Multi-objective optimal design of hybrid renewable energy systems ...

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ScienceDirect Solar Energy 118 (2015) 96–106 www.elsevier.com/locate/solener

Multi-objective optimal design of hybrid renewable energy systems using preference-inspired coevolutionary approach Zhichao Shi a,⇑, Rui Wang a, Tao Zhang a,b b

a College of Information System and Management, National University of Defense Technology, Changsha 410073, China State Key Laboratory of High Performance Computing, National University of Defense Technology, Changsha 410073, China

Received 5 January 2015; received in revised form 6 March 2015; accepted 30 March 2015 Available online 7 June 2015 Communicated by: Associate Editor Mukund R. Patel

Abstract As the increasing energy demand and rapid depletion of conventional fossil fuel resources, renewable energy has caused great attention of the public. The main drawback of the renewable resources is their unpredictable nature. A hybrid renewable energy system (HRES) that integrates different resources in proper combination is a promising solution to overcome this challenge. In this context, the preference-inspired coevolutionary algorithm (PICEA) has been applied for the first time to the design of multi-objective hybrid renewable energy system. We propose an enhanced fitness assignment method to improve the preference-inspired coevolutionary algorithm using goal vectors (PICEA-g) in the optimization process minimizing, simultaneously, the annualized cost of system (ACS), the loss of power supply probability (LPSP) and the fuel emissions. As an example of application, a stand-alone hybrid system including PV panels, wind turbines, batteries and diesel generators has been designed to find the best combination of components, achieving a set of non-dominated solutions from which the decision maker can select a most adequate one. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Hybrid renewable energy systems; Optimization; Preference-inspired coevolutionary algorithm

1. Introduction The worldwide rapid depletion of conventional energy sources such as coal and natural gas has made it an urgency to search for alternative energy resources to meet the present energy demand. Alternative energy resources like solar and wind have attracted energy sectors due to their advantages over conventional energy sources such as a decrease in external energy dependence and carbon emissions. However, a common drawback of solar and wind energy is their unpredictable nature and dependence on weather ⇑ Corresponding author. Tel.: +86 8457 3554.

E-mail addresses: [email protected] (Z. Shi), [email protected] (R. Wang), [email protected] (T. Zhang). http://dx.doi.org/10.1016/j.solener.2015.03.052 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

and climatic conditions. A hybrid renewable energy system (HRES), integrating different energy resources in a proper combination, can overcome the problems caused by the uncertainties of solar and wind. HRESs are becoming increasingly popular both in theory and engineering due to their higher reliability and lower cost. The optimal design of HRESs is a multi-objective optimization problem (MOP) in nature, that is, multiple objectives need to be optimized simultaneously. Due to the complexity of the optimal design of an HRES, traditional optimization methods cannot solve it either effectively or efficiently (Dufo et al., 2007). Hence, different meta-heuristics methods were developed to find the optimal sizing of an HRES in the last decade. These studies can be divided into single objective and multi-objective

Z. Shi et al. / Solar Energy 118 (2015) 96–106

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Nomenclature PICEA ACS LPSP MOP MOEA SOC d h h u s lt St S Sp

preference-inspired coevolutionary algorithm the annualized cost of system ($) loss of power supply probability multi-objective optimization problem multi-objective evolutionary algorithm battery state of charge solar declination (°) earth’s inclination to the plane of its orbit (°) solar elevation angle (°) geography of the latitude (°) hour angle (°) local time incident radiation on the tilted surface (W/m2) horizontal component of solar radiation (W/m2) solar radiation perpendicular to the tilted panel (W/m2) TC(t) cell temperature (°C) TA(t) ambient temperature (°C) NCOT nominal cell operating temperature (°C) ISC short-circuit current (A) ISC,STC short-circuit current under STC (A) VOC open-circuit voltage (V) VOC,STC open-circuit voltage under STC (V) KI short-circuit current temperature coefficient (A/°C) KV open-circuit voltage temperature coefficient (V/°C) PM(t,b) power output of PV (W) NP number of PV modules connected in parallel NS number of PV modules connected in series FF(t) fill factor Cainv annualized cost of initial investment ($) Caom annualized cost of operation and maintenance ($) Carep annualized replacement cost ($) Cinv initial investment cost of each component ($) Com operation and maintenance cost ($) Crep replacement cost of each component ($) Pavail(t) available power supply at time t (W) Pload(t) load demand at time t (W) Femission fuel emissions (kg) optimization problems according to the number of objectives in the model. Single objective optimization problems are considered in many articles, for example, genetic algorithm (Koutroulis et al., 2006) and stochastic simulated annealing algorithm (Giannakoudis et al., 2010) are used to minimize the system cost objective, respectively. Unlike single objective optimization, there are only a few articles using MOPs for optimal design of an HRES. Katsigiannis et al. (2010) developed a bi-objective optimization model to generate Pareto front of an HRES minimizing the total cost and total greenhouse emissions

Ef Pnr (t) PWG v CP q PWGR Vc Vr Vf Hwg vr Hr c Pbat(t) Vbus gbat Cn Nbat nbs Cbat Vbat Fcons Pr_dg Pdg Fs Fg ng Gc G PnL(t) Fobj Npv Nwg Ndg b Hlow Hhigh SBX PM

emission factor total power produced by renewable output power of wind turbine (W) wind velocity (m/s) performance coefficient air density (kg/m3) wind turbine rated power (W) cut-in wind speed (m/s) rated wind speed (m/s) cut-off wind speed (m/s) wind turbine height (m) measured reference wind speed (m/s) reference height (m) power law coefficient battery input/output power (W) DC bus voltage (V) round-trip efficiency total nominal capacity of the battery bank (A h) total number of batteries number of batteries connected in series nominal capacity of each battery (A h) nominal voltage of individual battery (V) fuel consumption of a diesel generator (l) generator’s rated power (W) generator’s output power (W) the fitness of a candidate solution s the fitness of a preference g number of solutions that satisfy the preference g goal vectors set after genetic variation initial goal vectors set resources (W) power consumed by the load (W) objective function number of PV panels number of wind turbines number of diesel generators PV panel slope angle (°) wind turbine tower lower limit (m) wind turbine tower upper limit (m) simulated binary crossover polynomial mutation

during its lifetime by using NSGA (Srinivas and Deb, 1994). An optimal sizing method based on genetic algorithm (GA) was developed by Yanget al. (2008) to calculate the optimum configuration of a hybrid solar-wind system employing battery banks, which aims to achieve the required LPSP with a minimum annualized cost of system (ACS). Trivedi (2007) applied the multi-objective genetic algorithm (MOGA) (Fonseca and Fleming, 1998) to solve a nonlinear multi-objective optimization problem for scheduling a wind/diesel system minimizing the fuel cost as well as SO2 and NOx emissions. With a tri-objective

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problem minimizing total cost, fuel emissions and unmet load, Dufo and Bernal (2008) applied strength Pareto evolutionary algorithm (SPEA) to determine the optimal size and optimal power management strategy parameters for an HRES. Abedi et al. (2012) established a multi-objective model to minimize simultaneously the total cost, unmet load and pollutant emissions. In their study, a differential evolution algorithm (DEA)/fuzzy technique is used to find the best combination of components and control strategies for the HRES. Sharafi and ELMekkawy (2014) proposed a novel approach combining the e-constraint approach with PSO method to determine the optimal size of an HRES. The idea of this approach is to minimize the total system cost while fuel emissions and unmet load acted as constraint bound by permissible levels. Unlike other studies where a MOP is usually solved by Pareto-based MOEAs which require expensive ranking and pairwise comparison operations, Wang and Zhang (2014) proposed a multi-objective combinatorial model and employed the multi-objective evolutionary algorithm based on decomposition (MOEA/D) (Zhang and Li, 2007) for the optimal design of an HRES. The objectives are to minimize the lifetime system cost, the CO2 emissions and the SO2 emissions and maximize the system output power. In addition to solar and wind energy in an HRES, there are also research on other renewable sources like ground energy and biogas (Esen and Yuksel, 2013) and relevant economic analysis (Esen et al., 2006). Esen et al. (2007) reported a techno-economic comparison between a ground-coupled heat pump (GCHP) system and an air-coupled heat pump (ACHP) system, the test results indicate that GCHP systems are economically preferable to ACHP systems for the purpose of space cooling. In this paper, a novel approach is presented for the optimal design of an HRES with diesel generators and battery storages. The modified preference-inspired coevolutionary algorithms using goal vectors (PICEA-ng) (Shi et al., 2014) is applied to minimize the annualized cost of the system (ACS), the loss of power supply probability (LPSP) and fuel emissions simultaneously. Preference-inspired coevolutionary algorithms using goal vectors (PICEA-g) (Wang et al., 2013) is an advanced search technique, and has the ability to attain better performance for multi-objective problems (especially many-objective problems) than other best-in-class MOEAs such as NSGA2 (Deb et al., 2002), SPEA2 (Zitzler et al., 2002) and MOEA/D. PICEA-ng is an enhanced version of the PICEA-g where a new fitness assignment method is employed. The features of this approach are its high performance and simplicity compared with Pareto-based and decomposition based evolutionary algorithms. In addition, the number of optimization objectives is flexible to be extended and more renewable energy sources and storage devices can be considered easily. The rest of this paper is organized as follows. The mathematical models of hybrid system components are presented in Section 2. Section 3 describes the system

optimization model and the proposed methodology. Section 4 shows and discusses the obtained results. Section 5 concludes this paper. 2. Mathimatical models of hybrid system components In this work, the considered hybrid renewable energy system consists of PV panels, wind turbines, diesel generators, the battery storage device and other accessory devices. A simple diagram of the system energy flow is depicted in Fig. 1. The available power produced by PV panels and wind turbines is directly delivered to the load to satisfy the load demand. When the energy from solar and wind is more than the load demand, the surplus energy is put into the battery storage system until it is fully charged. On the contrary, when the energy from renewable sources cannot meet the load, the battery bank will supply power to the load based on the state of charge (SOC) of batteries. If the batteries cannot meet the deficit energy, diesel generators are used as emergency power-supply. In case the diesel generators are not able to cover the surplus load requirements, the unmet load will be cut. In order to find the optimal design of the hybrid system, it is necessary to model individual components before evaluating the performance of their combination. The mathematical models of hybrid system components used in the simulation and optimization process are summarized below. 2.1. PV panel model In general, the total solar radiation on a tilted surface is the sum of the beam, diffuse and reflected solar radiation components on the tilted surface (Yang et al., 2008). The diffuse and reflected parts are neglected in this study as they only have a small proportion. The incident irradiation on a tilted panel can be available by the following equations. Eq. (1) is employed to calculate the solar declination (d) with earth’s inclination to the plane of its orbit h (h = 23.44°) (Sharafi and ELMekkawy, 2014).

Fig. 1. The system energy flow.


284 þ n d ¼ h sin 360 365

ð1Þ

where n is the number of days in one year when January 1st is recorded as one. Then the solar elevation angle (h) that is the angle between the direction of the sun and the horizon can be estimated using the following equations (Sharafi and ELMekkawy, 2014). sin h ¼ sin u sin d þ cos u cos d cos s s¼

360 ð12 ltÞ 24

ð2Þ ð3Þ

where u is the geography of the latitude, s is hour angle and lt is local time (0 6 lt 6 23). As shown in Fig. 2, the incident radiation on the tilted surface (St) can be calculated according to horizontal component of solar radiation (S) as follows (Abedi et al., 2012). St ¼

S sin h

ð4Þ

S p ¼ S t sinðh þ bÞ

ð5Þ

where Sp is the effective component of the solar radiation perpendicular to the tilted panel. Using the calculated Sp, the maximum output power of PV panels at time step t considering the ambient temperature effect can be determined by the following equations (Koutroulis et al., 2006): T C ðtÞ ¼ T A ðtÞ þ

NCOT 20 S p ðt; bÞ 800

I SC ðtÞ ¼ ½I SC;STC þ K I ðT C ðtÞ 25Þ

S p ðt; bÞ 1000

ð6Þ ð7Þ

V OC ðtÞ ¼ V OC;STC K V T C ðtÞ

ð8Þ

P M ðt; bÞ ¼ N S N P V OC ðtÞ I SC ðt; bÞ FF ðtÞ

ð9Þ

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8 0; > > >1 < C P qAWG v3 ; P WG ðv; tÞ ¼ 2 > P WGR ; > > : 0;

v