Biogeography-based learning particle swarm optimization for combined heat and power economic dispatch problem

Highlights

• BLPSO algorithm is applied for solving CHPED problem with various constraints.

• The interdependence of heat and power outputs of cogeneration units impose great complication.

• Non-convex CHPED problems with/without prohibited operating zones are considered.

• Comprehensive simulation results demonstrate the effectiveness of the BLPSO algorithm.

Abstract

Combined heat and power economic dispatch (CHPED) is an important optimization task in the economic operation of power systems. The interdependence of heat and power outputs of cogeneration units and valve-point effects of thermal units impose non-convexity, nonlinearity and complication in the dispatch modeling and optimization. In this paper, a novel PSO algorithm called biogeography-based learning particle swarm optimization (BLPSO) is applied to solve the CHPED problem considering various constraints including power output balance, heat production balance, feasible operation area of cogeneration unit and prohibited operation zones. In BLPSO, based on a biogeography-based learning model, each particle uses a migration operator to update itself based on the personal best position of all particles. This updating strategy helps BLPSO overcome premature convergence and improve solution accuracy. Moreover, a repair technique is employed to handle the system constraints and guide the solutions toward feasible zones. The effectiveness of the proposed method is evaluated by testing on four CHPED problems containing 5, 7, 24, and 48 units. The experimental results show that BLPSO outperforms the state-of-the-art methods in terms of solution accuracy and stability. Therefore, BLPSO can be regarded as a promising alternative for the CHPED problem.

Introduction

For decades, economic dispatch has become one of the most important issues in the operation of power systems, because it enables the thermal units to generate electricity at the lowest possible fuel cost for power generation. In the traditional thermal generation system, not all the heat energy is converted into electrical energy. By contrast, a considerable part of the power energy is lost in the form of heat loss. Therefore, combined heat and power (CHP) cogeneration system is introduced to improve the efficiency of traditional generation systems. In CHP system, electrical and heat energy can be generated simultaneously from a single source. According to the Ref. [1], [2], the use of CHP system can significantly improve fuel efficiency by 90%, reduce production costs by 10$\sim$40%, and reduce environmental pollution by 13$\sim$18%. Therefore, to effectively use the cogeneration units, the combined heat and power economic dispatch (CHPED) plays a very important role in the power systems.

CHPED involves the optimal production of three kinds of units, i.e., conventional thermal power units, CHP (cogeneration) units, and heat-only units. For cogeneration units, power generation and heat production are dual dependent [3], which adds complexity to the solution of CHPED. In addition, CHPED needs to consider more practical constraints, such as valve-point effects of conventional power units, feasible operating area of cogeneration units, system transmission loss and prohibited operating zones. All these factors lead a more difficult solution of the CHPED problem [4].

Different optimization methods have been developed to solve the CHPED problem. They can be divided into two groups: mathematical and meta-heuristic. Mathematical methods include quadratic programming [5], Lagrangian relaxation [6], benders decomposition [7], branch and bound algorithms [8], etc. These methods can converge to accurate solutions within a small number of iterations. Unfortunately, they often cannot efficiently tackle the CHPED problem with non-convex fuel cost functions.

To overcome the drawback of mathematical methods, metaheuristic algorithms (MHAs) have been proposed as modern optimization methods for the CHPED problem. MHAs have strong global search ability, and they also have no restrictions such as continuity and differentiability on the problem formulation [9], [10], [11]. The popular MHAs include particle swarm optimization (PSO) [12], [13], genetic algorithm (GA) [14], [15], differential evolution (DE) [16], [17] and others.

In the early years, MHAs were developed for the small-scale CHPED problem. For example, Subbaraj et al. [18] presented a self-adaptive real-coded GA (SARGA) to solve the CHPED problem. In SARGA, the mutation, crossover, and selection operators are self-adapted, and a parameterless penalty method is used to deal with the equality and inequality constraints. Khorram et al. [19] solved the CHPED problem by harmony search (HS) algorithm. HS mainly employs two search operators namely harmony memory consideration and pitch adjustment rate. Yazdani et al. [20] proposed the firefly algorithm (FA) for the CHPED problem. The FA algorithm is inspired by the behavior of fireflies, which uses an attraction updating operator. Mellal et al. [21] developed a penalty function based cuckoo optimization algorithm (PFCOA), and PFCOA exhibited very efficient performance for the CHPED problem. Basu [22] applied the DE algorithm to solve the CHPED problem considering transmission loss. DE is evolutionary technique with simple structure and robust performance, and it provided better results than basic PSO and evolutionary programming. Although promising results have been obtained by those methods in  [18], [19], [20], [21], [22], they were only tested in the small-scale CHPED problem with the number of units less than 10.

Several researchers proposed MHAs to handle both small-scale and large-scale CHPED problems with more difficulty. Ivatloo et al. [23] proposed PSO with time varying acceleration coefficients (PSOTVAC) for solving the CHPED problems with 4$\sim$48 units. The acceleration coefficients in PSOTVAC are adjusted during the iterations to overcome the premature convergence. Roy et al. [24] incorporated the opposition based learning into teaching-learning-based optimization (TLBO), and developed an oppositional TLBO (OTLBO) algorithm for the CHPED problems with 7$\sim$48 units. OTLBO has search operators called teacher phase and learner phase, and the opposition based learning is used to accelerate the convergence. Meng et al. [4] implemented a crisscross optimization (CSO) algorithm to solve the CHPED problem. CSO mainly employs two interacting search operators namely horizontal crossover and vertical crossover. The effectiveness of CSO was verified on six CHPED problems with 4$\sim$192 units. Beigvand et al. [25] solved the non-convex CHPED problem using a gravitational search algorithm (GSA). GSA is based on the gravitational law and the law of particles motion. The simulation results revealed that GSA provided better solutions on the CHPED problems with 4$\sim$48 units. Ghorbani [1] applied an exchange market algorithm (EMA) for solving the CHPED problems with 4$\sim$48 units. EMA is a powerful optimization algorithm with two absorbing operators pulling solutions toward optimality. However, In these research works [1], [4], [23], [24], [25], the practical constraints such as prohibited operating zones (POZs) are not considered .

Several researchers developed efficient MHAs for the CHPED problem with complex constraints such as prohibited operating zones (POZs). Basu [26] introduced the POZs into the CHPED, and also developed an opposition-based group search optimization (OGSO) to improve the solution quality of four CHPED problems with POZs. Narang et al. [27] devised a hybrid algorithm CSO-PPS based on civilized swarm optimization and Powells pattern search. In CSO-PPS, CSO is used as the global search optimizer and PPS is used as the local search optimizer. CSO-PPS was applied to solve five CHPED problems considering POZs and achieved high solution performance. Zou et al. [28] presented an improved GA using novel crossover and mutation (IGA-NCM) for the CHPED problem. A constraint handling technique was also given to guide the mutated offspring toward feasible regions. IGA-NCM was employed to solve ten CHPED problems considering POZs, and showed strong convergence and stability.

Some other MHAs used for solving the CHPED problem include SRPSO (PSO with self-regulating parameter setting) [29], MPHS (multi-player harmony search) [30], BBO (biogeography-based optimization) [31], CSA (cuckoo search algorithm) [32], GWO (gray wolf optimization) [33], HTS (heat transfer search) [34], and WOA (whale optimization algorithm) [35]. Although these methods have been proposed, the CHPED problem with non-convex objective function and complex generator constraints is still a high challenging global optimization problem [36]. To improve the solution accuracy of the existing methods, it is still necessary to investigate more search algorithms to deal with the CHPED problem.

PSO algorithm is one powerful MHA proposed by Kennedy and Eberhart [37]. Due to its simplicity, fast convergence and high solution quality, PSO has been successfully used for many power system problems. In this paper, an novel PSO algorithm called biogeography-based learning PSO (BLPSO) is proposed to solve the CHPED problem considering various constraints. BLPSO is our recently-developed PSO algorithm for continues optimization [38]. Compared with basic PSO, BLPSO uses a biogeography-based learning model, in which each particle uses a migration operator to update itself based on the personal best positions of all particles. This updating strategy helps BLPSO overcome premature convergence and improve solution accuracy. The BLPSO algorithm is applied to solve four CHPED problem considering constraints including power output balance, heat production balance, feasible operating area of CHP units, system transmission loss and prohibited operating zones. To handle these constraints, a repair technique is also employed which can guide the solutions toward feasible zones. The results of BLPSO are compared with those well-established methods in the literature, and the effectiveness and superiority of BLPSO are demonstrated.

The rest of this paper is organized as follows. Section 2 describes the mathematical model of the CHPED problem. Section 3 presents the BLPSO algorithm in detail. Section 4 provides the BLPSO implementation for solving the CHPED problem. The comparison results are provided in Section 5. Finally, the conclusion is given in Section 6.