1. Introduction
Environmental concerns like global warming are becoming more eminent each day. Means of diminishing carbon emissions are the objectives of industries and governments, as they are trying to find techniques for solving this problem. Coal-powered units or central steam are getting old since distributed generation is the trend and motivation towards it is increasing. Penetration of different renewable sources can be enabled by a distributed generation where the location of consumers is closer to these sources of renewable energy [
1]. Nevertheless, implementing renewable generation has its downsides and comes with different challenges.
Lasseter [
2] introduced the microgrids concept as a way of implementing dispersed energy resources in a supervised and safe manner. A group of interlinked distributed energy resources and loads within distinctly established electrical borderlines that performs as an individual tractable unit vis-a-vis the grid is often defined as a microgrid. Operation of a microgrid can have two cases of grid-connected or islanded-mode since they can connect to the grid or disconnect from it to enable this feature. High penetration of different renewable energy sources adds to the instability of the system because of the stochastic nature of them. Having implemented more than one class of renewable energy source like wind, solar or hydro will increase the uncertainty of the system even more. Since prediction error is the main relation of these uncertainties, reducing the instability of the network is important and can be achieved by studying different scenarios for each renewable type that exists within the system.
Economic Dispatch (ED) is the determination of the minimum possible cost for the required power from each committed power plant. In ED, there is usually one objective to be focused on: cost. The main objective in optimizing an ED problem is to reduce the total cost of generation as much as possible, to have an economic dispatch as the name suggests. In economic emission dispatch (EED), the main objective is to minimize the total price of generation as well as the emission degree. In both ED and EED, fulfilling electricity demand from the power units must be satisfied. Usually, the difference between ED and EED is that the former is a single-objective problem while the latter is a multi-objective problem. In EED one objective is to reduce emissions, and climatic contamination is mostly caused by thermal power units which produce Sulphur dioxide, a toxic gas, represented by SO
2, and other similar gases like Nitrogen oxide and Carbon dioxide represented by NOx and CO
2, respectively [
3]. There can be three different ways of solving EED according to Refs. [
3,
4,
5]. Firstly, the problem is considered to be a single objective, only containing emissions, since in many countries environmental laws impose a carbon tax, hence practicing emission control is of more importance. This approach of reducing emissions at any cost is not an ideal solution and it should not be called EED anymore since there would not be a concern to reduce cost. The second way is to mix emission and cost into a single objective optimization and reduce them at the same time by considering different weights, and thirdly, with multi-objective optimization which has different and separate functions, in this case, cost and emission.
A solution to the EED problem falls into the two parts of economic dispatch and emission optimization. In the first part, optimal scheduling of generator units is performed to reduce electricity demand while in the second part, the same task is performed to diminish the number of harmful gases. Furthermore, an optimization method is needed to compute the optimal output for EED since there can be too many numbers of generation units in the system to be enumerated one by one. Diminishing cost or emission alone is also a single objective problem but reducing both of them at the same time, makes the problem very non-convex. Hence, there is more than one solution to the problem and specific methods must be used to extract those answers for a trade-off between emission and cost. This means that by reducing emissions, the cost will increase and vice versa. In the following paragraphs, previous studies that solved ED and EED problems will be mentioned. Their optimization technique will be reviewed and we will point out what renewable energy source was incorporated and what consideration has been taken into account for system limitations.
Adarsh et al. [
6] solved ED by chaotic bat algorithm, a variant of swarm intelligence technique combined with chaotic sequences for tuning and controlling the parameters resulting in convergence and diversity enhancement. Jayabarathi et al. [
7] implemented the hybrid gray wolf algorithm to solve the ED problem. They acquired genetic operators (crossover and mutation) for enhancing the algorithms’ performance and they also considered prohibited operating zones (POZs), and valve point effect, but they did not consider a multi-fuel option. The introduction of the multi-fuel option was performed in Ref. [
8], and they used crisscross optimization to solve the ED problem but without considering POZs. Delshad et al. [
9] utilized a backtracking search algorithm (BSA) containing various feed options and valve-point effects. They added more complexity to the ED problem by considering POZs, and generators ramp-up and ramp-down since BSA is promoted to solve very non-convex functions. Even though their formulation for the ED problem was good, it lacked consideration of reducing emissions.
Implementing emission into the formula requires multi-objective optimization. Di Somma et al. [
10] used a stochastic multi-objective optimization to reduce the cost and emission and prioritized environmental aspects with a focus on optimal scheduling. Secui [
11] used an approach known as the weighted sum, with a newly altered artificial bee colony algorithm to approach the ED problem. Aside from the valve-point effect, other restrictions like transmission losses, POZ, and ramp-rate boundaries have been considered to improve the mathematical model. However, no renewable energy sources were considered in the formulation of the problem. Ghasemi et al. [
12] considered wind units in their formulation and they implemented a 2m-point practical model for the uncertainty in wind power. This was a multi-objective economic emission dispatch (MOEED) problem and they solved it by using the honey bee mating optimization technique. However, they compared the results with very old optimization methods that have poor constraint-handling techniques. Qu et al. [
13] used the summation-based differential evolution technique in a multi-objective form and considered the uncertainty of wind to be a limitation of the system while applying the superiority of a feasible solution as a constraint-handling method. Only the implementation of the wind plant was considered up to this point. Khan et al. [
14] solved EED with thermal and solar power by applying the particle swarm method while converting the multi-objective function to a single-objective function. This can hurt the performance of the optimization since a trade-off must happen between cost and emission. Kheshti et al. [
15] introduced Lightning Flash Algorithm. A new evolutionary algorithm for solving non-convex large-scale EED problems considering valve-point effects and multiple fuel options. However, they did not consider any wind plant in their problem formulation. Not too much literature can be traced regarding the model of solar, thermal, and wind plant in power systems and this is true for a combination of wind and hydro energy sources. Hence, more research is required.
Reddy et al. [
16] considered wind, thermal and solar power in the system and approached the scheduling problem with the best-fit evaluation of participation factors. However, they performed single objective optimization of the system and did not consider emission reduction. Reddy [
17] executed optimal scheduling of a hybrid system (wind-solar-thermal) together by using a two-point estimate method and genetic algorithm. To consider emission reduction, battery storage was proposed but this still is a single objective problem. Biswas et al. [
18] used the success history-based adaptation technique to solve the optimal flow problem incorporated with solar and wind plants. However, the problem formulation was a single objective problem but they used separate probability density functions to estimate the stochastic behavior of renewable energy sources as well as the underestimation and overestimation price of them. Liu et al. [
19] integrated the improved gradient descent with an evolutionary algorithm to solve the dynamic economic dispatch problem containing small hydro and wind energy sources. Gumbel and Weibull probability density functions were used to represent the random behavior of the mentioned energy sources, respectively. Up to here, no multi-objective optimization was performed for EED.
Salkuti [
20] computed single and multi-objective EED problems by adding thermal-wind-solar power in the system and implemented prohibited operating zones and valve point loading effect but he did not use a proper constrain handling technique and the optimization algorithm (particle swarm optimization) was too old. Yalcinoz et al. [
21] used improved particle swarm optimization to solve the MOEED problem while implementing wind energy in the system and considering generator limitations, valve point effect, ramp restrictions, transmission losses, and prohibited operating zones. Nevertheless, they did not consider a proper constraint-handling method nor an appropriate decision-making solution for optimization results. When the problem requires multi-objective optimization, a method of extracting compromised solutions is needed. It is important to take into account how the decision-making of extracting results is going to take place. Decision-making methods that can consider multiple objectives at the same time are needed in order to create energy planning scenarios that take into account social, economic, environmental, and technical aspects related to human development [
22].
Renewable energy sources like wind and solar can fluctuate randomly, which makes it risky for a single unit to participate in the energy market. If the unit is unable to produce power, purchasing power at a high price from the balancing markets is needed [
23], and this shows the importance of implementing different renewable energy units in the system. Until here, a combination of wind, small-hydro, solar, and thermal power plants has not been mentioned and many of these articles did not consider a proper constraint handling technique nor a proper technique to extract the compromised solution. To the best of our knowledge combination of these energy sources altogether, considering different aspects of system limitations while taking into account different probability density functions for predicting the stochastic behavior of renewables has been demonstrated only in Ref. [
24].
In this study, we considered many system limitations such as generator limits, POZs, valve point effects, network security, etc. while performing MOEED with thermal generators, the solar, wind, and hydro renewable sources. In this approach, we also considered a proper constraint-handling method and emphasized the importance of carefully selecting different optimization parameters. This study aims to:
Contemplate forecasting of renewable energy sources of different types and their implementation in the system.
Formulate and demonstrate a solution to MOEED that is a very non-convex and non-linear problem.
Give in-depth knowledge of optimization since developing an algorithm that is reliable, fast, robust, and able to handle multi-objective optimization requires a deep understanding of the underlying principles and techniques.
Satisfy many system constraints and network securities that go beyond the classical approach by using a proper constraint-handling method.
Analyze the results in detail and compare them with previous studies to assess the robustness, stability, and quality of this strategy.
This paper is categorized in the following manner. In
Section 1, we begin with an introduction to the problem and its significance, highlighting the research background and outlining the main objectives of this study. We then delve deeper into the topic with a thorough literature review, discussing the latest developments and trends in this area. Different methods of optimization are reviewed and key concepts and ideas behind the problem formulation are stated. The limitations of previous articles are mentioned.
Section 2 formally presents the detailed methodology that is practiced in this study. It states the proposed R-NSGA-II and its elitist characteristics alongside the genetic operators that are carefully selected and incorporated within. It also includes an explanation of different methods which are used to forecast renewable energy sources and their implementation in the modified IEEE 30 bus system. Furthermore, it provides methods of extracting the best-compromised solution integrated with the algorithm. It talks about a proper and strong constraint-handling technique.
Section 3 presents the outcomes of the simulation for the developed algorithm on the modified IEEE 30 bus network combined with renewable energy sources. It also shows the compared results with two other algorithms (which are newer and supposed to be better) to assess the accomplishments of the suggested approach.
Section 4 summarizes and concludes the presented study. It suggests possible future work that can be implemented and studied, and the limitations of this study.
4. Conclusions
In this study, the MOEED (multi-objective economic and emission dispatch) which is a non-convex and non-linear problem was solved using the R-NSGA-II (real non-dominated sorting algorithm II), which was modified to include a better constraint handling method called “constraint domination”, and more suitable genetic operators: a mutation operator called “polynomial mutation”, and a crossover operator called simulated binary crossover (SBX). We used a standard IEEE 30-bus system and modified it to be incorporated with different renewable energy sources such as stochastic solar, small hydro, and wind units. With increasing concerns about clean energy and the policies of companies and governments, it is important to consider renewable energy sources in energy systems. To forecast the stochastic behavior of these sources, we used suitable probability density functions. We also embodied prohibited operating zones, valve point effect, and generator limitation in the design of a thermal unit. Network security was considered. MOEED was calculated by applying R-NSGA-II and results were compared to two previously studied algorithms: SMODE-SF and MOEA/D-SF. Even though R-NSGA-II is older than MOEA/D-SF and SMODE-SF, the results showed that R-NSGA-II outperforms the other two algorithms in terms of cost and emission, and this superiority was consistently observed in 21 runs of the algorithm and did not happen by chance. Not only that, R-NSGA-II also provided more security, stability, and quality of the system. This superiority was due to careful study of the subject matter, and selection of the genetic operators and constraint handling technique.
This study is beneficial in the energy sector since there is a limited number of articles that studied the process of optimizing MOEED in depth. Going emission-free is a serious issue and it is the goal of many countries and governments. The authors plan to continue studying MOEED in future works, possibly using newer approaches such as NSGA-III, etc. As smart grids become more prevalent, it is important to expand the literature on MOEED and its potential for emulating the behavior of energy systems, by using new technologies like digital twins.
Some limitations of this approach can be enhanced in future studies. These limitations/suggestions are: Taking into account life cycle cost analysis of renewable sources as part of the objective function since maintenance and disposal costs can impact the overall optimization process. It can be a good idea to consider electrical vehicles and battery systems for energy flexibility [
53], this can be beneficial for MOEED and future smart grids. Decision-makers must also know the overall impact to see whether an investment in renewable units is beneficial/feasible or not, or how many renewables of different types must be considered to make the project feasible. A better policy for decision-making must be considered since policymakers need to pay attention to the lack of precise and certain data and the presence of conflicting goals when evaluating investments [
22]. This again, can impact the overall process of calculation, optimization, and investment and consequently reduce emission and saving costs.