# A Hybrid Approach for Model Order Reduction and Controller Design of Large-Scale Power Systems

**Rishabh Singhal**

Roorkee Institute of Technology

**Yashonidhi Srivastava, Shini Agarwal, Abhimanyu Kumar, and Souvik Canguli**

Thapar Institute of Engineering and Technology

## Introduction

Higher-order differential equations transform most physical phenomena into a mathematical model. They are usually preferred to reduce the order of this model while preserving the behaviour of the original system. It helps in complexity reduction of its hardware, which in turn makes designing of controller feasible [I]. Several methods have been developed for reducing certain systems in the domain of both time and frequency [2,3]. Numerous composite techniques have also been proposed [4,5]. Soft computing methods have been applied in the field of model reduction [6-8].

Large systems are exposed to declination in performance due to hindrance caused by load fluctuations, variations in parameters, and other uncertainties. Generation takes place in different areas, and transmission takes place over huge distances. In this entire interconnected system, both frequency and power variations occur due to imbalance in power demand and generation. This mismatch may be treated by kinetic energy extraction, which gradually decreases the frequency. But the gamble of frequency reduction to obtain equilibrium seems huge [9].

In this regard, the field of load frequency control (LFC) aims to provide an effective solution. The principal roles of LFC are the prevention of sudden load disturbances, ensuring zero steady-state error, minimizing unscheduled power exchanges, and ensuring system nonlinearities to lie within the specified tolerance [9].

With the fast headway in electrical power technology, the complete power system has developed into a complicated entity and is hence of higher order. Consequently, its order reduction has become equally important. Some related works are discussed below.

Gallehdari et al. [Ю] applied particle swarm optimization (PSO) to address the order reduction of a power system model. Outcomes of PSO were compared with those of Hankel norm method as well. Sturk et al. [11] proposed a structured model reduction scheme. The algorithm was tested on a three-machine, nine-bus system. Saxena and Hote [12] adapted Routh approximation method to reduce a single-area model and further proposed an internal model control (IMC)-based approach for smooth LFC operation. Kumar and Nagar [13] developed a new version of balanced truncation method to reduce large-scale power system model preventing the interaction between the study and the external area. Biradar et al. [14] compared around ten model reduction schemes to simplify the automatic voltage regulator model. Sambariya and Arvind [15] proposed a mixed method to reduce single-machine infinite bus system. The coefficients of the denominator polynomial were obtained by the stability equation method, whereas those of the numerator polynomial were determined using firefly algorithm (FA). Semerow et al. [16] stated a modal analysis approach based on the known dominant modes to reduce single- and multimachine infinite bus systems. Singh et al. [17] applied a balanced realization method to reduce an inherently unstable power system model having several input-output states. Saxena [9] further developed reduced model and its controller for multi-area network. Acle et al. [18] presented a new method to reduce higher-order practical power system stabilizers.

From the literature, it seems that only few works have been reported the use of soft computing for reduced-order modelling (ROM). Moreover, efficacy was not tested using some of the recently developed metaheuristic algorithms. Only step/impulse responses of the original and reduced order systems were considered to estimate the unknown model parameters. Being an unbiased signal, pseudo-random binary sequence (PRBS) has been taken up to obtain the ROM parameters.

Thus, a composite method for order reduction has been employed combining stability equation approach [19] and grey wolf optimizer (GWO) [20] for a two-area system. Stability equation method is used to obtain the coefficients of denominator polynomial, while GWO is used to determine the coefficients of the numerator polynomial. A proportional integral derivative (PID) controller is synthesized using

GWO technique by applying approximate model matching (AMM) framework [21]. Further, the proposed technique is compared with some of the latest heuristic methods used and cited in the literature [22-28].

The remainder of this chapter is structured as follows. Section 13.2 gives an overview of the modelling issues of the single-area and two-area power system networks. Section 13.3 briefs the proposed methodology of work. Section 13.4 presents the relevant results. Section 13.5 concludes this chapter with a discussion on the future scope work.