Hybrid Simulated Annealing–Tabu Search Method for Optimal Sizing of Autonomous Power Systems with Renewables Yiannis A

330 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 3, JULY 2012 Hybrid Simulated Annealing–Tabu Search Method for Optimal Sizing of Autonomous Power Systems With Renewables Yiannis A. Katsigiannis, Pavlos S. Georgilakis, Senior Member, IEEE, and Emmanuel S. Karapidakis, Member, IEEE Abstract—Small autonomous power systems (SAPS) that in- of WTs and PVs may not match with the load demand, so there clude renewable energy sources are a promising option for isolated is an impact on the reliability of the electric energy system. power generation at remote locations. The optimal sizing problem This reliability problem can be solved by a proper combination of SAPS is a challenging combinatorial optimization problem, and its solution may prove a very time-consuming process. This paper of the two resources (WTs and PVs) together with the use initially investigates the performance of two popular metaheuristic of an energy storage system, such as batteries, as a type of methods, namely, simulated annealing (SA) and tabu search (TS), energy-balancing medium [2]. Such a system, which is called for the solution of SAPS optimal sizing problem. Moreover, this a small autonomous power system (SAPS), is a promising paper proposes a hybrid SA-TS method that combines the advan- option for isolated power generation at remote locations [3]. tages of each one of the above-mentioned metaheuristic methods. The proposed method has been successfully applied to design To be more precise, an SAPS is an isolated hybrid system an SAPS in Chania region, Greece. In the study, the objective with renewable energy sources, conventional power sources function is the minimization of SAPS cost of energy (€/kWh), and (usually diesel generators), and energy storage. Proper sizing the design variables are: 1) wind turbines size, 2) photovoltaics of the overall SAPS is challenging, due to the large number of size, 3) diesel generator size, 4) biodiesel generator size, 5) fuel cells design options and the uncertainty in key parameters, such as size, 6) batteries size, 7) converter size, and 8) dispatch strategy. The performance of the proposed hybrid optimization method- load size and future fuel price. Renewable energy sources add ology is studied for a large number of alternative scenarios via further complexity because their power output is unpredictable sensitivity analysis, and the conclusion is that the proposed hybrid and intermittent. SA-TS improves the obtained solutions, in terms of quality and The problem of SAPS optimal sizing belongs to the cate- convergence, compared to the solutions provided by individual SA gory of combinatorial optimization problems, since the sizes of or individual TS methods. system’s components, which constitute the design variables, can Index Terms—Hybrid power systems, optimal sizing, opti- take only discrete values. For the solution of this problem, var- mization methods, power generation dispatch, renewable energy ious deterministic optimization techniques have been proposed sources, simulated annealing (SA), small autonomous power systems (SAPS), solar energy, tabu search (TS), wind energy. [4]; however, these methods may provide suboptimal solutions, which are usually combined with increased computational complexity. The most direct method for solving the SAPS sizing I. INTRODUCTION problem is the complete enumeration method that is used by HOMER software [5]; however,itcanprovetobeextremely ODAY more diverse challenges have emerged: climate time consuming. Moreover, a recent review of computer tools T change, economic recession, and security of energy has shown that there is no energy tool that addresses all issues supply. Moreover, the rapid depletion of fossil fuels and their related to SAPS optimal sizing, but instead the “ideal” energy high and volatile prices have necessitated an urgent need for tool highly depends on the specific objectives that must be ful- alternative energy sources to meet the energy demands [1]. filled [6]. Renewable energy sources (RES), such as wind and solar, are In recent years, new methods have been developed, in order clean, inexhaustible, and environmentally friendly alternative to solve many types of complex optimization problems, partic- energy sources with negligible fuel cost. However, RES tech- ularly those of combinatorial nature. These methods are called nologies, such as wind turbines (WTs) and solar photovoltaics metaheuristics and include genetic algorithms (GAs), simulated (PVs), are dependent on a resource that is unpredictable and annealing (SA), tabu search (TS), and particle swarm optimiza- depends on weather and climatic changes, and the production tion (PSO) among others. Metaheuristics orchestrate an inter- action between local improvement procedures and higher-level strategies to create a process capable of escaping from local op- Manuscript received July 14, 2011; revised November 21, 2011; accepted tima and performing a robust search of a solution space. From January 12, 2012. Date of publication April 06, 2012; date of current version June 15, 2012. the area of metaheuristics, GAs [7]–[9], SA [10], TS [11], as Y. A. Katsigiannis and E. S. Karapidakis are with the Department of Nat- well as PSO [12], have been proposed for the solution of SAPS ural Resources and Environment, Technological Educational Institute of Crete, optimal sizing. Chania 73133, Greece (e-mail: [email protected]). P. S. Georgilakis is with the School of Electrical and Computer Engineering, This paper initially investigates the application of two meta- National Technical University of Athens (NTUA), Athens 15780, Greece heuristic methods, namely SA and TS, for solving the SAPS (e-mail: [email protected]). sizing problem. SA transposes the technique of annealing to the Digital Object Identifier 10.1109/TSTE.2012.2184840 1949-3029/$31.00 © 2012 IEEE KATSIGIANNIS et al.: HYBRID SA-TS METHOD FOR OPTIMAL SIZING OF AUTONOMOUS POWER SYSTEMS WITH RENEWABLES 331 solution of an optimization problem. TS is a powerful iterative 2) Unmet load constraint optimization procedure that is characterized by its ability to escape from local optima (which usually cause conventional algorithms to terminate) by using a flexible memory system. (4) Moreover, this paper proposes a hybrid optimization methodology that combines the above-mentioned methods (SA and where is the annual unmet load fraction, (kW) TS) for solving the SAPS sizing problem. Hybrid methods is the unmet load during the simulation time step (h), that contain SA and TS have been applied in various areas, (kWh) is the total annual electric energy demand, including unit commitment [13], optimal capacitor placement and is the maximum allowable annual unmet load [14], and nonpermutation flowshop scheduling [15]. The fraction. In this paper, so 52 560 summa- proposed method has been successfully applied to design an tions are needed for the entire year to compute ,as(4) SAPS in the Chania region, Greece. In the study, the objective implies. function is the minimization of SAPS cost of energy (€/kWh), 3) Capacity shortage constraint and the design variables are: 1) WTs size, 2) PVs size, 3) diesel generator size, 4) biodiesel generator size, 5) fuel cells size, 6) batteries size, 7) converter size, and 8) dispatch strategy. (5) The performance of the proposed hybrid SA-TS optimization methodology is studied for a large number of alternative where is the annual capacity shortage fraction, scenarios, and it is concluded that it improves the obtained (kW) is the capacity shortage during ,and is the solutions, in terms of quality and convergence, compared to the maximum allowable annual capacity shortage fraction. Ca- solutions provided by individual SA or individual TS method. pacity shortage is defined as a shortfall that occurs between the required amount of operating capacity (load plus required operating reserve) and the actual operating capacity II. PROBLEM FORMULATION the system can provide. Operating reserve in an SAPS with The SAPS optimal sizing problem has to fulfil the objective RES technologies is the surplus electrical generation ca- defined by (1) subject to the constraints (3)–(9). The computa- pacity (above that required to meet the current electric tions of the objective function and the constraints of the problem load) that is operating and is able to respond instantly to are related with the results obtained by simulating the operation a sudden increase in the electric load or a sudden decrease of SAPS for a given time step , taking into account compo- in the renewable power output. nents’ type, cost, and technical characteristics. 4) Fuel consumption constraint A. Objective Function (6) Minimization of the system’s cost of energy (COE) where is the fuel consumption of a generator (1) during ,and is the maximum allowable annual fuel consumption of the generator. The COE (€/kWh) of SAPS is calculated as follows: 5) Minimum renewable fraction constraint (2) (7) where (€) is the total annualized cost and where is the RES fraction of the system, (kWh) is the total annual useful electric energy production. (kWh) is the total annual renewable energy production, takes into account the annualized capital costs, the annu- (kWh) is the total annual energy production of the alized replacement costs, the annual operation and maintenance system, and is the minimum allowable RES frac- (O&M) costs, and the annual fuel costs (if applicable) of the tion. system’s components. COE is adopted since it is a very good 6) Components’ size constraints measure of system cost for SAPS sizing [16]. (8) B. Constraints (9) where is the size of system’s component , 1) Initial cost constraint and is the maximum allowable size of . (3) III. SAPS COMPONENTS AND MODELING The considered SAPS has to serve electrical load, and it can where IC (€) is the initial installation cost of the system, contain seven component types: and (€) is the maximum acceptable initial cost of 1) WTs. the system. 2) Amorphous silicon (a-Si) PVs. 332 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 3, NO. 3, JULY 2012 3) Generator with diesel fuel. needing replacement. Batteries have been modeled according to 4) Generator with biodiesel fuel.

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