Sizing of a standalone photovoltaic water pumping system using a multi-objective evolutionary algorithm Dhiaa Halboot Muhsen a, b, * , Abu Bakar Ghazali a , Tamer Khatib c , Issa Ahmed Abed d , Emad M. Natsheh e a Department of EC Engineering, University of Tenaga Nasional, Malaysia b Department of Computer and Software Engineering, University of Al-Mustansiriyah, Iraq c Department of Energy Engineering and Environment, An-Najah National University, Nablus, Palestine d Engineering Technical College Basrah, Southern Technical University, Iraq e Department of Computer Engineering, An-Najah National University, Nablus, Palestine article info Article history: Received 30 December 2015 Received in revised form 17 May 2016 Accepted 20 May 2016 Keywords: Pumping system Photovoltaic Multi-objective optimization Differential evolution Loss of load probability abstract In this paper, a differential evolution based multi-objective optimization algorithm is proposed to optimally size a photovoltaic water pumping system (PVPS). Non-dominated sorting and crowding distance concepts are used to increase the elitism and diversity of the proposed algorithm. The proposed objective function is composed of technical and economic objectives. Loss of load probability is used as a technical objective, whereas life cycle cost is considered as an economic objective. The proposed PVPS is designed to provide a daily water demand of 30 m 3 with a 20 m static head and a drawdown level. The optimal configuration of the system is selected from an optimal Pareto set of configurations to achieve balance between reliability, cost, and excess water of the system. The performance of the system is tested using hourly metorological data for one year time. Results show that the loss of load probability of the proposed system is around 0.5%. The life cycle cost, water deficit, and cost of water unit of the system are 9910 USD, 55 m 3 , and 0.045 USD/m 3 , respectively. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction One of the most popular and promising applications of stand- alone photovoltaic (PV) systems is PV water pumping system (PVPS) [1]. Previous research has been dedicated to study the performance of PVPSs. These research works prove that PVPSs are more feasible than systems which are based on diesel generator and grid connection. Moreover, the average daily water flow rate of PVPSs is in the range of 5.3 m 3 /kWpe26 m 3 /kWp, and their overall efficiency is in the range of 1.3%e5% [2e6]. However, the high initial cost of the PV array is one of the main drawbacks of PVPSs [7,8]. Random vicissitudes and the lack of predictability of solar energy amount cause difficulty in optimally sizing such systems [9]. Therefore, an optimal sizing approach is important to ensure the satisfactory performance of PVPSs [10]. Researchers have focused on the optimal size of the PV array, as well as other components, such as the storage unit and inverter so as to meet the required load at a minimum cost [11,12]. In general, PV system sizing methods can be classified into intuitive, analytical, and numerical methods [13]. The intuitive method is the simplest one, which is based on the worst month or the average monthly solar radiation [14e16]. This method may lead to an over or under sizing of the PVPS, which consequently either increases the cost or decreases the reliability of the system. As a result, the intuitive method is only convenient to be used for estimating initial and rough approximation size of PV system [17]. In the analytical method, equations for the PV system size in terms of system reliability can be developed and utilized [18e20]. The calculation of system's size on the basis of an analytical method is simple and accurate, but the complexity of deriving the coefficient of these equations is the main drawback of this method. L opez et al. [21] proposed an analytical design method for sizing a direct PV pumping system to substitute the deficit water to irrigate an olive orchards. One of the most drawbacks of method presented in Ref. [21] is the efficiency of motor-pump set as it is * Corresponding author. Department of EC Engineering, University of Tenaga Nasional, Malaysia. E-mail addresses: deia_mohussen@yahoo.com (D.H. Muhsen), abakar@uniten. edu.my (A.B. Ghazali), t.khatib@najah.edu (T. Khatib), issaahmedabd80@yahoo. com (I.A. Abed), e.natsheh@najah.edu (E.M. Natsheh). Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy http://dx.doi.org/10.1016/j.energy.2016.05.070 0360-5442/© 2016 Elsevier Ltd. All rights reserved. Energy 109 (2016) 961e973