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# Particle Swarm Optimization Solution for Power System Operation Problems

By Mostafa Kheshti and Lei Ding

Submitted: June 2nd 2017Reviewed: November 13th 2017Published: December 20th 2017

DOI: 10.5772/intechopen.72409

## Abstract

Application of particle swarm optimization (PSO) algorithm on power system operation is studied in this chapter. Relay protection coordination in distribution networks and economic dispatch of generators in the grid are defined as two of power system-related optimization problems where they are solved using PSO. Two case study systems are conducted. The first case study system investigates applicability of PSO on providing proper overcurrent relay settings in the grid, while in the second case study system, the economic dispatch of a 15-unit system is solved where PSO successfully provides the optimum power output of generators with minimum fuel costs to satisfy the load demands and operation constraints. The simulation results in comparison with other methods show the effectiveness of PSO against other algorithms with higher quality of solution and less fuel costs on the same test system.

### Keywords

• power system
• economic dispatch
• relay coordination
• particle swarm optimization

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

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.

## 2. Problem formulation

In this section, overcurrent relay coordination and economic dispatch problems are formulated separately as optimization problems.

### 2.1. Relay coordination problem

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, which can be depicted as an optimization objective function:

OF=mini=1nwitiE1

where tiis the operation time of relay Ri, wiis the probability of the occurrence of fault on transmission line in the zone of protection, and it is normally set to 1; nis the total number of relays in the system.

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

ti=λ×TMSiIFiPSiη1+LE2

where IFiis the fault current seen by the appropriate relay Riafter being transformed through the secondary winding of corresponding current transformer (CT). Depending on the type of relays, the characteristic constants λ, Land ηare 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 characteristic function approximated by:

ti=0.14×TMSiIiPSi0.021E3

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:

timintitimax;i=1,,nE4

where, respectively, timinand timaxare 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), tiis 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 setting is chosen not greater than the minimum fault current [19]. Therefore, there are constraints on TMS and PS as follows:

TMSiminTMSiTMSimax;i=1,,nE5
PSiminPSiPSimax;i=1,,nE6

where TMSimax, PSimax, TMSiminand PSiminare the maximum and minimum values of TMS and PS of relay Ri. Although the constraints in Eqs. (4)(6) seem to provide satisfactory limits on performance of each relay, they are not enough to guarantee correct performance of the protection scheme as the coordination between primary-backup relays has not been considered.

The constraints can only ensure the operation of an individual relay not a primary-backup pair. To coordinate adjacent relays as primary and backup relays, the primary relay should operate as fast as possible within its acceptable boundaries. If it fails to act, its backup relay needs to take over the tripping action with a minimum time. The minimum operating time of the backup relay must be small but yet bigger than the operating time of primary relay. Therefore, a coordination time interval (CTI) is added to the constraints to satisfy the proper coordination scheme.

tjbackuptiprimaryCTIE7

where tiand tjare the operation time of primary and backup relays, respectively. CTI depends upon the relay type, circuit breaker speed, relay over-travel time and the safety factor time for CT saturation, setting errors, contact gaps and so on. According to the IEEE standard [21], CTI is set to 0.2 s for the digital relays. Figure 1 shows the backup-primary pair of relays in a radial network.

### 2.2. Economic dispatch

How to allocate the available generators in the grid to respond to the load demand with minimum fuel costs is an economical aspect of power dispatch in the electric power system that annually costs millions of dollars to operate.

In a practical ED optimization, the generator constraints and network limits such as ramp rate limit, the prohibited zones of operation, generation capacity constraints and valve point effects are considered. Single quadratic equation is used to formulate the ED optimization problem:

minFt=i=1mFPi=i=1mαi+βiPi+γiPi2E8

### Table 7.

Optimum solution of PSO compared with other methods in case study two.

The optimum cost of 15-unit system with the proposed PSO solution is 32701.282 (\$), which has better result than other methods. GA has the most deviating results compared with other hybrid and improved methods in this test system. Also, the mean value of final fuel cost of generators using PSO over 100 trials is less than minimum values obtained by other method, which indicates higher quality of solution and better performance of PSO compared with other algorithms on the same test system. The power loss in the grid obtained from PSO is less than other algorithms, which shows better dispatching scheme using PSO. The best convergence of PSO to the minimum fuel cost of generators in the grid while satisfying the constraints is shown in Figure 6.

In case study two, PSO achieves better results when compared with other hybrid or improved methods. It is worth mentioning that the maximum iteration number is 500 and the population size is 100. In most of the quoted methods, the iteration and population sizes vary that can affect the final results. For example, the PSO in [4] has population size and iteration number of 100 and 500, respectively. The population size, iteration, crossover rate, mute rate and crossover parameter of GA [4] are 100, 200, 0.8, 0.01 and 0.5, respectively.

Different system configuration and programming language frameworks can also influence the results in which MATLAB 2015Ra was used for programming.

## 5. Conclusions

Distribution network relay coordination and the economic dispatch of generators in the electric power system were modeled as optimization problems. Particle swarm optimization (PSO) was successfully employed to solve the defined problems where two case study systems were conducted to validate the results. In the first case study system, PSO provided proper relay settings that allow all the relays in a system to perform with high reliability and accuracy. In the second case, the optimal power outputs of thermal generators in the grid were scheduled to satisfy the load demands and other practical constraints on the generators and the grid with minimum fuel costs. The compared results with other methods demonstrated higher quality of solution, and less fuel costs obtained by PSO. The general performance of PSO in this chapter indicates applicability of this method on practical power system-related problems that are difficult to be handled by conventional methods.

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© 2017 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mostafa Kheshti and Lei Ding (December 20th 2017). Particle Swarm Optimization Solution for Power System Operation Problems, Particle Swarm Optimization with Applications, Pakize Erdoğmuş, IntechOpen, DOI: 10.5772/intechopen.72409. Available from:

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