8.1.1 Load Shedding: Concept and Review

The LS is an emergency control action to ensure system stability by curtailing system load. The emergency LS would only be used if the frequency/voltage falls below a specified frequency/voltage threshold. Typically, the LS protects the system against excessive frequency or voltage decline by attempting to balance real and reactive power supply and demand in the system.

If the power system is unable to supply its active and reactive load demands, the underfrequency and undervoltage conditions will be intense. To prevent the postload shedding problems and overloading, the location bus for the LS will be determined based on the load importance, cost, and distance to the contingency location.

The number of LS steps, amount of load that should be shed in each step, the delay between the stages, and the location of shed load are the important issues that should be determined in an LS algorithm. An LS scheme is usually composed of several stages. Each stage is characterized by frequency/voltage threshold, amount of load, and delay before tripping. The objective of an effective LS scheme is to curtail a minimum amount of load, and provide a quick, smooth, and safe transition of the system from an emergency situation to a normal equilibrium state.

Most common LS schemes are the UFLS schemes, which involve shedding predetermined amounts of load if the frequency drops below specified frequency thresholds. The UVLS schemes, in a similar manner, are used to protect against excessive voltage decline. A comprehensive and useful guideline for UFLS strategies can be found in Ref. [1]. The UFLS schemes typically curtail a predetermined amount of load at specific frequency thresholds. In comparison with the UVLS, the UFLS time delays are small; they are about 0.2 s.

There are many published research reports on the UVLS schemes. A guideline for the UVLS can be found in Ref. [2]. In Ref. [3] some reasons about using UVLS beside UFLS are given. In this article, the transmission line outage is introduced as a case in which voltage may drop before observing excessive depression in system frequency. In this situation, frequency may drop slowly and voltage may collapse before UFLS relays can sense the contingency situation.

It is noteworthy that the UVLS schemes are commonly used to avoid voltage collapse problems. Furthermore, the dip voltage transients are local problems where some practical methods such as the use of special protective relays can be used to avoid voltage collapses following a local voltage drop. These protective relays should cover the function standards to sense voltage magnitude and to trip the breaker if a dip voltage drop is observed. The UVLS schemes should consider such breaker-interlock protective functions by coordinating their time delay and thresholds.

The time delays in UVLS schemes should be set above 3 s to avoid false tripping [2]. In Ref. [4], it is mentioned that the UVLS time delays must not be too small to mitigate the reliability criteria introduced by the National Electrical Reliability Coordinating Council (NERCC). Furthermore, Ref. [4] proposes a slope permissive UVLS design to solve the problem by shedding load before this long time delay following prediction of a considerable voltage drop.

To represent the dynamics of emergency control actions, the incremented/decremented step behavior is usually used. For instance, for a fixed UFLS scheme, the function of LS in the time domain could be considered as a sum of the incremental step functions of , as given in Equation (5.8).

There are various types of UFLS/UVLS schemes discussed in literature and applied by the electric utilities around the world. A classification divides the existing schemes into static and dynamic (or fixed and adaptive) LS types. Static LS curtails the constant block of load at each stage, while dynamic LS curtails a dynamic amount of load by taking into account the magnitude of disturbance and dynamic characteristics of the system at each stage. Although the dynamic LS schemes are more flexible and have several advantages, most real-world LS plans are of static type. The improved UFLS/UVLS algorithms are usually adaptive. The adaptive schemes usually offer larger amount of load at the first LS step following large disturbances [5]. The frequency thresholds can also be biased to using disturbance magnitude to shed load at higher frequency levels in dangerous contingencies [5–9]. The rate of frequency change is a frequent additional parameter for estimating the disturbance magnitude and adjusting the frequency thresholds [6–12].

There are two basic paradigms for LS [5,9]: a shared LS paradigm and a targeted LS paradigm. The first paradigm appears in the well-known UFLS schemes, and the second paradigm in some recently proposed wide-area LS approaches. Using simulations for a multiarea power system, it is easy to illustrate the difference between these two paradigms, following generation loss in one area.

Sharing LS responsibilities (such as that induced by the UFLS) is not necessarily an undesirable feature and can be justified on a number of grounds. For example, shared LS schemes tend to improve the security of the interconnected regions by allowing generation reserve to be shared. Furthermore, the LS approaches can be indirectly used to preferentially shed the least important load in the system. However, sharing the LS can have a significant impact on interregion power flows and, in certain situations, might increase the risk of cascade failure.

Although both shared and targeted LS schemes may be able to stabilize overall system frequency/voltage, the shared LS response leads to a situation requiring more power transmission requirements. In some situations, this increased power flow might cause line overloading and increase the risk of cascade failure.

8.1.2 Some Key Issues

As the use of RES increases worldwide, there is also a rising interest in their impacts on power system operation and control. The important impacts of a large penetration of variable power generators in the area of operation and control can be summarized in the directions of regional overloading of transmission lines in normal operation as well as in emergency conditions, reduction of available tie-line capacities due to the large load flows, frequency performance, grid congestions, increasing need for balance power and reserve capacity, increasing power system losses, increasing reactive power compensation, and impact on the system security and economic issues [6].

The distributed power fluctuation (due to the use of variable generations) negatively contributes to the power imbalance, frequency, and voltage deviations. Significant disturbance can cause under/over frequency/voltage relaying and disconnect some lines, loads, and generators. Under unfavorable conditions, this may result in a cascading failure and system collapse. There are few reports on the role of distributed RESs in emergency conditions.

Among all RESs, wind power has attracted more attention over the last three decades. Increasing the penetration of wind turbine generators (WTGs) in a power system may affect its security/stability limits, frequency, voltage, and dynamic behavior [13–18]. The WTGs commonly use the induction generators (IG) to convert wind energy into electrical energy [16,17]. The induction generators can be considered as reactive power consumers. Therefore, the voltage of the system (as well as UVLS) would be affected in the presence of wind turbines, especially in the case of fixed-speed-type WTGs. In Ref. [17], the effects of the doubly fed induction generator (DFIG) and IG type of WTGs on the voltage transient behavior are explained and the disadvantages of the IG type are shown. Some notes are also given in Chapter 5. The loadability of various types of WTGs is compared in Refs [13,14,18], and it is shown that the DFIG has larger loadability than IGs. Frequency nadir in the presence of different types of the WTGs has been compared in Ref. [16]. As argued in the mentioned references, wind turbines affect frequency behavior (and in result UFLS scheme) because they add the amount of inertia in the power system. Both stator and rotor windings of IG-type WTGs are connected directly with the power grid, but in the DFIG type only the stator is directly connected and the rotor is connected through a power electronic-type converter. The IG-type WTGs in turn add much inertia than the DFIG in the power system; and in conclusion, the IG-type WTG's frequency response is better than systems with the DFIG type, with the same conditions.

Some reports have also addressed the impacts of various WTG technologies on the voltage deviation following a contingency event, and have analyzed their influences on the transient voltage stability. It is illustrated that the P–V curve is significantly affected by changing the network topology. Some parameters such as power system reserve and inertia constant are influenced by interconnecting the WTGs on the power system. Therefore, the frequency deviation will be also affected in the presence of the wind turbine [19]. Following a disturbance, the frequency decline and initial rate of frequency change in the presence of IGs is smaller than the DFIGs case. Because of their structure, the IGs add more inertial response to the power system than DFIGs.

Recent works indicate that using frequency gradient for the power system emergency control in the presence of wind turbines needs to be revised. Since in the presence of WTGs, the undesirable oscillations are added to the frequency deviation, the measuring of frequency gradient introduces another difficulty to achieve this variable in emergency control strategies. This issue encourages power design engineers to use instead of [14].

Furthermore, as it is discussed in Section 5.5, as well as in the next section, the voltage and frequency behavior does not address the same results about contingency conditions. This phenomenon encourages researchers to reevaluate the emergency control schemes for the future of the power systems that are integrated with a high penetration of wind power.

Most LS schemes proposed so far separately use voltage and frequency information via the UFLS and UVLS schemes. A majority of published works on the UFLS schemes only consider the active part of load while, by considering the reactive power part, frequency decline is also affected [19]. Furthermore, in the actual power system, the loads contain both active and reactive parts. It is noteworthy that coupling between the active and reactive parts of load (P–Q coupling) can significantly affect the LS schemes. Recently, some research works have been conducted on the necessity of considering both voltage and frequency indices to achieve an effective and comprehensive LS strategy [14].

Another important issue following a severe disturbance in a power system is the coordination between the amount of available spinning reserve and the required emergency control action. Coordination between the amount of spinning reserve allocation and the LS can reduce total costs that generation companies should pay in the emergency conditions.

8.3.1 Proposed LS Scheme

As mentioned, the UFLS and UVLS schemes work in the power system without any coordination. The interaction between voltage and frequency responses is neglected in these schemes. Therefore, the risk of LS schemes malfunction can appear in real-world power systems. From previous descriptions and the performed simulation results, it is realized that considering just frequency or voltage indices cannot lead to an effective/optimal LS plan, especially when the reactive power is incorporated in the studies.

Since the coordination between conventional UFLS and UVLS as separate algorithms is difficult and even impossible, both voltage and frequency should be used in the same LS program simultaneously. With this target in mind, one can define a new graphical analysis tool to monitor both voltage and frequency in one LS algorithm. As shown in Chapter 4 (Section 4.4), the frequency–voltage Δv–Δf graph can be used as a useful graphical tool to see the state of the system following a contingency.

Here, for calculation of the LSCS_i (4.21), the and parameters are considered as given in Table 8.1. It can be seen that in order to present a reasonable comparison between the UFLS scheme and the proposed underfrequency/voltage LS (UFVLS) scheme, the LS parameters are selected as close as possible to the LS strategy introduced by the FRCC [21]. The maximum number of LS steps and the amount of needed loads for shedding per step are also considered similar to the FRCC control plan. Furthermore, the parameters are selected the same as the frequency thresholds used in the FRCC scheme. Therefore, by fixing variable in (4.21) at zero, the proposed algorithm acts similar to the FRCC's UFLS program.

LS Steps			LS, %
A	0.3/60	0.05	9
B	0.6/60	0.12	7
C	0.9/60	0.15	7
D	1.2/60	0.18	6
E	1.5/60	0.2	5
F	1.8/60	0.21	7

Each step is determined by an ellipse and when the phase trajectory reaches each ellipse, the corresponding LS step will be triggered. Figure 8.4 shows the result of the applied LS steps on the Δv–Δf trajectory plane in the case of G2 outage. The time delay parameter between steps should be considered in the LS algorithm. The voltage and frequency may need to pass through a low-pass filter before entering the algorithm. Existing practical constraints should be also considered in the proposed scheme.

The loads are selected to be triggered at the zones where their LSCS parameter (4.21) leads to an LS step triggering. Actually, when a disturbance happens, the voltage and frequency of a zone will change faster than others; therefore, the loads in this zone will find the highest priority for the LS.

Fine adjustment of delay is significant for achieving a soft frequency/voltage improvement scenario to avoid overshedding and false shedding problems. The UFLS and UVLS schemes are considerably different in time delay magnitudes. The UVLS time delays should be set at about 2–3 s to avoid false shedding. However, typical UFLS time delays are about 0.2–0.3 s [13,14,21]. In order to establish a comprehensive LS scheme, the introduced Δv–Δf plane is divided into four regions, as illustrated in Fig. 8.4.

This partitioning lets us define different time delays for different conditions. Region 1 introduces an area with significant drop of voltage and small frequency change. If the Δv–Δf trajectory falls in this region, similar to the UVLS plans, the time delay should be long enough to avoid false shedding. Here, it is fixed at 2 s. On the other hand, region 2 introduces a situation with a high frequency drop and small voltage changes. Time delay in this condition should be also long; however, to prevent LS schemes from falling in a trap made by voltage support devices, it should not be considered too long. Here, similar to the UFLS plans, the time delay is fixed at 0.28 s. The upper and lower borders of this region and the associated time delay may also depend on the magnitude of available reactive power supports, wind power penetration, and wind turbine types. Region 3 introduces an area with significant drop in both voltage and frequency. Therefore, the time delay in curtailing of loads should be reduced. However, to avoid overshedding, it is not permitted to be too small. Here, the time delay for region 3 is fixed at 0.2 s. The LS is blocked in the remaining region (region 4). This region may demonstrate a good condition for the load restoration problem.

8.3.2 Implementation

It is clear that the conventional underfrequency and undervoltage relays cannot support the mentioned graphical tool (elliptical curves). Therefore, it is important to clarify how the proposed methodology can be implemented. The existing practical LS schemes in real power systems mostly use the following technologies [1,2]:

1. – Breaker interlock LS
2. – Underfrequency relay LS
3. – Undervoltage relay LS
4. – Programmable logic controller (PLC)-based LS

The first method, which is the simplest practical LS method, uses the trip signals of the special generators/tie-lines to directly shed off some load blocks. The second and third methods use undervoltage/underfrequency relays to shed specified load blocks when the locally measured voltage or frequency drops down under some predefined threshold. The most important defect of these three methods is that they do not consider the overall power system circumstance when they produce a command to trip a load. Therefore, they cannot present an optimal and effective LS response for all situations.

The PLC devices have opened a new window to realize new power system control solutions such as the proposed LS in the present chapter. The idea of using PLC is a practical solution for more complicated LS schemes. The PLC-based LS scheme is a more flexible LS method, which uses underfrequency/voltage relay commands as input signals, and then decides to trip some loads based on its predefined priority load levels. The PLC devices can use frequency and voltage signals as analog input (AI) variables to perform the parameter from (4.21). The result should be evaluated to determine the trigger time of the LS step.

As described beforehand, the proposed UFVLS program uses system frequency and voltage values of different buses. Because the voltage drop is a local problem, the source of the voltage value that would be used in the UFVLS program is not yet determined. It should be updated based on the real-time measured voltages and the location of maximum voltage drop. Figure 8.5 illustrates the flowchart diagram of the proposed UFVLS scheme.

As shown, the selected bus contains the maximum voltage drop. Based on the frequency and selected voltage value, the LSCS_i is calculated. If the LSCS_i is larger than 1, for a proper time period, a predetermined amount of load should be shed from buses near the selected one. This period of time is known as time delay, which is determined based on the real-time Δv–Δf trajectory. The forbidden regions and different time delays are considered as described in the previous subsection.

In the flowchart diagram, the flag parameter is a temporary variable, which used to control the set/reset of timers to adjust the time delays. The timers start if the LSCS_i > 1, and stop when they reach a predetermined value (timer (i) > delay (i)). The timer should immediately be reset if LSCS_i < 1. The i and i_max are the number and maximum number of the LS steps, respectively. It is noteworthy that the illustrated flowchart is completely implementable by standard PLC's programming languages.

8.3.3 Case Studies and Simulation Results

The 9-bus and 24-bus test systems are simulated in the MATLAB/SimPower environment. In both systems, the proposed LS scheme is simulated in two cases: first, it is examined when no WTG is connected to the power grid; second, the ability of the algorithm is examined in the presence of WTGs by another example in each test system.

8.3.3.1 Nine-Bus Test System

The described LS scheme in the previous section is applied to the nine-bus power grid as a test system, following loss of G2 at t = 10 s. The proposed LS scheme is used as an emergency control plan. For the sake of comparison, the conventional UFLS, developed by FRCC [21], is also examined. As shown in Fig. 8.6, both LS methodologies are able to save system stability but the proposed LS presents a better performance.

Overshedding can be seen as a problem of the UFLS scheme. It causes the voltage at bus 4 to stay above its normal level. As shown, in the proposed LS scheme the problem of overshedding is initially removed. Figure 8.4 shows the system state trajectory on the Δv–Δf plane during the LS process. Simultaneous use of voltage and frequency data and good adjustment of the region's time delays are the reasons for this improvement. Figures 8.4 and 8.6 illustrate the response of the system without WTG penetration. However, the proposed scheme is validated on a nine-bus power grid in the presence of high-penetration DFIG-type WTGs with a variable wind speed as another example; the time domain system frequency and voltage response for the new LS scheme are shown in Fig. 8.7.

8.3.3.2 24-Bus Test System

A single line diagram of the 24-bus reliability test system (RTS) is illustrated in Fig. 8.8. The RTS with its full data is introduced in Refs [22,23], and the generators data are selected the same as the given typical data in Ref. [20]. Here, the test system is divided into three areas. While most of the generation is located in area 1 and most of the load is located in area 3, in area 2, the amount of load and generation are approximately equal. Area 1 delivers its overgeneration into areas 2 and 3 through three tie-lines: line 16–19, line 16–14, and line 24–3. All generators use governors with 0.05 pu droop value (R); and also for the generators wherein their nominal output power is larger than 50 MW, a PSS is considered. The load model is a three-phase parallel RLC load, which implements a three-phase balanced load as a parallel combination of the RLC elements. At the specified frequency, the load exhibits constant impedance. The active and reactive powers absorbed by the load are proportional to the square of the applied voltage. Four wind farms are connected with the system to introduce a high wind power penetration power system. They supply about 10% of total system demand. All of the wind turbines are of DFIG type.

To validate the proposed LS scheme, several contingencies have been applied to the 24-bus test system. It is investigated that some contingencies affect frequency response more considerably than voltage behavior (a large generator loss near a voltage support device, that is, synchronous condenser at bus 14, like G15 outage), some contingencies affect voltage more considerably than frequency (a far generator like G7), and finally some contingencies significantly affect both voltage and frequency (G23 outage). Contrary to the conventional LS plans, the proposed scheme is expected to stabilize the system in all the mentioned scenarios by curtailing a minimum amount of load.

To have an obvious simulation result, first, the test system without including WTGs is considered. Then, an example will validate it in the presence of WTGs. To demonstrate the capability of the proposed scheme, a large disturbance is applied; outage of lines 16–19 and 16–14 at t = 2 s. Following this large disturbance, line 3–24 will be encountered with a high overloading problem. This overloading is larger than its angle stability limit. Therefore, the angle of G1 and G15, which are approximately located at two sides of the line, are separated, and the angle instability phenomena will immediately happen. To save the system in this circumstance, one solution is the use of islanding control.

Islanding control is practically implementable by controlling the interarea coupling devices. If an area observes an external large disturbance from an interconnected area, the islanding control function commands to decouple the connection with that faulted area immediately. These functions can be implemented using hardwired interlocks, breakers, and some special protective relays.

Therefore, the remaining tie-line is tripped and saving the resulting two systems is attempted separately. The main concern is on areas 2 and 3, which encounter an excess load condition. The LS schedule should be used in these areas. This is a large disturbance and the simulation results show that application of the conventional LS schemes is not able to restore the system stability. Therefore, an improved version of the previous methods should be used to have a reasonable validation.

As mentioned, most of the recent published works on the emergency control techniques suggest an LS methodology that sheds a larger amount of load with shorter time delay in dangerous contingencies. Here, these points are used to examine the proposed method and to compare it with other works. Therefore, the LS schemes examined here for the mentioned contingency shed a larger amount of load at the first LS step (9% + 7% instead of 9%). The first frequency threshold is also modified ( instead of 59.7 Hz for the UFLS scheme and instead of 0.03/60 for the proposed scheme).

On the other hand, as in the emergency control plans, time is a vital parameter; there is a critical value for the time of emergency control actions to restore the system conditions. With this point in mind, the following scenarios are tested here following the mentioned contingency:

1. The islanding control is done with a 0.4 s time delay at T_ic = 2.4 s (T_ic is the time of islanding control);
2. T_ic = 2.6 s;
3. T_ic = 2.7 s; in the 24-bus test system, there is more than one generator at some buses. All of those that have sizes larger than 30 MW are equipped with the PSS in the mentioned cases (cases 1–3). However, in order to have a more critical situation, case 4 is designed.
4. In this case, only one of the generators that is connected to the same bus is equipped with the PSS, and also the T_ic is assumed to be 2.4 s.

For the sake of comparison, the UFLS and the proposed LS schemes are used here when the system conditions are completely similar in both LS scenarios with the same shed load amount per step. The simulation results are illustrated in Fig. 8.9. For short islanding control time delays (T_ic = 2.4–2.6 s), both LS plans succeed in maintaining system stability; however, the proposed scheme presents a more soft post contingency frequency behavior. The advantages of the proposed scheme will be more clarified in the case of worse situations. Increasing time delay and/or decreasing the number of PSS forces the system condition into a critical situation where the UFLS scheme cannot stabilize it, but the proposed scheme is still successful. For larger islanding control time delays (), none of the schemes are able to protect the system.

To clarify why the (conventional) UFLS plans work worse than the proposed LS scheme, the voltage and frequency response of the fourth case are illustrated in Fig. 8.10. As shown in this figure, in the first few seconds following the contingency and before loss of line 3–24, voltage drops quickly, while frequency declines slowly. The UVLS time delays do not allow the related (UVLS) relays to cut the loads quickly. Furthermore, the UFLS relays cannot immediately sense the frequency drop. Therefore, although it is a very large disturbance, the LS actions cannot be run on time. It may be dangerous when the time delay of emergency actions is long and the system falls into a critical situation. On the other hand, the voltage is temporarily recovered following manual tripping of line 3–24, but frequency drop is intensified (this shows another demonstrative example to justify the existing conflict between voltage and frequency behaviors). The system frequency quickly drops and it leads the UFLS relays to trip more loads. This is another reason that causes the conventional UFLS schemes to be unsuccessful. Here, it is assumed that there are no load restoration requirements in the system.

Figures 8.11 and 8.12 are presented to answer why the proposed LS is more effective. The elliptic lines in Fig. 8.11 depict the LS thresholds. These lines cross the left-hand side of the x-axis at some points, which are actually the UFLS thresholds. The Δv–Δf trajectory following the mentioned contingency is also illustrated in the figure. Its map on the left-hand side of the x-axis is the frequency trajectory used in the UFLS, as a conventional LS scheme. It is shown in Fig. 8.11 that the proposed LS thresholds are reached much faster than the UFLS thresholds. If both voltage and frequency parameters decline, the new LS also present a shorter time delay. It is obvious that earlier LS action following a dangerous disturbance, with a large load/generation imbalance, presents a better performance because it blocks voltage/frequency depression. On the other hand, if frequency drops while the voltage stays at a higher level, the LS action is blocked (Fig. 8.4). All of these points help the proposed LS to shed load at an appropriate time and to avoid overshedding, as shown in Fig. 8.12. This figure compares the LS steps versus time for the UFLS and the proposed LS schemes, in case 4.

The contingency and emergency control actions on the 24-bus test system, which have been described earlier, are examined here, but in the presence of high-penetration DFIG-type WTGs (about 10%) with a variable wind speed (line 16–19 and 16–14 are loosed at t = 10 s, and also, as an islanding control action, line 3–24 is manually tripped at t = 10.4 s). Voltage and frequency behavior in this situation are illustrated in Fig. 8.13. The figure shows the ability of the proposed method to restore the system voltage and frequency responses.

Furthermore, as shown, the variable wind speed makes voltage/frequency have oscillations. The magnitude of oscillations can be amplified by increasing the WTG penetration. They may deceive LS actions to shed unnecessary amount of load when a frequency/voltage drop emanating from falling of wind speed takes place exactly at the duration of frequency/voltage drop derived from a contingency. Figure 8.13 (like Fig. 8.7) shows that the voltage/frequency behaviors that are affected by variation on wind speed and the existence of the contingency are varied approximately in two opposite directions; voltage improves while frequency is becoming worse and vice versa. It shows that simultaneous consideration of both voltage and frequency parameters for a load shedding scheme makes it powerful to prevent the overshedding problem in the presence of a high penetration of variable speed WTGs.

8.3.4 An Approach for Optimal UFVLS

In the optimal LS programs, the LS thresholds and the amount of LS in each step should be adjusted in order to minimize an objective function. In the conventional UFLS algorithms, the thresholds to be fixed at some frequencies and the objective function will be considered as a function of system frequency behavior and total curtailed loads [24,25].

Based on what has been illustrated in this section, using only frequency data (thresholds and frequency behavior) for finding an optimal LS solution does not lead to the global optimal results. Improving the frequency behavior may disprove the voltage behavior (see the simulation results for the nine-bus test system). Even when improving frequency behavior following large disturbances, just using frequency data may not be effective enough because of voltage behavior that prevents frequency response to drop quickly (see the simulation results for the 24-bus test system).

The proposed UFVLS algorithm, using both voltage and frequency data, makes it possible to adjust the LS parameters optimally. Here, the variables of an optimal UFVLS program that should be adjusted are , , and . The objective function, which demonstrates simultaneous frequency and voltage behavior, can be considered as follows:

(8.1)

where, is the objective function, is the LS amount in step i, Z consists of adjustable variables (, , and ). and are the maximum drops in frequency and voltage response, respectively. The variables , , , , and are bounded variables. Furthermore, C₁–C₃ are constant weights that should be determined by the designer to achieve a desirable LS performance.

8.3.5 Discussion

8.4.1 Proposed Control Scheme

The overall framework of the proposed control methodology is demonstrated in Fig. 8.14. This figure summarizes the process of using islanding formation, performing a continuum model for system stability assessment, and predicting suitable emergency actions following a contingency.

Angle instability is a fast instability phenomenon. Therefore, predicting its situation and performing suitable actions are very important. As mentioned in Section 4.6, having a continuum model of a power system can be helpful for predicting the trajectory of the disturbances by using disturbance conditions as initial states of the continuum model. Here, the power system continuum model is used to provide a powerful descriptive tool for stability analysis in emergency conditions.

The slow coherency theory can be used to identify the system islands. Determining the islands leads to identification of the weak links or critical cutset. Having knowledge of the weak links/islands helps one to determine the most suitable connections/locations for performing a more careful islanding plan, when the system needs to be separated. Here, a slow coherency is suggested to find the weak links/islands. The weak links are used to check whether islanding is needed or not. The weak links can be considered as those links that should be tripped when the islanding is recommended.

It is noteworthy that the overall stability can be evaluated by monitoring just a few links, that is, the weak links and the links near the contingency location. Furthermore, observing the trajectory of bus voltage angles helps the system operators to choose a suitable islanding plan. Following an islanding action, the power system is divided into some islands with excess load/generation. Therefore, other emergency control actions [13,27] such as the LS and generation tripping should be performed, as shown in Fig. 8.14.

Indeed, following a certain contingency, the most important goal of the proposed algorithm is to determine if islanding is needed or not. If the contingency is not dangerous and the angle across a link does not exceed a certain value (e.g., 30° for noncompensated lines), islanding is not needed.

However, for the higher value of transmission angles, the other emergency action will not be able to restore system stability. For more clarification, assume the angle across a link is increasing and exceeds 90°. After that, a decrease of the active power, for example, using LS, could not restore the system because the angle may track the power at the low side of the power–angle (P–δ) curve. Therefore, δ increases and thus instability occurs. In these circumstances, the islanding is strongly needed. The critical angle values (thresholds) should be determined based on the specified level of security.

Operators and engineers can validate the power system stability at the monitoring/control (SCADA) center by observing the wave propagation at the human–machine interface (HMI). Three modes may be defined for this tool: real-time, prediction, and test modes.

In real-time mode, the real-time data gathered from the network by the PMUs are shown as a surface. The operator can see the real-time states of the whole network. In prediction mode, the online data are used as initial values of a continuum model, and then the system states at a certain time value will be predicted. In the test mode, the operator or engineer can validate a certain contingency based on the real states of the system. In this mode the real-time data are used as initial values of a continuum model and a certain test is used as a deviation from initial state; then the post contingency condition will be shown in HMI for a certain time interval.

8.4.2 Simulation Results

8.4.2.1 Ring Systems and Islanding

To illustrate the concept of a coherent group of generators following a contingency, a 200-bus ring system is simulated. For simplicity, it is assumed that there is only one generator or one load at each bus. All generators are similar with equal amount of power and all loads are also equal. The number of generators () is equal to the number of loads (), so . The system data are determined the same as considered in Ref. [27].

The system is examined under two different configurations. In the first configuration (config-1), all generators and loads are distributed throughout the power system by a uniform random function. In the second configuration (config-2), the generators and loads are distributed in a three-area ring system, as shown in Fig. 8.15. In this case, all line impedances are assumed to be fixed at 0.1 pu, except three lines where their impedances are , , . For both configurations, a large disturbance, that is, tripping line 200–1, is applied. The angle deviations are illustrated in Fig. 8.16. The ring system is opened due to occurred disturbance.

As shown in Ref. [27], for the unstable case (config-2), the angle across link 75–76, that is, , is continually growing and finally this situation leads toward separation and instability. However, for the stable case (config-1), although the angle across the link deviates, the system remains in a limited boundary and moves to a constant value. The kinetic energy, potential energy, and total energy across link 75–76 are also given in Ref. [27]. As already mentioned, the system will be stable if it can be able to convert all amount of its kinetic energy achieved during a contingency into potential energy. This simulation also shows that following the mentioned fault, config-2 goes to an unstable condition, while config-1 maintains its stability.

As another example, assume a Gaussian distribution that affects the angles of a system depicted in Fig. 8.15 (config-2). Postcontingency wave propagation is illustrated in Fig. 8.17. In this case, the center of disturbance is located at bus 60; however, it can be seen that the system is separated at line 75–76, which is a weak link. Actually, when a disturbance reaches a weak link through its propagation trajectory, this may lead to an unstable operating point.

Figure 8.17 clearly shows the behavior of wave propagation when it reaches a weak link. For plotting this figure, the angle variations versus bus number for each time slot is calculated. As can be seen, angle wave is reflected when it reaches a transmission line without enough stability margin, and the system is separated exactly at the weak point.

8.4.2.2 Application to 24-Bus Test System

Here, the well-known 24-bus reliability test system (Fig. 8.8) is used to investigate the effectiveness of the proposed strategy. To make a serious fault, the connections between area 1 and area 2 are loosened. Now, the angle instability on link 24–3 can be considered as a useful example to examine the proposed methodology. Assume lines 16–19 and 16–14 are disconnected at t = 2 s. Following this large disturbance, line 3–24 will encounter a high overloading problem. This overloading is larger than its angle stability limit. Therefore, as shown in Ref. [27], the angles of generators G1 and G15 located at two sides of the line are separated, and the angle instability phenomena immediately occurs. To save the system, one solution is the use of islanding control.

Figure 8.18 illustrates how to use the proposed control scheme; an islanding plan improves the voltage behavior that has been suddenly depressed following the mentioned event. Therefore, the remaining tie-lines may be tripped when appropriate algorithms are not used to stabilize the resulting two islands. To save an island with excess load, a UFLS algorithm, like those suggested by the FRCC or addressed in Refs [6,10,13,19] should be used. However, for the islands with excess generation, some loads must be switched on.