1. Introduction

Electric power system is the most complex man-made system, and the modern society depends heavily on continuous and reliable operation of this system to supply electricity to commercial, residential and industrial consumers. Operation of the power grid involves a balanced platform in generation, transmission and distribution, which costs billions of dollars to run. The reliable and continuous availability of electricity with minimum costs is the major objective of utility grids and energy providers. Two of the important complex problems in power system are economic dispatch and power system protection.

The power plants and utility grids need to allocate the available generation units in an efficient and economical way to respond to the load demand in order to provide continuous power supply in stable conditions and with minimum power production costs. This is addressed as

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economic dispatch (ED) [1, 2]. With the practical constraints on the generators, finding optimum power outputs with minimum fuel costs is challenging.

2. Problem formulation

separately as optimization problems.

where ti is the operation time of relay Ri

characteristic function approximated by:

relays in the system.

which can be depicted as an optimization objective function:

Generally, the operation time of DOCRs is defined in (2):

2.1. Relay coordination problem

In this section, overcurrent relay coordination and economic dispatch problems are formulated

In a protection scheme, each primary relay should operate as fast as possible to clear the fault in a system. If the operation time of the relay takes longer than an acceptable time, the damage on the faulty equipment would be severe with serious consequences. In other words, minimizing the total operation time of relays decreases the risk and stress on the protected apparatus,

OF <sup>¼</sup> minX<sup>n</sup>

transmission line in the zone of protection, and it is normally set to 1; n is the total number of

ti <sup>¼</sup> <sup>λ</sup> � TMSi IFi PSi � �<sup>η</sup>

where IFi is the fault current seen by the appropriate relay Ri after being transformed through the secondary winding of corresponding current transformer (CT). Depending on the type of relays, the characteristic constants λ, L and η are selected [16]. In this chapter, continuous form of TMS and PS is considered with relay type of standard inverse definite minimum time (IDMT). Based on that, all the relays in the system are assumed identical with a common

> ti <sup>¼</sup> <sup>0</sup>:<sup>14</sup> � TMSi Ii PSi � �<sup>0</sup>:<sup>02</sup>

To ensure that the operation time of an individual relay is proper enough to mitigate the damage impact of faults on the apparatus, the time must be within an acceptable range:

where, respectively, timin and timax are the minimum and maximum operating time of the relay Ri. Each overcurrent relay has a manufactured TMS range to provide controllability of response to faults with different speeds. As shown in (3), ti is proportional to TMS values. Also, the PS has nonlinear effect on the operating time. Within a security margin and to avoid maloperation of an individual relay with normal load or slight overload current, the minimum pickup current setting is selected bigger than the maximum load current. The maximum plug

� 1

timin ≤ ti ≤ timax ; i ¼ 1, …, n (4)

i¼1

� 1

witi (1)

http://dx.doi.org/10.5772/intechopen.72409

27

þ L (2)

(3)

, wi is the probability of the occurrence of fault on

Particle Swarm Optimization Solution for Power System Operation Problems

In addition, as the occurrence of failures and faults in the power grid is inevitable, the entire power system must be protected. The relay protection scheme is designed to detect faults and isolate the faulty parts of the grid from the healthy sections in order to mitigate the consequences of the faults and maintain continuity of service. If a fault occurs, the nearest corresponding relays must operate as fast as possible to clear the fault. If due to any reason these primary relays fail to react, their backup relays must operate and accomplish the task. Directional overcurrent relays (DOCRs) are a suitable and economical protection scheme for distribution systems [3]. The protection design of DOCRs is based on two parameters, time multiplier setting (TMS) and plug setting (PS). Proper settings of TMS and PS allow a primary relay to clear the faults in its protection zone as fast as possible and in case of failure, its backup relay operates immediately after a time interval to clear the fault. TMS and PS values of each relay must be coordinated with other backup relays, where again relays act with different current settings, which make the coordination a complex task. Each pairs of relays include four variables (TMS, PS) and the complexity of coordination will be intense in bigger systems with more relays and constraints. Due to the complex interconnection of the distribution systems and also nonlinear characteristics of operation time of relays, finding best relay settings could be very difficult.

Considering the non-convex and nonlinear nature of these problems, traditional methods fail to feasibly or optimally solve them. Therefore, evolutionary algorithms have gained more attentions as solutions to such optimization problems. Some of the recent related works on ED problem have been studied with the metaheuristic methods such as Genetic Algorithm (GA) [4], Particle Swarm Optimization (PSO) [4], Imperialist Competitive Algorithm (ICA) [5], Artificial Bee Colony (ABC) [6], Bacterial Foraging Optimization (BF) [7], Hybrid Harmony Search with Arithmetic Crossover (ACHS) [8], GA with a special class of ant colony optimization (GAAPI) [9] and so on. The modified and hybrid models of PSO such as Modified PSO (MPSO) [10], guaranteed convergence PSO (GCPSO) [10], Species-based Quantum Particle Swarm Optimization (SQPSO) [11], Iteration PSO (IPSO) [12], Parallel PSO with Modified Stochastic Acceleration Factors (PSO-MSAF) [13], Distributed Sobol PSO and Tabu Search Algorithm (DSPSO-TSA) [14], Self-Organizing Hierarchical PSO (SOH-PSO) [15], Passive Congregation-based PSO (PC-PSO) [15] and Simple PSO (SPSO) [15] have also been employed to address the ED problem.

Application of metaheuristic algorithms on power system protection and particularly, DOCR coordination in distribution networks has been introduced in literature such as PSO [3, 16], Harmony Search Algorithm (HSA) [17], Cuckoo Algorithm [18], chaotic firefly algorithm [19], differential evolution [20] and so on.

In this chapter, PSO is applied as a solution to the introduced power system operation problems, namely ED and DOCR coordination. The rest of the chapter is organized as follows: in Section 2, these power system problems are defined and formulated as optimization problems. PSO algorithm is explained in Section 3. In Section 4, PSO is applied in two case study systems to conduct the performance and feasibility of this method. Finally, Section 5 concludes the chapter with the results in pervious sections.
