**5. Optimization of the control system for fractional order SVC-based system**

The derived fractional order control system is shown in Eq. (24). For best control performance, it is vital to choose the optimal control parameters. This work compares the performance of the proposed controller (Eq. 24) to the conventional PID control system. The parameters of the proposed control scheme are optimized using Latin Hypercube method and Simulink response optimization toolbox. The order of the fractional operator is chosen constant as *α* ¼ 0*:*8.

To optimize the parameters, the cost function chosen is the integral of square of the error (ISE) between the reference command and the feedback signal. The initial values of the controller parameters are chosen as *C*<sup>1</sup> ¼ 0*:*58, *C*<sup>2</sup> ¼ 0*:*78, and *Ks* ¼ 0*:*48. The convergence of the parameters to the optimal values is shown in **Figure 3**. The optimal parameters after convergence of the optimization algorithm are: *C*<sup>1</sup> ¼ 0*:*35, *C*<sup>2</sup> ¼ 0*:*86 and *Ks* ¼ 0*:*625. The optimized step response of the closed system is shown in **Figure 4**.

The step response and optimized parameters of the PID controllers are shown in **Figures 5** and **6**. **Figure 5** shows the response of the system with optimized PID under nominal conditions. The optimal parameters are given in the table of **Figure 6**.

**Figure 3.** *Optimized parameters of the proposed scheme.*

**6. Results and discussions**

*Parameters of the optimized PID controller.*

**Figure 5.**

**Figure 6.**

**277**

*PID step response optimization.*

*DOI: http://dx.doi.org/10.5772/intechopen.79615*

**6.1 Step response comparison**

and the profile of the load demand is shown in **Figure 8**.

For numerical simulations, the nominal parameters of the power system including the SVC configuration are given as following [18]: *M* ¼ 1, *X* ¼ 0*:*5, *V*<sup>1</sup> ¼ 1, *τ* ¼ 8, *k* ¼ 0*:*25, *D* ¼ 0*:*1, and *Pm* ¼ *Pd*. The Simulink simulation setup is shown in **Figure 7**

*Static Var Compensator with Fractional Order Dynamics for Enhanced Stability and Control*

The control performance of the SVC-based power system under the step response is compared in **Figure 9**. The comparison is done for the error of the bus voltage stabilization response under the proposed fractional order control system and optimized PID. From the simulation results, it is concluded that the proposed

**Figure 4.** *Step response optimization.*

*Static Var Compensator with Fractional Order Dynamics for Enhanced Stability and Control DOI: http://dx.doi.org/10.5772/intechopen.79615*

**Figure 5.**

**5. Optimization of the control system for fractional order SVC-based**

The derived fractional order control system is shown in Eq. (24). For best control performance, it is vital to choose the optimal control parameters. This work compares the performance of the proposed controller (Eq. 24) to the conventional PID control system. The parameters of the proposed control scheme are optimized using Latin Hypercube method and Simulink response optimization toolbox. The

To optimize the parameters, the cost function chosen is the integral of square of the error (ISE) between the reference command and the feedback signal. The initial values of the controller parameters are chosen as *C*<sup>1</sup> ¼ 0*:*58, *C*<sup>2</sup> ¼ 0*:*78, and *Ks* ¼ 0*:*48. The convergence of the parameters to the optimal values is shown in **Figure 3**. The optimal parameters after convergence of the optimization algorithm are: *C*<sup>1</sup> ¼ 0*:*35, *C*<sup>2</sup> ¼ 0*:*86 and *Ks* ¼ 0*:*625. The optimized step response of the closed system is

The step response and optimized parameters of the PID controllers are shown in **Figures 5** and **6**. **Figure 5** shows the response of the system with optimized PID under nominal conditions. The optimal parameters are given in the table of **Figure 6**.

order of the fractional operator is chosen constant as *α* ¼ 0*:*8.

**system**

*Control Theory in Engineering*

shown in **Figure 4**.

**Figure 3.**

**Figure 4.**

**276**

*Step response optimization.*

*Optimized parameters of the proposed scheme.*

*PID step response optimization.*



#### **Figure 6.**

*Parameters of the optimized PID controller.*

### **6. Results and discussions**

For numerical simulations, the nominal parameters of the power system including the SVC configuration are given as following [18]: *M* ¼ 1, *X* ¼ 0*:*5, *V*<sup>1</sup> ¼ 1, *τ* ¼ 8, *k* ¼ 0*:*25, *D* ¼ 0*:*1, and *Pm* ¼ *Pd*. The Simulink simulation setup is shown in **Figure 7** and the profile of the load demand is shown in **Figure 8**.

#### **6.1 Step response comparison**

The control performance of the SVC-based power system under the step response is compared in **Figure 9**. The comparison is done for the error of the bus voltage stabilization response under the proposed fractional order control system and optimized PID. From the simulation results, it is concluded that the proposed

PID. The comparative results are shown in **Figure 10**. From the results provided, it is clear that the system under the proposed control scheme perfectly tracks the reference command while the system under the PID controller exhibits tracking

*Static Var Compensator with Fractional Order Dynamics for Enhanced Stability and Control*

The system's bus voltage stabilization under heavy inductive loads is compared under the action of the proposed control and the optimized PID. The simulation results are shown in **Figure 10**. The inductive load is varied gradually from time t = 60 sec and increased step wise till t = 100 sec. The proposed controller is robust against the dynamics introduced due to the heavy inductive loads. From **Figure 11**, it is clear that the response of the power system with PID-based SVC system suffers from voltage sage condition. The proposed controller-based SVC system is efficient in handling the situation and thus, the bus voltage error is very small with no

The control signals comparison is given in **Figure 12**. The proposed control system offers low frequency oscillations, which shows the robustness of the proposed method as compared to the PID method. Usually, in classical sliding mode control method, the robust term excites high frequency oscillations. Due to the high frequency oscillations, the classical sliding mode control is not feasible for practical

**6.3 Performance comparison under inductive variable loading condition**

errors of considerable magnitudes.

*DOI: http://dx.doi.org/10.5772/intechopen.79615*

voltage dips.

**Figure 10.**

**Figure 11.**

**279**

*Tracking response (a) proposed scheme (b) optimized PID.*

*Step response under heavy inductive loads (a) proposed scheme (b) optimized PID.*

**Figure 7.** *MATLAB/SIMULINK simulation setup.*

**Figure 8.** *Load demand profile.*

**Figure 9.**

*Step response error (a) proposed scheme (b) optimized PID.*

control system is more robust against the load demand variation profile as compared to the optimized PID control system.

### **6.2 Tracking response comparison**

In this section, the bus voltage tracking performance of the SVC-based power network is compared under the action of the proposed control and the optimized *Static Var Compensator with Fractional Order Dynamics for Enhanced Stability and Control DOI: http://dx.doi.org/10.5772/intechopen.79615*

PID. The comparative results are shown in **Figure 10**. From the results provided, it is clear that the system under the proposed control scheme perfectly tracks the reference command while the system under the PID controller exhibits tracking errors of considerable magnitudes.

### **6.3 Performance comparison under inductive variable loading condition**

The system's bus voltage stabilization under heavy inductive loads is compared under the action of the proposed control and the optimized PID. The simulation results are shown in **Figure 10**. The inductive load is varied gradually from time t = 60 sec and increased step wise till t = 100 sec. The proposed controller is robust against the dynamics introduced due to the heavy inductive loads. From **Figure 11**, it is clear that the response of the power system with PID-based SVC system suffers from voltage sage condition. The proposed controller-based SVC system is efficient in handling the situation and thus, the bus voltage error is very small with no voltage dips.

The control signals comparison is given in **Figure 12**. The proposed control system offers low frequency oscillations, which shows the robustness of the proposed method as compared to the PID method. Usually, in classical sliding mode control method, the robust term excites high frequency oscillations. Due to the high frequency oscillations, the classical sliding mode control is not feasible for practical

**Figure 10.** *Tracking response (a) proposed scheme (b) optimized PID.*

**Figure 11.** *Step response under heavy inductive loads (a) proposed scheme (b) optimized PID.*

control system is more robust against the load demand variation profile as com-

In this section, the bus voltage tracking performance of the SVC-based power network is compared under the action of the proposed control and the optimized

pared to the optimized PID control system.

*Step response error (a) proposed scheme (b) optimized PID.*

**6.2 Tracking response comparison**

**Figure 7.**

**Figure 8.**

**Figure 9.**

**278**

*Load demand profile.*

*MATLAB/SIMULINK simulation setup.*

*Control Theory in Engineering*

**Figure 12.** *Control signal comparison.*

implementations. The proposed control method is noninteger in nature and from the control law given in Eq. (24), there is an integral term around the robust term, that is, signum function. So, it excites low frequency oscillations and thus it is very feasible for practical implementation over the microprocessor.
