7.3.1 Control Framework

The overall control structure using the SOF control design for a given power system is shown in Fig. 7.5, where the PSS and AVR blocks represent the existing conventional power system stabilizer and voltage regulator. Here, the electrical power signal is considered as the input signal for the PSS unit. The static feedback controller (optimal gain vector) uses the terminal voltage , electrical power and machine speed as input signals. The and show the reference voltage deviation and system disturbance inputs, respectively.

Consider the linearized model of a given power system “i” in the following state-space form:

(7.6)

where is the state variable vector, is the disturbance and area interface vector, is the control input vector, is the controlled output vector, and is the measured output vector. The , , , , , and are real matrices/vectors with appropriate dimensions.

Using standard H_∞-SOF configuration [1] while considering appropriate controlled output signals results in an effective control framework, which is shown in Fig. 7.6. This control structure adapts the H_∞-SOF control technique with the described power system control targets and allows direct trade-off between voltage regulation and closed-loop stability by mere tuning of a gain vector.

Here, disturbance input vector , controlled output vector , and measured output vector are considered as follows:

(7.7)

(7.8)

(7.9)

The and can be easily expressed in terms of system states, and the , , and are constant weights that must be chosen by the designer to get the desired closed-loop performance. Since the vector properly covers all significant controlled signals that must be minimized by an ideal AVR–PSS design, it is expected that the proposed robust controller could be able to satisfy the voltage regulation and stabilizing objectives, simultaneously. Since the solution must be obtained through minimizing of the H_∞ optimization problem, the designed feedback system should satisfy the robust stability and voltage regulation performance for the overall closed-loop system. Moreover, the developed ILMI algorithm (which is described in the next section) provides an effective and flexible tool to find an appropriate solution in the form of a simple static gain controller.

7.3.2 Developed Algorithm

The formulation of static output feedback stabilization generally leads to a bilinear matrix inequalities (BMI) problem, which is a nonconvex problem. As described in Ref. [21], system (A, B, C) is stabilizable via the SOF if and only if there exist P > 0, X > 0 (symmetric and positive-definite matrices) and satisfying the following quadratic matrix inequality:

(7.10)

This kind of problem can be solved by an iterative algorithm that may not converge to an optimal solution. Here, in order to solve the H_∞-SOF, an iterative LMI algorithm has been used. The key point is to formulate the H_∞ problem via a generalized static output stabilization feedback such that all eigenvalues of (A−B C) shift toward the left half plane in the complex s-plane, to close to feasibility of (7.10). The general static output feedback control theory [1] gives a family of internally stabilizing SOF gain matrix defined as . Here, the desirable solution is an admissible SOF law

(7.11)

such that

(7.12)

where is a small positive number. The performance index indicates a lower bound such that the closed-loop system is H_∞ stabilizable. The optimal performance index (), can be obtained from the application of a full dynamic H_∞ dynamic output feedback control method. The proposed algorithm, which gives an ILMI solution for the mentioned optimization problem includes the following steps [1]:

1. Step 1: Set initial values and compute the generalized system () and as given in (7.13), for the given power system including conventional AVR and PSS units.
   (7.13)

   For this purpose, the matrix has the following form, and the elements of other matrices in (7.13) can be obtained based on the structure of the used excitation system, AVR and PSS units:

   (7.14)

   The “c” is used for the conventional AVR–PSS system, is obtained from the linearized state space model of targeted generator, which can be expressed as . A modeling method to obtain a fourth-order linear state-space model for a typical generator is explained in Appendix C.

2. Step 2: Set i = 1, and let . and are positive real numbers.
3. Step 3: Select , and solve from the following ARE:
   (7.15)

   Set .

4. Step 4: Solve the following optimization problem for , , and .

   Minimize subject to the LMI constraints

   (7.16)
   (7.17)

   Denote as the minimized value of .

5. Step 5: If , go to step 8.
6. Step 6: For , if , is an H_∞ controller and indicates a lower bound such that the system is H_∞ stabilizable via SOF control. Go to step 10.
7. Step 7: If , solve the following optimization problem for and :

   Minimize trace () subject to the LMI constraints (7.16–7.17) with . Denote as the that minimized trace (). Go to step 9.

8. Step 8: Set , i = i + 1. Then do steps 3–5.
9. Step 9: Set i = i + 1 and , then go to step 4.
10. Step 10: If the obtained solution () satisfies the gain constraint, it is desirable; otherwise, retune constant weights () and go to step 1.

The vector is a constant weight vector that must be chosen by the designer to get the desired closed-loop performance. The selection of these weights depends on the specified voltage regulation and damping performance objectives. In fact an important issue with regard to the selection of the weights is the degree to which they can guarantee the satisfaction of design performance objectives. It is notable that sets a limit on the allowed control signal to penalize fast changes, large overshoot with a reasonable control gain to meet the feasibility and corresponding physical constraints. Therefore, the selection of constant weights entails a compromise among several performance requirements.

One can simply fix the weights to unity and use the method with regional pole placement technique for performance tuning. Here, for the sake of weight selection, the following steps are simply considered through the proposed ILMI algorithm:

1. Step 1: Set initial values for , for example, [1 1 1].
2. Step 2: Run the ILMI algorithm.
3. Step 3: If the ILMI algorithm gives a feasible solution such that it satisfies the robust H_∞ performance and gain constraints, the assigned weights vector is acceptable. Otherwise, retune and go to step 2.

The proposed iterative LMI algorithm shows that if we simply perturb to for some , then we will find a solution of the matrix inequality (7.16) for the performed generalized plant. That is, there exist a real number () and a matrix P > 0 to satisfy inequality (7.16). Consequently, the closed-loop system matrix has eigenvalues on the left-hand side of the line in the complex s-plane. Based on the idea that all eigenvalues of are shifted progressively toward the left half plane through the reduction of . The given generalized eigenvalue minimization in the proposed iterative LMI algorithm guarantees this progressive reduction.

7.3.3 Real-Time Implementation

To illustrate the effectiveness of the proposed control strategy, a real-time experiment was performed at the ANS laboratory. For the purpose of this study, a longitudinal four-machine infinite bus system is considered as the test system. A single line representation of the study system is shown in Fig. 7.7. Although in the given model the number of generators is reduced to four, it closely represents the dynamic behavior of the West Japan Power System [1]. The most important global and local oscillation modes of the actual system are included. For the study system, the local and global low-frequency oscillation modes are around 1.5 and 0.3 Hz, respectively. Each unit is a thermal unit and has its own conventional excitation control system as shown in Fig. 7.1a (for units 2 and 3) and Fig. 7.8 (for units 1 and 4).

Each unit has a full set of governor–turbine system (governor, steam valve servo-system, high-pressure turbine, intermediate-pressure turbine, and low-pressure turbine), which is shown in Fig. 7.9. The generators, lines, conventional excitation system, and governor–turbine parameters are given in Table C.1 to Table C.5 in Appendix C.

Unit 1 is selected to be equipped with a robust controller, and therefore our objective is to apply the control strategy described in the previous section to the controller design for unit 1. The whole power system has been implemented in the ANS laboratory. Figure 7.10 shows the overview of the applied laboratory experiment devices including the control/monitoring desks. A digital oscilloscope and a notebook computer are used for monitoring purposes.

The proposed control loop (Fig. 7.11) has been built in a personal computer connected to the power system using a digital signal processing (DSP) board equipped with the analog to digital (A/D) and digital to analog (D/A) converters as the physical interfaces between the personal computer and the ANS hardware. In Fig. 7.11, the input/output scaling blocks are used to match the PC-based controller and the ANS hardware, signally. High-frequency noises are removed by appropriate low-pass filters.

Then, applying the proposed H_∞-SOF control methodology, an optimal gain vector is obtained as . The considered constraints on limiters and control loop gains are set according to the real power system control units and close to ones that exist in the conventional AVR and PSS units. The constant weight vector is obtained as .

7.3.4 Experiment Results

The performance of the closed-loop system using the proposed optimal gain vector (OGV) in comparison with a pure conventional AVR–PSS system is tested in the presence of voltage deviation, faults, and system disturbance. The configuration of the applied conventional PSS, which was accurately tuned by the system operators, is illustrated in Fig. 7.1b. The conventional PSS parameters are listed in Table C.5 (Appendix C).

During the first test scenario, the output setting of unit 1 is fixed at 0.5 pu. Figure 7.12 shows the electrical power, terminal voltage, and machine speed of unit 1, following a fault on the line between buses 11 and 12 at 2 s. To have a more critical situation, the faulted line is isolated from the network just after four cycles from the fault. It can be seen that the system response is quite improved using the designed feedback gains.

Furthermore, the size of the resulting stable region by the proposed method is significantly enlarged in comparison with the conventional AVR–PSS controller. To show this fact, the critical power output from unit 1 in the presence of a three-phase to ground fault is considered as a good measure. To investigate the critical point, the real power output of unit 1 is increased from 0.3 pu (the setting of the real power output from the other units is fixed at the values shown in Fig. 7.7). Using the conventional AVR–PSS structure, the resulting critical power output from unit 1 will be 0.31 pu [1]; and in the case of tight tuning of conventional control parameters it cannot be higher than 0.52 pu. For the proposed control method, the critical power output, as shown in Table 7.1, is increased to 0.94 pu. The system response for a fault between buses 11 and 12, when the output setting of unit 1 is increased to 0.7 pu, is shown in Fig. 7.13.

In the second test case, the performance of the designed controllers was evaluated in the presence of a 0.05 pu step disturbance injected into the voltage reference input of unit 1 at 20 s. Figure 7.14 shows the closed-loop response of the power systems fitted with the conventional control and the proposed robust control design. Better performance is achieved by the developed control strategy. In the next scenario, the closed-loop system response is examined in the face of a step disturbance () at 20 s. The result is shown in Fig. 7.15. Comparing the experiment results shows that the robust design achieves robustness against the voltage deviation, disturbance, and line fault with a quite good voltage regulation and damping performance.

Finally, to demonstrate the simultaneous damping of local (fast) and global (slow) oscillation modes, filtering analysis has been performed. The laboratory results for the speed deviation of unit 1, following a fault on the line between buses 11 and 12, are shown in Fig. 7.16 (in this experiment, the fault happened at 2 s and the output setting of unit 1 was fixed at 0.45 pu).

7.4.1 High Penetration of Wind Power

Impacts of renewable energy options especially wind power on the power system dynamics and control are discussed in Section 5.5. References [25] and [26] show that the associated controllers with doubly fed induction generators (DFIGs) separate the mechanical dynamics from the electrical ones, and therefore no electromechanical mode exists. In other words, the DFIGs do not have a detrimental impact on the small-signal stability. Moreover, the transient stability is not of concern considering the DFIGs, and also the fault performance or ride through of the synchronous generator will be even better. Therefore, the DFIGs cannot affect power system dynamics seriously in such a way that it would be an appropriate case study to demonstrate the ability of the proposed coordination strategy. However, as previously stated the fixed speed induction generators (FSIGs) directly affect power system dynamics by interchanging reactive power with the connected system and hence significantly influence the controller performance. Implementation of auxiliary controllers such as a static VAR compensator (SVC) is mandatory to maintain power system integrity as addressed in this section.

7.4.2 Developed Algorithm [2]

Figure 7.17 demonstrates the generalized version of Fig. 4.3 (given in Chapter 4), which describes the operating region of the AVR, PSS, and SVC. After a description of the required borders to design a coordinated controller, the mechanism on how the variation of the AVR, PSS, and SVC gains could improve power system performance is explained. As already mentioned, the controller gains are retuned in order to conduct each connected generator to the (1, 1) point in the normalized () plane. Owing to the detrimental impact of torques in phase with rotor angle deviations on oscillatory stability and also taking into account subsynchronous resonance, the control strategy should be considered in such a way that the AVRs always encounter gains reduction. For a generator with less voltage deviation, variation of AVR gain could enhance the system performance. In other words, if voltage deviation for a generator is smaller than 0.707, decreasing of AVR gain causes an increment of voltage deviation and hence, the generator is conducted to the desired region. The mechanism on which the PSS gain affects the power system dynamics is described next.

Consider the swing equation as follows:

(7.18)

where , , , , are inertia constant, synchronize speed, rotor angle, mechanical power input, and electrical power output, respectively.

The reference for the rotor rotation is considered as a frame that rotates at the synchronized speed. Therefore, could be explained by

(7.19)

where is the initial position of the rotor. By replacing Equation (7.19) in (7.18), the following equation is obtained based on the speed variations:

(7.20)

It is well known that the PSS produces a torque in phase with positive deviations of speed [1]. For a negative speed deviation, that is, , decreasing of PSS gain accelerates the rotor and increases the rotor angle deviations. Therefore, for a generator with a normalized phase difference smaller than 0.707, the PSS gain should be reduced during the control process. For positive speed deviations, that is, , the PSS gain should be increased in order to conduct the generator with less phase deviations to the desired region. For a generator with both variations smaller than 0.707, a minor variation identifies the required control action to improve system performance. Regarding the above statements, three control laws could be explained as

1. Every generator located in the IHEDC area encounters decreasing of PSS gain in the proposed control strategy.
2. Every generator located in the GAFEH area encounters decreasing of AVR gain in the proposed control strategy.
3. Every generator located in the OGHI area encounters increasing of SVC gain in the proposed control strategy.

The proposed control methodology updates the controller gains by adding a correction term to the old ones in order to improve the system performance. Later, the details on calculating the controller gains are given.

Here, for a located generator in the SVC reaction region, increasing of SVC gain forces the generator operation to the reaction region of the AVR and PSS. Thereafter, the same procedure as steps 1 and 2 enhances the system performance. Therefore, the proposed criterion could be used for the coordinated design of the AVR, PSS, and SVC in multimachine power systems.

For the implementation of the proposed online control strategy, a combination of switching strategy and simple negative feedback in a discrete manner is employed. First, according to the position of each generator in the normalized plane (Chapter 4), an appropriate control action is selected based on the three control laws presented earlier. Then, the applied feedback tries to conduct generators to the desired region. The implemented feedback employs the angle between phase and voltage deviations () as input signal. Note that the set point for the employed feedback is considered as 45°, which is an ideal at the (1, 1) point. Regarding the time horizon of voltage instability (about 20 s) and transient instability (2 s [27]), the sampling time interval could be selected equal to 2 s. However, the proposed control strategy employs the first sample at a smaller time (less than 2 s) to improve its reliability. The proposed control algorithm can be explained as follows:

1. Step 1: Set the first sample interval ().
2. Step 2: Determine the position of each generator in the normalized plane by , , and .
3. Step 3: Select a proper control action based on the generators position and control laws.
4. Step 4: Calculate new control parameters (K_PSS, K_AVR, K_SVC) as follows:
   (7.21)
   (7.22)
   (7.23)
5. Step 5: Set and return to step 2.

where .

Note that, the proposed method is applicable for any load/generation changes. However, as already mentioned for the positive phase deviations, the PSS gain must be increased instead of decreasing. In other words, for the positive phase deviations, that is, , Equation (7.21) will change to

(7.24)

The flow chart representation of the proposed algorithm is shown in Fig. 7.18. Here, the K_PSS, K_AVR, and K_SVC are the AVR, PSS, and SVC gains, respectively. In fact, the problem of a coordinated AVR–PSS design is reduced to the design of a simple switching/feedback-based method, which is quite easy for implementation.

7.4.3 An Application Example

The capability of the proposed criterion and control strategy is investigated after application on several large-scale interconnected power systems. Here, this issue is illustrated using the New York/New England system, a 16-machine, 5-area test system, as shown in Fig. 4.4 (Chapter 4). As mentioned, all generators are represented by a two-axis model and equipped with PSS. The applied model for the AVR and PSS is shown in Fig. 4.5. The SVC block diagram is also presented in Fig. 7.19. The efficiency of the proposed control strategy is examined in the presence of wind turbines (WTs). To investigate the impact of WTs on the coordination problem, two wind farms are employed at buses 9 and 15. The implemented wind farms use simple squirrel cage induction generators without any control capability, which operate at a substantially constant speed, normally referred as the FSIGs [2] (Fig. 7.19).

7.4.4 Simulation Results

In Section 4.3, several disturbance scenarios in both generation and demand sides are applied to the considered case study and the importance of the Δδ–Δv graph in stability assessment is demonstrated. Here, the effectiveness of the introduced Δδ–Δv graph-based tuning approach for coordination of existing control devices (PSS, AVR, and SVC) to enhance oscillation damping and synchronization of the power system with and without wind power penetration are examined.

7.4.4.1 Case A: Without Wind Power

In the performed simulations without wind power penetration, the first sample is used at 1.5 s (T_S1 = 1.5 s). First, the behavior of the power system after the outage of generator 12 is investigated. Note that without applying the proposed control strategy, as shown in Figs. 4.10 and 4.11, the system encounters transient instability, that is, first swing instability. The system response for this disturbance when using the explained tuning-based coordination strategy is shown in Fig. 7.20. The results demonstrate the efficiency of the proposed criterion and control strategy. Figure 7.20a shows the performance of the power system after applying the proposed control strategy within 4 s for the sake of comparison with the first swing instability without applying the strategy. It can be seen that the proposed control strategy aids the system to keep its transient stability. Figure 7.20b explains the behavior of the system within 30 s in the Δδ–Δv plane. It is clear that after a number of control reactions, the system conducts to a stable mode at the steady state. Distribution of the voltage–angle indexes in the normalized Δδ–Δv plane is also shown in Fig. 7.20. It can be seen that generators 14–16 are located in the PSS reaction region at the first control action. Therefore, decreasing the PSS gains of these generators besides decreasing the AVR gains for some others makes the system stable. It can be seen that the system response is quite improved using the proposed coordination methodology (Fig. 7.20d).

The simulation results show the satisfactory performance of the control strategy and success of the proposed criterion against the load changes as well as generation changes.

As another example, Fig. 7.21 shows the dynamics of the system after outage of generator 16. It can be seen that the system experiences disorders in the oscillatory, angle, and transient stability behavior during simulation time. The applied control strategy eliminates the voltage/rotor angle oscillations and conducts the system to a stable mode in the steady state. Note that without applying the proposed control strategy the system encounters instability. Distribution of the voltage–angle indexes related to the outage of generator 16 in the normalized () plane is also shown in Fig. 7.21. At t = 1.5 s (Fig. 7.21c), except for two generators, the others are out of the desired region. According to the assigned control laws, by decreasing the PSS gains for this set of generators at the first control action, the system tries to keep its integrity. It can be seen that all the generators have been located in the desired region at the steady state (Fig. 7.21d).

7.4.4.2 Case B: With Wind Power

Case B is performed to emphasize the efficiency of the proposed method for the power system in the presence of wind farms. In the performed simulations concerning wind power penetration, the T_S1 will be fixed at 1.8 s. Figure 7.22 shows the dynamic response of the power system following outage of G12, concerning 8% wind power penetration. It can be seen that by the penetration of wind power, generators 14–16 try to be isolated from the system and operate in islanding mode. Therefore, the system is going into an unstable mode. The nonsimilar phase characteristics of generators besides the diverged terminals voltage behavior in Fig. 7.22b also exhibit instability of the system. Distribution of the voltage–angle indexes in the normalized () plane is shown in Fig. 7.22c.

It can be seen that generators 14–16 are located in the operating region of the SVC. Therefore, the SVC should be implemented in the areas related to these generators. However, because of fewer deviations for generator 16 and taking into account the economic reasons, it seems that the SVC in this region could return the system to a stable mode. For this purpose, at the beginning of simulation, the SVC is considered in the model and after that, increasing of SVC gain improves the system performance.

The dynamic behavior of the power system after applying the proposed control strategy is shown in Fig. 7.23. The proposed control strategy conducts the system to a stable mode within several tuning steps. The initial and final values (controller gains at steady state) of control parameters are given in Table 7.2. Distribution of the normalized parameters in the proposed criterion for outage of G12 in the presence of wind farms and SVC can be seen in Fig. 7.23. From Fig. 7.23c, it is quite clear that all the generators are moved to the desired region at steady state.

	PSS Gains (KPSS)		AVR Gains (KAVR)		SVC Gains (KSVC)
Generator Number	Initial	Final	Initial	Final	Initial	Final
1	100	100	100	100.000	–	–
2	100	100	100	81.7805	–	–
3	100	100	100	80.2319	–	–
4	100	100	100	76.6451	–	–
5	100	100	100	75.1585	–	–
6	100	100	100	74.4325	–	–
7	100	100	100	76.0875	–	–
8	100	100	100	82.0945	–	–
9	100	100	100	80.1594	–	–
10	100	100	100	100.000	–	–
11	50	50	100	82.2249	–	–
13	110	110	100	81.7274	–	–
14	100	75.8369	100	64.7924	–	–
15	100	79.9705	100	64.8628	–	–
16	100	82.3612	100	81.5471	50	58.3413

7.5.1 Fuzzy Logic-Based Coordination System

Figure 7.24a shows the overall scheme for the proposed fuzzy logic-based coordinator. The normalization and scaling blocks are not fuzzy variables and have been designed to improve the coordination performance. As shown, the fuzzy unit contains four major components: fuzzification, fuzzy rule-base, inference mechanism, and defuzzification.

Here, terminal voltage deviation and angle deviations are considered as input signals of the fuzzy system. These input signals are selected to guarantee the synchronism and stability enhancement of the power system. Furthermore, to limit the input signal deviations, a normalization method is applied. For this purpose, a method, which is conceptually shown in Fig. 7.24b, is used for both voltage and angle deviations. The Δδ_i−N (ΔV_i−N) demonstrates the normalized phase difference (voltage deviation). The Δδ_i−N and ΔV_i−N can vary in the range of [−1, 1] for all generators.

Fuzzification plays an important role in dealing with uncertain information, which might be objective or subjective in nature. The fuzzification block represents the process of making crisp quantity into fuzzy variables. In fact, the fuzzifier converts the crisp input to a linguistic variable using the assigned membership functions in the fuzzy knowledge base. Fuzziness in a fuzzy set is characterized by the membership functions. Using appropriate membership functions, the input/output quantities are converted to desirable linguistic variables, which finally specify the quality of control commands.

Here, the membership functions corresponding to the input variables are arranged as negative large (NL), negative small (NS), zero (ZR), positive small (PS) and positive large (PL), and for the output variables they are arranged as very small (VS), small (S), medium (M), and large (L). The number of membership functions for each variable may affect the quality of the output control command. In the present work, five membership functions are defined for the input signals and four membership functions are defined for output signals. The membership functions of input and output variables (for the case study shown in Fig. 6.8) are demonstrated in Fig. 7.25.

The knowledge rule base consists of information for linguistic variables definitions (database) and fuzzy rules (control commands). The concepts associated with a database are used to characterize fuzzy control rules and a fuzzy data manipulation in the fuzzy logic controller. A lookup table is made based on discrete universes that define the output of a controller for all possible combinations of the input signals. A fuzzy system is characterized by a set of linguistic statements in the form of “if–then” rules. Fuzzy conditional statements make the rules or the rule set of the fuzzy controller. Finally, the inference engine uses the if–then rules to convert the fuzzy input to the fuzzy output.

Fuzzy inference is the kernel of a fuzzy logic system. With two inputs and five linguistic terms, 25 rules were developed for each output, which is given in Table 7.3 [17]. The antecedent parts of each rule are composed by using the AND function. Here, the Mamdani fuzzy inference system is employed. The centroid method is used for defuzzification.

7.5.2 Simulation Results

The efficiency of the fuzzy logic-based coordinated control for AVR–PSS is tested on the 2-area, 4-machine, 11-bus test system, which is shown in Fig. 6.8. The detailed bus data, line data, and dynamic characteristics for the machines, exciters, and loads are given in Ref. [27]. All generators use AVR and PSS controllers with the following transfer functions:

(7.25)

(7.26)

The power system has two areas with two generators in each area. The nominal system is operating with 413 MW being sent from area 1 to area 2. The AVR–PSS units of generator 2 in area 1 (connected to the swing bus in the system) and generator 4 at area 2 (with a high power rate) are considered to be coordinated/controlled by the designed fuzzy system.

Since, the time horizon for transient instability is almost about 3–5 s and this time horizon for small-signal instability is about 10–20 s, the fuzzy control unit will be activated in the system following 1 s after faults. As the first test scenario, the power system performance is investigated after outage of generator 3; and at the second test scenario, 1000 MW load has been suddenly added to the power system [17].

Outage of generator 3 can be accounted for as a severe fault in the present power system. Figure 7.26 shows the time domain responses of the generator outputs following a fault without the fuzzy coordinator system. Here, the P_a is accelerator power, V_t is terminal voltage and w is generator speed. Strong oscillations in accelerator powers are shown. It can be also seen that the power system loses its synchronism, and two areas are separated. Therefore, generator 4 cannot be able to supply whole the load in area 2 and voltage is collapsed in this area.

Figure 7.27 shows the system response (voltage, speed, and accelerator power) for the same fault in the presence of using a fuzzy logic system for tuning the AVR–PSS units in generators 2 and 4. The fuzzy systems maintain the synchronism and return the terminal voltages to the acceptable levels.

In the second test scenario, 1000 MW load step disturbance is applied to the system. The system responses without and with the proposed fuzzy logic-based coordination system are shown in Figs. 7.28 and 7.29. It is shown that using conventional AVR–PSS control, the system falls to an oscillatory instability and the synchronism is also lost. On the other hand, with the fuzzy logic-based coordination, the synchronism remains and the oscillations are successfully removed.