Optimal sizing of a stand-alone photovoltaic, wind turbine and fuel cell systems

Abstract

In this paper, Jaya algorithm is applied to find an optimal unit sizing of renewable energy resources, including photovoltaic (PV) panels, wind turbines (WTs), and fuel cells (FCs) with the objective of reducing the consumer’s total annual cost in a stand-alone system. The system’s reliability is considered using the maximum allowable loss of power supply probability (LPSP^max) concept. The methodology is applied to real solar irradiation and wind speed data taken from Hawksbay, Pakistan. Simulation results achieved for low and high consumer’s load profiles show that when LPSP^max values are set to be 0% and 2%, the PV-FC is the most cost-effective system as compared to PV-WT-FC and WT-FC systems. Further, the results of Jaya algorithm are compared with a genetic algorithm, backtracking search algorithm, and particle swarm optimization.

Introduction

Traditional energy generation is widely dependent on the use of fossil-fuel resources such as oil, coal, and natural gas. These resources are depleted with consumption. Further, the usage of these sources are causing problems like environmental pollution and global warming. The present-day demands new ways of creating energy resources that are more environment-friendly, clean, sustainable, and inexhaustible by nature. Generation of energy through renewable energy resources (RERs) is one of the solutions to tackle the aforementioned problems. The RERs are widely used to generate electricity from solar, wind, geothermal, hydropower, and other sources that are naturally replenished and also have great potential to produce energy. Among the other RERs, photovoltaic (PV) panels and wind turbines (WTs) are the most dominant and encouraging technologies that are used to meet the consumer’s load demand [1].

The RERs can be implemented in two ways: grid-connected (GC) and stand-alone (SA) modes. In GC mode, the RERs inject the produced electricity to a power utility network, while in the SA mode, it directly powers up the consumer’s electrical demands. The SA system causes reliability concerns due to the non-availability of electricity backup from a utility network. Further, the intermittent nature of solar and wind cause a non-linear and unpredictable RERs’ output power. Thus, using a single renewable energy system (RES) in a SA environment results in energy variations due to varying weather conditions. This effect causes an energy mismatch situation where the consumer’s load requirements are not met by the generation capacity. To overcome the aforesaid challenge, hybrid RES (HRES) along with an energy storage system (ESS) is used to meet the consumer’s load demand [2]. The ESS comprises fuel cells (FCs), batteries, etc. Thus, the complementary features of wind and solar energies are combined with the backup of ESS to further make the system more sustainable and reliable as compared to the single RES.

The major issue in HRES is an optimal unit sizing of individual components comprising of PVs, WTs, and batteries. The proper combination of HRES is required for the strategic decisions, including feasibility study or an initial capital investment cost calculation. A methodology used to determine the right and accurate sizing of HRES components by maintaining the system’s reliability at a minimum cost is called as unit sizing. Oversizing and undersizing of the system’s components are two options when unit sizing is not considered. Oversizing of the system’s components can overcome the reliability problem; however, it increases the system’s cost. On the other side, undersizing of the system’s components can lead to the loss of supply problem, where electricity generation is less than the consumer’s load requirement. Therefore, an optimal unit sizing of HRES is essential for the determination of the exact number of system’s components that leads to the reliability of the system at reduced cost [3].

In the literature, software-based, classical, and meta-heuristic are some popular techniques used frequently by the research community for the unit sizing of HRES. A hybrid optimization model for multiple energy resources (HOMER) is a popular software-based tool used for the unit sizing of HRES. In [4], Ahmad et al. investigate the potential of HRES for inhabitants of Kallar Kahar, located in the province of Pakistan named as Punjab. The authors perform a techno-economic analysis of WTs, PVs, and biomass systems using HOMER. The authors conclude that Kallar Kahar provides significant potential for energy-production via HRES because of the suitable availability of solar irradiation, wind, and sufficient animal manure. The cost of HRES is calculated as 180.2 million USD ($) for a peak load of 73.6 megawatts (MW). Similarly, in [5], the authors apply the HOMER software tool to find unit sizing of PV-FC-battery system for an un-electrified village in India. The load variations in summer, winter, and rainy seasons are considered to reduce total net percent cost (TNPC). The cost of energy obtained from the optimized solution is estimated by 0.1959 $ per kilowatt ($/kW). However, the HOMER software tool suffers from some limitations, for instance, it does not support multi-objective problems, its formulation, depth of discharge of the battery bank, and ranking of HRES based on energy levelized cost. Further, it also does not consider intra-hour and bus voltage variations which makes it difficult to apply in many situations [6].

While considering the classical approaches, the authors in [7] propose an iterative-based method which achieves optimal configuration by searching all possible outcomes iteratively on the basis of the objective function. Okoye et al. in [8] apply mixed-integer linear programming (MILP) technique to find the accurate sizing of PVs in Bursari, Nigeria. The objective is to reduce the annual cost of finding the unit size of PV’s components. The results show that the use of the PV’s system is 30% cheaper as compared to the usage of diesel generators. These classical and formal approaches are good in finding the optimal solution in a deterministic environment, yet, are highly complex by nature, as every solution is computed and checked in the given search space. For a stochastic environment, where consumer’s behavior and intermittent nature of RERs add unknown variables to the environment, then these classical approaches become inefficient. Therefore, the meta-heuristic approaches based on computational intelligence and inherent randomness are widely used in literature to have an optimal solution at low computational complexity [9].

In [10], the authors perform optimal sizing of the SA PV’s system and its components using firefly algorithm-based sizing algorithm (FASA). The sizing problem considers four decision variables: PV modules, inverters, charge controllers, and batteries. The target of the objective function is to reduce the loss of power supply probability (LPSP). The FASA results are compared with the conventional iterative approach and other meta-heuristic schemes: particle swarm optimization (PSO), genetic algorithm (GA), and evolutionary programming (EP). The simulations are performed by considering two different cases, i.e., systems with the maximum power point tracking (MPPT) and standard charge controller. The results depict that the iterative method achieves the highest computational time by taking every solution into account, i.e. 14 and 16 hours at LPSP values 0.0259 and 0.0235 in the two different scenarios, respectively. Whereas, FASA obtains the same output values with the computational time of 11.66 seconds (s) and 40.51 s for the two scenarios, respectively. The FASA is also 1.93 times faster as compared to the GA, EP, and PSO. In [6], harmony search (HS) optimization technique is proposed for obtaining an off-grid hybrid solution consisting of PVs and biomass power generators. Agricultural wells located in Bardsir, Iran are considered with an objective function that reveals minimization of the system’s TNPC while also considering the reliability factor. The comparison of results with PSO and GA optimization schemes depict that HS performs better in terms of reducing TNPC. In [11], Maleki and Pourfayaz investigate optimal unit sizing of HRES, including PVs, WTs, and batteries. The authors analyze and compare evolutionary algorithms: simulated annealing, PSO, tabu search, and artificial bee swarm optimization (ABSO). The results show that ABSO performs better among other meta-heuristic algorithms with minimum system’s cost. In [12], the authors use an improved ant colony optimization (ACO) scheme for unit sizing of HRES consisting of PVs, WTs, batteries, and FCs. However, the iterative method used as a benchmark in [10] and MILP technique applied in [8] for unit sizing problems are highly computational. Also, these classical approaches suffer from the curse of dimensionality problem and do not find the optimal solution within a reasonable amount of time [12].

In [13], the authors consider a hybrid combination of PVs, WTs, and FCs. In unit sizing of this optimization problem, the decision variables are having integer values. A yearly data consisting of solar irradiation, wind speed at height 10 m (m), and users’ load profiles are taken for simulation. A population-based meta-heuristic scheme based on ABSO algorithm is applied to obtain a globally optimal solution. Using different LPSP values: 0%, 0.3%, 1%, and 2%, ABSO is applied to have a cost-effective hybrid system combination in three different combinations, including PV-WT-FC, PV-FC, and WT-FC systems. The results show that at lower LPSP values, the most cost-effective solution is obtained by a combination of PV-WT-FC system. In [14], Maleki considers the economic aspect of using a diesel generator with other RERs: PVs, WTs, and FCs for the electrification of a remote area. The total annual generation cost is optimized using a discrete simulated annealing algorithm.

All the above proposed meta-heuristic algorithms used for unit sizing require algorithmic-specific parameters for their functioning. For instance, the HS scheme uses harmony memory, pitch adjustment and consideration rate along with several improvisations. The GA requires crossover and mutation probabilities with a selection operator. The PSO algorithm needs cognitive and social parameters in addition to the inertia weight. The ABSO algorithm uses many scouts, employed, and onlooker bees with a limit specifier. Also, the ACO and other algorithms require performance tuning of these algorithmic-specific parameters, otherwise, may halt in locally optimal solutions or yield an increased computational time. Therefore, the meta-heuristic algorithms, including Jaya [15] and teaching learning-based optimization [16] are some other techniques that do not depend on the algorithmic-specific parameters for their execution.

Pakistan is one of the South Asian countries which is situated at a latitude of $23.{45}^{\circ }N-36.{75}^{\circ }N$ and longitude of ${61}^{\circ }E-75.5^{\circ }E$. Pakistan is geographically located in an area where solar irradiation is immense, i.e., 5–5.5kW-h per square meter per day (kWh/m²/day) in Punjab and 7–7.5 kWh/m²/day in Baluchistan, respectively. Further, it is having great potential of 346 gigawatt (GW) of wind power production [4]. Alternative energy development board (AEDB) is established in Pakistan to support, facilitate and encourage the implementation of RERs in the country. With the support of the World Bank, AEDB is carrying out an assessment and mapping activities in major areas of the country. In this paper, by considering these RERs’ potentials, a recently proposed algorithm Jaya is implemented to find an optimal unit sizing of HRES using real wind speed and solar irradiance data collected from Hawksbay, Pakistan. The unit sizing problem is considered with environmental concerns to have a green electricity generation and ESS. In this paper, time slot and hour are used synonymously. The previous work [17] is enhanced and the contributions are given below.

• System’s components are formulated and elaborated using an informative HRES model.

• Motivated from non-algorithmic-specific meta-heuristic approaches, Jaya algorithm is implemented to find the optimal number of components required in HRES to minimize consumer’s annual cost of energy.

• The real data for wind speed and solar irradiance is used to find out the optimal unit sizing of PV-WT-FC, PV-FC, and WT-FC systems for Hawksbay, Pakistan. The reliability of the system is considered using different LPSP values provided by the consumer.

• To test the efficacy of the proposed methodology, Jaya is implemented in two different consumer’s scenarios, i.e., low and high users’ load profiles.

• Further, results of Jaya algorithm are also compared with three algorithmic-specific schemes: GA, backtracking search algorithm (BSA), and PSO.

The rest of the paper is organized as follows. Section 2 models various system’s components of HRES and also formulates the optimization problem. The proposed methodology is elaborated and presented in Section 3. Section 4 depicts simulation results. Finally, in Section 5, a conclusion along with future work is stated.