1. Introduction
It is evident that energy has always been an indispensable part of nations’ plans. Several decades ago, it used to supply energy for a limited number of household items chiefly. In parallel with advances in technology and industry, consumption and dependence on electricity have boomed throughout the years. Therefore, having an optimal strategy for the future structure of industries that generate electricity is momentous. For this reason, the generation expansion planning (GEP) problem can be considered to ensure that a fraction of future load demand would be supplied. For years, different optimization techniques have been investigated in order to provide an optimal plan for the expansion of generation [
1].
Among related works, Ref. [
2] provides a new method with game theory approach in order to regard the electricity market adjacent to the GEP problem with PSO optimization algorithm to provide the optimal plan for expanding the generation and reducing the CO
2 gas emission. In [
3] Corrected Normal Boundary Intersection to diagnose pareto optimal solutions, a contributory lexico-graphic optimization method is applied to improve the NBI method modeled on a synthetic test system over a 6-year period. Ref. [
4] proposes a new hybrid model next to GEP for the case study in Iran to estimate the GEP problem for the long term (2016–2030). Furthermore, it directs at improving the combination of renewable energy resources in the network. For mentioned purpose, it uses a hybrid fuzzy analytic network and NSGA-II in two stages, respectively. Finally, it demonstrates the high importance of renewable energy plants in the future power system of Iran. Ref. [
5] simultaneously considers the electricity demand forecasting and generation expansion planning to promote the power system planning. In this study, genetic algorithm, artificial immune system, and differential evolution solve the problem during two periods, long-term (12 years) and short-term (6 years). Its main aim is to minimize the cost and environmental effects.
Due to the importance of renewable energies, Ref. [
6] introduces a new model for GEP to increase the incorporation of renewable energy resources over the planning. This survey is in the case study of China with considering uncertainties of load and renewable energies. In [
7], a new technique is presented for the GEP problem to integrate distributed and centralized generation units. Moreover, this study considers the genetic algorithm to discover the optimal resolution for a combined objective function. Ref. [
8] provides a model for expanding the power systems by simulating over the 15-year period. In this study, the applied algorithm to establish the optimal solution is a meta-model assisted evolutionarily. Results of this paper exhibit that it is an efficient approach.
Because of the penetrating the renewable power plants in power systems considering the energy storage systems in networks is necessary [
9]. In [
10], the GEP problem is considered with hourly variability of the wind and solar power. Ref. [
11] introduces a model for GEP that the units of the generation that energy storage systems are considered to diminish the reliability of the power system. In this kind of model, the cost of reliability is calculated by the amount of the lost load and the anticipated energy not supplied in which, a novel linear expected energy not supplied model is employed that is simulated on the IEEE-RTS system to display the efficiency of this new formulation. In [
12], different models of GEP combined with renewable energy resources are reviewed. It divides them based on the employed techniques of optimization. The key point about this paper is comparing them with their merits and demerits. Ref. [
13] suggests an optimum plan for the generation expansion to lessen the total cost. This goal is obtained by ensuring the power system operates correctly and considering the requisite conditions of integrating renewable energy resources in the power grid (model for thermal–wind–photovoltaic). In [
14], the expansion is considered for the transmission and generation problem for an energy hub (electricity and natural gas). The regarded way for this problem in this study is an improved genetic algorithm.
The influence of solar and wind integration and distinct reliability aims is analyzed in [
15] for the electricity generation expansion planning. The applied model for expanding generation capacity is national electricity market optimizer (NEMO) through the covariance matrix adaptation evolution strategy (CMA-ES) algorithm considered for all candidates in the case study of Indonesia’s Java–Bali. Differential evolution (DE), opposition-based differential evolution (ODE) and self-adaptive differential evolution (SaDE) algorithms are considered in [
16] to find the optimized plan for generation expansion of the case study in Indian state Tamil over a 6-year and a 12-year period. The key point about this study is considering the penalty costs on emissions and new technologies for generating the electricity and comparing them in different strategies.
Considering the presence of renewable energy resources for environmental reasons in the future of a system is necessary, in [
17], the differential evolution algorithm (DE) is exerted to GEP problem with the wind power plant for different goals.
By considering the unit commitment as one of the most important problems in the operation of power systems, in [
18] influence of unit commitment with load and renewable energy unpredictability on the GEP problem is studied. In this study, the regarded method for the GEP problem is a robust model and for unit commitment is a data-driven robust model.
It is obvious that in parallel with the expansion of the generation units, the transmission should be expanded [
19]. In [
20], the planning of renewable energy resources is considered adjacent to the expansion of the transmission to promote the system’s flexibility. Mixed-integer linear programming (MILP) model is exerted for finding the optimal answer for this issue. In [
21] a mixed-integer linear programming formulation is provided for the generation and transmission expansion planning problem simultaneously, which is resolved by a nested benders decomposition and a tailored benders decomposition algorithm in the case study of Texas.
Due to the consequences of the carbon environment having an optimal plan for the expansion of the generation units is necessary to decrease the amount of carbon. So, in [
22], a low carbon model for GEP is introduced. The problem is modelled as a mixed-integer linear programming (MILP) which is resolved through the CPLEX algorithm.
Since climate mitigation has become an important issue throughout the world, in [
23], it is considered with a GEP problem which is modelled as a multi-level optimization problem with a risk-averse agent for balancing. In [
24], a framework for the GEP problem with the mixed energy system is provided. The problem is solved by formulating a mixed-integer linear programming problem to decrease the cost of the mixed energy system. With increasingly integrating renewable energy resources in the power systems, the importance of their uncertainty increases. Ref. [
25] plans generation expansion for stochastic wind–thermal power plant of which the probabilistic characteristics are considered. In this study, a MILP also is introduced which is solved with the branch-and-cut algorithm. Ref. [
26] provides a two-stage nested bilevel model for the GEP problem. Furthermore, a novel algorithm is introduced in order to convert the provided model to a mixed-integer quadratic programming (MIQP) problem.
Having enough information about the different dimensions of the conducted works about the GEP problem for providing a novel technique can be useful. Hence, Ref. [
27] carry outs a review about the distinct dimensions of the state-of-the-art generation expansion planning such as the plan for expansion of the transmission, the systems work with gas, interim activities of markets for power, electric automobile and that sort of things. In [
28], the GEP problem is considered in the presence of the renewable energy market. In this study, the provided problem is solved by the integration of the Karush–Kuhn–Tucker (KKT) method and the fixed-point iterative algorithm. The uncertainty of renewable energy resources is one of the most important criteria that should be considered. In [
29], a two-stage robust plan is proposed for generation expansion regarding the probability of the immense amount of wind energy. In this paper, the provided GEP problem is resolved with mixed-integer linear programming (MILP).
The hydropower plant is one of the useful power plants for areas with enough hydropower. In [
30], the GEP problem for hydropower is considered in the case study of the Sulawesi power system. Ref. [
31] in a multi-objective model for the GEP problem focuses on the operational flexibility in the presence of renewable energy resources. The applied way for solving this problem is the non-dominated sorting genetic algorithm version II (NSGA-II).
Along with advances in technologies in power systems, the appliances and structure of these kinds of systems will change. In [
32], the GEP problem is considered with microgrid aggregators. In this study, the applied algorithm to find the best solution is the gravitational search algorithm (GSA).
To create a competitive situation in the GEP problem, different game theory (GT) approaches such as Nash–Cournot (NC), Nash–Bertrand (NB), and bi-level are used. In [
33], the Cournot–Bertrand model is applied for the GEP problem and categorizes 12 primary models of this theory. In a similar study [
34], a novel bi-level technique is regarded for GT to provide an optimal plan for the generation expansion of the power systems. In [
35], a game theoretical approach is considered to provide an optimal plan simultaneously for sub-transmission and generation expansion.
The increasing presence of distributed generation in power systems demands a key point that should be considered in the generation expansion planning problem. This key point is coordination and interaction between the transmission and distribution systems that in [
36] GEP problem is regarded with this criterion. Additionally, in [
37] is used a new way which is called Bayesian network for the dynamic behavior of the system with considering uncertainties of renewable power plants in a multi-objective generation expansion planning decision model regarding permanent development. Because of the changeable output of renewable energy resources, considering flexibility requirements with respect to the power system is an important issue. Ref. [
38] introduces a power-based GEP model that improves this issue.
Consequently, significant contributions of this study proposed a novel algorithm and a developed model to solve the GEP problem by a game theory approach. First, we analyzed the GEP problem with a TLBO algorithm that outperformed in the quality of solutions and convergence speed under the condition of our problem and compared the results with previous methods. Next, we have modelled the problem by GT to maximize each power plant’s profit. In the end, we considered carbon emission parameters in the NC model, met the peak demand and formulated the government’s objective under a unique strategy, namely with the carbon tax and government subsidy. We analyzed the effect of applied regulation on the optimal decisions of the NC model in the GEP problem.
In conclusion, we applied mentioned scenarios regarding the structure of the GEP and government regulations. We comprehensively compared the effects of different governmental carbon and subsidy regulations by sensitivity analysis.
The rest of the paper is organized as follows:
Section 2 describes the problem.
Section 3 applies the TLBO algorithm to the GEP problem and compares it with other prominent algorithms. In
Section 4, the results of the simulation are illustrated, then the results are discussed and analyzed. In the last section, the conclusion is presented.