Control System Anand Kumar Pdf

[Thedore Rosa]

Inthis paper, a Sliding mode controller design method for frequency regulation in an interconnected power system is presented. A sliding surface having four parameters has been selected for the load frequency control (LFC) system model. In order to achieve an optimal result, the parameter of the controller is obtained by grey wolf optimization (GWO) and particle swarm optimization (PSO) techniques. The objective function for optimization has been considered as the integral of square of error of deviation in frequency and tie-line power exchange. The method has been validated through simulation of a single area as well as a multi-area power system. The performance of the Sliding mode controller has also been analyzed for parametric variation and random loading patterns. The performance of the proposed method is better than recently reported methods. The performance of the proposed Sliding mode controller via GWO has 88.91% improvement in peak value of frequency deviation over the method of Anwar and Pan in case study 1 and similar improvement has been observed over different case studies taken from the literature.

The main objective of LFC is to regulate the frequency and tie-line power flow within the control area. The main control challenges in LFC are system model parametric uncertainty, non-linearity present in a realistic power system, and load-disturbances [4,5,6].

Various control techniques have been used in LFC to address these control issues, like model predictive control (MPC) [7], internal model control (IMC) [8], two-degree of freedom IMC (2DoF-IMC) [9], H-infinity control [10, 11], SMC [12,13,14,15], active disturbance rejection control (ADRC) [16, 17], the direct synthesis (DS) approach [18, 19] and artificial intelligence techniques [20] etc.

In recent times, the SMC design technique has gained more attention for being robust to modeling error, parametric variation, and external disturbance. These properties make SMC quite effective in many applications such as automotive systems [21], robotics [22], electric drives [23], wind-energy conversion systems [24, 25], process control [26, 27], unmanned aerial vehicles [28], etc. Recently the SMC technique has been used by many researchers to address the control issues of LFC [29,30,31,32,33,34,35,36,37,38,39].

Decentralized SMC has been designed for frequency control in a multi-area power system (MAPS), considering unmatched uncertainty, by Mi et al. [29]. Qian et al. [30] have improved control performance by using neural network-based integral SMC for the LFC of a non-linear power system. The method has been extended by Qian and Fan [31] for frequency control of a power system with renewable energy. A non-linear Sliding mode controller with matched and unmatched uncertainty has been proposed by Prasad et al. [32] for LFC of a three-area interconnected power system. Further, Prasad et al. [33] have extended their SMC design method to control the frequency of wind-integrated power systems.

This paper is organized as follows: the LFC model for a single-area as well as a multi-area power system along with the proposed controller design method is given in Section 2. The simulation results are shown in Section 3 and the paper is concluded in Section 4.

The SMC technique is a special type of variable structure control that was initially presented by Utkin and Vadim [12]. The SMC is a robust control technique that can effectively compensate for plant model mismatch and load-disturbances. The desired behavior is represented through sliding surface s(t) and the objective of the sliding mode controller is to drag the state of the system to the surface and keep it there.

The tuning parameters k1, k2, k3, k4, KD, and δ are obtained with the use of the metaheuristic optimization technique. Several researchers have used the metaheuristic optimization algorithm to determine the controller parameters in different control problems. The particle swarm optimization (PSO) technique is used by Mehta and Kaya [40] while the cuckoo search (CS) algorithm is adopted by Mehta and Rojas [41] to obtain the controller setting. The democratic joint operation algorithm [42], grouped grey wolf optimization [43], the dynamic leader-based collective intelligence algorithm [44] are some recently reported optimization techniques which have been successfully implemented in different control problems. Here, we have used PSO and GWO optimization techniques to obtain the controller parameters in Eq. (12).

The proposed controller design method is implemented for the LFC problem. The plant model for the LFC consists of governor, turbine, generator, and load. The schematic diagram of a single area power system (SAPS) is shown in Fig. 2.

The block diagram of a multi-area power system (MAPS) is shown in Fig. 3. The proposed controller design method can also be extended to MAPS where the goal of LFC is to regulate the frequency of each area and further to maintain the tie-line power flow exchange between the areas. With the variation of load in the power system the area frequency and tie-line power interchange vary. So, a combined parameter, area control error (ACE), is a linear combination of deviation in frequency response and tie-line power flow exchange, and is used in each LFC of MAPS.

In this section, three SAPS, one two-area power system (TAPS), and one FAPS is considered for the simulation. The response obtained with the proposed method is compared with the recently reported methods in the literature. The performance has been evaluated in terms of peak value, settling time, percentage improvement in peak value, integral absolute error (IAE), integral of square error (ISE), integral time absolute error (ITAE) of the output response.

From the above three case studies, it is seen clearly that the proposed method gave faster response with lower peak value. The performance of the proposed1-GWO method is observed in terms of IAE, ISE, ITAE, and it is better than that of the proposed2-PSO, Anwar and Pan [18].

As a non-linear component like GRC is added to a power system it will produce oscillation and sometimes it may become unstable. In the case study 4, Fig. 7 shows the GRC block is cascaded in a turbine transfer function model.

The frequency deviation in area 1, area 2 and tie-line power flow between the two areas for case 5a is shown in Figs. 10, 11 and 12, respectively, and its response is compared with K. Lu et al. [6] and shows that the proposed1-GWO method gives the faster response and lower peak value for frequency regulation in TAPS.

The frequency deviation in area 1, area 2 and tie-line power flow between the two areas for case 5b is shown in Figs. 13, 14 and 15 respectively, and its response is compared with that of the proposed2-PSO, K. Lu et al. [6] and show that the proposed1-GWO method has the faster transient speed for frequency regulation in TAPS.

Figure 16 shows the frequency regulation in area 1 and ACE in area 1 is shown in Fig. 17. Figures 16 and 17 show that the proposed1-GWO controller has much-improved performance over that of the proposed2-PSO, K. Lu et al. [6].

Random step load variation in area 2 is shown in Fig. 21. Frequency deviation in area-1, area 2 and tie-line power flow between the two areas for case 5e is shown in Figs. 22, 23 and 24 respectively, and its response is compared with that of the proposed2-PSO, K. Lu et al. [6] and confirm that the proposed1-GWO and the proposed2-PSO method is more robust for frequency regulation in TAPS.

In this paper, the sliding mode controller has been designed for a third-order system and implemented for frequency regulation in single-area, two-area, and four-area power systems. The optimal value of SMC controller parameters is obtained via the GWO and PSO optimization techniques. The efficacy of the proposed method has been analyzed with consideration of GRC, parametric uncertainty, and a random loading pattern. The proposed SMC controller via GWO performs better than the proposed SMC controller via PSO and other recently reported methods. From the simulation study, it is seen that the proposed method via GWO has 88.91% improvement in peak value of frequency deviation with that of Anwar and Pan while the proposed method via PSO has 84.80% improvement in case study 1. Future work on the proposed method is to implement in LFC problem considering wind energy, hydro-energy, and photo-voltaic systems.

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