voltage in normal operation mode and −5%～+10% of system rated voltage in emergency operation mode. For the 10.5, 35, or 110 kV bus in the substation (S/S), the permissive voltage deviation is −3%～+7% of system rated voltage in normal operation mode.

Considering the actual operating requirements of the Northwest Grid, the permissive voltage deviation of the wind farm in normal operation mode shall be as follows:

750 kV bus voltage: 750～800 kV;

330 kV bus voltage: 330～363 kV;

110 kV bus voltage: 106.7～117.7 kV;

35 kV bus voltage of the wind farm: 33.95～37.45 kV;

10.5 kV bus voltage of the wind farm: 10.185～11.235 kV.

3.1.3. Requirements for System Frequency

In accordance with GB/T 15945–2008 “Power quality: Permissive deviation of power system frequency,” the permissive normal frequency deviation of the power system is ±0.2 Hz.

3.1.4. Requirements for Relay Protection and Security Automation Devices

It says in DL 755–2001 “Guideline for security and stability of power system” that for the lines of 220 kV and above, the fault clearance time from fault occurrence to fault cleared by the circuit breaker shall be no larger than 0.1 s and 0.1～0.15 s, respectively, at the sides close to and far away from the fault point.

3.1.5. Low Voltage Ride-Through (LVRT) Capability

The low voltage ride-through (LVRT) capability refers to WTG or wind farm to maintain integrated with power grid in case of voltage reduction. In accordance with “Technical code on integration of SGCC's wind farms (Revised)” (State Grid Development, 2009, #327), it shall be able to continue running for 0.625 s in case the voltage of the WTG and the wind farm reduces to 20% of rated voltage. See Figure 3.1.

Figure 3.1 LVRT capability of wind turbine generators (WTGs) and wind farms.

3.2. Mathematical Model of WTGs and Wind Farms

The WTGs in Jiuquan Wind Power Base consist of three types commonly used at home and abroad. The first type is those at constant speed with asynchronous generators (FSIGs), the second is those at variable speed and constant frequency with doubly fed WTGs (DFIGs), and the third is those at variable speed and constant frequency with permanent magnet direct-driven wind turbine generators (D-PMSGs). The FSIGs are all located in the wind farms built earlier and integrated to the grid at 110 kV, and those wind farms integrated to the grid at 330 kV are all installed with D-PMSGs or DFIGs. The FSIGs generate the active power while absorbing the reactive power and thus have no voltage regulation capability; the voltage is regulated via reactive power compensators (mainly the capacitor installed at the generator end), which will make the WTG run approximately to the unit power factor. The DFIGs and D-PMSGs can generate reactive power via control of the frequency converter, and they can regulate the reactive output in a certain range as demanded by the system. For example, FD77A DFIGs can support up to ±0.95 power factor, i.e., the FD77A DFIGs of 1.5 MW-rated capacity can generate inductive and capacitive power up to 493 Kvar.

3.2.1. Modeling of FSIGs

See Figure 3.2 for the block diagram of FSIG model. The mathematical model consists of four basic links: wind turbine model, asynchronous generator model, pitch control system model, and wind velocity model.

The wind turbine model consists of those mechanical devices with speed rise, integration, and drive functions such as the WTG blades, hub, gearbox, drive shaft, and coupling, etc. The pitch control system model is used for variable-pitch WTGs. For the WTG with fixed pitch, the blade shall be designed according to the stall effect, and it can automatically regulate the power output according to the wind velocity; in addition it is not provided with a pitch control system and the other parts of the model are similar to the variable-pitch WTGs.

3.2.1.1. Wind turbines

For the blades of the wind turbine, when the dynamic characteristics of the blades are not taken into account, the relations between the wind velocity and the output torque are as follows:

$M_{W} = {\begin{matrix} 0 & v_{w} < v_{in} \\ \frac{1}{2} C_{p} ρ A \frac{v_{w}^{3}}{Ω} \times \frac{Ω_{N}}{B_{MVA}} \times 10^{- 6} & v_{in} \leq v_{w} < v_{out} \\ 0 & v_{out} \leq v_{w} \end{matrix}$ $M_{W} = {\begin{matrix} 0 & v_{w} < v_{in} \\ \frac{1}{2} C_{p} ρ A \frac{v_{w}^{3}}{Ω} \times \frac{Ω_{N}}{B_{MVA}} \times 10^{- 6} & v_{in} \leq v_{w} < v_{out} \\ 0 & v_{out} \leq v_{w} \end{matrix}$

(3.1)

where, A = πR². Where, M_w is the per-unit value of the blade output torque (p.u.); ρ is the air density, kg/m³; Ω is the mechanical speed of the wind turbine, rad/s; A is the swept area of the wind turbine blade; R is the radius of the wind turbine, m; v_w is the wind velocity, m/s; v_in, v_out is the cut-in/cut-out wind velocity of the wind turbine, respectively, m/s; Ω_N is the rated mechanical angle speed of the wind turbine, rad/s; B_MVA is the system reference capacity, MVA; C_p is the wind power utilization coefficient of the wind turbine, i.e., the ratio of the wind power absorbed by the wind turbine to all the wind power passing the rotating surface of the blades at unit time.

According to the Betz law, the maximum of C_p is 0.593, and it has relations to the tip speed ratio λ (i.e., the ratio of the linear speed at the blade top of the wind turbine to the wind velocity, λ = ΩR/v_w) and the pitch angle β of the wind turbine, and thus it is expressed as the nonlinear function of λ and β. See Figure 3.3 for C_p characteristics of the typical WTGs.

Generally, the C_p characteristics are given by the wind turbine manufacturer based on tests, and they can be simulated by the empirical formula in case the actual C_p data are unavailable.

For WTGs with constant pitch, C_p can be expressed by the following formula:

$C_{p} = \frac{16}{17} \frac{λ}{λ + \frac{1.32 + {[(λ - 8) / 20]}^{2}}{B}} - 0.57 \frac{λ^{2}}{\frac{L}{D} (λ + \frac{1}{2 B})}$ $C_{p} = \frac{16}{17} \frac{λ}{λ + \frac{1.32 + {[(λ - 8) / 20]}^{2}}{B}} - 0.57 \frac{λ^{2}}{\frac{L}{D} (λ + \frac{1}{2 B})}$

(3.2)

where, B is the quantity of blades, and L/D is the lift ratio.

Eqn (3.2) has higher accuracy with error no larger than 0.005 when the quantity of blades is 1, 2 or 3, 4 ≤ λ ≤ 20 and L/D ≥ 25.

Figure 3.3 C_p characteristics of typical WTGs.

For the variable-pitch WTGs, the C_p characteristics can be approximately expressed as Eqn (3.3):

$C_{p} = 0.5 (\frac{R C_{f}}{λ} - 0.022 β - 2) e^{- 0.255 \frac{R C_{f}}{λ}}$ $C_{p} = 0.5 (\frac{R C_{f}}{λ} - 0.022 β - 2) e^{- 0.255 \frac{R C_{f}}{λ}}$

(3.3)

where, C_f is the design constant of blades, generally 1～3.

For the mechanical transmission mechanism of the wind turbine, it is unnecessary to build the detailed mathematical model in electromechanically transient simulation of power system and the losses of the drive part can be ignored. Since the blades and the hub are not rigid, it has some time lag effect when the wind torque is transmitted from the blades to the hub, similar to the middle reheat process of the steam turbine.

Here it is simplified, i.e., a 1-order inertial link is used to express the time-lag of the wind power transmitted from the blades to the hub, and the flexibility of the drive shaft and the losses of the coupling are ignored. The model of the simplified drive part is as follows:

$\frac{ⅆ M_{t}}{ⅆ t} = \frac{1}{T_{h}} (M_{w} - M_{t})$ $\frac{ⅆ M_{t}}{ⅆ t} = \frac{1}{T_{h}} (M_{w} - M_{t})$

(3.4)

$M_{m} = M_{t}$ $M_{m} = M_{t}$

(3.5)

where, M_t is the per-unit value of the hub torque (p.u.); M_w is the per-unit value of the blade torque (p.u.); T_h is the time constant of time lag effect, s; M_m is the per-unit value of the mechanical torque input to the generator side for power (p.u.).

3.2.1.2. Asynchronous generators

Below is the voltage equation of the asynchronous generator stator where the stator electromagnetic transient process is ignored:

${\dot{U}}_{s} = - (r_{s} + j x^{'}) {\dot{I}}_{s} + {\dot{E}}^{'}$ ${\dot{U}}_{s} = - (r_{s} + j x^{'}) {\dot{I}}_{s} + {\dot{E}}^{'}$

(3.6)

$x^{'} = x_{s} + \frac{x_{r} x_{m}}{r_{r} + x_{m}}$ $x^{'} = x_{s} + \frac{x_{r} x_{m}}{r_{r} + x_{m}}$

where,

{\dot{U}}_{s}

${\dot{U}}_{s}$

{\dot{I}}_{s}

${\dot{I}}_{s}$

, r_s is the per-unit value of stator voltage, current, and resistance (p.u.), respectively; x′ is the per-unit value of the transient reactance (p.u.); x_s, x_r, x_m is the per-unit value of the stator leakage reactance, rotor leakage reactance, and excitation reactance (p.u.), respectively.

See Eqn (3.7) for the 3-order mathematical model of the asynchronous generator where the electromagnetic transient process is ignored.

$\begin{matrix} \frac{ⅆ s}{ⅆ t} = \frac{1}{T_{j}} (M_{e} - M_{m}) \\ \frac{ⅆ {E^{'}}_{x}}{ⅆ t} = \frac{1}{{T^{'}}_{d 0}} [- {E^{'}}_{x} + j (x - x^{'}) I_{sy} + 2 π f_{0} {T^{'}}_{d 0} s {E^{'}}_{y}] \\ \frac{ⅆ {E^{'}}_{y}}{ⅆ t} = \frac{1}{{T^{'}}_{d 0}} [- {E^{'}}_{y} - j (x - x^{'}) I_{sx} - 2 π f_{0} {T^{'}}_{d 0} s {E^{'}}_{x}] \end{matrix}}$ $\begin{matrix} \frac{ⅆ s}{ⅆ t} = \frac{1}{T_{j}} (M_{e} - M_{m}) \\ \frac{ⅆ {E^{'}}_{x}}{ⅆ t} = \frac{1}{{T^{'}}_{d 0}} [- {E^{'}}_{x} + j (x - x^{'}) I_{sy} + 2 π f_{0} {T^{'}}_{d 0} s {E^{'}}_{y}] \\ \frac{ⅆ {E^{'}}_{y}}{ⅆ t} = \frac{1}{{T^{'}}_{d 0}} [- {E^{'}}_{y} - j (x - x^{'}) I_{sx} - 2 π f_{0} {T^{'}}_{d 0} s {E^{'}}_{x}] \end{matrix}}$

(3.7)

where,

{T^{'}}_{d 0} = \frac{x_{r} + x_{m}}{2 π f_{0} r_{r}}, x = x_{s} + x_{m}

${T^{'}}_{d 0} = \frac{x_{r} + x_{m}}{2 π f_{0} r_{r}}, x = x_{s} + x_{m}$

where, M_e is the electromagnetic torque of the generator; T_j is the inertia time constant; the slip differences will still use the definition of the motor convention, i.e.,

s = \frac{ω_{0} - ω_{r}}{ω_{0}}

$s = \frac{ω_{0} - ω_{r}}{ω_{0}}$

, which shall be negative when the generator is running;

{T^{'}}_{d 0}

${T^{'}}_{d 0}$

is the time constant of the rotor winding during the stator winding in open circuit, s;

{E^{'}}_{x}, {E^{'}}_{y}

${E^{'}}_{x}, {E^{'}}_{y}$

are the real and the virtual component of the transient electromotive force, respectively

{\dot{E}}^{'}

${\dot{E}}^{'}$

; I_sx, I_sy are the real and the virtual component of stator current, respectively

{\dot{I}}_{s}

${\dot{I}}_{s}$

; x_s is the stator winding leakage reactance; x_m is excitation reactance.

The per-unit value of the generator electromagnetic torque M_e is as follows:

$M_{e} = - Re [{\dot{E}}^{'} \hat{{\dot{I}}_{s}}] / ω$ $M_{e} = - Re [{\dot{E}}^{'} \hat{{\dot{I}}_{s}}] / ω$

(3.8)

where, Re is the real component (•); and ω is the electrical angular speed (p.u.).

3.2.1.3. Pitch control systems

To minimize the fluctuation of the wind power output, the variable-pitch WTG is also provided with pitch angle control system. Generally, the pitch angle control system shall measure the wind velocity and compare the output power to change the pitch angle of the blade and realize regulation and control of the WTG output. See Figure 3.4 for the typical pitch control system of the variable-pitch WTG.

The mathematical model of the control system can be expressed as:

$\frac{ⅆ β}{ⅆ t} = \frac{1}{T_{B}} (β_{c} - β)$ $\frac{ⅆ β}{ⅆ t} = \frac{1}{T_{B}} (β_{c} - β)$

(3.9)

$\frac{ⅆ X}{ⅆ t} = k_{pi} (P_{s} - P_{ref})$ $\frac{ⅆ X}{ⅆ t} = k_{pi} (P_{s} - P_{ref})$

(3.10)

$β_{c} = k_{ω} V_{w} + k_{pp} (P_{s} - P_{ref}) + X$ $β_{c} = k_{ω} V_{w} + k_{pp} (P_{s} - P_{ref}) + X$

(3.11)

where, X is the intermediate status variable introduced to the integration link; T_B is the time constant of the control servo mechanism, s; k_ω, k_pi, k_pp is the parameter of the controller; P_s, P_ref refers to the reference active power output by the WTG and the per-unit value of the given reference active power (p.u.), respectively; β is the pitch angle; β_c is the intermediate variable controlled by the pitch angle.

3.2.2. Modeling of DFIG

See Figure 3.5 for the block diagram of DFIG dynamic model, and the mathematical model consists of the following five basic links: wind turbine, pitch control system, generator and frequency converter, excitation control system, and velocity.

Figure 3.4 Typical pitch control system of variable-pitch WTGs.

Figure 3.5 Block diagram of DFIG dynamic model.

3.2.2.1. Wind turbines

The wind turbine blade model of the DFIG is the same as that of the constant-speed WTG except that the expression is slightly different. In addition, the DFIG model also adopts a different simulation method for wind power conversion efficiency coefficient.

$C_{p} (β, λ) = \sum_{i = 0}^{4} \sum_{j = 0}^{4} α_{i, j} β^{i} λ^{j}$ $C_{p} (β, λ) = \sum_{i = 0}^{4} \sum_{j = 0}^{4} α_{i, j} β^{i} λ^{j}$

(3.12)

where, β is the pitch angle; λ is the gear ratio at the blade tip; α_i,j is the fitting parameter.

See Table 3.1 for α_i,j values.

3.2.2.2. Generators and converters

The generator and converter model of the DFIG is the interface between the WGTS and the grid; see Figure 3.6 for the model block diagram. Since the frequency converter control system has rapid response speed, the system dynamic status is simplified in the model. In addition, different from the traditional generator model, the model does not include the mechanical status of the generator rotor.

Suppose that in the converter control, the action time corresponding to the transient e.m.f. E″_q and stator current active component I_p on q axis is T_EQ and T_IP (generally 20 ms), respectively, the transient e.m.f. E″_q and stator current active component I_p on q axis is:

$\frac{ⅆ {E^{″}}_{q}}{ⅆ t} = \frac{1}{T_{EQ}} ({E^{″}}_{qcmd} - {E^{″}}_{q})$ $\frac{ⅆ {E^{″}}_{q}}{ⅆ t} = \frac{1}{T_{EQ}} ({E^{″}}_{qcmd} - {E^{″}}_{q})$

(3.13)

$\frac{ⅆ I_{p}}{ⅆ t} = \frac{1}{T_{IP}} (I_{pcmd} - I_{p})$ $\frac{ⅆ I_{p}}{ⅆ t} = \frac{1}{T_{IP}} (I_{pcmd} - I_{p})$

(3.14)

where,

{E^{″}}_{qcmd}

${E^{″}}_{qcmd}$

and I_pcmd are the output of the excitation control system.

Table 3.1

α_i,j Values for the DFIG Model

i	j	α_i,j	i	j	α_i,j	i	j	α_i,j	i	j	α_i,j	i	j	α_i,j
0	0	−4.1909 × 10⁻¹	1	0	−6.7606 × 10⁻²	2	0	1.5727 × 10⁻²	3	0	−8.6018 × 10⁻⁴	4	0	1.4787 × 10⁻⁵
	1	2.1808 × 10⁻¹		1	6.0405 × 10⁻²		1	−1.0996 × 10⁻²		1	5.7051 × 10⁻⁴		1	−9.4839 × 10⁻⁶
	2	−1.2406 × 10⁻²		2	−1.3934 × 10⁻²		2	2.1495 × 10⁻³		2	−1.0479 × 10⁻⁴		2	1.6167 × 10⁻⁶
	3	−1.3365 × 10⁻⁴		3	1.0683 × 10⁻³		3	−1.4855 × 10⁻⁴		3	5.9924 × 10⁻⁶		3	−7.1535 × 10⁻⁸
	4	1.1524 × 10⁻⁵		4	−2.3895 × 10⁻⁵		4	2.7937 × 10⁻⁶		4	−8.9194 × 10⁻⁸		4	4.9686 × 10⁻¹⁰

Figure 3.6 Block diagram of DFIG generator and frequency converter model.

The generator model shall read the generator end voltage from the system and work out the current injected to point of common coupling (PCC) Isorc by the following formula based on the transient e.m.f.

{E^{″}}_{q}

${E^{″}}_{q}$

and stator current active component I_p:

$\begin{matrix} I_{sorc, re} = \frac{P V_{term . re} + Q V_{term . im}}{V_{term . re}^{2} + V_{term . im}^{2}} \\ I_{sorc, im} = \frac{Q V_{term . re} - P V_{term . im}}{V_{term . re}^{2} + V_{term . im}^{2}} \end{matrix}}$ $\begin{matrix} I_{sorc, re} = \frac{P V_{term . re} + Q V_{term . im}}{V_{term . re}^{2} + V_{term . im}^{2}} \\ I_{sorc, im} = \frac{Q V_{term . re} - P V_{term . im}}{V_{term . re}^{2} + V_{term . im}^{2}} \end{matrix}}$

(3.15)

where,

Q = \frac{V_{term}}{X^{″}} {E^{″}}_{q}, P = V_{term} I_{p}

$Q = \frac{V_{term}}{X^{″}} {E^{″}}_{q}, P = V_{term} I_{p}$

where, X″ is the equivalent reactance.

3.2.2.3. Excitation control systems

See Figure 3.7 for the overall block diagram of DFIG excitation control system. The input signals are the generator active power P_gen, reactive power Q_gen, the voltage at the monitoring node V_reg and the active power demand output by the pitch control system P_ord; and the output are the transient e.m.f.

{E^{″}}_{q}

${E^{″}}_{q}$

and stator current active component control commands

{E^{″}}_{qcmd}

${E^{″}}_{qcmd}$

and I_pcmd, which will be input to the generator model.

The excitation control system model consists of two parts. The first part is the wind power management system (WPMS); see Figure 3.8. The part is a simple simulation to the reactive power detection and control module of the whole wind farm where the input signal is the voltage of a certain node (subject to line voltage reduction compensation), T_r is the time constant in the measurement link, and the difference with the reference voltage shall be subject to the PI link and one delay link T_V.

The second part is the electrical control part, which is a simple simulation to the excitation/converter system; see Figure 3.9. The reactive power Q_gen and the end voltage V_term shall be monitored, and the WTG voltage command

{E^{″}}_{qcmd}

${E^{″}}_{qcmd}$

shall be calculated. When V_ltflg = 0, the generator reactive power shall be controlled only by WPMS and the open-loop control system; and when V_ltflg = 1, the closed-loop control is simultaneously available. The limiting link of the output control signal reflects the limits of the hardware. The active power current control command I_pcmd can be obtained by P_ord output from the wind turbine model divided by the generator-end voltage V_term. I_pcmd is limited to the short-time active current output capacity of the converter. See Table 3.2 for the recommended parameters of the excitation model.

Figure 3.7 Overall block diagram of DFIG excitation control system.

Figure 3.8 Block diagram of WPMS simulation system.

Figure 3.9 Block diagram of WTG electrical control system.

Table 3.2

Excitation Parameters of the DFIG Model

Name of Variable	Recommended Parameter	Name of Variable	Recommended Parameter
T_r	0.05	Q_min	−0.436(1.5 MW)/–0.39(3.6 MW)
T_V	0.15	XI_Qmax	0.30
K_pv	20	XI_Qmin	−0.35
K_iv	2.0	V_max	1.10
K_Qi	0.05	V_min	0.90
K_Vi	30.0	I_pmax	1.1
Q_max	0.312(1.5 MW)/0.52(3.6 MW)

3.2.2.4. Pitch control system models

See Figure 3.10 for the block diagram of the mathematical model of the DFIG pitch control system. When the wind power available exceeds the ratings of the WTG, the pitch control system will regulate the pitch angle to control the wind power at the ratings; and when the wind power available is less than the ratings of the WTG, the pitch control system will regulate the pitch angle to the minimum value and keep the maximum mechanical power.

The input signals of the model are the wind velocity and the electromagnetic power output from the generator P_elec, and the output signals are the active power demand P_ord and the shutdown signal. See Table 3.3 for the recommended values of the control parameters.

3.2.3. Modeling of D-PMSG

Since the common FSIG and the DFIG are provided with gearboxes, and the DFIG is also provided with carbon brushes and slip rings, the system suffers from high cost, poor reliability, a large amount of maintenance, and serious noise pollution. When it runs at low load, the efficiency is low, and especially as the unit capacity increases, the problem becomes more serious. As a result, the direct-driven and brushless design has become the focus, and the D-PMSG based on variable-speed operation, variable-pitch regulation, low speed, high efficiency, and high power factor has become the hot point of research and development. The generator adopts permanent-magnet excitation, which eliminates the excitation losses and improves the efficiency, realizing brushless generators. Besides, during operation, it does not need to absorb reactive power to build the field, improving the power factor of the grid. The wind turbine directly drives the generator where the gearbox is eliminated, improving the WTG efficiency and reliability and reducing the equipment maintenance and noise pollution.

Figure 3.10 Block diagram of the mathematical model of the DFIG pitch control system.

Table 3.3

Pitch Angle Control Parameters of DFIG Model

Name of Variable	Recommended Parameter	Name of Variable	Recommended Parameter
K_pp	150	P_min(p.u.)	0.1
K_ip	25	dP/dt_max(p.u./s)	0.45
Tp(s)	0.30	dP/dt_max(p.u./s)	−0.45
θ_max(°)	27	k_pc	3.0
θ_min(°)	0.0	K_ic	30.0
d/dt_max(°/s)	10.0	k_ptrq	3.0
d/dt_min(°/s)	−10.0	k_itrq	0.6
P_max(p.u.)	1.12	T_pc	0.05

For the D-PMSG, the rotor and the generator shafts are fixed on the same shaft, and thus the generator runs at low speed, 10～25 r/min for the WTG at MW level. It is inappropriate for the generator to run at low speed because it must increase the torque corresponding to the desired power. As a result, the standard generator cannot be used and special design is necessary. The direct-driven generator is heavier than the traditional one, and the efficiency is lower due to higher rated torque. To improve the efficiency and reduce the weight, the direct-driven generator is generally provided with larger rotor diameter and several poles so that it can obtain the appropriate frequency at low speed. The size and loss of the generator are greatly dependent on the desired torque. If the asynchronous motor has many poles, the excitation reactance will become small. This means that the multipole asynchronous generator needs larger excitation current than the traditional asynchronous generator. Accordingly, the multipole synchronous generator is generally used.

The multipole synchronous generator can adopt the electrical excitation or the permanent magnet, and almost all the large generators adopt the electrical excitation. The permanent magnet is more competitive for the low-speed gearless WTG than the traditional synchronous generators because it has more pairs of poles. Since the permanent magnet does not need excitation winding, it reduces the copper losses caused by the excitation current of the rotor and the slip ring. The disadvantages of the permanent magnet include that it cannot control excitation and the cost is high.

See Figure 3.11 for the typical structural diagram of the D-PMSG, which includes the mechanical part and the electrical part: (1) The mechanical part consists of the aerodynamics part, the gearbox-free drive link, and the pitch angle control part, etc.; (2) The electrical part consists of multipole permanent-magnet synchronous generator, full-power variable-frequency converter and its control system, the pad-mounted transformer, etc.

The synchronous generator is integrated with the grid via the frequency converter, which is used to control the generator speed and the active power exchanged with the grid. The frequency converter includes two back-to-back voltage-source converters, which are integrated via the DC capacitor, and the DC capacitor shall serve as the energy storage element. The voltage-source converters allow the generator to control its own end voltage and frequency according to the ideal optimal rotating speed of the wind turbine, which is not related to the voltage and frequency of the grid.

The rotor of the wind turbine is directly coupled to the generator where no gearbox is used. The permanent magnet is installed on the generator rotor shaft, and the stator winding is directly integrated to the frequency converter. Since the frequency converter enables the generator to be separated from the grid, the electrical frequency of the generator can vary with the change of the wind velocity while the network frequency can remain constant. The capacity of the voltage-source converters is equal to the sum of the generator-rated capacity and the losses.

Figure 3.11 Typical structure diagram of D-PMSG.

The whole system consists of the controller of the wind turbine itself (i.e., the pitch angle controller) and the frequency converter controller, both of which adopt the generator speed as the control signal. The frequency converter controller can control the output active power based on the speed and the power control characteristics and then further control the generator speed. The pitch angle controller also can be used to control the rotor speed, which, however, is only used in case of high wind velocity to prevent the frequency converter and generator from overloading whereas the pitch angle can be adjusted to reduce the power.

All the power generated by the generator will be transmitted to the system via the frequency converter, and the frequency converter can convert the variable frequency to the fixed frequency of the grid. The inverter on the grid side can control the reactive power and the system voltage exchanged with the grid. As a result, it can take full control of the active/reactive power like the double-fed generator.

3.2.3.1. Permanent-magnet synchronous generators

See Figure 3.12 for the single-phase equivalent circuit of synchronous generators.

In power system analysis, the synchronous generator model is based on the assumption that the rotor flux is sinusoidal. In this assumption, the flux can be expressed in vector. For the permanent-magnet synchronous generator, the field generated by the permanent magnet can induce a voltage, which can be expressed as follows:

$| \dot{E} | = ω_{e} ψ_{PM} = 2 π f_{e} ψ_{PM}$ $| \dot{E} | = ω_{e} ψ_{PM} = 2 π f_{e} ψ_{PM}$

(3.16)

where, ω_e is the electrical speed; ψ_PM is the amplitude of the flux induced in the rotor; and f_e is the electrical frequency.

The current in the stator winding will result in losses and voltage drop, which can be expressed as R_s. In addition, the electronic current will also generate its own field, which will be superposed to the field generated by the permanent magnet. As a result, the terminal voltage of the permanent-magnet generator U_s has relations to the voltage induced by the whole field. The whole field will increase or decrease with change of the stator current, and the effect will be expressed by the synchronous reactance X_s in the model. Because R_s is generally far less than X_s, it is generally ignored. The stator reactance of the multipole synchronous generator is generally high.

Figure 3.12 Single-phase equivalent circuit of synchronous generators.

With the rotor d-axis, q-axis as the reference coordinates, the voltage formula of the permanent-magnet synchronous generator can be expressed as:

$\begin{matrix} u_{sd} = R_{s} i_{sd} - ω_{e} ψ_{sq} + {\dot{ψ}}_{sd} \\ u_{sq} = R_{s} i_{sq} + ω_{e} ψ_{sd} + {\dot{ψ}}_{sq} \end{matrix}}$ $\begin{matrix} u_{sd} = R_{s} i_{sd} - ω_{e} ψ_{sq} + {\dot{ψ}}_{sd} \\ u_{sq} = R_{s} i_{sq} + ω_{e} ψ_{sd} + {\dot{ψ}}_{sq} \end{matrix}}$

(3.17)

$\begin{matrix} ψ_{sd} = L_{d} i_{sd} + ψ_{PM} \\ ψ_{sq} = L_{q} i_{sq} \end{matrix}}$ $\begin{matrix} ψ_{sd} = L_{d} i_{sd} + ψ_{PM} \\ ψ_{sq} = L_{q} i_{sq} \end{matrix}}$

(3.18)

where, u_sd and u_sq are the stator voltage, i_sd and i_sq are the stator current; L_d and L_q are the stator induction.

3.2.3.2. Frequency converters

The frequency converter can independently control the active and reactive power, including control of the rectifier on the generator side and the inverter on the grid side.

1. Control of the rectifier on the generator side. There are many control schemes for the rectifier on the generator side. Figure 3.13 shows a control system structure that can be used to control the DC-side voltage and the generator electronic voltage.

2. Control of the inverter on the grid side. The main function of the inverter on the grid side is to control the active and reactive power exchanged with the grid; see Figure 3.14 for the general control scheme.

The reference active power is based on the power-speed characteristic curve to ensure that the WTG can automatically run at the operating point with maximum efficiency. The variable-speed WTG can run in the constant power factor or the constant voltage modes. When the grid voltage deviates from the rated voltage and the grid needs reactive support, the voltage control can be used to set the reference reactive power.

Figure 3.13 Control system structure of the rectifier on the generator side.

Figure 3.14 Control system structure of the inverter on the grid side.

3.2.4. Model of Wind Farms

In Jiuquan Wind Power Base, each wind farm is composed of several WTGs. For example, a typical 200 MW wind farm is installed with 134 × 1.5 MW variable-speed WTGs. The special research of China Electric Power Research Institute in 2000, the special report for national “9th Five-year Plan” key technological plan “Research on planning methods and operation technologies of wind power integration system,” shows, “it is technically feasible to replace the wind farm of equivalent capacity by single WTG of large capacity.” With extensive research on wind power and massive building of wind farms and wind power bases, the simplified wind farm modeling methods can no longer meet the demand on system analysis, and it is necessary to build more practical wind farm models, i.e., the wind farm model including the detailed internal wiring of the wind farm. See Figure 3.15.

For a 200 MW wind farm composed of 134 × WTGs, the wind turbines in the wind farm are divided into 12 groups, each integrated to 11～12 × WTGs. Each generator is integrated to the 35 kV overhead line (OHL) in the form of single set to the pad-mounted transformer 0.69/35 kV, and 1 c/c (circuit) overhead line collects the 11～12 × WTGs of each group, and then integrates to the 35 kV bus of the step-up substation of the wind farm via 1 × 35 kV cable. The same modeling method shall be used for the wind farms of other scales and integrated at 110 kV.

3.2.4.1. Combined method of the single WTG and the pad-mounted transformer

The unit wiring method of one turbine and one transformer shall be used as the main electrical wiring of the WTG and the pad-mounted transformer. The output voltage of the WTG is 0.69 kV, which is boosted by the pad-mounted transformer and then transmitted to the 35 kV OHL. The 1 kV LV cable shall be used to connect the LV side of the pad-mounted transformer with the WTG, and a total of 134 pad-mounted transformers shall be used. For the pad-mounted transformers, the capacity is 1600 kVA, and the voltage is 0.69/35 kV. During integration analysis on wind farms, the key model for single WTG and pad-mounted transformer is the 0.69/35 kV pad-mounted transformer model where the 1 kV cable and the outgoing line from the transformer to the 35 kV OHL are ignored.

Figure 3.15 Detailed model diagram of wind farms.

3.2.4.2. Wiring method of HV side of the pad-mounted transformer

The 35 kV OHL is used to connect the HV side of the 11～12 × pad-mounted transformers of one group. In this part, the focus is the 35 kV OHL model on the HV side of the 11～12 × pad-mounted transformers of one group.

3.2.4.3. Wiring method of one group of WTGs with the step-up substation at PCC

Each group of WTGs shall be integrated to the 35 kV bus of the step-up substation of the wind farm via 1 × 35 kV cable, and there is a total of 12 × 35 kV cables in a 200 MW wind farm. It has charge capacitor of large capacity, and the impact of the reactive power injected by the charge capacitor on the integration analysis cannot be ignored; in the electrical wiring model of the wind farm, it shall focus on the 35 kV cable.

3.3. Security and Stability Analysis on Wind Power Integration of Simple Systems

3.3.1. Introduction to Simple Systems

Figure 3.16 shows the wiring diagram of a simple system with wind power integration. The installed capacity of the wind farm at the sending end (TE) is 700 MW, the installed capacity of the hydropower plant is 400 MW, the WTGs are integrated to the main grid via the OHL, the cable and two step-up transformers: 0.69/35 kV and 35/363 kV, and the hydropower plant is integrated to the main grid via the step-up transformer 10/363 kV, and the wind farm and the hydropower plant transmit the power via the 45-km line to the sending-end substation, and then via the 300-km line to the receiving end (RE) system. The load level of the TE system is 100 MW ＋ j30 Mvar, and the load level of the RE system is 900 MW ＋ j300 Mvar, and the installed capacity of the thermal units at RE is 1000 MW. See Table 3.4 for the information of the WTGs in the wind farm.

Figure 3.16 Simple system wiring sketch of wind farm integrations.

Table 3.4

Information of WTGs in Wind Farms

Wind Farm	Information of WTGs
1	200 MW DFIGs
2	200 MW DFIGs
3	300 MW D-PMSGs
Total of installed capacity	700 MW WTGs

3.3.2. Wind Power Integration Capability Analysis by Multiple and Detailed Models

The detailed model of wind farms is the method mostly close to the actual situation for integration analysis, i.e., the detailed models, including the static/dynamic models of each WTG and the internal electrical wiring of the wind farm, shall be built. For the thousands of WTGs in Jiuquan Wind Power Base, the detailed models shall be built with consideration of the associated electrical wiring, during which, the workload for modeling and program maintenance will be huge, and the reliability of power flow and stability calculation algorithm also will be a problem. The equivalent model of the wind farm can be used to substitute the detailed model, and the common “multiple” equivalent model is an alternative.

Table 3.5 shows the limit output of WTGs in the detailed wind farm model and the multiple wind farm equivalent model where the WTGs are in constant control mode and the limit fault is “TE-RE system” double-circuit 3-phase permanent (“3 permanent” for short) N-1 fault.

The calculation results of Table 3.5 show that the limit output of WTGs corresponding to the detailed wind farm model is 651 MW, which is larger than that corresponding to the multiple wind farm equivalent model (620 MW). Many example checks show that the limit output of WTGs calculated by the detailed wind farm model is larger than that by the multiple wind farm equivalent model. Accordingly, the conclusion is to some extent universal.

See Figure 3.17 for the power angle swing curve of hydropower plant versus thermal plant by means of the multiple wind farm equivalent model and the detailed wind farm model. The calculation results of Figure 3.17 show that the power angle curve of the detailed wind farm model compared with that of the multiple wind farm equivalent model is characterized by small swing amplitude and fast damping, which indicates in the identical calculation boundary conditions that the system based on the detailed wind farm model is more stable and the wind power output limits are larger. See Figure 3.18 for the voltage at PCC and the reactive power output of the wind farm when the WTGs are in the constant voltage control mode. Figure 3.18 shows that the results based on the detailed wind farm model compared with those based on the multiple wind farm equivalent model have characteristics such as small swing amplitude of the voltage at PCC and the reactive power output, which can rapidly become smooth, offering stronger support to system stability.

Set the control mode of the WTGs as constant power factor 1, and see Tables 3.6 and 3.7 for the results of simulation calculation. Table 3.6 shows that the limit output of WTGs based on the detailed wind farm model is larger than that based on the multiple wind farm equivalent model.

Table 3.5

Transient Stable Limits of Detailed and Multiple Wind Farm Models in Constant Control Mode

Various Wind Farm Models	Hydropower Output: Fixed at 350 MW; Thermal Power as the Balance Node; Wind Power Output: Continuously Rise
Limit output of WTGs in the detailed wind farm model (MW)	651
Limit output of WTGs in the multiple wind farm equivalent model (MW)	620

Figure 3.17 Power angle swing curve of hydropower plant versus thermal plant by means of the multiple wind farm equivalent model and the detailed wind farm model.

Figure 3.18 Voltage at PCC and the reactive output of the wind farm when the WTGs are in the constant voltage control mode. (a) Voltage at PCC of the wind farm; (b) Reactive output of the wind farm LBD—code of the wind farm.

The following primary conclusions can be drawn on the basis of the above large amount of calculations and analysis in various boundary conditions: (1) The calculation results by the multiple wind farm equivalent model show no big difference from that by the detailed wind farm model; (2) The limit output of WTGs by the multiple wind farm equivalent model is slightly smaller than that by the detailed wind farm model. Accordingly, the multiple wind farm equivalent model is more conservative for stability calculation, and it is reasonable that the conclusions based on the multiple wind farm equivalent model can play a leading role in wind farm operation and production.

Table 3.6

Transient Stable Limits of Detailed and Multiple Wind Farm Models in the Constant Power Factor Control Mode

Various Wind Farm Models	Hydropower Output: Fixed at 350 MW; Thermal Power as the Balance Node; Wind Power Output: Continuously Rise
Limit output of WTGs in the detailed wind farm model (MW)	478
Limit output of WTGs in the multiple wind farm equivalent model (MW)	462

Table 3.7

Simulation Results of WTGs Disintegrated from the Grid and Shut Down due to Insufficient LVRT Capability

No.	Simulation Results
1	7.0 cycle, generator “1Z101 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z101 0.7” power 0.12 MW (1 set)
2	7.0 cycle, generator “1Z102 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z102 0.7” power 0.12 MW (1 set)
3	7.0 cycle, generator “1Z103 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z103 0.7” power 0.12 MW (1 set)
4	7.0 cycle, generator “1Z104 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z104 0.7” power 0.12 MW (1 set)
……	……
Total output of WTGs disintegrated (MW)	27.72

3.4. Security and Stability Analysis on Integration of Jiuquan Wind Power Base, Gansu, 2010

3.4.1. Transmission Plan

Based on uncertain grid structures and transmission plans of the Northwest Grid, the security and stability analysis has been carried out for several wind power transmission plans, e.g., the various plans for Xinjiang integrated to the Northwest, the Hexi 750 kV channel provided with serial compensating capacitors or controllable HV reactor, and so on.

3.4.1.1. Serial compensating capacitor plan

The Hexi 750 kV channel has low transmission capacity, and the serial compensating capacitors can be installed to improve the wind power transmission capacity. Based on the results of special studies and the outgoing scale of Jiuquan Wind Power Base, the serial compensating capacitors shall be provided as follows: Dunhuang–Jiuquan: 30%, Jiuquan–Hexi: 50%, Hexi–Wusheng: 40%, where in the section of Jiuquan–Hexi: 50%, the serial compensating capacitors shall be provided on both sides of the line in sections; and for Dunhuang–Jiuquan: 30% and Hexi–Wusheng: 40%, the serial compensating capacitors shall be concentrated at the receiving end of the line. For the Wusheng-Hexi line, the serial compensating capacitors shall be provided on the HV reactor line side of Wusheng side; and for the Hexi-Jiuquan line, the serial compensating capacitors shall be provided on the HV reactor line side of both sides of the lines; and for the Jiuquan-Dunhuang line, the serial compensating capacitors shall be provided on the Jiuquan HV reactor line side.

3.4.1.2. Controllable HV reactor plan

In the Dunhuang–Jiuquan-Hexi-Wusheng transmission and substation system, the Jiuquan-Hexi line is the longest with serious problems of reactive power and voltage control. Accordingly, the provision of controllable HV reactors will play a big role. In the Jiuquan-Hexi line, the controllable HV reactors account for 50% of the total capacity of the HV reactors, which is 2 × 210 Mvar for one side of the circuit, and the capacity of the controllable HV reactor is 210 Mvar. The stage regulation mode is used, and the controllable HV reactors are divided into four stages, and the double-circuit controllable HV reactors are divided into 16 stages. The HV reactor capacity variation and the line reactive power characteristics are similar to that of the continuously regulated controllable HV reactors.

In addition, in case Dunhuang Substation is not provided with controllable HV reactors, the 750 kV bus voltage is very high in case of small load of the wind farm. Primarily, it is proposed to install the 300 Mvar controllable HV reactors on the bus of Dunhuang Substation to settle the problem. In this case, the voltage level of the 750 kV system can be controlled in the permissive range.

The calculations and analysis are based on the detailed wind farm model, and the type, control mode, and LVRT capability of the WTGs are based on the data supplied by Gansu Power Corporation. The WTG mathematical model built on the simulation platform by the software of China Electric Power Research Institute Power System Department-Bonneville Power Administration (PSD-BPA), which is maximally close to the actual physical conditions and takes into account the internal electrical wiring model of the wind farm.

3.4.2. Integration Capability of Jiuquan Wind Power System Installed with Serial Compensating Capacitors/Controllable HV Reactors

3.4.2.1. Xinjiang integrated with Northwest Grid, WTGs in constant voltage control mode

When Xinjiang is integrated with the Northwest Main Grid to transmit 1000 MW, and the Hexi 750 kV channel is provided with serial compensating capacitors and controllable HV reactors, the WTGs (including the DFIGs and the D-PMSGs) of the wind farms integrated to the Northwest Main Grid at 330 kV are in constant voltage control mode. The integration capacity of Jiuquan Wind Power System is calculated in the maximum power loads in summer, 2010 (summer maximum, for short). The Jiuquan-Hexi line is the section with the longest electrical distance in the Hexi transmission channel, and the limit fault is the “three permanent” N-1 of the Jiuquan-Hexi line. With gradual rise of Jiuquan wind power output, the power flow of the Hexi transmission channel will gradually increase. When the wind power output rises up to 3400 MW, the “three permanent” N-1 on the Jiuquan-Hexi line will result in excessively low voltage of Dunhuang, Jiuquan Substations, and out of stability of power angle of the thermal power units in Jiuquan in terms of the Northwest Main Grid, further causing out of stability of power angle of Xinjiang grid in terms of the Northwest Main Grid. See Figure 3.19 for the generator power angle curve. That is to say, the limit of the outgoing capacity of Jiuquan Wind Power System is 3400 MW in the boundary conditions.

Figure 3.19 Calculated results of generator power angle at limit output of WTGs in summer maximum, 2010.

The fault of the Hexi transmission channel has significant impact on the bus voltage near the fault point. When the voltage reduces to a certain threshold and holds on for some time, it will result in the WTG not designed with LVRT capability disintegrated from the grid and shut down; and if the voltage further reduces to a certain threshold and holds on for a long time, it is likely to make the WTG designed with LVRT capability disintegrated from the grid. When the wind power transmitted outwards is 3400 MW and a three permanent N-1 fault occurs in the Jiuquan-Hexi system, some WTGs not designed with LVRT capability that are integrated to Guazhou, Yumen 330 kV Substations at 110 kV will be disintegrated from the grid and shut down. See Figure 3.7 for the simulation calculation results. See Figure 3.20 for the active output and voltage curves of the single WTG that is not designed with LVRT capability disintegrated from the grid and shut down.

Work out the outward transmission limits at the minimum load in summer (summer minimum, for short), the maximum load in winter (winter maximum, for short), and the minimum load in winter (winter minimum, for short) in the same boundary conditions; see Table 3.8 for detailed calculation results. In the above four modes and at the maximum wind power integration capacity, the limit fault and the out-of-stability modes are consistent. At the same time, they will affect the WTGs not designed with LVRT capability and integrated at 110 kV to disintegrate from the grid.

Figure 3.20 Active output and voltage curves of the single WTG that is not designed with LVRT capability disintegrated from the grid and shut down. (a) Active output of WTGs; (b) Generator-end voltage of WTGs.

Table 3.8

Calculation Results of Grid Stability in Case of WTGs Integrated to the Grid at 330 kV in Constant Voltage Mode, Xinjiang Integrated with Northwest Grid, Provided with Serial Compensating Capacitors/Controllable HV Reactors, 2010

Operating Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Summer maximum	3400	4912	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the voltage of Dunhuang, Jiuquan Substations is excessively low, and the power angle of the thermal units in Jiuquan loses stability in terms of the Northwest Main Grid	Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down
Summer minimum	3520	4972
Winter minimum	3492	5010
Winter maximum	3444	4911

Based on the above calculation results in the four operating modes, the limit transmission capacity of Jiuquan Wind Power System is 3400 MW in case Xinjiang is integrated with the Northwest Grid, the serial compensating capacitors and controllable HV reactors are provided and the 4100 MW WTGs (800 MW direct-driven; 3300 MW double-fed) are operated in constant voltage control mode and integrated to the grid at 330 kV.

3.4.2.2. Xinjiang integrated with Northwest Grid, WTGs in constant power factor control mode

Xinjiang is integrated with the Northwest Main Grid to transmit 1000 MW, and the 750 kV transmission channel is provided with serial compensating capacitors and controllable HV reactors, and the WTGs integrated to the grid at 330 kV are in constant power factor 1 control mode. In this case, work out the WTG limit transmission capacity in 2010 in four operating modes—summer maximum, summer minimum, winter maximum, and winter minimum—respectively; see Table 3.9 for the detailed calculation results. In the boundary conditions, the limit transmission capacity of the Jiuquan wind power system is about 2100 MW, which is far smaller than that in the constant voltage control mode (3400 MW). Obviously, it will significantly improve the transmission capacity of the Hexi wind power system to propose the access requirement of constant voltage control mode for the 410 MW WTGs integrated to the Northwest Grid at 330 kV.

3.4.3. Integration Capacity of Jiuquan Wind Power System Not Provided with Serial Compensating Capacitors/Controllable HV Reactors

3.4.3.1. Xinjiang integrated with Northwest Grid, WTGs in constant voltage control mode

Xinjiang is integrated with the Northwest Grid to transmit 1000 MW, and the 750 kV transmission channel is not provided with serial compensating capacitors and controllable HV reactors, and the WTGs integrated to the grid at 330 kV are in constant voltage control mode. In this case, work out the WTG limit transmission capacity in 2010 in four operating modes—summer maximum, summer minimum, winter maximum, and winter minimum—respectively; see Table 3.10 for the detailed calculation results. In the boundary conditions, the limit transmission capacity of Jiuquan wind power system in 2010 is 1736 MW, which is 1664 MW less than that of the system provided with serial compensating capacitors and controllable HV reactors (3400 MW). Obviously, it is good for wind power transmission to provide the Hexi 750 kV channel with serial compensating capacitors and controllable HV reactors.

Table 3.9

Calculation Results of Grid Stability in Case of WTGs Integrated to the Grid at 330 kV in Constant Power Factor Mode, Xinjiang Integrated with the Northwest Grid, Provided with Serial Compensating Capacitors/Controllable HV Reactors, 2010

Operating Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Summer maximum	2142	3710	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the voltage of Dunhuang, Jiuquan Substations is excessively low, and subsequently the power angle of the thermal units in Jiuquan loses stability in terms of the Northwest Main Grid	Some FSIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen substations at 110 kV are shut down
Summer minimum	2142	3629		Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down; and some DFIGs, D-PMSGs that are designed with LVRT capability and integrated to Dunhuang Substation at 330 kV are shut down (less than 0.9 p.u. 150 cycles).
Winter maximum	2084	3604
Winter minimum	2170	3740		Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down (the constant power factor can offer weak support to voltage).

Table 3.10 shows that the limit fault of the four modes is all the “three permanent” N-1 fault on Jiuquan side of the Hexi-Jiuquan line, and the out-of-stability mode is all the power angle of the thermal units in Jiuquan Region, and Xinjiang loses stability in terms of the Northwest Main Grid. After the fault, it will result in voltage reduction of the bus in the substation on the Hexi 750 kV transmission channel and shutdown of some WTGs not designed with LVRT capability and integrated to Guazhou and Yumen Substations at 110 kV.

Table 3.10

Calculation Results of Grid Stability in Case of WTGs Integrated to the Grid at 330 kV in Constant Voltage Mode, Xinjiang Integrated with Northwest Grid, Not Provided with Serial Compensating Capacitors/Controllable HV Reactors, 2010

Operating Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Summer maximum	1736	3287	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the power angle of the thermal units in Jiuquan Region and Xinjiang loses stability in terms of the Northwest Main Grid	Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down
Summer minimum	1820	3312
Winter maximum	1778	3356
Winter minimum	1794	3320

3.4.3.2. Xinjiang integrated with Northwest Grid, WTGs in constant power factor control mode

Xinjiang is integrated with the Northwest Grid to transmit 1000 MW, and the 750 kV transmission channel is not provided with serial compensating capacitors and controllable HV reactors, and the WTGs integrated to the grid at 330 kV are in constant power factor control mode. In this case, work out the WTG limit transmission capacity in 2010 in four operating modes—summer maximum, summer minimum, winter maximum and winter minimum—respectively; see Table 3.11 for the detailed calculation results. In the boundary conditions, the limit transmission capacity of Jiuquan wind power system in 2010 is 1210 MW, which is 890 MW less than that of the system provided with serial compensating capacitors and controllable HV reactors (2100 MW). Obviously, it is good for wind power transmission to provide the Hexi 750 kV channel with serial compensating capacitors and controllable HV reactors.

Table 3.11

Calculation Results of Grid Stability in Case of WTGs Integrated to the Grid at 330 kV in Constant Power Factor Mode, Xinjiang Integrated with Northwest Grid, Not Provided with Serial Compensating Capacitors/Controllable HV Reactors, 2010

Operating Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Summer maximum	1210	2802	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the voltage of Dunhuang and Jiuquan is excessively low, and the power angle of the thermal units in Jiuquan Region and Xinjiang loses stability in terms of the Northwest Main Grid	Most of the FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down.
Summer minimum	1289	2832
Winter maximum	1217	2756
Winter minimum	1243	2838

Table 3.11 shows that the limit fault of the four modes is all the “three permanent” N-1 fault on Jiuquan side of the Hexi-Jiuquan line, and the out-of-stability mode is all that the power angle of the thermal units in Jiuquan Region, and Xinjiang loses stability in terms of the Northwest Main Grid. After the fault, it will result in voltage reduction of the bus in the substation on the Hexi 750 kV transmission channel and shutdown of some WTGs not designed with LVRT capability and integrated to Guazhou and Yumen Substations at 110 kV.

3.4.4. Effect of Various Integration Plans between Xinjiang and the Northwest Grid on the Wind Power Integration Capacity

3.4.4.1. WTGs not provided with serial compensating capacitors/controllable HV reactors and operated in constant voltage control mode

In the two plans—Xinjiang is not integrated to the Northwest Grid, and Hami is integrated to the Northwest Grid (Hami not integrated to Xinjiang) to transmit 1000 MW—the Hexi 750 kV transmission channel is not provided with serial compensating capacitors/controllable HV reactors, and the WTGs are integrated to the grid at 330 kV in constant voltage control mode, work out the WTG limit transmission capacity in summer maximum in 2010; see Table 3.12 for results.

Table 3.12 shows, the WTG limit transmission capacity is 1693 MW when Xinjiang is not integrated with the Northwest Grid, which, compared with that when Xinjiang is integrated with the Northwest Grid to transmit 1000 MW and the other boundary conditions are kept unchanged (1736 MW, see Table 3.10), is slightly smaller. When Hami is integrated with the Northwest Grid, the WTG limit transmission capacity is only 760 MW, which, compared with that when Xinjiang is not integrated with the Northwest Grid, is almost 1000 MW less. This is mainly because Hami is integrated with the Northwest Grid in point-to-grid mode, which plays a small role in improving the transmission capacity of Hexi, and that the 1000 MW power transmitted from Hami to the Northwest Grid uses the Hexi transmission channel. As a result, the wind power transmission capacity sees significant reduction.

Table 3.12

Calculation Results of Grid Stability in Summer Maximum, 2010, in Case of WTGs Integrated to the Grid at 330 kV in Constant Voltage Mode, Xinjiang Not Integrated with Northwest Grid, Not Provided with Serial Compensating Capacitors/Controllable HV Reactors

Integration Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Xinjiang not integrated to the Northwest Grid	1693	2264	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the power angle of the thermal units in Jiuquan Region loses stability in terms of the Northwest Main Grid	Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down
Hami integrated to the Northwest Grid	760	2331

In the three plans—Xinjiang is integrated with the Northwest Grid to transmit 1000 MW, Xinjiang is not integrated with the Northwest Grid, and Hami is integrated with the Northwest Grid to transmit 1000 MW—the transmission power of the Jiuquan-Hexi line is 3287, 2264, and 2331 MW, respectively. The transmission capacity of the first plan is about 1000 MW larger than the latter two plans, and the latter two have similar transmission capacity. That is to say, when it does not consider that Xinjiang and Hami transmit the power via the Hexi 750 kV transmission channel, the wind power transmission capacity of the first plan is about 1000 MW larger than the latter two plans, and the wind power transmission capacity of the latter two is similar.

3.4.4.2. WTGs not provided with serial compensating capacitors/controllable HV reactors and operated in constant power factor control mode

In the two plans—Xinjiang is not integrated to the Northwest Grid, and Hami is integrated to the Northwest Grid (Hami not integrated to Xinjiang)—to transmit 1000 MW, the Hexi 750 kV transmission channel is not provided with serial compensating capacitors/controllable HV reactors, and the WTGs are integrated to the grid at 330 kV in constant power factor 1 control mode, work out the WTG limit transmission capacity in summer maximum in 2010; see Table 3.13 for results. In this case, both plans have very small WTG limit capacity, which, compared with the expected capacity of Jiuquan Phase I, is far less.

Table 3.13

Calculation Results of Grid Stability in Summer Maximum, 2010, in Case of WTGs Integrated to the Grid at 330 kV in Constant Power Factor Mode, Xinjiang Not Integrated with Northwest Grid, Not Provided with Serial Compensating Capacitors/Controllable HV Reactors

Integration Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Xinjiang not integrated to the Northwest Grid	580	1192	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the voltage of Dunhuang and Jiuquan is excessively low, and the power angle of the thermal units in Jiuquan Region loses stability in terms of the Northwest Main Grid	Most of the FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down; and some D-PMSGs integrated at 110 kV are shut down. Some DFIGs that are designed with LVRT capability and integrated at 330 kV are shut down
Hami integrated to the Northwest grid	260	1816

3.4.5. Effect of WTG LVRT Capability on Integration Capacity of Jiuquan Wind Power System

The LVRT capability of WTGs is one of the key indexes to evaluate the WTG performance. Based on the 4100 MW WTGs in Jiuquan integrated to the grid at 330 kV in 2010, the following calculation boundary conditions are given: the 800 MW D-PMSGs are provided with LVRT capability; and for the 3300 MW DFIGs, the 1250 MW WTGs in Hekou Wind Farm are not provided with LVRT capability, and the rest 2050 MW WTGs are provided with LVRT capability. When Xinjiang is integrated with the Northwest Grid to transmit 1000 MW, the serial compensating capacitors and the controllable HV reactors are provided, the summer maximum mode in 2010 serves as the calculation level year, and the 4100 MW WTGs integrated at 330 kV are in two control modes—constant power factor 1 and constant voltage, work out the effect of WTG LVRT capability on the WTG limit transmission capacity in the two control modes.

Note that setting of WTG LVRT capability is only used for simulation calculation and it has nothing to do with the actual situation. In 2010, the LVRT capability improvement had not been carried out on the WTGs in Jiuquan Wind Power Base, and most WTGs did not possess LVRT capability. By early 2012, most WTGs in Jiuquan Wind Power Base had completed the technical improvements and basically possessed LVRT capability.

3.4.5.1. WTGs in constant power factor control mode

The WTGs integrated to the grid at 330 kV are set in constant power factor control mode, the 1250 MW DFIGs originally provided with LVRT capability are changed as not provided with LVRT capability. In the same wind power output (summer maximum limit output: 2142 MW) before and after the change, after the Jiuquan-Hexi line has three permanent N-1 fault on Jiuquan side, it will exert great significance on the WTGs integrated to Dunhuang Substation at 750 kV. Moreover, the WTGs can offer weak voltage support in the constant power factor control mode, which results in the per-unit value of the generator-end voltage of more DFIGs not provided with LVRT capability less than 0.85 for seven cycles (0.14 s) and then disintegrated from the grid. See Table 3.14 for the total output of the WTGs disintegrated from the grid before and after the change.

Table 3.14

Total Output Comparisons of WTGs Disintegrated from the Grid Before/After LVRT Capability Change on WTGs

Originally Provided with LVRT Capability	Changed as Not Provided with LVRT Capability
Some FSIGs, DFIGs (156.4 MW) that are integrated to Guazhou, Yumen Substations at 110 kV and not provided with LVRT capability are disintegrated from the grid	Some FSIGs, DFIGs (132.1 MW) that are integrated to Guazhou, Yumen Substations at 110 kV and not provided with LVRT capability are disintegrated from the grid; and some DFIGs (729 MW) that are integrated to Dunhuang Substation at 330 kV and changed as not provided with LVRT capability are disintegrated from the grid; the total output of the above two is 861.1 MW

In the same wind power output and the same fault, the capacity of the WTGs with changed LVRT capability disintegrated from the grid is larger than that with unchanged LVRT capability (equivalent to the stability control effect of WTG disintegration), and thus the WTG limit output after the LVRT capability is changed will be consequently larger than that before the change 2142 MW.

Continue to increase the wind power output and set the limit fault until the power angle loses stability. In this case, work out the WTG limit output in summer maximum and constant power factor after the LVRT capability is changed, which is 3000 MW. Since the WTG limit output is 2142 MW larger than that of the original WTGs, it will exert great impact on the voltage of the main grid after fault, and it will result in the WTGs with LVRT capability disintegrated from the grid in addition to the WTGs not provided with LVRT capability. See Figure 3.21 and Table 3.15 for some simulation results. Because the output of WTGs disintegrated is large, up to 1468.6 MW, it will have some impact on the system frequency. Figure 3.22 shows the frequency simulation output result during transient transitional process, and it shows that the frequency falls in the reasonable range.

3.4.6. WTGs in Constant Voltage Control Mode

The WTGs integrated to the grid at 330 kV are set in constant voltage control mode, and the 1250 MW DFIGs originally provided with LVRT capability are changed as not provided with LVRT capability. Since the DFIGs have strong voltage support capacity in the constant voltage control mode, the generator-end voltage will not reduce to the per-unit value 0.85 and hold on for more than seven cycles (0.14 s) in case of fault, even the changed WTGs not provided with LVRT capability will not be disintegrated from the grid. Accordingly, the limit output of WTGs with changed LVRT capability will stay unchanged, still 3400 MW, in summer maximum, 2010, in the constant voltage control mode.

See Table 3.16 for the detailed calculation result summary of WTG limit output in constant voltage/power factor control modes, in summer maximum, 2010, after the LVRT capability of WTGs is changed.

Figure 3.21 Power angle curve at WTG limit output in summer maximum, 2010, in constant power factor control mode, after LVRT capability is changed.

Table 3.15

Simulation Results of WTGs Disintegrated Concerning LVRT, at WTG Limit Output in Summer Maximum, 2010, in Constant Power Factor Control Mode, After LVRT Capability is Changed

No.	Simulation Results
1	7.0 cycle, generator “1Z101 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z101 0.7” power 0.12 MW (1 set)
2	7.0 cycle, generator “1Z102 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “1Z102 0.7” power 0.12 MW (1 set)
……	……
Cut off the output of FSIGs, DFIGs not provided with LVRT capability and disintegrated from the grid (MW)	156.42
1	7.0 cycle, generator “7GX∗01 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “7GX∗01 0.7” power 1.35 MW (1 set)
2	7.0 cycle, generator “7GX∗02 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.8500 p.u.). 7.0 cycle, disintegrate WTG “7GX∗02 0.7” power 1.35 MW (1 set)
……	……
Cut off the output of DFIGs changed to not provided with LVRT capability and disintegrated (MW)	1131.3
1	150 cycle, generator “5BX001 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.9000 p.u.). 150.0 cycle, disintegrate WTG “5BX001 0.7” power 1.35 MW (1 set)
2	150 cycle, generator “5BX002 0.7” undervoltage and overvoltage relay RE act (acting voltage: 0.9000 p.u.). 150.0 cycle, disintegrate WTG “5BX002 0.7” power 1.35 MW (1 set)
……	……
Cut off the output of DFIGs provided with LVRT capability disintegrated (MW)	180.9
Cut off the output of total of the WTGs disintegrated (MW)	1468.62

Figure 3.22 Bus frequency and system minimum frequency variation curves during transient process. (a) Bus frequency variation during transient process; (b) System minimum frequency variation during transient process.

Table 3.16

Effect of WTG LVRT Capability on Limit Transmission Capacity of WTGs

Control Mode	Limit Output of WTGs (MW)	Power of Jiuquan-Hexi Line (MW)	Out-of-Stability Mode	Remarks
Constant power factor control	3000	4533	The Jiuquan-Hexi line has “three permanent” N-1 fault on Jiuquan side, the voltage of Dunhuang and Jiuquan Substations is excessively low, and the power angle of the thermal units in Jiuquan Region loses stability in terms of the Northwest Main Grid, and the Xinjiang Grid is out of step in terms of the Northwest Main Grid	Most FSIGs, DFIGs that are integrated to Guazhou, Yumen Substations at 110 kV and not provided with LVRT capability are shut down; and most DFIGs that are integrated to Dunhuang Substation at 330 kV and not provided with LVRT capability are shut down (less than 0.85 p.u. for 7 cycles); and some DFIGs that are integrated to Dunhuang Substation at 330 kV and provided with LVRT capability are shut down (less than 0.9 p.u. for 150 cycles)
Constant voltage control	3400	4912		Some FSIGs, DFIGs that are not designed with LVRT capability and integrated to Guazhou, Yumen Substations at 110 kV are shut down

3.5. Analysis on Reactive Voltage Characteristics with Consideration to Internal Electrical Wiring of Wind Farms

The overhead lines and cables are used for electrical wiring in the wind farm. More importantly, the resistance is larger than or approximate to the reactance of the cable, and the cable has large charging power. These electrical characteristics will affect the system steady-state power flow. Since the electrical wiring length is short in the wind farm, it is reasonable to ignore the electrical wiring model during building the static model of the wind farm when the wind farm has small capacity and scale. Gradual increase of wind farm capacity and scale, however, will exert some impact on the power flow analysis result after integration to ignore it again during modeling, and the conclusion based on it will have large errors. In the following section, the impact of internal electrical wiring of the wind farm on the reactive voltage characteristics will be analyzed by a simple system.

3.5.1. Introduction to Simple Systems

Figure 3.23 shows the wiring diagram of a simple system. The installed capacity of wind power of wind farm subsystem 1, 2, 3 is 200, 200, 300 MW, respectively, for a total of 700 MW, and in the wind farm subsystems, the detailed electrical wiring is taken into account. The three subsystems of wind farms will be stepped up via 0.69/35 kV and 35/363 kV to the collecting bus and then to the 45-km line and finally integrated to the infinite system. The infinite system is a thermal power plant with installed capacity of 1000 MW, the generator-end voltage is set as the per-unit value of 1, and the bus of the infinite system is provided with loads 800 MW + j250 Mvar.

3.5.2. Impact of Internal Electrical Wiring of the Wind Farm on the Reactive Voltage Characteristics

For the wind farm that ignores the internal electrical wiring, the WTGs shall be directly integrated to the grid via two stages of transformers 0.69/35 kV and 35/363 kV, and the electrical wiring of overhead lines and cables inside the wind farm shall be ignored. The wind farm shall start from 0 MW and increase at an interval of 150 MW to the full output 700 MW. At the section gradually increased output of the wind farm, compare the calculated results of the system in terms of the voltage at PCC of the wind farm, the active/reactive power output by the integrated line in case of considering and ignoring the electrical wiring, and based on it, analyze the impact of the electrical wiring (considering and ignoring) on the reactive voltage characteristics of the wind farm integration system. See Table 3.17 for results.

Figure 3.23 Wiring diagram of a simple system.

Table 3.17 shows that the output of the wind farm increases at an interval of 150 MW, and when the output is in the range of 0～450 MW, since the output of the wind farm is small and the charging reactive power of the wind farm cables is larger than the reactance losses of the overhead lines and cables of the wind farm, the reactive power injected to the grid by the wind farm considering the electrical wiring after integration is larger than that ignoring the internal electrical wiring, or the reactive power absorbed from the grid side is less than that ignoring the internal electrical wiring, resulting in slightly higher voltage at PCC; when it falls in a range of 450～700 MW, since the output of the wind farm is relatively heavy and the charging reactive power of the wind farm cables is less than the reactance losses of the wind farm overhead lines and cables, the wind farm considering the electrical wiring, compared with that ignoring the electrical wiring, absorbs more reactive power from the grid side after integration, and subsequently the voltage at PCC is lower. From 150 MW, the voltage fluctuation range of the wind farm considering the electrical wiring is 0.9695–0.9291 = 0.0404 (p.u.), and that of the wind farm ignoring the electrical wiring is 0.9682–0.9318 = 0.0364 (p.u.). Obviously, the wind farm considering the internal electrical wiring sees larger voltage fluctuation range, which is bad for voltage control. Moreover, the voltage fluctuation difference will become more dramatic with growing scale and capacity of integrated wind farms. As a result, the analysis result on reactive voltage characteristics of the integrated wind farm will become “optimistic” when ignoring the internal electrical wiring of the wind farm.

In Figure 3.24, the comparisons of integration physical output variation trends of wind farms with increased output show that the wind farm considering the electrical wiring has larger voltage fluctuation at PCC and integration reactive power output fluctuation than that of the wind farm ignoring the electrical wiring.

3.5.3. Reactive Voltage Control Considering the Electrical Wiring of the Wind Farm

The substation of the wind farm is provided with static var compensator (SVC). Suppose the capacity of the SVC has no upper/lower limits, and the 363 kV bus at PCC of the wind farm is controlled at 0.97 p.u. Table 3.18 shows the calculation results of SVC-controlled quantities considering and ignoring the electrical wiring.

Table 3.18 shows that during the variation process of the wind farm output, when the voltage at PCC of the wind farm is controlled at the expected value, the SVC control range is 137.5–11.6 = 125.9 (Mvar) in case the internal electrical wiring of the wind farm is considered, and it is 130.4–17.5 = 112.9 (Mvar) in case the internal electrical wiring of the wind farm is ignored. Obviously, it is more difficult to control the voltage at PCC when the internal electrical wiring of the wind farm is considered from the angle of operation control, and the capacity required for provision of SVC is larger than the capacity required by the internal electrical wiring of the wind farm from the angle of planning. As a result, it further indicates that the analysis on reactive voltage characteristics is “optimistic” when the internal electrical wiring of the wind farm is ignored. Figure 3.25 shows the comparisons of calculation output for SVC-controlled quantities, which proves the above conclusions in a more visualized way.

Table 3.17

Voltage at PCC, Active/Reactive Output of the Integrated Line in Case of Output Variation of Wind Farms

Electrical Quantity	Treatment of Electrical Wiring
Electrical Quantity	Integration of Wind Farm with Consideration to the Electrical Wiring						Integration of Wind Farm Ignoring Electrical Wiring
Output of wind farm (MW)	0	150	300	450	600	700	0	150	300	450	600	700
Voltage at PCC of wind farm (p.u.)	0.9671	0.9695	0.9669	0.9589	0.9442	0.9291	0.9656	0.9682	0.9661	0.9589	0.9455	0.9318
Reactive power of the integrated line (Mvar)	5.8	−1	−21.7	−57.9	−112.8	−163.6	0	−6.2	−25.1	−58.1	−107.8	−153.5
Active power of the integrated line (MW)	0	149.8	298.9	447.4	595.5	695.6	0	150	300	450	600	700

Figure 3.24 Comparisons of integration physical output variation trends of wind farms with increased output (I). (a) Comparisons of voltage variation trend at PCC with increased wind farm output. Comparisons of integration physical output variation trends of wind farms with increased output (II). (b) Comparisons of reactive output variation trend of integrated lines with increased wind farm output. (c) Comparisons of active output variation trend of integrated lines with increased wind farm output.

Table 3.18

Comparisons of Reactive Voltage Control Output Results

Output of Wind Farm (MW)	0	150	300	450	600	700
SVC-controlled quantities considering the internal electrical wiring of the wind farm (Mvar)	11.6	2.1	12.0	41.8	92.0	137.5
SVC-controlled quantities ignoring the internal electrical wiring of the wind farm (Mvar)	17.5	7.3	15.4	42.3	88.3	130.4

Figure 3.25 Comparisons of SVC control output required to control the voltage of the wind farm at PCC at the expected value when the output of the wind farm varies.

3.6. Evaluation Software for Wind Power Accommodation Capability

In different typical operation modes, the wind power accommodation and transmission capability of the Gansu grid is different. After the WTGs of Jiuquan Phase I, Gansu, are integrated to the grid, the wind power accommodation capability in each typical mode shall be evaluated in a quantitative method from the views of dispatching, production and operation, and the output plan of each wind farm shall be determined with consideration to the wind power prediction of wind farms. It is good for improvement of wind power generation, energy saving, and emission reduction to receive the maximal integrated wind power in the precondition of grid security. The quantitative evaluation software system for wind power accommodation and transmission capability of the Gansu Grid in various operation modes (the evaluation software, for short) can offer technical support for integration operation of Jiuquan Wind Power Base with gradually increased capacity.

3.6.1. Software Design Process

To evaluate the wind power accommodation and transmission capability, continuous calculation and analysis shall be carried out for the continuously changed grid modes to plot the evaluation capability curve, indicating the additional wind power that can be received in the continuously changed grid modes. As a result, the single section limit calculations cannot meet the requirements of wind power accommodation and transmission capability evaluation, and the software must consider the continuous section transmission capability calculation, analysis, and comprehensive evaluation in multiple modes of the grid. In this way, it can approach the actual operation of wind power integration and better discover the leading factors affecting safe and smooth operation as well as transmission capacity during wind power accommodation and transmission process.

To carry out evaluation of wind power accommodation and transmission capability, the following five steps shall be followed:

1. Building of typical and fundamental modes: Build the model according to the actual grid situation; the typical operation modes of summer maximum, summer minimum, winter maximum, and winter minimum shall be generally used according to the actual power system project, and the typical operation modes serve as the basis to build various mode sets, and accordingly, the building of typical modes must reflect the actual grid operation and be representative in a period.

2. Setting of evaluation constraint and limit conditions: Mainly including formation of sections in the wind power integration conditions, startup regulation direction and regulation priority, startup limit range, section transmission limit prediction, leading fault set, evaluation stability type and security limit conditions, etc.

3. Calculation of single section accommodation and transmission capability: After the sections are defined in advance in a reasonable manner, match the operation mode, startup constraints and stability conditions, and based on it, work out the calculation configuration and then start the section calculation process in turn to carry out serialization calculation in various modes.

4. Evaluation, statistics, and analysis of section calculation results: Based on the section calculation results, categorize the results, and carry out statistics to the section transmission information, including the initial power flow, transmission limit values and limit factors, margin difference of power between transmission limit status and fundamental status, etc.

5. Comparison analysis on WTGs: Based on the calculation results of single section transmission capability, carry out comparison analysis and statistics for the output of WTGs in the fundamental mode and the transmission limit mode.

See Figure 3.26 for the complete design process of evaluation software.

3.6.1.1. Quantitative evaluation of single section

The quantitative evaluation process of single section is a continuously regulated process where the power flow at the section shall be regulated by changing the balance relations between power generation and loads based on stability calculation results in the precondition of the overall balance between power generation and loads in the whole system. During the regulating process, other factors shall be taken into account, including the system voltage level, startup mode arrangement, load distribution and load level, etc. Calculation evaluation of single section consists of two stages: search stage and check stage. Below shows the core algorithm corresponding to the two stages.

3.6.1.2. Conclusions of quantitative evaluation

The evaluation software for wind power accommodation and transmission capability will work out the detailed calculation and analysis conclusions of single section. A set of calculation results, including the power flow in the fundamental mode, the transmission limit values and limit factors, the margin difference of power between transmission limit status and fundamental status, and the files of the corresponding mode, will be drawn for each operation mode. The files in the transmission limit mode can offer the necessary data for analysis on grid security and stability in single mode.

Figure 3.26 Complete design process of evaluation software.

3.6.1.3. Relations with the large power system simulation platform PSD-BPA

The evaluation software is a software system that can run independently, and it can directly use the modes and the fundamental data of the stability model provided by the PSD-BPA platform of the power system analysis software of China Electric Power Research Institute, and it can use the core calculation modules such as power flow and stability modules to carry out batch calculation, analysis, and comprehensive judgment, including the power angle, voltage, frequency, and other transient stability judgments. Based on various stability judgments and analyses, the accommodation and transmission capability of the wind power system under various limit conditions can be judged.

3.6.2. Core Algorithm of Software

Single section evaluation is the core module of the software and includes the core algorithm of the software—“grid section transmission capability” calculation. The algorithm of grid section transmission limit calculation can be expressed as:

$\lim_{n \to \infty} P_{n} = F (G_{i}, F_{i}, N, P_{step})$ $\lim_{n \to \infty} P_{n} = F (G_{i}, F_{i}, N, P_{step})$

(3.19)

where, P_n is the power value at a certain tap; G_i is the adjustable WTG and its order; F_i is the fault disturbance; N is the step of successive approximation; P_step is the increasing step of power approximation.

When carrying out the calculation, based on the basic power flow transmitted on the given section and the expected upper limit, divide the range between the expected upper limit of the section and the current transmission power value into N × taps at the step of increasing power, and use the given F × associated faults to form N × F calculation tasks for each section. If more than one section is present, ∑N_i × F_i tasks shall be formed for the several sections. Work out each task, and summarize and analyze the calculation results to find out the transmission capability limits of the section. After the limit search is finished, if the check fault is present, the program will enter the check stage. In section transmission capacity search, the upper limits shall take the section N-1 thermal stability limits. See Figure 3.27 for transmission limit calculation diagram.

3.6.3. Functions of Software

The evaluation software is mainly designed to carry out the wind power accommodation capability evaluation and thus it has the following main functions:

1. Setting and operation of evaluation work sets of grid wind power capacity;

2. Storage of evaluation work sets of grid wind power capacity;

3. Setting of evaluation sections of grid wind power capacity;

4. Definition of control quantities on unit adjustment for grid wind power capacity evaluation;

5. Appointment and selection of check faults for grid wind power capacity evaluation and calculation;

6. Setting of control parameters for grid wind power capacity evaluation;

7. Single-work calculation and analysis for grid wind power capacity evaluation;

Figure 3.27 Transmission limit calculation diagram.

8. Several-work calculation and analysis for grid wind power capacity evaluation;

9. Calculation stop control for grid wind power capacity evaluation;

10. Results and conclusions for grid wind power capacity evaluation;

11. WTG presence comparison statistics and analysis for grid wind power capacity evaluation;

12. Monitoring of calculation process for grid wind power capacity evaluation.

3.6.4. Performance of Software

3.6.4.1. Calculation accuracy

The input power flow data shall meet the requirement on convergence accuracy, the input stability data shall correspond to the power flow data and be able to carry out normal stability calculation, and the input fault set shall correspond to the power flow data files and the setting content shall be correct and complete, meet the requirement on prescribed form, and the configured section information shall correspond to the power flow files, and the output range and limits of WTGs shall match with the actual grid, and the check fault of the section shall be reasonably selected according to the problems present in the grid.

3.6.4.2. Calculation efficiency

Based on the grid scale and complexity, the details of grid stability model, specified output, specified quantity of sections, and the difference between the fault set and the section adjustment, it will take several seconds or dozens of minutes or even several hours to finish the wind power evaluation calculations for one mode.

3.6.4.3. Flexibility of software

The evaluation software can make direct use of the matured PSD-BPA software and build the transmission capacity calculation modules based on the distributive parallel architecture mode. It can be integrated to the integrated environment of the wind power capacity evaluation software. It can offer a very flexible application package while each model can be independently developed and operated. The evaluation software can run in various environments such as Windows XP and the compatible Windows operating system, and the resulting accuracy can fully meet the demand of project applications on calculation.

3.6.5. Use of Software

Since the evaluation software includes the power flow calculation program, the stability calculation program, the wind power capacity evaluation and calculation program, and the support library in its integrated environment, the programs must be complete; otherwise, the evaluation software cannot start and run normally.

3.6.5.1. Integrated environment

The evaluation consists of appointed calculation method, appointed fault set, definition of relevant section, calculation of wind power transmission performance and statistics, and analysis of WTG output. To make it flexible and extendable, the operating environment of wind power evaluation calculations adopts the standard Windows operating method. See Figure 3.28 for the integrated environment interface of the evaluation software.

Figure 3.28 Integrated environment interface of the evaluation software.

The integrated environment includes the following main elements:

1. Title bar: indicate the application title and the latest program compilation and release time, including System menu, Min., Max., and Close buttons.

2. Menu bar: indicate the prompts on operation function category of wind power evaluation, including Evaluation (P), Edit (E), View (V), Help (H), etc. If the function is unavailable or temporarily invalid, the menu shall be displayed in gray.

3. Toolbar: indicate the shortcut buttons of the functions of wind power evaluation. If the function is unavailable or temporarily invalid, the menu shall be displayed in gray.

4. Method appointment and setting window: set the methods of several time periods to be calculated for wind power evaluation, and it shall select the power flow data, the stability data, the check fault data, the section definition data, and the calculation result file data for each mode. The section definition data include formation of section line, basic regulatory style of section, adjusting units of section, check fault of section, etc. The window is provided with an independent toolbar and it can set the information in the window.

5. Report of evaluation calculation results: indicate the calculation results of wind power evaluation. It can display the evaluation results of several sections in one mode in case of calculation and evaluation of one single mode; and it can display in turn the evaluation results of several sections in several modes in case of calculation and evaluation of multieffective modes.

6. Running process monitoring window: indicate the operation prompts during system running, which can be the alarm information on file setting or the prompt information on operation. After the wind power evaluation calculation starts, it will show the information of the internal calculation process for wind power evaluation.

7. Status bar: indicate the simple prompt information on development and the functions of the menu toolbar. After the wind power evaluation calculation starts, it will show the dynamic prompt information of calculation process. In case several modes need evaluation, the prompt status bar will pop up after each start and disappear after stop.

3.6.5.2. Brief introduction of menu and toolbars

See Table 3.19 for brief introduction and fast index of functions of the evaluation software.

3.6.5.3. Work steps

To rapidly and smoothly carry out the calculations for wind power accommodation capability evaluation, some operation steps and processes shall be followed; see Figure 3.29 for the work process. The calculations for wind power accommodation capability evaluation generally consists of the following five steps:

1. Select and set the associated files for wind power accommodation capability evaluation. Select (set) the power flow, stability, fault set, section setting files, and the wind power result record files. Before working out the wind power accommodation capability, the content of the wind power transmission or accommodation section must be manually set. See the follow-up chapters for detailed selection and setting methods.

2. Set the sections. Set the reasonable section and regulatory style as well as the mode (or relevant mode set) corresponding to the section according to the architecture and modes, and set the section capacity evaluation method, calculation step, formation of section line, type of check fault, adjusting units, adjusting direction and adjusting range, etc.

Table 3.19

Brief Introduction and Fast Index of Functions of the Evaluation Software

Category	Function Menu	Tool Button	Shortcut Key	Description
Evaluation (P)	Evaluation of current mode (B)		F5	Evaluate the currently selected mode in the evaluation configuration list of wind power modes
	Evaluate all the modes (M)		Ctrl + F5	Evaluate the files of the mode checked qualified in the evaluation configuration list of wind power modes
	End the calculation (E)		Shift + F5	After the calculation for wind power evaluation starts, it may cause no result available or incomplete result if the limit calculation is stopped during calculation
	Statistics of WTG output (W)		F3	Extract the options in the report of evaluation results for WTGs and carry out statistics and analysis on WTG output
	Export the result to Excel (X)			To output the evaluation result to Excel, the Excel software shall be preinstalled in the system
				Realize the function by sub-toolbar
Setting operation	Select the file associated with the column			According to the edit items in the table, select the associated data file
	Select several files			Several files can be selected at one time and they can be filled into the selected table by the suffix of the file; when the default suffix is used, all the configuration files can be selected at one time
	Definition of section			It is an indispensable configuration item for wind power evaluation to set the formation of sections and unit adjustment in the current mode
Table Continued

Category	Function Menu	Tool Button	Shortcut Key	Description
	Create a new blank mode record			To create a new blank mode record, the software will automatically show the serial number and the mode time number, where the time number can be manually modified and the serial number system will be automatically executed
	Create a mode record by paste			If there is the associated information on the mode clipboard, a new mode record can be created by direct use of the information on the clipboard
	Cut a mode record			Copy the currently selected mode record to the mode clipboard and delete the current record
	Copy a mode record			Copy the currently selected mode record to the mode clipboard
	Paste a mode record			Copy the record in the mode clipboard (if any) to the currently selected mode record
	Delete the selected record			Delete the currently selected mode record
	Delete all the mode records			Delete the mode records in all tables
	Open the configuration list			Open the configuration list previously saved
	Save the configuration list			Save the content of the current configuration list to the file
View (V)	Main toolbar			Display and hide the main toolbar
	Status bar (S)			Display and hide the status bar
	Wind power evaluation guide (W)		Alt + W	Display the closed wind power evaluation guide window
Help (H)	About the software (A)			Display the development information of the software

Figure 3.29 Work process of calculations for wind power accommodation capability evaluation.

3. Start the calculation for wind power accommodation capability evaluation. After the file is set or modified, execute the wind power evaluation calculation program, and the program will automatically carry out calculations and the calculation process will be displayed on the software output window. There are two basic calculation methods for wind power evaluation: one is for single mode and the other for the whole mode set. No matter which calculation method is used, the basic rationality of the setting content will be checked, and those configuration items failing in the check cannot start normal calculations.

4. Display and analyze the evaluation result report. No matter which calculation method is used, the software will generate the report on wind power transmission and accommodation capability of each section after the calculations are finished, and the analysis operations such as sorting and so on are available to the report contents, and the WTG output comparison statistics and analysis are also available for the given sections.

5. Export the results of wind power accommodation capability evaluation to Microsoft Excel or save as a file.

3.6.6. Case Analysis for Automatic Calculation of Evaluation Software

Based on the summer maximum typical mode of the Northwest Grid in the end of 2010 where Xinjiang is integrated with the Northwest Grid to transmit 1000 MW and the WTGs are in the control mode of constant power factor 1, work out the wind power accommodation capability automatically by the evaluation software.

3.6.6.1. Setting mode of transmission limit section

1. Basic information of transmission limit section

See Figure 3.30 for setting of the basic information of the transmission limit section where the relevant information of a transmission limit section to be studied can be set for a certain operation mode. The setting information is as follows:

a. Set a section with number of 1;

b. Section name: “Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV”;

c. Preset the upper limit value of the transmission limits as 7000 MW and the step accuracy of the search limit as 50 MW;

2. Formation of transmission limit section lines

See Figure 3.31 for the input interface of the transmission limit section line formation where the lines related to the transmission limit section can be set. The formation of lines related to the section of the “Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV” electromagnetic ring grid is as follows according to the calculations of this method:

a. Jiuquan-Hexi 750 kV double-circuit lines where the lines corresponding to the mode data are Ganjiuquan 71–Ganjiujin K1, Ganjiuquan 71–Ganjiujin K2;

b. Jiuquan-Zhangye 330 kV double-circuit lines where the lines corresponding to the mode data are Ganjiuquan 31–Ganzhangjiu K1, Ganjiuquan 31–Ganjiuzhang K1;

3. Relevant fault of transmission limit section

See Figure 3.32 for the setting interface of the relevant fault of transmission limit section. Select the calculating fault for the transmission section from the candidate fault set. In this mode calculation, the relevant faults for “Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV” electromagnetic ring grid section are set as below:

a. Jiuquan-Hexi 750 kV double-circuit line has three permanent N-1 fault at the start and terminal ends;

Figure 3.30 Interface on setting of basic information for transmission limit section.

Figure 3.31 Input interface on formation of transmission limit section lines.

Figure 3.32 Setting interface of relevant faults of transmission limit section.

b. Jiuquan-Zhangye 330 kV double-circuit line has three permanent N-1 fault at the start and terminal ends.

4. Setting of adjustable WTGs at RE/TE of transmission limit section

See Figure 3.33 for the setting interface of the adjustable WTGs at the receiving end (RE) and the sending end (TE) of the transmission limit section, and select the WTGs at RE/TE, and the WTG maximum active output, the adjusting lower limit of the active output, and the adjusting upper limit of the active output from the grid WTGs.

Since the study target is the accommodation capability of the WTGs, the other traditional power sources at the sending end are viewed as nonadjustable by default and only the WTGs are adjustable. According to the power generation schedule of traditional power sources with response to the WTG output in the Gansu Grid, the traditional main power sources in the Gansu grid are selected to participate in adjustment at the receiving end.

See Table 3.20 for the relevant information of the WTGs at TE related to “Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV” electromagnetic ring grid section, including the adjustable upper/lower limits of WTG output, increasing WTG output sequence in order, etc.

See Table 3.21 for the relevant information of the WTGs at RE related to the section, including the adjustable upper/lower limits of WTG output, increasing WTG output sequence in order, etc.

Figure 3.33 Setting interface of adjustable WTGs at TE/RE of transmission limit section.

Table 3.20

Information of Adjustable WTGs at TE (MW)

Adjusting and Control Sequence	Name of WTG	Maximum Active Output	Adjustable Lower Limit of Active Output	Adjustable Upper Limit of Active Output
1	Ganganhe G7	200	0	200
2	Ganganhe G6	200	0	200
3	Ganganhe G5	200	0	200
4	Ganganhe G4	200	0	200
5	Ganganhe G2	200	0	200
6	Ganganhe G3	200	0	200
7	Ganganhe G1	200	0	200
8	Ganganhe G8	200	0	200
9	Ganbeida G5	200	0	200

Table 3.21

Information of Adjustable WTGs at RE (MW)

Adjusting and Control Sequence	Name of WTG	Maximum Active Output	Adjustable Lower Limit of Active Output	Adjustable Upper Limit of Active Output
1	Ganjingyuan G6	300	0	300
2	Ganjingyuan G5	300	200	300
3	Ganjingyuan G4	200	0	200
4	Ganjingyuan G3	200	0	200
5	Ganjingyuan G2	200	0	200
6	Ganjingyuan G1	200	0	200
7	Ganjingyuan G7	300	0	300
8	Ganjingyuan G8	300	0	300

3.6.6.2. Comparisons of auto/manual calculation results

The evaluation software is used to automatically work out the wind power accommodation capability in this mode, and the interface of calculation finish is showed in Figure 3.34.

Figure 3.34 Interface of calculation finish by evaluation software.

Compare the results by software automatic and manual calculation of the wind power accommodation capability in this mode, and see Table 3.22 for the results. The limit reasons of the two results are different where the limit reason of the automatic calculation result by software is transient stability limit. This is mainly because the program automatically considers them as transient stability limit as long as the persistent or increasing oscillation is present. In the follow-up software development and improvement, the output of limit reasons can be further divided according to the stability forms, making it more practical.

See Figure 3.35 for comparisons of the power angle output curves of some WTGs by auto/manual calculations.

Table 3.22 and Figure 3.35 show that the calculation results of the two means are similar with error falling in the acceptable range. As a result, it is reasonable to automatically work out the wind power accommodation capability by the evaluation software.

Table 3.22

Comparisons of Manual and Software Automatic Calculation Results

Means of Calculation	No. of Section	Name of Section	Present Power Flow (MW)	Capacity of Section (MW)	Reason of Limit
Software automatic calculation	1	“Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV”	2566.98	3734.92	Transient stability limit
Manual calculation	1	“Jiuquan-Hexi 750 kV, Jiuquan-Zhangye 330 kV”	2569.9	3759.1	After transient persistent, increasing oscillation, the oscillation will slowly attenuate

Figure 3.35 Comparisons of the power angle output curves of some WTGs by auto/manual calculations.

Figure 3.36 Interface of output list of wind power accommodation capability by automatic calculation.

The evaluation software can automatically evaluate the maximum accepted wind power capacity after the section transmission capacity reaches the limits and output the list as shown in Figure 3.36. In the current mode, the maximum accepted wind power capacity is 1250 MW.

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Table of Contents for Chapter 3. Simulation Calculations for Wind Power Transmission Capability

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Abstract

Keywords

3.1. Technical Specifications on Integration Operation of Wind Turbine Generators (WTGs)

3.1.1. Requirements on Voltage and Power Factor of WTG Integration

3.1.2. Requirements for Grid Voltage

3.1.3. Requirements for System Frequency

3.1.4. Requirements for Relay Protection and Security Automation Devices

3.1.5. Low Voltage Ride-Through (LVRT) Capability

3.2. Mathematical Model of WTGs and Wind Farms

3.2.1. Modeling of FSIGs

3.2.1.1. Wind turbines

3.2.1.2. Asynchronous generators

3.2.1.3. Pitch control systems

3.2.2. Modeling of DFIG

3.2.2.1. Wind turbines

3.2.2.2. Generators and converters

3.2.2.3. Excitation control systems

3.2.2.4. Pitch control system models

3.2.3. Modeling of D-PMSG

3.2.3.1. Permanent-magnet synchronous generators

3.2.3.2. Frequency converters

3.2.4. Model of Wind Farms

3.2.4.1. Combined method of the single WTG and the pad-mounted transformer

3.2.4.2. Wiring method of HV side of the pad-mounted transformer

3.2.4.3. Wiring method of one group of WTGs with the step-up substation at PCC

3.3. Security and Stability Analysis on Wind Power Integration of Simple Systems

3.3.1. Introduction to Simple Systems

3.3.2. Wind Power Integration Capability Analysis by Multiple and Detailed Models

3.4. Security and Stability Analysis on Integration of Jiuquan Wind Power Base, Gansu, 2010

3.4.1. Transmission Plan

3.4.1.1. Serial compensating capacitor plan

3.4.1.2. Controllable HV reactor plan

3.4.2. Integration Capability of Jiuquan Wind Power System Installed with Serial Compensating Capacitors/Controllable HV Reactors

3.4.2.1. Xinjiang integrated with Northwest Grid, WTGs in constant voltage control mode

3.4.2.2. Xinjiang integrated with Northwest Grid, WTGs in constant power factor control mode

3.4.3. Integration Capacity of Jiuquan Wind Power System Not Provided with Serial Compensating Capacitors/Controllable HV Reactors

3.4.3.1. Xinjiang integrated with Northwest Grid, WTGs in constant voltage control mode

3.4.3.2. Xinjiang integrated with Northwest Grid, WTGs in constant power factor control mode

3.4.4. Effect of Various Integration Plans between Xinjiang and the Northwest Grid on the Wind Power Integration Capacity

3.4.4.1. WTGs not provided with serial compensating capacitors/controllable HV reactors and operated in constant voltage control mode

3.4.4.2. WTGs not provided with serial compensating capacitors/controllable HV reactors and operated in constant power factor control mode

3.4.5. Effect of WTG LVRT Capability on Integration Capacity of Jiuquan Wind Power System

3.4.5.1. WTGs in constant power factor control mode

3.4.6. WTGs in Constant Voltage Control Mode

3.5. Analysis on Reactive Voltage Characteristics with Consideration to Internal Electrical Wiring of Wind Farms

3.5.1. Introduction to Simple Systems

3.5.2. Impact of Internal Electrical Wiring of the Wind Farm on the Reactive Voltage Characteristics

3.5.3. Reactive Voltage Control Considering the Electrical Wiring of the Wind Farm

3.6. Evaluation Software for Wind Power Accommodation Capability

3.6.1. Software Design Process

3.6.1.1. Quantitative evaluation of single section

3.6.1.2. Conclusions of quantitative evaluation

3.6.1.3. Relations with the large power system simulation platform PSD-BPA

3.6.2. Core Algorithm of Software

3.6.3. Functions of Software

3.6.4. Performance of Software

3.6.4.1. Calculation accuracy

3.6.4.2. Calculation efficiency

3.6.4.3. Flexibility of software

3.6.5. Use of Software

3.6.5.1. Integrated environment

3.6.5.2. Brief introduction of menu and toolbars

3.6.5.3. Work steps

3.6.6. Case Analysis for Automatic Calculation of Evaluation Software

3.6.6.1. Setting mode of transmission limit section

3.6.6.2. Comparisons of auto/manual calculation results

Table of Contents for
Chapter 3. Simulation Calculations for Wind Power Transmission Capability