2.1. Studies about Cost Optimization of Renewable Energy Systems
Several studies on cost optimization and planning of RESs have been conducted in literature. Ho et al. [
19] developed a cost optimization model for RE-based distributed energy generation (DEG) system. Mixed Integer Linear Programming (MILP) method was used to determine the optimum cost of integrated solar and biomass system. The proposed model considered actual operation constraints due to availability of biomass, thermal power plant restriction and weather variation. The results elaborated that for optimum generation, biogas thermal power plant, direct fired biomass power plant and PV plant should generate 412 kW, 417 kW and 136 kW respectively. Similarly, Ferrer-Martí et al. [
20] proposed a MILP model to solve the optimal cost of hybrid PV-wind plant in Peru. The mathematical model was used to design the micro grid that selects the best generation combination or option under certain constraints such as RE potential and load demand. The results show very significant cost reductions as the model can explore and allocate optimal design of micro grids. Milan et al. [
21] focused on optimal sizing of renewable systems. Linear programming was used to find the overall system costs of three technology options that include PV, solar thermal collectors and heat pump. The study results revealed that heat pump combined with PV is the optimal configuration with the optimal cost of 75,200 euros.
Askarzadeh and Dos Santos [
22] developed an optimal grid independent hybrid RESs in Kerman, Iran. Particle swarm optimization (PSO) was used to find the optimal values of the variables that include number of batteries, turbine swept area, and total area of PV panels. The results showed that wind/PV/battery system was the most cost-effective. Similarly, Lai et al. [
23] developed an optimal sizing of stand-alone solar PV and storage system with anaerobic digestion biogas power plants in Kenya. PSO was used to determine the optimum size of PV and energy storage system (ESS) with biogas power plant. The proposed model considered the levelized cost of energy (LCOE) of the system while minimizing the energy imbalance between demand and generation due to intermittency of solar energy and anaerobic digestion constraints. The results showed that for optimum sizing, the PV plants, inverter, controller and vanadium redox flow battery should be 5 MW, 5000 kW, 5000 kW, and 5 MWh respectively. Also, Senjyu et al. [
24] presented an optimal configuration of a power system with RE power production plants. The system comprised PV, battery, wind and diesel generators. The optimal configuration of the system was achieved by using genetic algorithm (GA). The simulation results showed that the total cost can be reduced by 10%.
Deshmukh and Deshmukh [
25] developed a micro-level integrated RESs planning model for a rural area in India. In the study, multi-objective goal programming (MOGP) algorithm was used to optimally allocate RESs while considering some parameters such as load requirement, emissions, RE potential, social acceptance level and employment factor. The study revealed that biomass energy should be promoted for electrical energy generation, while solar thermal and biogas should be supported for cooking purposes. Similarly, Deshmukh and Deshmukh [
26] proposed a MOGP approach to optimally allocate RESs that can meet the energy needs of three districts in India (Panthadiya, Bisanpura, and Morva). The study considered the optimal energy resource allocation for various end-uses. The simulation results revealed biomass, biogas and solar thermal as the preferred sources that can meet the load requirement of the Panthadiya, Bisanpura, and Morva. Niknam et al. [
27] presented a Modified Honey Bee (MOP) algorithm for sizing and siting renewable generators. A modified honey bee mating algorithm was used to solve the optimization problem that consists of cost minimization, losses, voltage profile and emissions of the distributed system. The results show that proper sizing and siting of renewable electricity generations (REGs) are vital for emission reduction, voltage profile and cost reduction associated with the distribution system.
Chang [
28] proposed an optimal design of hybrid RESs using Monte Carlo optimization technique. The model considered not only the equipment installation, including wind, PV, storage system and diesel generator, but also transmission and power allocation within the hybrid RESs in order to achieve minimum equipment cost. Similarly, Sharafi et al. [
29] developed an optimal design of hybrid RESs in a building, with low to high RE ratio. Meta heuristic approach was used to model the potential use of PV panels, heat pump, wind turbine, biomass boiler, heat storage tank and solar heat collectors to produce RE for the building. The study showed that installing 73 kW wind turbine and 200 kW biomass boiler is the optimal option with a net present cost of C
$705,180.
Iniyan and Sumathy [
30] proposed an Optimal RE Model (OREM) that allocates different RESs for several end users. The energy demand, acceptance level, RE potential and reliability are used as constraints in the model. The results indicated that PV system could be used to cover the demand for pumping, cooling, lighting and heating to an extent of 16%, 12%, 6%, and 2% respectively. According to the authors, the bioenergy systems could generate 1%, 17%, 9%, 17%, and 14% of the total energy needed for cooking, heating, lighting, pumping and transportation respectively. Furthermore, 4% of the total energy required by pumping could be generated by using wind energy. Li et al. [
31] developed a dynamic sizing and modeling optimization of stand-alone PV systems. Three different stand-alone PV systems that include PV/battery hybrid system, PV/fuel cell hybrid system and PV/battery/fuel cell hybrid system were evaluated. The simulation results showed that the optimal configuration was PV/battery/fuel cell hybrid system.
Jeppesen et al. [
32] studied least cost and utility scale abatement from Australia’s national electricity market (NEM). The planning model formulated has many constraints which are vital when considering greenhouse gas abatement and widespread uptake of intermittent RE generation. The least cost pathways were evaluated by numerical optimization of utility scale generation, transmission, distribution and storage. The authors revealed that the estimated wholesale market cost of energy was found to be
$ 37 per MWh. Rozali, et al. [
33] developed a novel method for the design of a cost-effective hybrid power systems (HPS). The study incorporates power pinch analysis with a systematic hierarchical approach for resilient process screening for the design of HPS. The results showed that HPS design with minimum electricity targets will have a simple payback period of 10 years. Also, Razak et al. [
34] developed an optimal design of RE hybrid system using HOMER simulation tool. The proposed model considered solar, hydro, wind, and storage system. The results revealed that if the demand load is increased to maximum capacity, the cost of energy can be reduced to about 50%. Also, the authors show that the net present cost, levelized cost of energy and total production was found to be RM 63,887, RM 1.019 kWh, and RM 8405 kWh respectively.
Yang and Nehorai [
35] proposed an optimal design of cost minimization of RES, diesel generator and storage system using alternating direction method of. The authors formulated an optimization problem with the objective of minimizing the investment cost; maintenance cost and operational cost of RESs, storage system and diesel generators. The hourly load data from 2008 to 2012 used in generating the load data was obtained from Electricity reliability council of Texas while the renewable energy data used in the study was obtained from national solar radiation database. The results showed that to generate of 0.3432 MWh of energy, the optimum investment cost, operation and maintenance cost are 0.2196 and 0.0088 million dollars respectively.
Khan et al. [
36] reviewed the optimal sizing techniques and cost analysis methodologies. The study focused on hybrid PV and wind energy systems. The authors shed light on various sizing strategies, various parameters of economic viability with logical advancements to improve their utilization, and future prospects of RESs. Also, the study reviewed the developments in optimization methods, cost analysis methods and reliability index for hybrid RE systems.
Kanase-Patil et al. [
37] analyzed RESs integrated for off-grid rural electrification of remote area in India by using LINGO optimization software. The optimal system cost, system reliability and cost of energy were evaluated for four different RE technologies that include biomass, micro hydro, wind and solar. The results revealed the optimum cost and the cost of energy as Rs 19.44 lacs and Rs 3.36/kWh respectively. Arnette and Zobel [
38] presented an optimization problem for RE development. In the paper, multi objective linear programming method was used to determine the optimal mix of RESs and the existing conventional facilities on a regional basis. The results revealed that the optimal cost and emissions were
$6.25 billion and 166.6 million tons respectively.
2.2. Studies about Renewable Energy Potential in Nigeria
There are some previously reported studies on RE potential in Nigeria, for example, Mohammed et al. [
12] reviewed the RE resources for distributed power generation in Nigeria and concluded that the country has vast RE resources with a potential of generating 697.15 TJ from crop residue and 455.80 PJ from animal waste in Lagos city alone. Ohunakin et al. [
39] studied the wind energy evaluation for electricity generation using wind energy conversion systems (WECS) in seven selected locations in Nigeria. Weibull probability distribution was used to statistically examine the wind speed and power density in Yelwa, Sokoto, Gusau, Kaduna, Katsina, Zaria, and Kano. The study revealed that the average wind speeds at 10 m height for Yelwa, Sokoto, Gusau, Kaduna, Katsina, Zaria, and Kano are 3.61, 7.61, 6.09, 5.27, 7.45, 6.08, and 7.77 m/s respectively. Also, the yearly average power density was found to be 43.77, 320.09, 178.48, 109.30, 339.85, 169.27, and 368.92 W/m
2 in Yelwa, Sokoto, Gusau, Kaduna, Katsina, Zaria, and Kano respectively. Similarly, Ohunakin, and Akinnawonu [
40] investigated the wind energy potential and economics of wind power generation in Jos, Plateau state, Nigeria, using 37 years (1971–2007) wind speed data at 10 m height. The analysis indicated that Jos has 8.6 m/s, 458 W/m
2 and 4013 kWh/year average wind speed, mean power density and energy production capacity respectively. Ajayi [
41] reviewed the prospects and challenges of wind energy utilization in Nigeria. The study focused on the potential of generating electricity from wind in the northern states, mountainous regions, and some locations in the central and south-eastern states. The study revealed that despite vast wind energy potential across the states, there is no wind energy generating plant in the country.
Ohunakin et al. [
42] studied the development of small hydro power (SHP) in Nigeria. The study examined the current development of hydropower in Nigeria with respect to the established energy sector reform act 2005. The authors revealed that from 1971 to 2005, hydropower sector has witnessed about 360% growth. Yet, SHP contributed only 5%. Similarly, Fagbohun [
43] investigated the potential of SHP in Itapaji dam in Ekiti, Nigeria. The study analyzed the discharge rate, effective head and other parameters that determine the power that can be generated from the site. The results revealed that the dam has a maximum yearly discharge rate of 23.24 m
3/s with a mean nominal flow discharge rate of 8.33 m
3/s, and mean minimal flow of 1.78 m
3/s. Also, the author showed that the dam has a potential of generating 1.30 MW of electricity.
Ohunakin et al. [
44] studied the solar energy development and applications in Nigeria. The study focused on current solar energy utilization, drivers for RE development and barriers to large scale deployment. The authors elaborated that currently, there are about 61 solar projects across the country with most of them being in the northern region. Also, the study showed that emission reductions, power sector reform act, electricity demand, electricity access level and energy security are the major RE drivers in the country. Furthermore, some barriers such as grid unreliability, high cost of investment, incentives and government policies affect the development of solar energy in the country. Abur and Duvuna [
45] studied the viability of solar energy in Benue state, Nigeria. The study revealed that the state receives its minimum and maximum solar radiation in the month of August and November with radiation of 14.57 MJ/m
2/day and 20.16 MJ/m
2/day respectively, and a yearly average solar radiation of 16.6 MJ/(m
2·day) to 18.07 MJ/(m
2·day).
It is vital to note that the above-mentioned approaches have been developed without novel methods on identifying the best technology for a location, the best location for a technology, available area for RESs installations, and electricity demand calculation. When necessary, these decisions/parameters have tended to contain simple estimates related to RESs potential, and available area for RESs installations, and, most often these data were derived from sources outside the provided research. This consists of a drawback to many optimization approaches which this study aims at solving. Unlike other studies, the objective of this study is to provide a general framework that can be used in any country or region. The framework is designed in a way that it considers the existing installed capacity and focuses on minimization of the total cost of installing RE technologies in different locations, to supply the gap between demand and supply, by using the best combination of various RE technologies. Thus, to the authors’ knowledge, there is no study in the literature that focus on developing a general cost optimization framework that can be used in deciding optimum amount of RE capacities to be installed in different locations in a region or country by considering the country’s peak power demand, and hence, the application of such a framework to Nigeria.