Sine-Cosine Algorithm for the Dynamic Economic Dispatch Problem With the Valve-Point Loading Effect

1. Introduction

The operation of a power system depends upon the system's security, reliability, and economy (Bhattacharjee ‎, Bhattacharya‎, & Nee Dey 2014). The Economic Dispatch (ED) is the main function of power system operation to reduce the cost of different fuel types. The main aim of the ED is to allocate load demand among committed thermal generators at a minimum price while satisfying power balance and other system constraints (Nourianfar & Abdi 2021). Thus, the ED problem is a highly complex and nonlinear optimization problem. The ED can be classified into Static Economic Dispatch (SED) and Dynamic Economic Dispatch (DED) (Verma et al. 1AD). In SED, the thermal generating units have been allocated economically to satisfy load demand for a specific time interval. The SED does not consider the fundamental relation of the system between the different periods (Soni et al., 2020). The DED, an extension of SED, issues time-varying load demand among the generators by satisfying various operating constraints. The DED considers the relation of different operating times to meet multiple constraints (Bhattacharjee, Shah, & Soni 2022a). Traditionally, the valve point loading effect (VPLE) has been ignored in DED to make the problem tractable (Bhattacharjee & Patel 2020). The solution becomes inaccurate and imprecise. The DED problem with VPLE has been considered to make the system more (Soni & Pandya, 2018).