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Combined Shunt and Series Active Power Filters

Abstract

This chapter describes the main features that can be achieved with the use of combined series and shunt active power filters. It studies the different strategies to provide balanced, sinusoidal, and regulated voltages at the load terminals, as well as to obtain balanced sinusoidal supply currents in phase with the supply voltages. These targets allow us to define the structure and control calculations of a unified power quality conditioner (UPQC). The analysis of the state- space model will show the behavior of the conditioner to tune the components and control parameters. This analysis is contrasted with the results obtained in simulation and experimental cases. The power flow control and the voltage regulation in power systems with the unified power flow controller (UPFC) are also revised here. This can be combined with the tasks of the UPQC to design a universal active power line conditioner (UPLC). The control implementation and a practical case are developed to show its behavior.

Keywords

electric power quality

combined active power filter

load conditioning

unified power quality conditioner

unified power flow controller

universal active power line conditioner

This chapter describes the main features that can be achieved by using combined series and shunt active power filters. The first section focuses on the concept of load conditioning and power quality. It studies the different strategies to provide balanced, sinusoidal, and regulated voltages at the load terminals, as well as to compensate the harmonic, unbalance, and reactive components of the load currents to obtain supply currents with the same waveform and in phase with the fundamental direct-sequence component of the supply voltages. These targets allow us to define the structure and control calculations of a unified power quality conditioner (UPQC) to provide this load conditioning and to enhance the electric power quality (EPQ) in the point of common coupling (PCC).

Analysis of the state-space model of the power circuit and the control implementation will show the filtering characteristics of the conditioner, so that the values of the passive components around both converters can be selected, and the control parameters tuned.

The theoretical analysis is contrasted with the results obtained in simulation cases, developed in a platform based on MATLAB-Simulink; as well as with the results of an experimental laboratory prototype.

The last section of the chapter focuses on another interesting application of the series-shunt power conditioner: power flow control and the voltage regulation in electric power systems with the unified power flow controller (UPFC). The control techniques of this device are compatible with the tasks of the UPQC and can be combined to design a universal active power line conditioner (UPLC) with both functions. The complete control implementation is now defined, and a practical case is developed to show the behavior of the combined conditioner.

7.1. Introduction

The increasing sophistication of APFs has allowed them to be used in an increasing number of compensating functions, and the experience obtained from their use has shaped the objectives of the conditioners, depending on their situation in the electrical networks [1,2]. Thus, the main objective of an active filters installed by individual users would be the harmonic and unbalance compensation of its own specific nonlinear loads. On the other hand, the main objective of active filters installed by the electrical companies would be the compensation of the supplied voltages, as well as a harmonic dumping between distribution systems.

Depending on the specific objectives, different appropriate configurations for each application can be selected:

1. Shunt active filter (Figure 7.1): This is the simplest configuration and the one now most commonly used. Its main purpose is to compensate for nonlinear loads, injecting in parallel the harmonic components of the load current. Thus, its control strategy would be:

i_{C} = i_{L h}

(7.1)

Further applications assigned them a more complete compensation of the load current, including the reactive components (i_LfQ) as well as the unbalance components (i_LfU) at the fundamental frequency:

i_{C} = i_{L h} + i_{L f U} + i_{L f Q}

(7.2)

This increase in performance does not imply necessarily higher intensity peak values for the electronic devices, although they may need a higher capacity in the dc side to compensate for higher oscillating instantaneous power.

Finally it is worth mentioning the ability of the shunt APF to dump harmonic resonances between existing passive components in the electrical networks [3], acting as a harmonic resistance:

$i_{C} = G \cdot v_{L h}$

(7.3)

2. Series active filter (Figure 7.2): This configuration is specifically appropriate for individual HVS loads [4] where this load acts as a source of harmonic voltages, instead of harmonic currents. In this case, the compensation strategy should be:

v_{C} = - v_{L h}

(7.4)

Another more general application is to compensate for the unbalances and voltage harmonics of the mains supply [5], in order to provide an enhanced voltage to the installation. In this case, the strategy should be:

v_{C} = v_{S h} + v_{S f U}

(7.5)

It is usual to include, in both applications, an additional harmonic current compensating term R·i_Sh; since in both cases there may be harmonic voltage sources on the side of the circuit that is intended to be compensated. This term has also a dumping effect against transients and resonances, giving the conditioner a more robust behavior.

3. Hybrid filters (Figures 7.3–7.5) [2]: The cost, complexity, and energy efficiency of active filters, compared to passive filters of equal power, has promoted the development of hybrid solutions that use the advantages of both elements. The basic idea is to minimize the rated power of the active components, assigning them a tuning and damping behavior of the passive filters.

The combination of parallel passive and active filters of Figure 7.3 allows us to use the active filter as a damper for the passive filter against possible resonances. (The passive filter generically includes tuned filters and high-pass filter.) The series combination of passive filters and active filter in Figure 7.4 tries to achieve similar objectives.

The configuration in Figure 7.5 follows a slightly different principle, in which the series active filter – acting as a harmonic resistance – aims to force the flow of the load harmonics through the passive filters, providing also a harmonic damping between source and load.

4. Combined series–parallel active filters (Figure 7.6): The dual properties of series and shunt active filters has led to combined designs, which have been generically called UPQC [6–10].

The configuration shown in Figure 7.6 is the most commonly used of the different options. Both converters share a common dc link, which is regulated through the shunt converter. The series converter usually compensates the supply magnitudes (v_S, i_S) and the shunt converter is mainly focused on the load side (v_L, i_L). There is another usual topology that is symmetrical to this one, where the series APF is at the load side of the circuit [7]. This topology is usually intended for specific loads and each converter compensates only one of the target magnitudes. The configuration of Figure 7.6 is particularly suitable for distribution systems and combines the functions of both filters to compensate the distortion and unbalances of the supply voltages, as well as the load currents. The control strategy would be:

v_{C} = v_{S h} + v_{S f U} + R \cdot i_{S h}

(7.6)

i_{C} = i_{L h} + i_{L f U} + i_{L f Q}

(7.7)

Thus, the series filter compensates the supply voltages and provides harmonic damping between source and load; and the parallel filter compensates the load currents. Furthermore, the topology of this conditioner allows to each converter to control both target variables – the load voltages and the supply currents – and to design a global control strategy that enhances the general behavior of the conditioner.

Figure 7.3 Parallel passive, parallel active hybrid filter.

Figure 7.4 Parallel active–passive hybrid filter.

Figure 7.5 Series active, parallel passive hybrid filter.

Figure 7.6 Series–parallel combined active filter.

7.2. Unified Power Quality Conditioner

This section explains and develops the design and control implementation of a UPQC to compensate a broad range of load types, improving the EPQ in the point of common coupling (PCC). This conditioner is called load compensation active conditioner (LCAC) and has a specific design to enhance the voltages applied to the load and the currents delivered by the electrical supply.

The general target is the compensation of the distortion and unbalance produced by nonlinear loads, and the supply network itself. With an adequate compensation strategy it is possible to obtain balanced sinusoidal supply currents in phase with the direct-sequence component of the supply voltages; and regulated and balanced sinusoidal voltages applied to the load terminals. From this point of view, the combination of series and parallel active filters is seen as one of the most appropriate configurations [1], and the topology shown in Figure 7.6 has the capability to achieve these requirements.

In the first stage, the series converter should apply a controlled voltage equal to the harmonic and unbalance components of the supply voltages (equation (7.8)) to isolate the load from this source of distortion; as well as a direct-sequence fundamental voltage to regulate the voltage level at the load side. On the other hand, the shunt converter should draw the harmonic, unbalance, and reactive components of the current required by the load (equation (7.9)) to avoid that they flow through the whole supply network. And the other task of the shunt converter is to maintain the voltages of the dc link, through an active component, i_adcreg, to compensate the internal losses of the conditioner.

$v_{C}^{*} = v_{S h} + v_{S f U} + ∆ v_{S f +}$

(7.8)

$i_{C}^{*} = i_{L h} + i_{L f U} + i_{L f Q} - i_{a d c r e g}$

(7.9)

In the second stage, it is advisable to consider the inclusion of the current harmonic dumping term (R · i_Sh) in the series converter due to the reasons explained in the previous section. This way, the presence of HVS loads in the generic distribution line is mitigated, and the additional control term provides damping against transients and possible resonances. At this point, it is important to state that pure HVS loads should have their own specific compensation methods, like active filters or smoothing reactors. Otherwise they could not be connected to pure sinusoidal voltage sources, when the resulting currents exceed the capabilities of their own electronic power devices. And when they are in the same line with another loads, strong voltage distortions and unbalance can be produced.

It is also convenient to include a corrective term for the load voltages in the reference current of the shunt converter (G·v_Lh). When the conditioner is applied to a strong HVS load or the changes in the load current are faster than the tracking capability of the shunt converter, the correcting term of the series filter reach significant values and therefore the load voltages differ substantially from their reference values. If the shunt converter can provide this requested current as fast as possible, the voltage gap will be minimized. Otherwise it must be assumed that the load voltages will remain distorted (it is a voltage distortion caused by the own load and remains only in the load side) and that the dumping effort will flow through the series converter and the supply network. With the additional term in the shunt converter, the stabilization efforts of the conditioner are shared between the converters and the part of these transients that flow through the supply is reduced.

$v_{C}^{*} = v_{S h} + v_{S f U} + ∆ v_{S f +} + R \cdot i_{S h}$

(7.10)

$i_{C}^{*} = i_{L h} + i_{L f U} + i_{L f Q} - i_{a d c r e g} - G \cdot v_{L h}$

(7.11)

These correcting terms, in both converters, should be limited in the control implementation to maintain the voltages and currents of the conditioner in affordable values. In any case, they act as a feedback of the general compensation process to improve the dynamic of the active conditioner, as will be shown later on. This way, each filter will develop a specific function using a unified control that treats the load compensation process globally.

7.2.1. Structure of the UPQC

Figure 7.7 shows the power circuit of the LCAC. It includes two full bridge power converters with a common dc link and passive elements for the filtering the high frequencies. One of the converters is connected is series with the supply, through a coupling transformer, and the other one is connected in parallel with the load. Both are voltage source converters, with pulse width modulation (PWM) control. In the most recent developments, for three-phase four-wire systems, these converters are made with IGBT devices with a three-leg configuration (see Section 4.3.3) and a split dc link to allow the neutral wire connection [8].

The figure also shows the location of the passive elements for the filtering of the higher harmonics. The harmonic traps (L_S1, R_S, C_S, L_S2) provide filtering of the voltage harmonics generated by the series inverter. The branches R_P, C_P in association with L_S2 provides a low impedance path for the higher harmonics of i_C or i_L. The same elements attenuate the effects of the noncontrollable harmonics of v_S over the load voltages v_L or the supply currents i_S.

The switching control of the converters is based in the reference signals

v_{C}^{*}

i_{C}^{*}

generated in the internal LCAC control, following the compensation strategy exposed previously.

The construction of the voltage waveform v_C for the series converter is made with the scheme shown in Figure 7.8. It is a PWM modulation control by comparison with a triangular wave for a switching frequency of 20 kHz. A sample and hold element is applied to the reference signal

v_{C}^{*}

, each 50 μs, to limit the maximum switching frequency. It also allows to implement this control by DSP as well as to show the robustness of the control strategy explained in this section.

Figure 7.8 PWM generation of the series converter voltage v_C.

Figure 7.9 shows the control scheme applied to the generation of the current i_C in the shunt converter. The switching control is made with periodic sampling, with a fixed switching frequency. Although this method is not the best for accurate wave generation, the criteria for its selection were the foregoing exposed for the series filter. Actually, both the acquisition of all the measurements as well as the generation of the signal references of the conditioner are sampled every 50 μs.

Figure 7.9 Generation of the shunt converter current i_C.

7.2.2. Control Strategy of the UPQC

The control of the LCAC allows the power circuit to develop a dual function. The series filter works as a controlled voltage source to compensate that part of the supply voltages that differs from a balanced and regulated sinusoidal waveform. That is, the series filter eliminates the voltage harmonics and unbalance to get a direct sequence system. And at the same time it regulates the voltage level applied to the load.

On the other hand, the shunt filter located downstream of the series filter, will compensate the harmonics, reactive and asymmetry components included in the load currents. As a consequence, it cancels the neutral current. It will be also responsible for regulating the voltages of the common dc link.

Figure 7.10 shows the overall scheme of the control reference calculations, wherein each filter develops a specialized function through a unified control that treats globally the load compensation process. Thus, the voltage signals that the control circuit uses for determining the compensation currents of the parallel filter (see Figure 7.12) are the reference voltages of the series filter. And, as will be explained in the next section, the crossed correcting signals between converters will be detailed; and their function as stabilizer against transients and possible imperfections in the generation of the reference waveforms will be shown.

Figure 7.10 Overall scheme of the LCAC control.

The reference voltage of the series compensation filter (

v_{C}^{*}

) is obtained by comparing the supply voltage (v_S) and its fundamental positive-sequence component with controlled amplitude (

v_{1, reg}^{+}

) as described later. This signal

v_{1, reg}^{+}

is also used for the determination of the compensation current (

i_{C}^{*}

) of the shunt converter, based in the calculation of the active current of the load [11] and the internal power balance of the conditioner. The use as voltage signal of

v_{1, reg}^{+}

makes the reference active currents (i_a) of each phase to be balanced and sinusoidal.

7.2.2.1. Calculation of the Load Voltage Reference ( $v_{L}^{*} = v_{1, r e g}^{+}$ )

The control of the series filter aims to obtain an ideal voltage supply: balanced voltages without distortion. Figure 7.11 shows the block diagram for this part of the control circuit.

Figure 7.11 Block diagram for the extraction of the fundamental positive-sequence amplitude regulated voltage component. (a) Obtaining the fundamental positive-sequence component; (b) Amplitude regulation and three-phase wave building.

The first stage is to obtain the positive-sequence component (v⁺) of the supply voltages. The phase shift of ±1/3 of a cycle of the voltage signals in phases 2 and 3, and the mean value of the three signals, results in a signal that has as fundamental harmonic the positive-sequence component of the voltages (

v_{1}^{+}

$\begin{array}{l} v^{+} (t) & = \frac{1}{3} (v_{1} (t) + v_{2} (t - \frac{T}{3}) + v_{3} (t + \frac{T}{3})) \\ = V^{+} \cos (ω t + ϕ^{+}) + \sum_{h = 2}^{\infty} V_{h} \cos (h ω t + ϕ_{h}) + V_{dc} \end{array}$

(7.12)

There are three terms in equation (7.12): the direct-sequence component of the fundamental harmonic, the rest of harmonic components, and an eventual nonzero average component. Subsequently, through a bandpass filter, the harmonic and dc components are removed and the signal

v_{1}^{+}

is obtained.

In the second stage, a control loop regulates the rms value of

v_{1}^{+}

to a preset value V_REF. The selection of the bandwidth of the bandpass filter (±2% f_N) is oriented to attenuate fast voltage amplitude variations (voltage flicker [7]). And the combination with the amplitude control loop allows a fine voltage regulation. Finally, the three-phase voltage waveforms are built (

v_{1 r 1}^{+} (t), v_{1 r 2}^{+} (t), v_{1 r 3}^{+} (t)

). The use of a double subtraction for phase 2 cancels instantaneously any remaining zero-sequence component and simplifies the scheme.

7.2.2.2. Calculation of the Active Current Reference ( $i_{S}^{*} = i_{a}$ )

The shunt filter control is based on the calculation of the active load current (i_a), and its block diagram is shown in Figure 7.12. The current reference

i_{S}^{*}

will be this active load current, and it is obtained from the calculation of the active load current using the voltage reference

v_{1, reg}^{+}

Figure 7.12 Block diagram for the calculation of the compensation currents for the shunt filter.

The transfer of an active power P from source to load requires the line currents (active currents) to be [11]:

$\begin{array}{c} i_{a 1} = \frac{P}{V^{2}} v_{1}; & i_{a 2} = \frac{P}{V^{2}} v_{2}; & i_{a 3} = \frac{P}{V^{2}} v_{3} \end{array}$

(7.13)

$V^{2} = \frac{1}{T} \int_{0}^{T} (v_{1}^{2} + v_{2}^{2} + v_{3}^{2}) d t$

(7.14)

where V is the three-phase voltage rms value. The difference between the load currents i_L and the active currents i_a determinate the components that do not transport useful power and are therefore compensable (

i_{CL}^{*}

)

$i_{CL}^{*} = i_{L} - i_{a}$

(7.15)

The determination of the active power P requires a low pass filter that eliminates the oscillatory component of the instantaneous power p(t), with a critical frequency at least the supply frequency. Using a feedback loop and an integrator it is possible to reach, in steady state, some values of

i_{C}^{*}

whose average power P_C is null. Therefore, the output of the integrator remains without change in the previous estimated value of P/V². This will be its state until the load changes. The adaptation speed against load variations depends mainly on the dynamic response of the set low pass filter + integrator. The use of

v_{1, reg}^{+}

allows the active currents references i_a to be balanced and sinusoidal, if the equivalent conductance G_C is constant. If there are unbalances and harmonics the instantaneous power is not constant and there must be a tradeoff between the adaptation speed of the control loop and the allowable oscillating components in G_C.

In the second stage, the power flow through the series filter (

v_{C}^{*} \cdot i_{S}^{*}

) is included in the instantaneous power to enhance the estimation of the power balance, as well as the necessary direct regulation of the dc side voltages of the conditioner (see Section 4.5.2). If the power balance is accurate the variation of the dc side voltages will be reduced and the corresponding control loop will set an equivalent conductance G_V with smaller oscillations.

Finally, the crossed correcting terms of equations (7.10) and (7.11) should be defined. These components have a strong damping effect in the power circuit and can be analyzed together with the dynamic behavior of the passive components around the PWM converters. This joint analysis will allow to enhance the selection of both components.

7.2.3. Parameters Design

In the first stage, the dynamic behavior of the passive components will be analyzed. This will be carried out using the state-space equations, to check if they mitigate adequately the high frequency switching harmonics and no amplifications occur with possible resonances. The damping terms can be included later, with a similar analysis, to study their joint behavior in the different frequency ranges.

Figure 7.7 has shown the location of the passive elements of the active conditioner. These passive components have the function of filtering the higher harmonics (those greater than f_C/10, where f_C is the maximum switching frequency of the converters). Among these harmonics are the harmonics generated by the converters themselves. The series converter generates harmonics with frequencies near the switching frequency [8], with an amplitude equal to the maximum assigned compensating voltage (20–30% of the rated voltage V_N). The shunt converter produces harmonics with lower amplitude but also lower frequencies [12,13]. In the same way, the passive components can be assigned the mitigation of those components noncontrollable by the converters (like sharp load current changes, etc.). On the other hand, they should interfere as little as possible with the tasks of the LCAC at low frequencies, mainly to maintain at maximum the energetic efficiency of the conditioner.

Figure 7.13 presents the single-phase equivalent circuit of the conditioner, where the series-coupling transformer has been considered as ideal, and the load as a current source. The series converter, with its PWM generation control, has been considered as a controlled voltage source; and the shunt converter with its output inductance has been considered as a controlled current source.

Figure 7.13 Single-phase equivalent circuit of the passive components.

7.2.3.1. Analysis of the Passive Circuit

The passive circuit of the active conditioner can be considered as a passive n-port network [9] that relates the one-port elements among each other, corresponding to the points of supply, load, series and shunt converters of the LCAC. This relation can be expressed with the state-space equations of the n-port:

$\begin{array}{c} \begin{array}{l} \frac{d}{d t} x = A x + B_{1} u + B_{2} w \\ y = C x + D_{1} u + D_{2} w \end{array} & \equiv & \begin{array}{l} \frac{d}{d t} [\begin{array}{c} v_{cap} \\ i_{ind} \end{array}] = A [\begin{array}{c} v_{cap} \\ i_{ind} \end{array}] + B_{1} [\begin{array}{c} v_{C} \\ i_{C} \end{array}] + B_{2} [\begin{array}{c} v_{S} \\ i_{L} \end{array}] \\ [\begin{array}{c} v_{L} \\ i_{S} \end{array}] = C [\begin{array}{c} v_{cap} \\ i_{ind} \end{array}] + D_{1} [\begin{array}{c} v_{C} \\ i_{C} \end{array}] + D_{2} [\begin{array}{c} v_{S} \\ i_{L} \end{array}] \end{array} \end{array}$

(7.16)

where u = [v_C, i_C ] are the variables controlled by the converters of the LCAC; w = [v_S, i_L] are the variables corresponding to the distortions introduced in the system from the supply or the load sides; y = [i_S, v_L] are the target variables of the control; and x are the state variables of the passive network that are usually identified with the energy storing elements (capacitance voltages, v_cap, and inductance currents, i_ind). For the case of the Figure 7.13 there are four state-space variables.

If the equations are expressed in the Laplace domain, we can calculate the transfer functions to evaluate the effect of the independent variables u and w over the target variables y of the control; through the passive elements of the conditioner:

$Y (s) = [C {(I_{S} - A)}^{- 1} B_{1} + D_{1}] U (s) + [C {(I_{S} - A)}^{- 1} B_{2} + D_{2}] W (s)$

(7.17)

If the n-port network is linear, its response can be considered as the superposition to different excitations. Thus, it is possible to split the response to the control sources u into two parts: the ideal value u* that could achieve the desired values of y (

v_{L}^{*}

and

i_{S}^{*}

); and the part of the control u_E, responsible of some deviations of the response y. The variable u_E includes the high frequency harmonics generated by the converters, as well as their control limitations. In this way, it is possible to model the behavior of the passive network against perturbations with a formulation similar to (7.16), with the difference that now u = u_E, and w = w_E are the deviations over the ideal control and ideal measurements, and y = y_E show the effects of these “noises” over the target values of v_L and i_S.

$\begin{array}{l} \frac{d}{d t} (x^{*} + x_{E}) = A (x^{*} + x_{E}) + B_{1} (u^{*} + u_{E}) + B_{2} (w^{*} + w_{E}) \\ (y^{*} + y_{E}) = C (x^{*} + x_{E}) + D_{1} (u^{*} + u_{E}) + D_{2} (w^{*} + w_{E}) \end{array}$

(7.18)

$\begin{array}{l} \frac{d}{d t} x_{E} = A x_{E} + B_{1} u_{E} + B_{2} w_{E} \\ y_{E} = C x_{E} + D_{1} u_{E} + D_{2} w_{E} \end{array}$

(7.19)

The analysis made on the passive circuit is based on two criteria:

• The eigenvalues of the matrix A are the poles of the characteristic equation of the system and show the natural responses of the passive circuit and also its stability. They define the dynamic response of the passive circuit during transients, like the start of the LCAC where the initial conditions of the internal states can be far from the reference values.

• The bode plots of the transfer functions of (7.19), between each element of the y_E vector, with respect to each element of u_E and w_E vectors, will show the attenuation degree obtained at the control targets.

The study has been made on an equivalent single-phase model (Figure 7.13), where the series converter has been modeled as a controlled voltage source and the shunt converter as a controlled current source. The values of the passive components have been chosen through their results with the eigenvalues and transfer functions of this model. As a general target, an attenuation of −40 dB (1%) has been aimed, especially over f_C/10. The values of these components are shown in Table 7.1, and the corresponding eigenvalues are shown in Table 7.2. After some initial state-space analysis like the one that is to be explained hereafter, the value of the resistance R_P has been finally set to zero, to reduce the influence of the high frequency components of i_C over the load voltage v_L.

Table 7.1

Values of the Passive Components for the State-Space Analysis

L_S1	25 mH	L_S2	5 mH
R_S	800 Ω	R_P	0 Ω
C_S	1 μF	C_P	15 μF

Table 7.2

Eigenvalues of A for the Passive Circuit of Figure 7.13

Eigenvalues of A (s⁻¹)

−16.84 ± 1.476j (235 Hz)

−1.283

−190.683

Figure 7.14 presents the magnitudes of the transfer functions of u_E and w_E over y_E, as a function of frequency. For a better interpretation of the results, the transfer functions have been plotted in per unit values, being 230 V and 1000 VA/230 V the base values for voltages and currents. Some solid lines have been included in Figure 7.14 for a better interpretation and resolution. Three vertical solid lines show the frequency references of 50 Hz, 2 kHz (f_c/10), and 20 kHz (f_c). There are also two horizontal lines at the attenuation levels of −30 and −40 dB.

Figure 7.14 Transfer functions of the passive network. Reference vertical solid lines at 50 Hz (f_N), 2 kHz (f_C/10), and 20 kHz (f_C). Reference horizontal solid lines at −30 and −40 dB.

A correct attenuation for frequencies greater than 2 kHz can be observed, but a strong resonance in 235 Hz is also appreciated, with a very slow transient response (see first eigenvalue of A in Table 7.2). Any inaccuracy in the generation of the compensating voltages v_C of currents i_C will be amplified in a factor greater than 10, and will deteriorate the compensation feature of the conditioner.

7.2.3.2. Control Modification

It is difficult to avoid these types of resonance in the choice of the values of the passive components, since these components should be dissipative the least possible. To enhance the behavior of the system in the range of the controllable frequencies, the basic control is modified with two correcting signals: over v_C, a signal

R (i_{S}^{*} - i_{S})

is added, and over i_C the value of

G (v_{L}^{*} - v_{L})

. That is, correcting signals proportional to the deviation of the targets respect to their control values, and applied in the opposite converter that should control them. These signals will act eliminating the resonances that could occur. Their effect can be analyzed including this control law over u_E in the state-space equations (7.19); and recalculating the transfer functions and eigenvalues.

The values of R and G can be chosen to make the adjustment of y to their control references as fast and stable as possible, as well as to reduce the magnitude of the transfer functions. On the other hand, it would be convenient if these values were not so large, in order to avoid unnecessary effort by the compensator. Figure 7.15 shows the effect of these parameters on the eigenvalues of the modified matrix A. This three-dimensional surface shows the minimum real part of the eigenvalues of A for each pair of values of the parameters R and G. The eigenvalue with a lower negative real part can be considered as the dominant pole of the system and it is associated with the slowest dynamic response. This graphic does not show if the eigenvalues are real or complex, but gives an initial selection of the control parameters. In the contour plot at the right side we can see that values for R greater than 50 and for G greater than 0.02 give a value for the minimum real part of −1.270 s⁻¹; which is equivalent to a time constant τ of 0.79 ms for the slowest pole. Larger values of R or G would not obtain much better results in terms of a faster response.

Figure 7.15 Minimum negative real part of A eigenvalues as a function of the parameters R (Ω) and G (Ω⁻¹). Three-dimensional and contour graphics.

Figure 7.16 shows the new transfer functions obtained with these values, and the effect of the modified control can be observed: The amplification at 235 Hz disappears and the system is better damped against possible perturbations. Table 7.3 presents the corresponding eigenvalues of the modified matrix A. The slowest pole has now a value of −1.302 s⁻¹, and the second one is complex but better damped than that of Table 7.2. However, considering the steady state behavior, the attenuation degree of the transfer functions shown in Figure 7.16 is quite low for the low frequency range. That means that, for instance, any inaccuracy in the compensation will appear almost in the same proportion in the target variables v_L and i_S.

Figure 7.16 Transfer functions of the passive network (- -), in comparison with that of the modified control (-), with R = 50 and G = 0.02. Reference vertical solid lines at 50 Hz (f_N), 2 kHz (f_C/10), and 20 kHz (f_C). Reference horizontal solid lines at −30 and −40 dB.

Table 7.3

Eigenvalues of Matrix A With R = 50 and G = 0.02

Eigenvalues of the modified A (s⁻¹)

−1.302

−1.521 ± 1.421j (226 Hz)

−190.683

To enhance this attenuation degree it is possible to increase the parameters R and G, without significantly changing the response speed, as shown in Figure 7.15. Table 7.4 shows the eigenvalues for values of R and G equal to 250 and 0.1, respectively and Figure 7.17 presents the corresponding transfer functions.

Table 7.4

Eigenvalues of Matrix A With R = 250 and G = 0.1

Eigenvalues of the modified A (s⁻¹)

−1.251

−7.767 ± 774.7j (123 Hz)

−181.881

Figure 7.17 Transfer functions of the passive network (- -), in comparison with that of the modified control (-), with R = 250 and G = 0.1. Reference vertical solid lines at 50 Hz (f_N), 2 kHz (f_C/10), and 20 kHz (f_C). Reference horizontal solid lines at −30 and −40 dB.

The first and last eigenvalues in Table 7.4 are similar to those shown in Table 7.3, and the pair of complex poles has a faster and much better damped dynamic response. And the attenuation degree of the transfer functions shown in Figure 7.17 is also enhanced in the low frequency range.

The analysis done so far has shown the capability of the crossed control terms of equations (7.10) and (7.11) to damp the system dynamic and to reduce the perturbations over the control targets. It is now convenient to include the direct compensation terms of equations (7.10) and (7.11) for a more complete analysis. The distortions of the supply voltage v_S and the load current i_L can be compensated directly and the corresponding transfer functions will be greatly reduced. However, it is usual to compensate only a fraction of these signals (typically 95%) to prevent positive feedbacks due to measurement inaccuracies or control delays. Another possibility is to filter out the high frequency components of these signals, which can be filtered by the passive components and damped with the crossed control terms. This can also reduce the efforts of the converters in the high frequency range.

Considering that the converters can build accurate compensating signals until f_C/10, the input signals v_S and i_L will be filtered with a second order Butterworth high-pass filter at 2 kHz:

$v_{C}^{*} = G_{1} (s) (v_{L}^{*} - v_{S}) + R \cdot (i_{S}^{*} - i_{S})$

(7.20)

$i_{C}^{*} = G_{1} (s) (i_{L} - i_{S}^{*}) + G \cdot (v_{L}^{*} - v_{L})$

(7.21)

where G₁(s) is:

$G_{1} (s) = \frac{\sqrt{2} \frac{s}{ω_{f}} + 1}{\frac{s^{2}}{ω_{f}^{2}} + \sqrt{2} \frac{s}{ω_{f}} + 1}$

(7.22)

Their effect can also be analyzed including this control law over u_E in the state-space equations (7.19); and recalculating the transfer functions and eigenvalues. Figure 7.18 presents the corresponding transfer functions, and the eigenvalues are shown in Table 7.5. The first four eigenvalues are equal to those in Table 7.4, and the last four of the double complex pole correspond to those introduced by the Butterworth filters (equation (7.22)). Looking at the transfer functions we can see that the ones for the noise sources in v_C or i_C remain unchanged, but those corresponding to v_S or i_L are greatly reduced, especially in the low frequency range.

Figure 7.18 Transfer functions of the passive network (- -), in comparison with that of the modified control (-), with R = 250, G = 0.1 and prefiltering of the input signals. Reference vertical solid lines at 50 Hz (f_N), 2 kHz (f_C/10), and 20 kHz (f_C). Reference horizontal solid lines at −30 and −40 dB.

Table 7.5

Eigenvalues of Matrix A With R = 250, G = 0.1 and Prefiltering of the Input Signals

Eigenvalues of the modified A (s⁻¹)

−1.251

−7.767 ± 774.7j (123 Hz)

−181.881

−8.886 ± 8.886j (1.414 Hz) (double)

Example 7.1

The UPQC with the control strategy described in this section will be simulated to check its behavior. The power circuit of the conditioner is shown in Figure 7.7 and the values of the passive components are shown in Table 7.1. The value of the parallel filter inductance L_P, that is not included in the state-space analysis, is 50 mH, 1 Ω. All the dc link capacitors are of 2200 μF, and will be precharged at the reference value at the beginning of the simulation. The UPQC will be applied to an unbalanced nonlinear load composed of three different single-phase loads. In the phase 1 it is a single-phase diode rectifier with a high capacitor and a resistive load in the dc side, and a smoothing reactor in the ac side. For the phase 2, it is a single-phase diode rectifier with a series RL load in the dc side. And ideal resistors for the phase 3, with an ideal switch to produce a load change. Figure 7.19 represents the simulation model.

This load is fed with an unbalanced set of voltages (214, 198, 225 V), and a 5th harmonic component of 10 V with inverse sequence. The equivalent impedance of the supply network has been modeled with a resistance of 1Ω and an inductance of 1 mH in series. This example has been simulated in MATLAB-Simulink using device models of the SymPowerSystem library.

This simulation case will show the behavior of the UPLC, to isolate the load from the harmonics and unbalance of the supply side, and to compensate the harmonics, unbalance, and reactive components of the load currents. The UPQC is activated at 100 ms, and before that the series part of the conditioner is short-circuited and the IGBTs of the shunt conditioner are off. The load changes at 200 ms to show also the dynamic response of the conditioner in those cases.

Figures 7.20 and 7.21 show the phase voltages v_L at the right side of the UPQC and the phase currents i_L of the nonlinear load that has to be compensated by the conditioner, during the whole simulation. Figures 7.22 and 7.23 show the waveforms of the phase voltages v_S at the supply side of the UPQC and the phase currents i_S that flow through the series converter. Before the activation of the UPQC, the supply currents are distorted and unbalanced, mainly due to the distortion produced by the nonlinear load and the harmonics and unbalance of the supply voltages. There is also some level of distortion produced by the resonances among the load, the passive components of the conditioner and the supply line impedance.

Figure 7.20 Phase voltages at the load side of the UPQC.

Figure 7.22 Phase voltages at the supply side of the UPQC.

Figure 7.23 Phase currents of the supply side.

Figure 7.24 shows in some detail the effects of the connection of the UPQC, in the supply side of the conditioner. These currents become sinusoidal and balanced, according to the active component of the load current and the power balance of the conditioner. In the first milliseconds of this transition, some high frequency peaks appear, due to the efforts of the converters to control quickly the target magnitudes. After this short transient, the supply voltages v_S remain distorted and unbalanced due to the characteristics of the own voltages sources. Figure 7.25 shows the variation of the load voltages and currents with the start of the UPLC. The resonances, distortion, and unbalance are strongly mitigated and the load voltages become sinusoidal, balanced, and regulated to its nominal value. The load currents seem to be quite robust against the distortion of the applied voltages, mainly because they have a strong distortion by themselves. Only in the resistive load of the third phase a clear enhancement can be observed due to the compensation of the load voltage. And the major visible change after the compensation is observed in the current of the first phase i_La. The load of this phase is the most sensible to the voltage variations, especially at the peak values, and the enhancement of this phase voltage produces a visible increase of the corresponding current, with a small transient of around two cycles.

Figure 7.24 Detail of the supply voltages and currents before and after the connection of the UPQC.

Figure 7.25 Detail of the load voltages and currents before and after the connection of the UPQC.

The load change is set at 200 ms, and is concentrated in a change of the resistance of the third phase (see Figure 7.21). This connection produces a fast change of this current that cannot be compensated instantaneously by the shunt converter and produces a small deviation of this phase voltage (see. Figure 7.20) that is compensated in few milliseconds. Afterwards, the induced transient is much smoother, while the control of the UPQC set the new value of the supply currents to deliver the active power of the load, in approximately two and a half cycles (see Figure 7.23).

On the other side, Figure 7.26 shows the neutral current of the load i_Ln and the supply i_Sn. Before compensation, the character of the load produces a considerable amount of zero-sequence currents, of the same order of the phase currents, which flow also through the supply line. The unbalance of the load is clearer when the applied voltages are compensated. Then, the neutral current is even greater; although the shunt converter of the UPQC can compensate this component and the neutral current of the supply line is reduced to a minimum value, mainly due to the voltage regulation of the dc side of the conditioner

Figure 7.26 Neutral currents of the load and the supply sides.

Figure 7.27 shows the compensating currents i_C produced by the shunt converter of the UPQC. With the activation of the converters, the conditioner delivers the harmonic, unbalance, and reactive components of the load currents, as well as an active component to regulate the power balance of the conditioner and the voltages on the dc side. The compensating current of the third phase is mainly a fundamental component to compensate the zero- and negative-sequence components of the three-phase load. And with the load change, the differences are mainly in fundamental unbalance components because the currents of the first and second phases of the load remain in similar values.

Figure 7.27 Compensating currents of the shunt converter of the UPQC.

Figure 7.28 shows the references of the compensating voltages

v_{C}^{*}

produced by the series converter of the UPLC to regulate the load voltage and to isolate the load side from the harmonics and unbalance of the supply side. They are around 25% of the amplitude of the base voltage and differ slightly in each phase, corresponding with the voltage regulation and voltage harmonic present in each one. They also show an increase after the load change at 200 ms to compensate the voltage drop of the increasing supply currents.

Figure 7.28 References of the compensating voltages of the series converter of the UPQC.

Figure 7.29 presents the instantaneous active and reactive powers required by the load during the simulation. They show during the whole period a clear shape of an unbalanced and distorted behavior. Even after the compensation of the load voltages, they indicate a stronger unbalance component that becomes greater with the load change. Figure 7.30 shows the instantaneous active and reactive powers in the point between the converters where both magnitudes are controlled: the load voltages v_L and the supply currents i_S. After the compensation both variables become balanced and sinusoidal, and therefore the instantaneous powers behave as constant values. The instantaneous reactive power is almost null because these voltages and currents are in phase. And the average value of the instantaneous active power increases after the beginning of the compensation due to a better voltage regulation of the load side.

Figure 7.29 Instantaneous active and reactive powers at the nonlinear load.

Figure 7.30 Instantaneous active and reactive powers between the converters of the UPQC.

Figure 7.31 presents the instantaneous active and reactive powers delivered by the supply. After the compensation of the UPQC, the oscillating components of the power are clearly reduced due to the enhancement of the supply currents. However they do not disappear completely because the supply voltages remain unbalanced and distorted.

Figure 7.31 Instantaneous active and reactive powers provided by supply side.

Figures 7.32 and 7.33 show the instantaneous active and reactive powers that flow through the series and shunt converters of the UPQC, respectively. The powers through the series converter are significantly lower, to compensate the relatively low values of voltage distortion, unbalance and lack of regulation of the supply side, and the supplementary efforts to control the supply currents. They are increased with the change of the load and the corresponding supply current. One significant part of the average value of the active power delivered by the series converter corresponds to the voltage drop of the supply voltages in its fundamental balanced component. The oscillating powers through the shunt converter reach significantly higher values. The strong unbalance of the load produces a visible 100 Hz component that must be delivered with the shunt converter along with the rest of high frequency components. With the change of the load, the active power shows a clear first order transient that lasts around two and a half cycles. This is produced by the power balance control of the conditioner. While the supply current reference does not reach the active current of the new load condition, the UPQC must provide this power to the load. This will reduce the voltage of the dc side capacitors, which will have to be recharged slowly along the new steady stage.

Figure 7.32 Instantaneous active and reactive powers of the series converter of the UPQC.

Figure 7.33 Instantaneous active and reactive powers of the shunt converter of the UPQC.

Figure 7.34 presents the evolution of the voltages of the dc side capacitors during the present case. At the beginning of the compensation they have a relatively slow decrease of their average value. The difference between them reaches a visible amount while the conditioner compensates the transient components of the currents and voltages during the first two cycles; until this values become balanced. In this stage an oscillating and alternating component remains due to the zero-sequence components of voltages and currents that are being compensated. After the load change, the average value has a greater variation. At the beginning of the compensation, the internal power balance was set to the previous values and the change of the load voltages in this step was not so great as to change significantly the active power of the load. In comparison, the load change implies a bigger variation of the active power of the load. In the first two cycles, the reference of the supply current is not high enough and the capacitors are being discharged. When the power balance is set again, this decrement stops and the dc voltages begin to recover to their reference values through the additional active current of the shunt converter that controls these parameters.

Figure 7.34 Voltages at the dc link of the UPQC.

Finally, a harmonic and unbalance analysis of the resultant voltage and current waveforms has been performed. Figure 7.35 shows the harmonic spectrum of the phase voltages and currents at the supply and load side after compensation, in a time window from 160 ms to 180 ms. The data is presented with the harmonic distortion index, HD, of each individual harmonic with respect to the fundamental value, and the harmonic order h has been used instead of the frequency. The values of the three phases of each magnitude are presented together to appreciate the global envelope of the harmonic spectrum of the three-phase set. Figure 7.36 shows a magnification of the harmonic spectrum of the supply currents for the first 20 harmonics, where the harmonic content of each phase can be distinguished.

Figure 7.35 Harmonic spectrum of voltages and currents.

Figure 7.36 Detail of the harmonic spectrum of the supply currents for the first 20 harmonics (50 Hz–1 kHz).

Table 7.6 shows the rms and total harmonic distortion (THD) values of these 12 variables obtained in this analysis. We can see that, after compensation, the load voltages v_Labc are much more balanced and regulated in amplitude than the supply voltages v_Sabc. The average voltage deviation respect to the nominal value is around 0.9%. The harmonic content of the load voltages is also greatly reduced. Looking at the harmonic spectrum, the fifth harmonic component of the supply voltages is clearly compensated by the series converter. The harmonic content of the load voltages is more spread, with small components around 0.2%. On the other side, the high THD values of the load currents of the first two phases indicate the nonlinear character of these two loads. After compensation, the supply currents become almost balanced and sinusoidal, with a low THD around 0.9%, and almost in phase with the supply voltages.

Table 7.6

Individual rms and THD Values After Compensation

	rms (V)	THD (%)		rms (A)	THD (%)
v_Sa	211.8	4.730	i_Sa	2.385	0.916
v_Sb	195.8	5.117	i_Sb	2.443	0.896
v_Sc	222.8	4.499	i_Sc	2.425	0.500
v_La	227.6	0.840	i_La	2.963	45.03
v_Lb	227.8	0.809	i_Lb	1.643	37.78
v_Lc	228.2	0.529	i_Lc	1.904	0.529

Table 7.7 shows some relevant three-phase indices of this analysis, as defined in Std. 1459, [14]: Three-phase rms effective voltage V_e; voltage total harmonic distortion, VTHD; voltage unbalance fundamental, VUF; three-phase rms effective current I_e; current total harmonic distortion, ITHD; current unbalance fundamental, IUF; active, reactive, and apparent powers of the fundamental components, P₁, Q₁, S₁; and total effective apparent power, S_e, of each three-phase set. These values have been calculated in the supply and load sides, as well as between the series and shunt converters; where the voltages are v_Labc and the compensated currents i_Sabc.

Table 7.7

Three-Phase Indices of the Harmonics and Unbalance Calculations

	Supply Side (v_S, i_S)	Between Conv. (v_L, i_S)	Load Side (v_L, i_L)
V_e	210.3 V	227.9 V	227.9 V
VTHD	4.763%	0.663%	0.663%
VUF	4.577%	0.113%	0.113%
I_e	2.418 A	2.418 A	2.425 A
ITHD	1.187%	1.187%	48.99%
IUF	2.208%	2.208%	44.43%
P₁	1521 W	1652 W	1306 W
Q₁	48 VAr	12 VAr	382 VAr
S₁	1522 VA	1653 VA	1361 VA
S_e	1526 VA	1653 VA	1658 VA

In Table 7.7, VUF is the voltage unbalance fundamental index and IUF is the current unbalance fundamental index [15], which are defined as:

Table 7.8

Individual rms and THD Values After Compensation

	rms (V)	THD (%)		rms (A)	THD (%)
v_Sa	212.6	2.804	i_Sa	3.861	4.124
v_Sb	196.7	2.640	i_Sb	3.896	3.623
v_Sc	224.7	2.808	i_Sc	3.887	4.762
v_La	229.2	2.294	i_La	2.712	39.70
v_Lb	231.9	3.371	i_Lb	2.849	29.41
v_Lc	230.1	1.887	i_Lc	2.821	1.900

$VUF = \frac{V_{u 1}}{V_{b 1}}, IUF = \frac{I_{u 1}}{I_{b 1}}$

(7.23)

These three-phase indices show that the unbalance, harmonics, and deregulation of the supply voltages are compensated in the load side, where the voltages have an unbalance fundamental index of only 0.11%, a total THD index of 0.66%, and an effective rms voltage of 227.9 V. On the other hand, the conditioner compensates the load currents and therefore the supply currents are much more balanced, with an unbalance fundamental index of 2.21% and with a low distortion, 1.19%. The effective value is slightly lower than at the load side due to the compensation of the unbalance and harmonic components. Although, the losses of the conditioner must be considered, as well as the low fundamental voltage at the supply side, that requires higher currents to deliver the same active power.

Regarding the power components during the active conditioning, we can see that the supply delivers an active power at the fundamental component equivalent to that requested by the load and the losses of the conditioner. The active power between the converters is higher than at the supply side because the series converter must inject a direct-sequence voltage to regulate the load voltages. It draws this power from the common dc link and the shunt converter equilibrates the power balance increasing the reference of the active current. On the other hand, the fundamental reactive power of the load is delivered mainly through the shunt converter. Between the converters and in the supply side the fundamental apparent power is almost equal to the active power and the displacement power factor is almost one. If we compare the fundamental apparent power, S₁, with the total effective apparent power, S_e, we can see that they are almost the same between the converters, where both voltages and currents are balanced and sinusoidal. At the load side the nonlinear currents imply relevant harmonic components in the apparent power and the total power factor is 0.787. At the supply side the distorted voltage sources increase slightly the effective apparent power, reducing the power factor to 0.997.

7.3. Experimental Prototype of UPQC

An experimental platform has been set to perform a validation of the proposed strategies and to verify the behavior of the conditioner. A series– parallel compensation has been applied to an unbalanced and nonlinear load supplied by an unbalanced set of voltages. Figure 7.37 shows the equivalent power circuit per phase of the series–parallel conditioner with their corresponding matching transformers and the passive elements for the filtering of the high frequency components. The series and shunt three-phase IGBT converters (Semikron SKM50GB123D) are connected back to back, with a common dc link composed by two electrolytic capacitors, C_dc+ and C_dc− of 2200 μF and 400 V each one [16,17]. The middle point of the dc link is connected with the neutral wire of the three-phase line. The turn ratio of the matching transformers T_P and T_S are 1:2 and 1:1, respectively, to achieve reasonable voltage values in the dc link. The filtering inductances L_P and L_S are 50 mH and 25 mH each one, and the values of the parallel filtering capacitor C_P and resistance R_P are 15 μF and 2.5 Ω, respectively. A panel selector switch allows to bypass the series converter to make tests with only parallel active compensation.

Figure 7.37 Single-phase equivalent power circuit of the active conditioner.

The switching control of the active converters and the calculation of the compensation references are made with a data acquisition and control system (dSPACE-DS1103). The sampling time of the main processor was set to 80 μs for the series–parallel compensation. The target references for the compensation are the fundamental positive-sequence components of the load currents i_L and supply voltages v_S, in order to achieve the lowest unbalance and harmonic components in the compensated system. When the series–parallel compensation is performed, the references for the series compensating voltage v_C and the shunt compensating current i_C are:

$v_{C}^{*} = G_{1} (s) (v_{L}^{*} - v_{S}) + R (i_{S}^{*} - i_{S})$

(7.24)

$i_{C}^{*} = G_{1} (s) (i_{L} - i_{S}^{*}) + G (v_{L}^{*} - v_{L})$

(7.25)

where

v_{L}^{*}

is reference for the load voltage: the fundamental direct sequence component of the supply voltage, regulated in amplitude to its nominal value, and

i_{S}^{*}

is a set of balanced currents in phase with the fundamental direct sequence component of the supply voltage, that transports the average active power of the load and the losses of the conditioner. This way, the unbalanced and harmonic components of the load current are compensated. The analysis made in Section 7.2.3 gives the prefiltering G₁(s) of the first terms of (7.24) and (7.25); and the second terms of these equations are the crossed correcting signals proportional to the deviation of the target magnitudes to the reference values, which damp the systems behavior in strong transients and with different kind of loads. With this kind of compensation, the load voltage v_L and the supply current i_S should have a very reduced content of unbalance and harmonic components.

The compensating voltage of the series converter v_C is built with a 20 kHz PWM generator (DS1103 slave), using its calculated reference

v_{C}^{*}

. The compensating current of the shunt converters is built with a periodic sampling control at 20 kHz, in an external circuit, using the deviation of the compensating current i_C respect to its reference

i_{C}^{*}

On the other side, an independent measurement system to calculate the indices is implemented [15] in another data acquisition card (dSPACE-DS1005), with a signal conditioning system formed by six voltage sensors (LEM-LV25-P) and eight current sensors (LEM LA35-NP). These signals are taken simultaneously to avoid phase differences between the measurements, to enhance the accuracy of the calculated results. The configuration of the virtual instrument was made following the IEC Std 61000-4-7 and IEC Std 61000-4-30 recommendations, using a window equal to five cycles of the fundamental component and a sampling frequency of 6400 Hz to avoid problems of aliasing and leakage errors.

Finally, the load is composed of three different single-phase loads. In the phase 1 it is a single-phase diode rectifier with a high capacitor and a resistive load in the dc side, and a smoothing reactor in the ac side. For the phase 2, it is a single-phase diode rectifier with a series RL load in the dc side; and a resistor for the phase 3. This load is fed through a variable autotransformer with an unbalanced set of voltages (214, 198, 225 V), considering a nominal phase to neutral voltage of 230 V_rms. These applied voltages have a small distortion similar to the existing in the supply network of the laboratory. Figure 7.38 shows the voltage and current waveforms of the load fed with this power supply.

Figure 7.38 Voltage and current waveforms of the load without compensation.

7.3.1. Results of Practical Case

Figures 7.39 and 7.40 show the resulting voltage and current waveforms with series–parallel compensation in the load and supply side, respectively. The supply currents i_Sabcn are practically balanced, sinusoidal and in phase with the fundamental positive-sequence component of the supply voltage. The load voltage is also enhanced, compensating the distortion and unbalance present in the supply voltage.

Figure 7.39 Voltage and current waveforms of the load side with active series–parallel compensation.

Figure 7.40 Voltage and current waveforms of the supply side with active series–parallel compensation.

Figure 7.41 shows the corresponding harmonic spectrum of the phase voltages and currents at the supply and load side after compensation, where the data is presented with the harmonic distortion index, HD, of each individual harmonic respect to the fundamental value, and the harmonic order h has been used instead of the frequency. The values of the three phases of each magnitude are presented together to appreciate the global envelope of the harmonic spectrum of the three-phase set.

Figure 7.41 Harmonic spectrum of voltages and currents.

Table 7.8 presents the rms value and the total harmonic distortion, THD, of these 12 variables. We can see that, after compensation, the load voltages v_Labc are much more balanced and regulated in amplitude that the supply voltages v_Sabc. The harmonic content of the load voltages is not so reduced, mainly is the phases a and b. Looking at the harmonic spectrum, the various harmonics present in the supply voltages are compensated by the series converter and the harmonic content of the load voltages is more reduced but more spread, with small components around 1%. On the other side, the high THD values of the load currents of the first two phases indicate the nonlinear character of these two loads. After compensation, the supply currents become almost balanced and sinusoidal, with a reduced THD around 4%, and almost in phase with the supply voltages.

Table 7.9 shows some relevant three-phase indices of this analysis, as defined in Std. 1459, [14]: Three-phase rms effective voltage V_e, voltage total harmonic distortion, VTHD, voltage unbalance fundamental, VUF, three-phase rms effective current I_e, current total harmonic distortion, ITHD, current unbalance fundamental, IUF, active and apparent powers of the fundamental components, P₁, S₁; and total effective apparent power, S_e, of each three-phase set. These three-phase indices show that the unbalance, harmonics, and deregulation of the supply voltages are compensated in the load side, where the voltages have an unbalance fundamental index of only 0.62%, a total THD index of 2.30%, and an effective rms voltage of 230.4 V. On the other hand, the conditioner compensates the load currents and therefore the supply currents are much more balanced, with an unbalance fundamental index of 0.95% and with a reduced distortion, 6.07% mainly due to the regulation of the dc link voltages. The effective value is higher than at the load side due to the losses of the conditioner but also due to the low fundamental voltage at the supply side, which requires higher currents to deliver the same active power.

Table 7.9

Three-Phase Indices of the Harmonics and Unbalance Calculations

	Supply Side (v_S, i_S)	Load Side (v_L, i_L)
V_e	211.6 V	230.4 V
VTHD	2.681%	2.296%
VUF	4.707%	0.619%
I_e	3.885 A	3.000 A
ITHD	6.066%	34.89%
IUF	0.947%	41.13%
P₁	2448 W	1732 W
S₁	2461 VA	1957 VA
S_e	2466 VA	2077 VA

Regarding the power components during the active conditioning, we can see that the supply delivers an active power at the fundamental component equivalent to that requested by the load and the losses of the conditioner. The reactive, unbalance, and harmonics powers of the load are delivered by the conditioner and the power factor at the supply side reaches a value of 0.993. At the load side the nonlinear currents imply relevant harmonic and unbalance components in the apparent power and the total power factor is 0.834, while the displacement power factor is 0.885.

7.4. Universal Active Power Line Conditioner

The concept of an active power line conditioner, APLC, emerges from the development of active power filters made with PWM force-commutated converters [2,8]. In the first proposals they were focused on the compensation of the currents of unbalanced nonlinear loads, including the reactive component. The capability of these PWM converters to produce controlled current or voltage waveforms in an important frequency range (∼1 kHz) with high fidelity and dynamic response, made them to be applied also in the field of flexible ac transmission systems (FACTS); for power flow control and dynamic and static stability enhancement. The UPFC is one of the most promising devices in the FACTS concept [18–22]. It is based on the combination of series and shunt power converters with a shared dc link, and has the potential of active and reactive power flow control and/or voltage stability in power transmission systems; inserting balanced fundamental voltages and currents in the line circuits.

When the combined series–shunt power conditioner includes also the tasks of a UPQC to compensate supply and load side harmonics and unbalances, it receives the name of universal active power line conditioner, UPLC [8,23].

Figure 7.42 shows an UPLC inserted in a line of the power system, near a nonlinear load. Acting as UPQC, it can compensate the distortion and unbalance of this nearby load, as well as to provide harmonic isolation and/or dumping for distortions and unbalances at both ends of the power line. When it works as UPFC, it can control the power flow of the line where the series converter is connected, and regulate the voltage V_L injecting fundamental reactive power with the shunt converter. The combination of both modes gives the UPLC the capability to compensate and to regulate the working conditions of this part of the network.

7.4.1. Unified Power Flow Controller

The UPFC device consists of a combination of series and shunt power converters with a common dc link, like that shown in Figure 7.42, where the series converter acts as a controllable voltage source V_C, whereas the shunt converter acts as a controllable current source I_C. The main purpose of the series converter is to regulate the active and reactive power flow of the controlled line L_S1, changing the receiving end voltage V_S1 with the series voltage V_C and therefore the current I_S1 of the line. The shunt converter can help to regulate the voltage at the bus where it is connected, injecting a current I_C that provides the necessary reactive power. The active power delivered by the shunt converter is not free, unless it had significant energy storage components because it must compensate the active power provided by the series converter and the internal losses of the conditioner.

The phasor diagram shown in Figure 7.43 illustrates the principle of voltage regulation with the shunt converter. When the current I_C leads 90° with respect the voltage V_L (Figure 7.43a), it produces a voltage V_LS2 in the equivalent impedance of the nearby network, thus increasing the voltage V_L. When the current I_C lags 90° (Figure 7.43b) it produces the opposite effect and reduces the voltage V_L. The amount of reactive power to be injected will be similar to other classical techniques to control the Q–V relation in electrical power systems.

Figure 7.43 Voltage regulation with reactive power.

Figure 7.44 shows a single-phase equivalent circuit of the series part of the UPFC to explain the principle of power flow control. The inductance L and the resistance R represent the series impedance of the transmission line, where it is usual to remove the resistance R because ω₀L ≫ R in this kind of line. Thus, the line current phasor I_S1 is given by:

Figure 7.44 Single-phase equivalent circuit.

$I_{S} = \frac{V_{S} - V_{L} + V_{C}}{j ω_{0} L}$

(7.26)

For the sake of simplicity, the assumption of V_S = V_L leads to the phasor diagram shown in Figure 7.45. When the series voltage V_C is in quadrature with the voltage V_L, it promotes the circulation of a current I_S1 in phase with this voltage, as shown in Figure 7.45a, and changes the flow of active power. Controlling V_C to be in phase with V_L, Figure 7.45b, makes the current I_S1 lag by 90° with respect to V_L, thus resulting in reactive power flow.

Figure 7.45 Phasor diagrams for series power control. (a) Active power control; (b) Reactive power control.

This power flow principle is most interesting feature of the UPFC. As we can derive from equation (7.26), the amount of power flow that the voltage source V_C can control is inversely proportional to the line fundamental impedance. Furthermore, the series converter will be working with balanced fundamental voltage waveforms, easier to achieve with low switching frequencies and reduces losses.

7.4.2. Power Flow Control, Voltage Regulation, and Power Quality Improvement

In this section, the control implementation of the UPFC principles will be discussed and detailed, as well as the integration of these control blocks in the general UPLC.

Considering the model exposed in Figures 7.44 and 7.45, and equation (7.26), the control can be made using the line current as target, with the corresponding active and reactive powers. An open loop determination of the control references for V_C can be made with equation (7.26), although a robust feedback scheme must be used because the voltages V_S at the other end of the line and its own impedance (or the Thevenin equivalent of the whole network at this side of the UPFC) are usually unknown in real time.

The simplest feedback scheme is the proportional control. On the d–q frame coordinates of the voltage and current vectors, the d-axis current i_d corresponds to the active power, and so it can be controlled by the q-axis voltage v_Cq. Therefore, the reference for the v_Cq component is:

$v_{C q}^{*} = K_{p} (i_{d}^{*} - i_{d})$

(7.27)

$i_{d}^{*} = \frac{P_{REF}}{v_{d}}$

(7.28)

where P_REF is the preset value for the active power and v_d is the d-axis component of the voltage (The d–q frame is supposed to be in phase with the fundamental direct-sequence component of the voltage and therefore the q-axis component is null).

The q-axis current i_q corresponds to the reactive power, and so it can be controlled by v_Cd. Therefore, the reference for the v_Cd component is:

$v_{C d}^{*} = K_{q} (i_{q}^{*} - i_{q})$

(7.29)

$i_{q}^{*} = \frac{Q_{REF}}{v_{d}}$

(7.30)

where Q_REF is the preset value for the reactive power, considered positive for leading currents.

These two control laws provide the base for an independent control of P and Q, but they are obtained from steady state phasor relations. In fact, this control scheme presents interferences between the d- and q-axis that induce poor damped transient behaviors [18]. The control scheme proposed in [18] includes a proportional control between the magnitudes of the same axes:

$[\begin{array}{c} v_{C d}^{*} \\ v_{C q}^{*} \end{array}] = [\begin{array}{c} - K_{r} & - K_{q} \\ K_{p} & - K_{r} \end{array}] \cdot [\begin{array}{c} i_{d}^{*} - i_{d} \\ i_{q}^{*} - i_{q} \end{array}]$

(7.31)

The new terms defined by K_r act as a damping resistor that enhances strongly the dynamic behavior. The transient analysis exposed in [18] deduces a second-order system for the series control of the UPFC and relates its damping factor with the line impedance and the proportional gains of the control:

$ς = \frac{K_{r} + R}{\sqrt{(ω_{0} L + K_{p}) (ω_{0} L + K_{q}) + {(K_{r} + R)}^{2}}}$

(7.32)

Using equations (7.32) and (7.26) the values of K_p, K_q, and K_r can be preset. The values of K_p and K_q should be of the same order as the line impedance, for an open loop control estimation based on equation (7.26). And for a given value of ζ, K_p, and K_q, the K_r gain should be:

$K_{r} \approx \frac{ς}{\sqrt{1 - ς^{2}}} \sqrt{{(X_{L} + K_{p q})}^{2}} - R \approx \frac{ς}{\sqrt{1 - ς^{2}}} (X_{L} + K_{p q})$

(7.33)

For instance, for a damping factor ζ = 0.8 and K_p = K_q = X_L, the corresponding value for K_r is 2.67 times the line reactance X_L.

Nonetheless, the results presented in [18] with the proportional control still have cross couplings between the P and Q controls in steady state. The addition of slow integral gains allows the system to set the final values in the preset references.

Similar considerations can be made for the implementation of the voltage regulation with the reactive power of the shunt converter. Taking references in the magnitudes presented in Figure 7.42, the equation that relates the phasor voltage V_L and the voltage of the right side subsystem V_S2 is:

$V_{L} = V_{S 2} - j ω_{0} L_{S 2} \cdot I_{S 2}$

(7.34)

If all the injected current I_Cq flows through the line S₂, the leading values of I_Cq will produce and increment of V_L and the lagging values of I_Cq will reduce the voltage (see Figure 7.43), and a similar control strategy could be applied:

$i_{C q}^{*} = K_{q v} (v_{d}^{*} - v_{d})$

(7.35)

However, there are important differences in the shunt converter control. The first one is that the control of the active power is not free because it is focused in the power balance of the conditioner. The second one, and maybe the most important, is that according to equation (7.34) the effect of the reactive current injected on the voltage to be regulated, is “reduced” by a factor equal to the line impedance, in per unit values; and there are easier and classical methods to provide the same amount of reactive power. Furthermore, the implementation of a control scheme similar to equation (7.31) would produce important oscillating values of the instantaneous power that will interfere in the power balance of the conditioner.

7.4.2.1. Integration in the UPLC Control

When the UPFC control is applied in a system with distortions and unbalances, additional requirements must be considered. First of all, the d–q components of the space vectors no longer behave as constant values. The dc components of these d–q coordinates must be obtained, in order to avoid the introduction of additional distortions through the control signals of the UPFC. And this filtering introduces a delay that changes the response of the damping factor K_r, deteriorating the transient response in the low frequency range. Finally, the existing unbalances and distortions mean that, even with an ideal compensation, the instantaneous power that flows through the converters could have important oscillatory components that must be considered in the dimensioning of the dc link of the conditioner.

When the features of an UPFC are to be included in a UPQC to set a UPLC, the last consideration is already included in the efforts of the harmonic and unbalance compensation. Furthermore, the harmonic damping term R·i_Sh (equation (7.10)) of the UPQC can be extended to give the response of the factor K_r because they have essentially the same role.

On the other hand, the control of the UPQC explained in Section 7.2 is formulated with the phase variables, instead of d–q frame variables. The adaptation of the control scheme to this approach implies to reorder the control calculations. The UPQC control has an internal variable,

v_{1, reg}^{+}

, that is in phase with the fundamental direct-sequence component of the load voltage. These internal signals have unity amplitude and can be used as a phase reference. And also, an instantaneous quadrature voltage vector can be defined with these signals [24]:

$\begin{array}{l} e_{d, abc} = v_{1, reg, abc}^{+} \\ e_{q} = [\begin{array}{c} e_{q a} \\ e_{q b} \\ e_{q c} \end{array}] = \frac{1}{\sqrt{3}} [\begin{array}{c} 0 & - 1 & 1 \\ 1 & 0 & - 1 \\ - 1 & 1 & 0 \end{array}] \cdot [\begin{array}{c} e_{d a} \\ e_{d b} \\ e_{d c} \end{array}] \end{array}$

(7.36)

The vector e_q leads 90° the signal vector e_d and has also unity amplitude. The instantaneous reference of the currents in the d–q axis can be calculated as:

$i_{d}^{*} = \frac{P_{REF}}{{\bar{v}}_{d}}$

(7.37)

$i_{q}^{*} = \frac{Q_{REF}}{{\bar{v}}_{d}}$

(7.38)

where v_d is the dc component of the d-axis component of the voltage vector:

${\bar{v}}_{d} = \frac{1}{T} \int_{0}^{T} (v_{a} e_{d a} + v_{b} e_{d b} + v_{c} e_{d c}) d t$

(7.39)

The average d–q components of the actual currents can be calculated as:

${\bar{i}}_{d} = \frac{1}{T} \int_{0}^{T} (i_{a} e_{d a} + i_{b} e_{d b} + i_{c} e_{d c}) d t$

(7.40)

${\bar{i}}_{q} = \frac{1}{T} \int_{0}^{T} (i_{a} e_{q a} + i_{b} e_{q b} + i_{c} e_{q c}) d t$

(7.41)

These components are related to the average values of the active and reactive instantaneous powers, produced by those currents that are in phase with the corresponding voltage waveforms. Thus, the voltage

v_{C}^{*}

references are:

$v_{C q}^{*} = K_{p} (i_{d}^{*} - {\bar{i}}_{d}) \cdot [\begin{array}{c} e_{q a} \\ e_{q b} \\ e_{q c} \end{array}], v_{C d}^{*} = K_{q} (i_{d}^{*} - {\bar{i}}_{q}) \cdot [\begin{array}{c} e_{d a} \\ e_{d b} \\ e_{d c} \end{array}]$

(7.42)

However, for the damping component K_r, the voltages references have been calculated directly by comparison of the phase current and their references:

$i_{S a b c}^{*} = i_{d}^{*} \cdot [\begin{array}{c} e_{d a} \\ e_{d b} \\ e_{d c} \end{array}] + i_{q}^{*} \cdot [\begin{array}{c} e_{q a} \\ e_{q b} \\ e_{q c} \end{array}] = \frac{P_{REF}}{{\bar{v}}_{d}} e_{d} + \frac{Q_{REF}}{{\bar{v}}_{d}} e_{q}$

(7.43)

$v_{C r}^{*} = - K_{r} [\begin{array}{c} i_{S a}^{*} - i_{S a} \\ i_{S b}^{*} - i_{S b} \\ i_{S c}^{*} - i_{S c} \end{array}]$

(7.44)

The direct use of the instantaneous values of the currents avoids the delay related with the calculation of average d–q components that deteriorate the dynamic response of the control. Furthermore, it includes the harmonic damping term that was incorporated in the series converter of the UPQC; and it has similar gain values.

Finally, the voltage references for the series converter of the UPLC will be:

$v_{C}^{*} = (v_{S} - v_{L}^{*}) + v_{C q}^{*} + v_{C d}^{*} + v_{C r}^{*}$

(7.45)

The control of the shunt converter of the UPLC has to be modified only to include the term i_Cq, and no substantial modifications in the power balance should be expected:

$i_{C}^{*} = (i_{L} - i_{S}^{*}) + G \cdot (v_{L}^{*} - v_{L}) + i_{C q}$

(7.46)

Example 7.2

The UPLC with the control strategy described in this section will be simulated to check its behavior. The power circuit of the conditioner is the same as in Example 7.1, with the connection of a second power supply in the load side that plays the role of the right side subsystem. Figure 7.46 shows the general power circuit for this case. The UPLC will be applied to the same load of Example 7.1, with the same unbalanced and distorted supply system in the left side of the conditioner. Only the line impedance has been changed to produce a 4% voltage drop with nominal load, through a resistance of 1Ω and an inductance of 7 mH. The power supply of the right side will provide balanced nominal voltages, but the line impedance will be greater, with a resistance of 1Ω and an inductance of 14 mH to produce an 8% voltage drop with nominal load.

The resultant waveforms of this simulation case will be presented in per unit values: the voltages and currents will be divided by the amplitude of their nominal references (400/230 V, 50 Hz, 3 kVA) and the instantaneous power will be referred to the nominal apparent power of the system. The gains K_p, K_q, K_r for the proportional control of the S1 line have been set to 0.2, 0.2, and 5 pu, respectively. The gain K_qv for the voltage regulation has been set to 1 pu.

This simulation case of 400 ms will show the behavior of the UPLC through the following events:

• Activation of the UPLC at 100 ms. Before that moment, the shunt converter is off and the voltage reference of the series converter is set to 0 V. When it starts, the reference for the instantaneous active and reactive powers of the controlled line are set to 0.5 and 0 pu, respectively.

• Change in the reference of the instantaneous active power P_REF from 0.6 pu to −0.6 pu, at 200 ms.

• Change in the reference of the instantaneous reactive power Q_REF from 0 pu to −0.3 pu, at 300 ms.

Figures 7.47 and 7.48 show the phase voltages v_L at the right side of the UPLC and the phase currents i_L of the nonlinear load that has to be compensated by the conditioner, during the whole simulation. Figures 7.49 and 7.50 show the waveforms of the phase voltages v_S1 at the left side of the UPLC and the phase currents i_S1 that flow through the series converter and the controlled line of the subsystem S1. Before the activation of the UPLC, the supply currents are strongly distorted and unbalanced, mainly due to the distortion and unbalance of the voltage sources of the S1 subsystem. There is also some level of distortion produced by the nonlinear load, as well as some resonances among the load and the subsystems S1 and S2.

Figure 7.47 Phase voltages at the right side of the UPLC (load voltages).

Figure 7.49 Phase voltages at the left side of the UPLC (controlled line).

Figure 7.50 Phase currents of the left side subsystem S1 (controlled line).

Figure 7.51 shows in some detail the effects of the activation of the UPLC in the left side of the conditioner. These currents become sinusoidal and balanced, according to the references of the active and reactive power of the controlled line. The v_S1 voltages remain distorted and unbalanced due to the characteristics of the own voltages sources of this subsystem. Figure 7.52 shows the variation of the load voltages and currents with the start of the UPLC. The resonances, distortion, and unbalance are strongly mitigated and the load voltages become sinusoidal and balanced. It shows how the UPLC isolates the load side from the distortion and unbalance of the S1 supply side. The load currents are quite robust against the distortion of the applied voltages, and the major change with the compensation is observed in the current of the first phase i_La. The load of this phase is the most sensible to the voltage variations, especially in the peak values, and the enhancement of this phase voltage produces a visible increase of the corresponding current, with a small transient.

Figure 7.51 Detail of the S1 supply voltages and currents before and after the activation of the UPLC.

Figure 7.52 Detail of the load voltages and currents before and after the activation of the UPLC.

On the other side, the UPLC compensates also the harmonic, unbalance, and reactive components of the load current, improving the working conditions of subsystem S2. Figure 7.53 shows the neutral current of the load i_Ln and the lines of both the supply subsystems, i_S1n and i_S2n. Before compensation, the unbalance in S1 produces a strong circulation of zero-sequence currents between both subsystems. With the activation of the conditioner, the neutral current of the controlled line is reduced to a minimum value. The compensation of the shunt converter enhances also the neutral current of the subsystem S2, after a small transient in the first cycle. The evolution of the neutral current of the load during the whole simulation indicates also a steady behavior after compensation that reflects the stability of the voltages applied to the load during the subsequent changes of the power references of the controlled line.

Figure 7.53 Neutral currents of the load, the supply S1 (controlled line) and the supply S2 (right side subsystem).

Figure 7.54 shows the compensating currents i_C produced by the shunt converter of the UPLC. In the first stage of the compensation, the conditioner delivers the harmonic, unbalance, and reactive components of the load currents, as well as an active component to regulate the power balance of the conditioner and the voltages on the dc side. This is quite accurate in this stage, from 100 ms to 200 ms because the references of the active and reactive powers of the controlled line are similar to those of the load with only an UPQC compensation. In the next stages, the differences are mainly in fundamental components, due to the changes in the controlled line and the power balance of the conditioner.

Figure 7.54 Compensating currents of the shunt converter of the UPLC.

Figure 7.55 shows the references of the compensating voltages

v_{C}^{*}

produced by the series converter of the UPLC to regulate the power flow in the controlled line and to isolate the load side from the harmonics and unbalance of the S1 subsystem. They are around 25% of the amplitude of the base voltage and differ slightly in each stage corresponding with the changes in the active and reactive power references. They show steady values among each step change, reflecting a very fast transient behavior of the power control. Figure 7.56 presents the instantaneous active and reactive powers in the controlled line. From the very beginning of the compensation they are set in the reference values with a very fast transient response. When the active power reference is changed from 0.6 pu to −0.6 pu at 200 ms, the transient is a little bit longer due to the fluctuations in the S2 subsystem, induced by the great change in the current of the controlled line. In the real systems the changes in the power references should be limited in a range and/or rate change to avoid these unnecessary short transients and provide a smoother transition.

Figure 7.55 References of the compensating voltages of the series converter of the UPLC.

Figure 7.56 Instantaneous active and reactive powers at the controlled line.

Figure 7.57 shows in detail the evolution of the voltages and currents of the right side subsystem S1 during the step change of the active power reference, from 0.6 pu to −0.6 pu. The transition of the supply current is very fast, in few milliseconds, to produce a complete reversion of the power. During this transition, small disturbances appear in the supply voltage, related to the larger changes produced in the currents, mainly in the second and third phases.

Figure 7.57 Voltages and currents in the S1 subsystem during the change of active power reference.

Figure 7.58 shows in detail the evolution of the voltages and currents of the right side subsystem S1, this time during the step change of the reactive power reference, from 0 pu to −0.3 pu. In this case, the controlled line demands active and reactive power to the left side subsystem; and the line currents increase their amplitude and phase. Again, the control transient is very fast; however the changes in the controlled currents are smaller and therefore the supply voltages of the left side exhibit smaller changes.

Figure 7.58 Voltages and currents in the S1 subsystem during the change of reactive power reference.

Figure 7.59 shows the voltages and currents of the nonlinear load in the stages of power reference changes. The active power reversion induced at 200 ms produces a voltage drop in the first half cycle. This short transient induces a longer transient in the current of the voltage sensitive load of the first phase that lasts around five cycles. The changes induced by the reactive power reference at 300 ms are not so sharp, and the corresponding transients are much smaller.

Figure 7.59 Voltages and currents in the load during the changes of the power references.

Figure 7.60 shows the instantaneous active and reactive powers demanded by the nonlinear load during the whole simulation. At a first glance, they show a very stable behavior, before and after the activation of the UPLC, and during the step changes of the power references. The average active power increases slightly with the start of the UPLC, from 0.42 pu to 0.44 pu, remaining quite constant afterwards. Meanwhile, the average reactive power has a similar behavior, with 0.13 pu before compensation and around 0.14 pu for the rest of the time.

Figure 7.60 Instantaneous active and reactive powers at the nonlinear load.

Figure 7.61 shows the instantaneous active and reactive powers provided by the left side subsystem S1. Before compensation, the system is strongly distorted and unbalanced, supplying an average active power of 0.06 pu and receiving a reactive power of 0.27 pu. After compensation, the instantaneous powers become very constant with a small ripple due to the distortion and unbalance of the supply voltage. Their average values follow very near the control references, with small differences due to the voltages that the series converter must apply to control the active and reactive power of the line.

Figure 7.61 Instantaneous active and reactive powers provided by the left side subsystem.

Figure 7.62 show the waveforms of the phase currents of subsystem S2. Before the start of the compensation they supply an important part of the load currents. After compensation, the references of active and reactive power of the controlled line make subsystem S1 to provide the major part of the active power of the load, and the currents of the S2 subsystem are reduced. When the active power reference changes from 0.6 pu to −0.6 pu at 200 ms, the S2 line must provide the total amount requested by the controlled line and the nonlinear load. The fast control of the current i_S1 (see Figure 7.57) induces a transient in the load side of the conditioner with the uncontrolled transmission line. The strong response of the currents of S2 due to its relatively small line impedance, is partially damped with the UPLC and the subsystem reach steady values after three cycles. The reaction produced by the change in the reactive power reference is smaller because the variations of the controlled currents i_S1 are also lower.

Figure 7.62 Phase currents of the right side subsystem (supply S2).

Figure 7.63 shows the square root of the instantaneous aggregate values of the load voltages. After compensation the oscillating component is strongly reduced and the average value is 1.02 pu. The transient induced by the active power reference of the controlled line produces a short voltage drop of about 12% during one cycle but it reaches quickly a steady value of 0.99 pu. And when the controlled line requires a reactive power of 0.3 pu the new steady value is 0.97 pu.

Figure 7.63 Instantaneous aggregate values of the load voltages v_L.

Figure 7.64 shows the voltages of the capacitors of the dc link of the UPLC and the total amount. It shows that the highest dc voltage variation occurs at the activation of the conditioner, where the instantaneous active power flow is bigger. The change in the references of the active and reactive powers of the controlled line does not imply great oscillations of the active power and the control of power balance of the conditioner manages it with lower variations. Figure 7.65 shows the instantaneous active and reactive powers that flow through the series converter of the conditioner. They present reduced average values along all the stages of the compensation and illustrate the effectiveness of the UPLC series converter to control the flow of the power line with a small effort. Figure 7.66 shows the instantaneous active and reactive powers that flow through the shunt converter of the conditioner. They have higher oscillating components due to the characteristics of the compensated load.

Figure 7.64 Voltages at the dc link of the UPLC.

Figure 7.65 Instantaneous active and reactive powers of the series converter of the UPLC.

Figure 7.66 Instantaneous active and reactive powers of the shunt converter of the UPLC.

The results of Example 7.2 illustrate the extended capabilities of the UPLC. It can provide a fast and accurate control of the power flow at the controlled line, which should be even slowed to reduce the transients induced in the nearby parts of the network. It regulates also the load voltages with reactive power from the shunt converter. At the same time it enhances the EPQ of the whole system. Before the activation of the UPLC, there was a strong spread flow of harmonics, resonances and unbalance. With the UPQC compensation the unbalances and distortions of the left side subsystem are isolated and the current is compensated, improving the working conditions in this side. In the right side subsystem, the distortion and unbalance introduced by the nonlinear load are compensated, and the voltages at this side are enhanced for nearby loads.

7.5. Summary

This chapter has illustrated various of the capabilities of the set made with the combination of series and shunt active power filters. It started with the considerations for adequate compensation strategies for a complete load compensation, with appropriate voltages and compensated currents. These considerations have led to the definition of the compensating control references and the power structure to achieve these targets.

The state-space model has allowed us to analyze the transient behavior of the conditioner, and has improved the selection of the passive components and control parameters. The theoretical analysis has been contrasted with the results obtained in simulation cases, developed in a platform based on MATLAB-Simulink; as well as with the results of an experimental laboratory prototype.

Finally, the extended capabilities of the UPFC concept have been included in a UPLC design. The power flow control and the reactive-voltage regulation have been adapted and implemented in the previous UPQC design, and the practical case has shown the enhanced features of the combined conditioner.

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Table of Contents for 7: Combined Shunt and Series Active Power Filters

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Abstract

Keywords

7.1. Introduction

7.2. Unified Power Quality Conditioner

7.2.1. Structure of the UPQC

7.2.2. Control Strategy of the UPQC

7.2.2.1. Calculation of the Load Voltage Reference (vL*=v1,reg+)

7.2.2.2. Calculation of the Active Current Reference (iS*=ia)

7.2.3. Parameters Design

7.2.3.1. Analysis of the Passive Circuit

7.2.3.2. Control Modification

7.3. Experimental Prototype of UPQC

7.3.1. Results of Practical Case

7.4. Universal Active Power Line Conditioner

7.4.1. Unified Power Flow Controller

7.4.2. Power Flow Control, Voltage Regulation, and Power Quality Improvement

7.4.2.1. Integration in the UPLC Control

7.5. Summary

Table of Contents for
7: Combined Shunt and Series Active Power Filters

7.2.2.1. Calculation of the Load Voltage Reference ( $v_{L}^{*} = v_{1, r e g}^{+}$ )

7.2.2.2. Calculation of the Active Current Reference ( $i_{S}^{*} = i_{a}$ )