A State-of-the-Art Review on Optimization Methods and Techniques for Economic Load Dispatch with Photovoltaic Systems: Progress, Challenges, and Recommendations

Abstract

Fossil fuel is considered to be the primary power generation source. As this source is not that eco- and environmentally friendly, researchers are constantly searching for an alternative source for power generation. Renewable energy has drawn much attention in this regard in recent times. For solving economic load dispatch issues, numerous operational constraints must be considered. Due to the restructuring of the power sector, there is competition between different power systems organizations. Increasing fossil fuel costs drive power-producing utilities to adopt a cost-effective technique for dispatching actual power output. Due to the presence of nonlinearity and non-convexity in the fuel of cost function of generators, the economic load dispatch is often considered a complex optimization problem. Many researchers have been optimizing fuel costs to solve the economic power dispatch problem. This paper offers a critical analysis of ELD that takes into account both traditional and non-traditional energy sources. The review covers a variety of algorithms, including hybrid algorithms for integrating renewable energy sources (RES). The paper also focuses on several restricted optimization techniques and contemporary algorithms including PSO, Jaya, GWO, SMO, TLBO, Rao, MRao-2, and MFO to reduce the fuel cost of generation units using large-scale solar PV. Moreover, this paper provides a comprehensive overview of the current state of economic load dispatch and provides valuable insights for electricity researchers and practitioners. It also discusses future technologies and next steps in the field of ELD, emphasizing the need for more environmentally friendly and cost-effective power generation and distribution solutions. Overall, the paper demonstrates the benefits of renewable energy sources as well as optimization techniques for creating a more sustainable and efficient power generation system.

1. Introduction

In recent times, power systems are facing numerous challenges due to the variability of power due to the integration of renewable energy sources. Hence, power companies are trying to determine new ways to optimize the cost of generation while maintaining all other operational requirements [1].

Economic load dispatch (ELD) is a technique used in power systems to determine the optimal generation schedule for a group of power plants in order to meet the load demand at the lowest possible cost. The objective of ELD is to minimize the total fuel cost of generation while satisfying a set of constraints, such as transmission line capacity and generator capacity limits. The process of ELD involves solving a mathematical optimization problem, which is typically achieved using numerical methods such as gradient descent or linear programming.

Minimizing the generation cost and reducing carbon emissions can be accomplished by integrating renewable energy sources such as solar power systems [2]. RES is considered environmentally friendly and non-harmful for electricity generation and supply [3]. Hence, integrating renewable energy sources such as solar and wind power into the energy generation dispatch mix has changed the direction of research on ELD in recent times [4].

Energy dispatch plays a vital role in the planning and control process of power generation [4]. Thus, maintaining optimal power flow is important in electrical networks to minimize the total cost generation while considering all constraints such as ramp rate limited, prohibited operating zones, spinning reserve, and voltage constraints [5]. Moreover, ELD plays a vital role in scheduling the generating units while maintaining minimal cost and considering the generator limits [6].

Usually, pollution factors are not taken into account in the conventional renewable-free ELD models [7]. To offset environmental emissions and move toward carbon neutrality, researchers are shifting their focus toward renewable integrated economic load dispatch [8]. Power generation companies are constantly trying to minimize the cost of generation and the same time looking for alternative pathways to offset carbon emissions [9]. This leads the researchers to optimally integrate and penetrate renewable sources into the conventional grid to obtain the best-optimized cost and at the same time offset a significant amount of carbon emissions [10]. In order to economically dispatch overall load demand among the generating units, the optimization of the ELD problem is a must [11]. Simultaneously, solving the economic load dispatch problem by integrating renewable sources such as solar power is vital.

This paper illustrates the optimization methods and formulation of problems for ELD taking into account thermal power units and solar power. Section 2 sheds light on the mathematical form of ELD with and without solar power. Section 3 discusses different optimization methods and algorithms that are in practice for the optimization problem. Section 4 provides an overview of the current practices of solving ELD problems by integrating renewables. Section 5 proposes technical solutions to generation dispatch with photovoltaic systems. Section 6 shed light on the challenges and technical solutions of large-scale PV integration. Discussion and recommendations are placed in Section 7 and Section 8, respectively. Finally, Section 9 concludes the paper.

2. Formulation of Economic Load Dispatch

2.1. Economic Dispatch with Thermal Units

ELD is a vital optimization problem to reduce the cost of generation. The primary objective of economic load dispatch is to minimize the total power generation cost while satisfying the operational constraints. The fuel cost function is optimized to obtain the optimum power generation conditions [1]. Overall fuel cost is expressed in the following terms [2]:

$$F_T={\displaystyle \sum }_{i=1}^{n}F\left(P_i\right)={\displaystyle \sum }_{i=1}^{n}a{P}_i^2+b_i{P}_i+c_i,$$

(1)

where $F_T$ is considered to be the total cost of power generation in $\mathrm{USD}/\mathrm{hr}$, $a_i,b_i and c_i$ are the fuel cost coefficient, and $P_{Gi}$ is the output unit $i$ of the real power generation.

If the valve point effect of the generator is taken into account, the above equation can be reiterated as

$$F_T={\displaystyle \sum }_{i=1}^{n}F\left(P_i\right)={\displaystyle \sum }_{i=1}^{n}a{P}_i^2+b_i{P}_i+c_i+\left|e_i\sin \left(f_i\left(P_{Gimin}-P_{Gi}\right)\right)\right|,$$

(2)

where $a_i, b_i, c_i,$ are the cost coefficients of the $i^{th}$ power generating unit and $e_i$ and $f_i$ are the coefficients of generator $i$ with valve point effect. Integrating valve point loading into the economic load dispatch quadratic cost function makes the cost function non-linear. Several methods have been suggested in the literature to take the valve point influence into account when calculating the economic load dispatch cost function. One common method is to represent the sections of the fuel cost curve as valve points using a piecewise linear or quadratic function. The use of a multi-objective optimization formulation as an alternative approach would take into account the effects of both fuel price and valve point loading. In reality, the valve point loading effect can be accounted for by including a series of binary variables in the ELD problem that represent each generator’s on/off state. These binary variables indicate whether a given generator should be operated at a specific output level or should be turned off completely to avoid operating near the valve point. The inclusion of these binary variables aids in ensuring that the best solution to the ELD problem is not skewed toward suboptimal options that entail operating generators at output levels near to their valve points.

2.2. Economic Dispatch Integrating Solar

Because of the challenges and opportunities, integrating solar power into the electrical grid is critical for economic load dispatch (ELD). While solar power is intermittent and requires careful coordination with conventional generators to maintain grid stability, it can also save money and reduce greenhouse gas emissions. A critical challenge in ELD with an integrated solar system is optimizing the dispatch of generators with solar energy while maintaining system stability.

According to the data presented in Figure 1 and obtained from Scopus Advanced Search, it seems that researchers are still very interested and active in the fields of “economic load dispatch” and “solar” energy.

With a peak of 228 citations in 2018 and a low of 0 citations in 2014, the number of citations received by publications in this field has fluctuated over time. With a total of 641 citations between 2013 and 2022, the number of citations has been continuously high over the past ten years.

With the increasing penetration of solar PV into the power grid in the recent years, integrating the variable and uncertain power generation from these sources into the traditional power system becomes more difficult. ELD must consider the characteristics of solar PV generation, such as variability and uncertainty, as well as the impact on overall power system operation. In a system with significant solar PV penetration, the goal of ELD is to minimize total operating costs while ensuring the reliability and stability of the power system and taking into account the power grid’s limitations in terms of transmission capacity, power flow control, and grid stability. ELD strategies that are effective can assist power systems in effectively integrating solar energy while minimizing operational costs and carbon emissions.

Therefore, the integration of solar PV into the power grid can be seen as a challenge for ELD and requires the development of new optimization algorithms and methods to ensure the efficient and effective dispatch of load in a system with high renewable energy penetration.

The maximum power solar photovoltaic panels are denoted as

$$E_t=3.24M_{pv}\left(1-0.0041\times \left(T_t-8\right)\times S_t\right).$$

(3)

Here $E_t$ is the output power of the solar panel, $M_{PV}$ is the output capacity of each panel, $S_t$ is the irradiation at time $t$ while $T_t$ is the temperature. The cost of solar generation comprises two parts. Part one is the investment cost, and the second is the generated energy’s operation and maintenance cost. Equation (4) presents the cost function for solar power, which is incorporated into the economic load dispatch calculation to determine the minimum total cost alongside the cost function for thermal units. If the capital investment of land is not considered, the cost function for solar can be written as

$$F\left(P_s\right)=a{I}^p{P}_s+G^E{P}_s,$$

(4)

where $a$ is called the dimensionless annuitization coefficient, which can be denoted as

$$a=\frac{r}{\left[1+{\left(1+r\right)}^{-N}\right]},$$

(5)

where $P_s$ is the solar power generation, $r$ is the interest rate, $N$ is the investment lifetime which is taken as 20 years. $I^P$ is the investment cost per unit of installed power in USD per kW. $G^E$ is the operation and maintenance cost of per unit dollar sated energy.

2.3. Integrated Cost Function Incorporating Solar PV

Adding the cost functions described in $\left(1\right),\left(2\right) \mathrm{and} \left(3\right)$ provides us

$$F_T=F_i\left(P_i\right)+F\left(P_s\right).$$

(6)

Several equalities and inequality constraints are considered while minimizing the overall cost of generation.

2.3.1. Power Balance

If system transmission loss is neglected, total generation from the thermal and PV units must be equal to the total system demand.

$${\displaystyle \sum }_{i=1}^n{P}_i=P_{Load}.$$

(7)

Generator Production Limit:

Power produced by each generating unit should be within the minimum and maximum range of each generating units,

$$P_{imin}<P_i<P_{imax},$$

(8)

where $P_{imin}$ is the minimum output power and $P_{imax}$ is the maximum output power from the $i^{th}$ generating units.

2.3.2. Ramping Rate Constraint

The active power output of each generator should be within an acceptable range. Subtracting the previous active output power from the current output power of the $i^{th}$ generating unit is called the ramping rate constraint and is denoted as

$$P_i-P_i^{pr}\le U{R}_i,$$

(9)

$$P_i^{pr}-P_i\le D{R}_i.$$

(10)

2.3.3. Prohibited Operating Zones

Generators cannot operate in the prohibited operating zone [3].

$$P_iϵ\left\{\begin{array}{c}{P}_{i,min}\le P_i\le P_{i,1}^L\\ P_{i,k-1}^U\le P_i\le P_{i,k}^L k=2,3,\dots ,p{z}_i\\ P_{i,p{z}_i}^U\le P_i\le P_{i,max}\end{array},\right.$$

(11)

where $p{z}_i$ is the number of prohibited operating zones of the $i^{th}$ generating unit, $P_{i,k}^L$ is the lower bound of the generator and $P_{i,k}^U$ is the upper bound of the $k-th$ prohibited zone [4].

Optimization methods for optimal power dispatch can be classified mainly into three categories.

2.3.4. Combatting the Intermittency and Uncertainties

Economic load dispatch (ELD) is a complex optimization problem with several unknowns that can affect the outcome. Among the key uncertainties in ELD are the following aspects.

Load Demand Uncertainty

Load demand is typically unpredictable and changes quickly in response to a variety of factors such as weather, consumer behavior, and industrial activity. Load uncertainty can have a significant impact on ELD performance and necessitates appropriate modeling and forecasting methods.

PV Generation Uncertainty

Solar photovoltaics (PV) are inherently uncertain and variable, which can have an impact on ELD performance. A sudden increase or decrease in solar PV generation, for example, can affect power system stability, and ELD algorithms must account for these fluctuations.

In several ways, an ELD algorithm can account for the uncertainty of renewable energy sources:

• Probabilistic forecasting: Based on historical data and current weather conditions, the ELD algorithm can use probabilistic forecasting techniques to predict the expected output of renewable energy sources. The algorithm can also account for forecast uncertainty by modeling forecast error as a probability distribution.
• Metaheuristic optimization: In the presence of uncertainty from photovoltaic (PV) generation, metaheuristics can be crucial in the solution of the economic load dispatch (ELD) problem. The ELD problem entails determining the ideal generator output combination to satisfy the power demand while reducing the overall cost of generation. Traditional deterministic optimization techniques may not be suitable in the presence of PV generating uncertainty because they do not account for the variability and unpredictability of the PV generation. By including the uncertainty of PV generation in the optimization problem and locating close to optimal solutions, metaheuristics can be applied to solve the ELD problem. They are particularly suited for ELD problems in the presence of PV generation uncertainty because they can manage big, complicated problems and handle uncertainty effectively.

In the economic load dispatch (ELD) process, the dispatch priority of renewable energy sources, such as solar photovoltaic (PV) and wind power, depends on various factors, including local regulations, market structures, and technical constraints.

In some cases, renewable energy sources may be dispatched first in the ELD process, to meet renewable energy targets and promote the use of clean and sustainable energy sources. In such cases, renewable energy sources may be considered as “must-run” units, and their generation may be given priority over conventional generation.

In other cases, the dispatch priority of renewable energy sources may be determined based on economic considerations, such as the cost of generation and the availability of storage. In such cases, renewable energy sources may be dispatched in the ELD process only if they are the least-cost option for meeting the load demand.

For a simple system with loss where solar power is dispatched at the first place can be mathematically modelled as follows:

$${\displaystyle \sum }_{i=1}^n{P}_i+{\displaystyle \sum }_{j=1}^n{P}_j=P_{Load}+Loss.$$

(12)

Therefore, the dispatch priority of renewable energy sources in the ELD process can vary based on the specific conditions and objectives of the power system. However, regardless of the dispatch priority, the overall aim of the ELD process is to minimize the total generation cost while ensuring that the load demand is met and the power system operates efficiently and reliably.

Several constraints, such as security constraints, voltage magnitude constraints, reactive power constraints, and line flow constraints, can be considered for economic load dispatch problems. However, for the purpose of simplicity and to avoid complexity in this paper, these constraints have been excluded from the scope. This is because considering these constraints would require accounting for numerous additional factors and data that may be difficult to obtain, which could impede the evaluation of algorithms.

3. Optimization Algorithms for Economic Power Dispatch

The process through which an optimal solution is determined is called optimization. Optimal power dispatch refers to delivering demanded power while considering the system constraint [5]. Optimization methods for optimal power dispatch can be classified mainly into three categories such as classical, hybrid, and nonconventional methods [5]. The conventional method is used for solving a convex optimization problem, while the nonconventional method is used to solve non-convex and practical ELD problems. In addition, to solve systems with more than two nonconventional methods, hybrid approaches are used to improve the performance of each method. Figure 2 shows the three commonly used optimization techniques for economic power dispatch.

One of the most commonly used classical methods for solving ELD is the Newton’s method [6]. Quadratic programming methods also perform well in solving economic load dispatch problem for multiobjective functions [7]. These algorithms have a combatively faster convergence rate and comparatively better solutions in terms of cost minimization. The Interior search method can solve the economic load dispatch problem with line flow limits as a single optimization without any penalty factors. This method avoids introducing augmented penalty terms which makes it more effective [8]. In [9], authors used lambda iteration method on two test systems. Lambda iteration method worked better for the lossless systems compared to the system with losses [10]. In a nutshell, it is asserted that the classical methods for ELD are pretty simple and easy to implement. One of the significant issues with these kinds of optimization is that they cannot handle non-convexity and non-smoothness. On top of that, another drawback of this method is that it only generates only one solution at a single run [11].

On the other hand, non-conventional methods are capable of handling complex ELD optimization problems. Numerous optimization problems such as bat algorithm [12], Genetic algorithm [13], Ant colony optimization [14], Particle Swarm Optimization [15], Grey Wolf Optimization [16] and Simulated Annealing [17] are used to solve this sort of problem.

However, in many real-world scenarios, the cost functions of power generation units are non-linear, making the problem more difficult. This review of the literature summarizes recent advances in ELD optimization techniques for non-linear cost functions.

In 2013, Kanagaraj et al. [18] proposed a new hybrid optimization technique for solving ELD with non-linear cost functions called the Cuckoo Search Algorithm with Genetic Algorithm (CSA-GA). To achieve an optimal solution with fewer iterations, the proposed method combines the Cuckoo Search Algorithm (CSA) with the GA. In terms of convergence rate and solution quality, the results show that CSA-GA outperforms traditional optimization techniques.

Mandal et al. [19] presented a novel methodology for explaining the complexities associated with the Dynamic Economic Load Dispatch (DELD) problem with non-convex cost function. The proposed methodology takes into account various factors such as operating limits, constraints, ramp rate boundaries, prohibited operating zones, and the effect of valve point loading, as well as the uncertainties of load requirement and wind power. The paper also investigated the impact on DELD of incorporating wind generators into the thermal generation structure. The proposed method was tested on conventional and non-conventional DELD, and its effectiveness was compared to that of other heuristic methods in the literature. The results show that the oppositional-based chaotic group search optimization (OCGOA) approach proposed in this paper yields a higher-quality solution while consuming less computational resources.

In addition to the aforementioned optimization techniques, several other methods have been proposed in the literature, including Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), and Harmony Search Algorithm (HSA). According to recent research, hybrid optimization techniques outperform traditional methods in solving non-linear ELD problems [20].

A study conducted by Kim et al. [21] presented a memetic scheme that combines a metaheuristic algorithm and a gradient-based technique to solve a benchmark problem of 40 generating-unit ELD with valve-point loading. The memetic approach outperformed other approaches in the literature, including metaheuristic-only and gradient-based-only approaches. The study also discovered that the memetic approach can be mutually beneficial in achieving better solutions than either metaheuristic or gradient-based solutions alone. The proposed method can be used to improve the simulation results of existing ELD and other optimization approaches.

In hybrid algorithms, two or more algorithms are used to exploit the strength of multiple algorithms and overcome individual weaknesses [22]. When combined, GA’s global search and GSA’s local search capability make it a perfect candidate for solving ELD problems [22]. However, the disadvantage of these hybrid methods is extended computational time. Therefore, there is a tradeoff between computation time and optimal result.

Table 1. Pros and cons of different optimization algorithms.

Refs	Optimization Algorithm	Survey	Research	Pros	Cons
[23,24]	PSO	√		▪ Easy to implement ▪ Well suited for fuel cost minimization	▪ Local searching capacity is weak ▪ Low convergence rate
[25]	ACO	√		▪ Guaranteed convergence ▪ Distributed computation helps to avoid premature convergence	▪ Slow convergence time ▪ Coding is difficult
[26,27]	GA	√		▪ Can deal with multiple local minima ▪ Handling capacity for non-smooth objective function ▪ Can deal with noisy and stochastic objective functions	▪ Slow CPU time for convergence
[28]	Simulated Annealing		√	▪ Coding is easy ▪ Can deal with nonlinear models ▪ Can provide optimal and robust solution	▪ Numerous hyper parameters need to be tuned ▪ Tradeoff between quality of the result and the time required to run the algorithm
[29]	Linear Programming		√	▪ Easy to understand and implement ▪ Adaptive in nature	▪ Cannot solve problem with multiple variables ▪ Unable to solve non-linear functions
[30]	DE		√	▪ Performs quite well with piecewise quadratic functions compared to other classical methods	▪ Combinatorial optimizations are not suited for DE
[31,32]	ABC		√	▪ Suitable candidate for non-smooth and non-convex ELD problems	▪ Comparatively slower rate in sequential processing
[33,34,35]	GWO		√	▪ Performs better even for non-convex objective functions	▪ Sometimes stuck in the local optima ▪ Convergence speed is slow
[36,37]	Jaya		√	▪ Great global exploration and searching capability ▪ Hyperparameter tuning not needed	▪ Researchers are still in the process of improvising the algorithm using hybridization and integration
[38]	Rao-1, Rao-2, MRao-2		√	▪ MRao-2 works on any scale of renewable integration	▪ The initial values of the decision variables have a significant impact on the performance of the Rao-1, Rao-2, and MRao-2 algorithms. The algorithms may not reach the ideal answer if the beginning values are not carefully chosen
[39,40]	SMO		√	▪ Global search capability ▪ State-of-the-art exploration and exploitation phase	▪ Supremacy in terms of GA and PSO yet to be found
[41,42,43]	MFO		√	▪ Faster convergence ▪ provides a large-scale search space	▪ Scope for further development
[44,45,46]	PSO-ACO		√	▪ Faster convergence ▪ Cost-effective and loss saving	▪ Further scope for improvement

illustrates the pros and cons of some of the recent and prominent algorithms used in economic load dispatch.

The algorithms discussed previously can be classified into two categories: deterministic algorithms and stochastic algorithms. Deterministic algorithms are characterized by their predictable and consistent behavior, as they produce the same output and follow the same process for a given input, regardless of the number of times they are executed. There is no random element involved in the output or process of a deterministic algorithm, as it is entirely determined by the input. On the other hand, stochastic algorithms involve a certain degree of randomness and are commonly used to approximate solutions to complex or large optimization problems. Evolutionary algorithms and metaheuristic algorithms fall under the category of stochastic algorithms. To determine a global optimal solution, deterministic algorithms such as Gradient-based techniques, Newton–Raphson, and Particle Swarm Optimization (PSO) have been extensively used. On the other hand, stochastic algorithms such as Simulated Annealing (SA), Genetic Algorithm (GA), Differential Evolution (DE), Jaya, and others have been used to move beyond the limitations of deterministic algorithms and achieve a solution that is close to ideal. Fuzzy logic, artificial neural networks, and multi-objective optimization have all been added to these algorithms to increase their functionality and make them better suited for use with real-world ELD issues. A comprehensive comparison between these two methods is presented in tabular format below in

Table 2. Deterministic vs Stochastic Methods [23,24,25,26,27,44,45,46].

Deterministic Methods	Stochastic Methods
Deterministic methods employ mathematical models to determine the best solution to the ELD problem.	Stochastic approaches use probabilistic models and algorithms to find the solution.
These methods offer a one-of-a-kind solution to the problem.	These methods offer a variety of potential solutions to the problem, allowing for more exploration of the solution space.
The solution obtained by these methods is deterministic and does not change when the algorithm is run multiple times.	These methods produce random solutions that change with each run of the algorithm, resulting in better results in optimization problems with complex, non-linear objectives.
These methods are computationally fast, but they can become stuck in local optima, resulting in suboptimal solutions.	These methods are slower in terms of computation, but they are better at escaping local optima and converge to near-optimal solutions for complex, large-scale problems.
Although deterministic methods are more precise, they may not always find the best solution to complex problems.	Stochastic methods are less precise but more robust and flexible in solving complex problems.

.

4. Recent Progress on Power Dispatch with PV

The last decade has seen an enormous improvement in integrating RES into the power system dispatch to reduce carbon footprint. Researchers are shifting their focus to optimally schedule thermal as well as PV generations to meet the power demand [46].

RES installation, including PV, is quite typical and available compared to other conventional power plants with a lower loss in transmission. However, the problem lies on the other side of the coin. In terms of regulated power generation, demand PV and other renewable sources are still not the right choices [47]. Another drawback is its high capital upfront investment cost [48].

In [49], researchers developed a comparatively new nature-inspired algorithm called the manta ray foraging algorithm (MRFO) applied on a microgrid to solve the Combined Economic and Emission Dispatch (CEED) problem. Results suggest that this algorithm has a prospect in solving CEED problems as it outperformed the results illustrated with other optimization models in the recent literature. It was concluded that MRFO provides better results than CSA, PSO, ABC, and DE.

In [50], researchers proposed a hybrid bat-crow algorithm on ten thermal generators and PV power plants to optimize the generation cost. On top of proposing this hybrid algorithm, the researchers also tested the solar plants ON and OFF conditions to develop a better approximation for the multi-area power network. From the simulation results, it was concluded that this hybrid algorithm was better performing than that of the PSO, bat algorithm, and crow search algorithm.

In [51], the authors tested the efficacy of the PSO optimization algorithm for solving CEED problems with three thermal and ten solar generating units. Test cases were observed for both with and without solar PV. Before implementation, this technique was validated with other optimization techniques to test its suitability. In the later part of this paper, the authors conducted a comparative analysis using the TLBO algorithm for solar thermal scheduling. In [52], the researchers suggested a new perspective in solving economic load dispatch for microgrids by combining binary PSO algorithm and Quadratic programming called BPSO-QP. The authors considered KKT conditions for optimal sizing of the battery energy storage system (BESS) and optimal scheduling of generators using BPSO-QP. The usefulness of this algorithm was verified through several experiments and simulations. Researchers further developed the application of another algorithm called the Flower pollination algorithm to solve the multi-constraint nonlinear optimization with 15 generating units. It performs better in terms of convergence speed, economy, and robustness. Experimental results show its efficacy and suitability compared to the other heuristic algorithms such as PSO, SCA, and WOA [53].

In [54], the authors implemented NSGA-II and RNSGA-II on six generator units with a load demand of 283.4 MW with 5% power loss. They validated the performance of GA, NSGA-II, and R-NSGA-II for loss and without loss conditions. It was concluded that NSGA-II and RNSGA-II are better than PSO as it implies intelligent Pareto optimization for multi-objective criteria.

However, not much research has yet been conducted using metaphor-less algorithms on ELD to check its efficacy. In [34], the authors implemented Rao-1,2,3 algorithms on test systems with 6, 40, and 110 units, respectively. Comparative results show that this metaphor-less algorithm performs quite well in terms of other algorithms used on these unit systems earlier. In [55], the authors implemented an adaptive Jaya Optimization algorithm for solving ELD with thermal, solar, and wind power. A 24-hour total demand was introduced for optimal scheduling. Furthermore, in [56], the researchers proposed an improved version of Jaya (IJaya) to solve ELD problems with multi-fuel and valve point constraints. This newly proposed algorithm performs even better in terms of convergence and optimal global solution due to its distance-varying acceleration coefficient and Gaussian Cauchy Mutation (GCM). The superiority of this algorithm was proved using 6, 10, 13, 15, and 40 generating units.

In [57], in one of the segments of their review, the authors suggested a CMOPEO method to optimize the hybrid system, including thermal, solar, and wind power. On top of equality and inequality constraints, the researchers also introduced a security constraint in their work.

Due to the reliability and classical nature of the PSO algorithm, researchers often try to adhere to this algorithm or its variant. A research team from China improvised the PSO algorithm, which they called improved symbiotic particle swarm optimization. (ICPSO). There are three swarms allocated for this improved PSO. Swarm-1 and Swarm-2 are used for iteration optimization. Swarm-3 used the position information to self-update the position. Simulation on benchmark test cases proves the superiority of the ISPSO compared to PSO [58]. In [59], the authors proposed a new hybrid PSO-SSA optimization algorithm to solve ELD problems for large-scale plants efficiently. Large-scale ELD suffers from converging prematurely to the local minima. This proposed method uses the levy flight to differentiate those local minima and convert towards the global optima. The proposed algorithm performs relatively well for large datasets. Furthermore, in [60], the authors combined two algorithms to solve ELD problems. Hybrid GWO-PSO is implemented on three- and six-generator systems which perform better than GWO and some other benchmark algorithms. One of the significant advantages of this optimization algorithm is its simplicity of application and faster convergence rate.

Table 3. Summary of recent economic load dispatch with renewables.

Reference	Type of Paper	Methods	Test Unit			Optimization Objective			Constraints
			Thermal	Solar	Wind	Cost	Emission	CEED
[57]	Research	MRFO	$\surd$	$\surd$	$\surd$	$\surd$		$\surd$	I and E
[58]	Research	Hybrid Bat-Crow	$\surd$	$\surd$				$\surd$	I and E
[59]	Research	PSO	$\surd$	$\surd$				$\surd$	I and E
[60]	Research	BPSO-QP	$\surd$			$\surd$			I and E
[61]	Research	EPFA	$\surd$			$\surd$			I
[62]	Research	NSGA-II and RNSGA-II	$\surd$			$\surd$	$\surd$		I
[44]	Research	Rao-1,2,3	$\surd$			$\surd$			I and E
[63]	Review	CMOPEO	$\surd$	$\surd$	$\surd$			$\surd$	I, E and S
[64]	Research	ISPSO	$\surd$			$\surd$			I
[65]	Research	PSO-SSA	$\surd$			$\surd$			I
[66]	Research	GWO-PSO	$\surd$			$\surd$			I
[67]	Research	IJAYA	$\surd$	$\surd$	$\surd$	$\surd$			I and E
[61]	Research	SSA	$\surd$	$\surd$		$\surd$			I and E
[62]	Research	Firefly	$\surd$	$\surd$		$\surd$		$\surd$	I and E
[36]	Research	MP-CJAYA	$\surd$			$\surd$			I and E
[67]	Research	JAYA-TLBO	$\surd$			$\surd$			I and E

Where I = Inequality Constraints; E = Equality Constraints; S = Security Constraints.

summarizes some of the recent algorithms used for economic load dispatch.

5. Current Practices in ELD

5.1. Large-Scale PV System Integration

Besides intermittency of power production, another critical problem in PV is its shading effect due to the moving clouds [56]. This causes significant complications in grid-connected solar PV plants’ power production. Researchers are continuously trying to develop solutions to combat this sudden change in PV power production due to the shading effect. Some of the commonly used techniques to combat this problem are listed below.

• Automatic Generation Control;
• Scheduling considering unit commitments;
• Regulation of Generation;
• Emphasis on the combined cycle generation where the response time of turning the units on and off is quite shorter.

Some of the significant challenges for combatting the sudden change in the generation are illustrated below in Figure 3.

Due to cloud cover and weather factors, large-scale PV transmission and sub-transmissions are not severely affected in contrast to the distribution system, where the output of the PV can drastically reduce to 50% in some instances [63].

A study conducted by the US Department of Energy determined that considering the diversity factor can minimize the short-term variability of output from the PV power plant. The diversity factor also contributes to minimizing costs and compensating for the variability. Some of the cost factors that are directly associated with the reliance on the factors illustrated in Figure 4.

Different studies suggest that the economic benefit decreases with the increase in the penetration of renewables due to the need for additional spinning reserves [64]. Geographic diversity can play an essential role in combating the variability of a single solar plant. Geographic diversity contributes to fewer balancing resources and reserves [65]. Researchers continuously focus on battery storage to make large-scale PV production and storage more efficient [66]. Fluctuating power output from the PV firms can be solved using a battery energy storage system (BESS) [68].

Different compensating techniques, such as ramp rate control using the inverter, limit the PV output fluctuations. This setup uses a compensated power output from the inverter to keep the output power constant. The equation can be written as follows [69]:

$$P_{inverter}={\mu }_{inverter}\left(P_{DC}+P_{compensator}\right),$$

where ${\mu }_{inverter}$ is the efficiency of the of the inverter. Power output from the inverter can be kept constant by controlling the $P_{DC} and P_{compensator}$. $P_{compensator}$ output power is raised whenever there is a sudden drop in power in the $P_{DC}$ due to the sudden cloud cover. Different converters can play an important role balancing the level of voltage and thus maintaining a desired power level [70]. Another way of compensating the power output from the inverter is to try out a conventional PID controller [71]. For improving the efficiency of the inverter, different combinations of buck and boost converter can be used [72].

In [73], the researchers suggested that to obtain the best benefit from a PV-battery system, demand side management, proper forecasting, and energy optimization are the prime factors.

Apart from load following dispatch, demand dispatch is becoming popular recently due to the wide-scale adoption of the internet and the internet of things. This method exploits the advantage of the internet to turn different loads on and off and adjusts different generator outputs [74].

Hybrid hydropower plants are becoming more popular in recent times. Longyangxia hydro-PV plant has a capacity of 2130 MW, out of which 850 MW accounts for solar PV. Researchers are trying to model and incorporate PV in this hybrid system efficiently. Hydropower units can be swiftly changed to compensate for the unpredictability of solar power [75].

5.2. Grid Code and Large-Scale PV System

Due to its variable and intermittent nature, there are numerous challenges in integrating large-scale PV into the grid [76]. Grid codes pave the way to successfully integrate large-scale PV into the grid considering the formulations already provided by the researchers. Some of the critical features for grid code in the future are listed below [77]:

• Size of the system;
• Voltage and current levels;
• Transmission and distribution;
• Characteristics of the generating units;
• Energy policy.

5.3. Economic Feasibility of Large-Scale Photo Voltaic Systems

Though solar cell technology has seen a drastic improvement recently, research gaps still need to be addressed, such as emerging solar cell technologies for high solar PV penetration. Solar irradiation and power forecasting are crucial for successfully operating solar EES systems. As there are still issues with grid instability and inertia, an improved energy storage system for PV integration can solve this issue. Revaluation of the grid structure is needed to make RES integration economically feasible in the future [78,79].

AGC is a type of control system used to keep the demand for and supply of electrical energy in a power system in balance. To adapt to shifting power demand, AGC continuously modifies the generator power output. AGC can be used to maintain the equilibrium between the power generation from conventional sources and the power generation from renewable sources, which are often more variable in nature, in a power system with renewables. Integrating large-scale PV faces significant complications such as varying impacts. It was determined in recent research that large-scale PV integration still lacks a proper control mechanism to control the varying loads promptly. The spinning reserve and AGC mechanism can be used to adjust the output power to meet the load demand [80].

In hybrid hydropower systems, faster ramping rates and availability of hydro play an essential role in a higher level of PV penetration [81,82].

5.4. Economic Dispatch of Large-Scale Solar PV System

Economic load dispatch is the process of allocating generation mix in the cheapest manner [78]. Commonly used ELD dispatch categories are

• Optimal Power Flow (OPF);
• AGC;
• Dynamic Economic Dispatch;
• Economic Dispatch with RES.

Economic dispatch with RES usually includes solar, wind, hydro, and a battery system for backup. Conventional AGC mechanisms cannot handle the spinning reserve constraints, load following requirements, and load frequency excursion, causing problems with the system stability [83,84].

Dynamic economic dispatch is provided as a solution to operational issues. An efficient solar power generation forecast is created ahead of each dispatch cycle using this method. High load generation balance is achieved using chain rule-based hydro, PV, turbine generation, and import [80].

One of the significant challenges of large-scale PV integration is the rescheduling or the displacement of conventional generators to operate the system efficiently. One research study at the U.S Western Electricity Coordinating Council (WECC) proposed an optimal dispatch ratio (ODR) for reliable and uninterruptible power system operation [85].

As output power from PV generation changes drastically due to the varying solar irradiation and other weather factors, power generation and production from PV vary significantly. To combat these problems, a probabilistic power flow model working on the conventional dispatching units can balance high PV power generation. This method solves fluctuations in voltage and frequency using a corrective measure [86].

Inverters play a crucial role in grid support regarding voltage and frequency regulation. Researchers suggested grid-friendly PV plants incorporating components such as SCADA HMI, DAS, PLC, and RTU. These interfaces and networks transmit inverter commands to the inverter unit. These functions perform automatic voltage control, reactive power injection, active power reduction, and frequency control [87].

In [88], the researchers illustrated the practical implementation of active power curtailment and reactive power injection for making the grid-connected large PV plants more effective. The distribution network’s local voltage regulation is achieved through the RPI-APC algorithm.

In [89,90], the authors pointed out some significant problems of PV integration, such as voltage fluctuations due to the fluctuations in solar radiation. Sudden tripping of the system due to the under-voltage capacity relays reduces the system’s overall generation. These problems can be overcome using a unity power factor and automatic voltage control (AVC). However, this system also has limitations. It only works well with the kilowatt size generators, not with the megawatt size generators.

6. Challenges and Technical Solution

6.1. Overview of the Technical Solution

There are two major techniques to generation dispatch when integrating large-scale PV: generation dispatch and economic dispatch. The techno-economic feasibility of large-scale PV integration is also investigated in order to arrive at a viable and feasible solution. The entire transmission performance is observed by examining the transmission systems’ load flow and other characteristics. The literature review suggests that some significant challenges in large-scale PV integration are uncertainty, variability, and system adequacy. Various techniques such as spinning reserve requirement, generation scheduling, power prediction of the solar plant, proper dispatch strategy, and different aspects of the transmission system are discussed to combat these challenges.

6.2. Spinning Reserve Requirement for Generation Dispatch

Various scheduling techniques are used to satisfy the generation and load demand. The role of operating reserve comes into play when the power generation differs from the load demand.

Some of the major causes of imbalance in power system are:

• Sudden loss in transmission line;
• Change in load demand;
• Change in power generation from PV panel due to the cloud cover.

Usually, the better the PV integration, the more operating reserves are needed, but due to different technicalities, it is difficult to assess the type and amount of operating reserve. Figure 5 classifies different operating reserves.

6.2.1. Regulating Reserve

Regulating reserve, often known as automatic generation control, is used to automatically balance the continuous and frequent changes in the demand and generation side [93]. This method can rectify the variations in the shortest possible time ranging from 5 min to an hour.

The objective of this method is to reduce the area control error. Solar forecast cannot still provide accurate forecasts due the intermittent nature of the solar. As more and more large-scale solar plants become integrated into the electricity grid, regulating reserves are play an even bigger role in the present.

6.2.2. Load following Reserve

Load-following reserves are almost similar to the regulating reserve, but the main difference is that they correct the anticipated changes in the load rather than the imbalance occurring instantaneously [94].

In most of the cases, automatic generation control is not required. Power grids are primarily directed by the system operator and engineers manually. In today’s world, power grids do not explicitly use load-following reserves as the loads are becoming reasonably predictable. However, due to the intermittent nature of the solar and the need for accurate solar power generation forecast for the longer time horizon, load following reserves may become good candidates soon.

6.2.3. Contingency Reserves

Contingency reserves are often called spinning reserves. Spinning reserves play a vital role in stabilizing the power system’s frequency due to the imbalance in load caused by sudden variations. Usually, solar power generation is not instantaneous, and thus it does not affect the contingency reserves. Spinning reserves can be split into primary, secondary, and tertiary.

6.3. Generation Scheduling with PV

The scheduling of generating units is determined by a number of actions, including the unit’s commitment, and other factors. Unit commitment is the scheduling of sufficient generating units to meet load demand while taking into account fuel costs, environmental costs, and other optimization parameters that are constrained. Economic load dispatch is dependent on unit commitment because the available generating units and their operating characteristics, such as their fuel cost, ramp-up and ramp-down rates, and minimum and maximum output levels, determine the feasible space for economic load dispatch. In other words, the economic load dispatch problem presupposes that the available generating units have already been determined via the unit commitment process.

If some generating units are not available because they have been turned off or are undergoing maintenance, for example, then their capacity is not available for use in the economic load dispatch problem, and the remaining units must make up for the shortfall. On the other hand, if some units are not yet running at full capacity because they are ramping up or ramping down, then the economic load dispatch problem must consider these constraints as well [95].

Any generation plant with integrated PV needs to have proper generation planning to efficiently deal with the loss of generation from the PV due to cloud cover and other weather factors. A mechanism should be in place to help balance the generation and load balance.

The forecasting mechanism should be as precise as possible to maintain this balance. Accurate measurement is needed to determine the load, water, solar irradiation, and wind speed. For thermal and solar power facilities, scheduling should be addressed seriously from an economic standpoint.

6.4. Solar Plant’s Power Prediction

Different literatures consider different kinds of time horizon prediction modeling for the dispatch. The most commonly used horizons are hourly, daily, weekly, monthly, and yearly predictions [96]. The prediction category can be classified into three major categories based on the time horizon: very short-term, short-term, and long-term or medium-term [96]. An algorithm based on AI can be leveraged to forecast solar power output [97].

Table 4. Summary of different forecasting methods used for solar power prediction.

	Very Short Term	Short Term	Long Term or Medium Term
Time horizon	5 min to 6 h	Up to 3 days	Up to number of months or years
Models Used	ANN,SVR,ARMA,ARIMA.LSTM	GFS,ECMWF,LSTM	Statistical models with processed data

summarizes various forecasting methods utilized for predicting solar power.

6.5. Generation Units’ Dispatch Selection

The prime objective of the generation dispatch in the power system is to minimize the cost of operation and fuel in USD/hour. Modern system operators continuously shift their focus from conventional thermal plants to non-conventional and green energy to reduce the optimal generation cost. However, the main problem lies in the substitution cost. The substitution cost for solar PV with the thermal unit is often relatively high. It is believed to be equivalent to the thermal generation unit’s avoided generation cost. This is due to renewable energy’s intermittency and forecasting complexity [98]. Figure 6 shows that it may be costly to completely replace a thermal plant with a solar or wind facility. But integrating it with the right mechanisms can make it affordable.

6.6. Operating Limits of Generator

Proper dispatching of the power system depends on the generation limits of the generators. Each generator has their upper and lower limits. Apart from the upper and lower limits, prohibited operating limit and spinning reserve limits are also important in effective dispatch of the power systems. Full power system consists of four major parts: generation, transmission, substation, distribution. Schematic diagram of the full system is depicted below in Figure 7.

6.7. Planning for Short Term Dispatch of Power System

In a power system, a process known as short-term generating dispatch determines the amount of electricity that will be produced the following day. Two crucial monitoring steps must be performed to ensure proper functionality, as shown in Figure 8.

For conducting the dispatch planning for a day, researchers have implemented real-time optimal power flow, often known as RT-OPF [99]. In this method, generators balance the load and generation according to their participation factor, which instantaneously balances the load and generation. This can be called a dynamic economic load dispatch based on participation factors. Different monitoring aspects for real-time dispatch are described below.

6.7.1. Monitoring of Load, Tie Line and Generation

For smooth generation dispatch, tie-line imports and exports must be monitored promptly. Monitoring promptly and implementing automatic generation control (AGC) to keep the frequency at 50 Hz all the time is an integral part of generation dispatch [100,101]. Schedule of hourly dispatch also needs to be monitored and looked upon timely to take necessary steps for optimal dispatch.

6.7.2. Transmission Line Flow Monitoring

As transmission systems and lines play a vital role in power dispatch, continuous monitoring of the transmission equipment and its parameters in terms of voltage, frequency, and rotor angle is crucial, as well as their ranges and limits [102]. Major monitoring parameters of transmission system is illustrated in Figure 9.

Transmission Voltage Stability

One significant problem with the large-scale PV plant is the voltage stability problem [103]. Often, voltage instability occurs due to the insufficient compensation of reactive power [104]. Keeping PV power plants provides better voltage stability compared to concentrated power plants [105].

Studies have reported that the integration mode voltage control strategies provide better results in terms of voltage stability and loading margin. On the other hand, power-factor-operated PV is slightly less effective in terms of those two parameters. Dynamic VAR devices are often used to improve system loading. Commonly used VAR devices are SVC and STATCOM. It has been discovered that STATCOM with short-term VAR, is more successful than placing STATCOM at the PV generator bus and the weakest bus for resolving the low voltage ride-through issue [98]. STATCOM improves the voltage stability margin. Researchers suggest placing SVCs at PV generator buses rather than placing them based on the short-term dynamic VAR support or placing them at the weakest bus [106,107].

Both active and reactive power contributes to the voltage drop in the transmission line due to the bifurcation with limits. Reactive power compensation units should be placed in a dispersed setup rather than a concentrated one to attain a better loading margin [108].

As suggested by researchers, shunt capacitor can be used to control static voltage stability and hence improve the voltage profile of the transmission system. The tap changer and PSS can improve the overall dynamic voltage stability on the controller using a capacitor. However, precaution should be taken regarding selecting the capacitor because a more significant value of the capacitance may cause oscillations, decreasing the transmission voltage stability. The parameter optimization method can play a vital role in reducing the oscillations and increasing the dynamic voltage stability [109].

Rotor Angle Stability of the Transmission System

One of the significant drawbacks of large-scale solar PV integration is the incapability of providing inertia. This is because there are no rotational masses in the PV generation system such as the conventional units. Inertial response directly influences the frequency change rate in the event of sudden load change. Researchers have conducted numerous researches on the rotor angle stability of the large-scale PV integration [110,111].

Transmission System Frequency Stability

Due to an imbalance between the load and generation, there can be an under-frequency load shedding. Load shedding occurs when the system frequency drops below the desired frequency level. By using economic load dispatch on microgrids with RES, BESS, and conventional generation schemes, switches were controlled considering the critical and non-critical loads in this study.

6.8. Factors for Effective Economic Dispatch

Dispatching mainly depends on the proper establishment of the infrastructure of renewable energy projects. A detailed study is conducted in [112,113,114,115]. Factors of effective economic load dispatch vary largely depending on different factors ranging from generation resources to geographic location of the plants and transmission resources [116]. Figure 10 illustrates some of the main factors that affect the economic load dispatch process, such as generation resources, geographic area, and transmission resources.

6.8.1. Generation Resources

Various interconnected generation resources are considered for effective planning and implementation of economic load dispatch. An optimally wide range of generation resources is considered to meet the demand and generation. In [117,118], the researchers proposed a model for flexible power dispatching incorporating wind, solar, thermal, and electric vehicles. Thermal power plants work on a flexible mechanism to trade off the intermittent power from the renewable sources.

6.8.2. Geographic Area

Depending on the size of the geographical area, economic dispatch can be classified mainly into two categories, single-area economic dispatch (SAED) and multi-area load dispatch (MAED). Single-area load dispatch was a popular method almost a few decades ago. Nowadays, however, it has lost its popularity as in this scheme customers have the right to choose the supplier of electrical energy [119]. On the contrary, multi-area economic load dispatch [120] seeks to determine the most feasible transmission facilities and generation resources considering all the significant system constraints. Several techniques have been used in the past to solve MAED problems, such as Mixed Integer Linear Programming [121], JAYA-TLBO [67], ImCSO [122], GOA [123], TLBO [124].

In [125,126], it was shown that passing clouds negatively affect PV generation. PV generation should not be built in a smaller area as it can affect the PV generation negatively due to poor diversity factor.

6.8.3. Transmission Resources

Transmission resources play an essential role in power system economic load dispatch. Reliability and security issues in the transmission line play an important role in successfully transferring power to households. However, investing in the transmission system does not necessarily offset the total cost of fuel savings. A revised, newly proposed approach is presented for the power system load dispatch in [127]. Before implementing large-scale PV integration for economic load dispatch, security and reliability issues should be considered rigorously. Another study conducted by researchers in [128] suggests having a proper export mechanism for large-scale PV integration with scattered and fluctuating renewable sources where the consumption of electricity is relatively low to avoid overloading. In [129], the researchers proposed a re-dispatch technique for highly variable power plants with wind and solar power. This online generation scheme reduces the generation cost and the loadability of elements in the power system. This proposed method includes two power sensitivity factors: LODF and PTDF. This method can minimize the overload risk created by N-1 contingencies. Numerous works are available for the conventional electrical device optimal placements. However, in regard to solar DG generators, there still seems to be a gap that needs to be filled. In [130], the researchers previewed the existing works published over the last 60 years, located the gaps, and proposed a few techniques to bridge the gaps and passively increase transmission loss. To effectively and practically implement the current distribution network, the authors suggested four solutions that can be used.

• Introduction of new terminology from the DG site to the connection point;
• Considering the geographic data and distribution infrastructure;
• Proper evaluation of all the network points;
• The original structure of the distribution business market.

6.9. Solar Tracker

To deal with the intermittency of solar power, researchers suggested operating the arrays intentionally at the maximum power point. In [131], comprehensive comparative study on the different solar maximum power point techniques and algorithms is discussed. MPPT is a technique of extracting maximum power from the PV using the PV system P-V and I-V characteristics [132]. Electrical and mechanical tracking is widely used among the most used techniques to extract the maximum power from the PV [133].

Mechanical tracking system uses the single or double axis of the panel to change the orientation to extract the maximum power output [134]. Most of the tracking is conducted on a daily, monthly or weekly basis [135]. Active and passive trackers can be used to tracking the sunshine, but active trackers are mostly recommended by researchers as the increased efficiency of these trackers is as high as 29.37% compared to that of the passive trackers [136].

In [137], the authors reviewed numerous optimization techniques and algorithms, including particle swarm optimization, for determining the best parameters, cell and materials, tilt angle of the sun, and the system design.

New and improved tracking strategies have been proposed by the researchers in recent years which can be adopted to obtain the best PV power output from the solar plant. An elaborate design criteria for designing solar PV plant and optimizing the tracking trajectory is proposed in [137]. According to [138], MPPT techniques under partial shading conditions can be classified into four major categories. The first one comprises the newly proposed MPPT optimization algorithms, the second group comprises the hybrid algorithms, the third category consists of the new modelling approach and the final one focuses on the various converter topologies. Therefore, while designing a specific system, proper MPPT technique should be used to obtain the maximized PV output power.

6.10. Adequate Protection of Solar PV System

There are numerous challenges associated with the distributed generations (DG), especially in the case of solar PV. One of the major challenges lie in the field of fault detection and isolation. Proper protection and islanding techniques are discussed in [139,140]. A novel technique was proposed to make the system stable by providing proper fault current for system fault detection [141]. In [142], the study clearly demonstrated that effective integration of solar PV arrays with DFIG-based energy systems has the potential to significantly increase system fault ride through capabilities while also lowering equipment costs by eliminating the requirement for power inverters for solar PV units. This method can be used while planning and integrating solar PV systems.

6.11. Voltage Stability in Large-Scale PV Integrated Systems

Grid-tied PV generation often causes voltage instability due to the intermittency of the distributed PV generation system. Conventional FACTS techniques and devices such as static VAR compensator and static synchronous compensator are used. VAR compensator provides a fast-acting reactive power on high-voltage transmission lines. On the contrary, static synchronous compensator is a fast-acting device that can provide or absorb reactive power, and hence it plays a vital role in regulating the point of connection voltage to a power grid [143]. In [144], the researchers determined that large-scale PV integration SVC performs better than the STATCOM.

7. Discussion

This paper critically reviewed the recent advancements in the renewable integrated economic load dispatch problem, one of the significant challenges of modern power system operation. The outcome of the paper shows that interest in conducting research in this field is growing daily, resulting in numerous research articles. Previously, researchers used to rely on GA and PSO. However, in recent times, experts in the field are showing more interest in evolutionary algorithms for solving this problem which is evident from numerous recent research articles. Specifically, researchers are putting more emphasis on swarm-based algorithms due to their ample search space and convergence rate, as demonstrated in Table 1 and Table 2. In the swarm-based intelligent-based algorithm category, PSO has gained enormous popularity, which is evident from [42]. A simplified tabular comparison of mathematical optimization (classical method) and metaheuristics (non-conventional method) is presented in

Table 5. Comparison between the metaheuristics and mathematical optimization.

Criteria	Metaheuristics [145]	Mathematical Optimization [146]
Global optimality	No guarantee	Guaranteed
Complexity	High	Low
Convergence speed	Slow	Fast
Handling constraints	May require modification	Directly handled
Handling non-linearity	Good	Good
Handling discrete variables	Good	Not always efficient
Handling multi-modal problems	Good	Not always efficient

below for better understanding.

From the table, it is evident that metaheuristics which fall under the non-conventional method outperform mathematical optimizations in terms of handling nonlinearity, discrete variables, and multi-modal problems. One major problem of metaheuristics and non-conventional methods is the absence of guarantee of global optimality, mainly due to its hyperparameters. That is where parameter-less non-conventional algorithms and hybrid algorithms come into play.

However, recently, researchers have been exploring the feasibility of parameter-less and hybrid algorithms for power system optimization. Jaya, Rao, and different variants of this algorithms are performing exceptionally well in this aspect, which is evident from Table 3 and [147].

8. Recommendation

The economic load dispatch (ELD) problem is a critical aspect of power system operation that seeks to reduce power generation costs while meeting operational constraints. Because of the non-linearity and non-smoothness of cost functions, the ELD problem has become more complex in recent years with the integration of renewable energy sources (RES) such as photovoltaics (PV).

Classical methods for ELD, such as Newton’s method and quadratic programming, are widely used because they provide relatively fast convergence rates and cost-effective solutions. These methods, however, have limitations in dealing with non-convex and non-smooth problems, and they only generate one solution in a single run.

Complex ELD problems can be solved using unconventional methods such as the bat algorithm, genetic algorithm, ant colony optimization, particle swarm optimization, grey wolf optimization, and simulated annealing. Recent research has demonstrated that hybrid optimization techniques such as the memetic approach, cuckoo search algorithm with genetic algorithm (CSA-GA), hybrid Jaya and oppositional-based chaotic group search optimization (OCGOA) outperform traditional methods in solving non-linear ELD problems.

PV and other renewable sources are still not the best options for regulated power generation due to their variable nature and high capital investment costs, even though the integration of RES into the power grid has decreased carbon footprint and transmission losses. The best way to schedule thermal and PV generating to meet demand for energy has been the subject of recent research. This paper illustrated various technical solutions and the benefits of large-scale PV integration for economic load dispatch. The important approaches are generation dispatch and economic dispatch, and the literature review suggests that there are some significant challenges in large-scale PV integration, such as uncertainty, variability, and system adequacy. Through analysis and thorough observation, it can be said that various techniques such as spinning reserve requirement, generation scheduling, solar plant power prediction, proper dispatch strategy, various transmission system aspects, regulating reserve, load-following reserve, contingency reserves, generation scheduling, solar plant power prediction, and dispatch unit selection are among the solutions. These technical solutions aid in dealing with issues such as variability, uncertainty, and system adequacy.

The choice of algorithm for economic load dispatch with large-scale PV integration is determined by the problem’s complexity and nonlinearity. Classical methods are simple and straightforward to implement, but non-traditional and hybrid metaheuristic methods can handle more complex problems. There is, however, a trade-off between computation time and optimal outcome.

However, in metaheuristic algorithms, there are mainly two phases: the exploration phase and the exploitation phase. In other words, these phases can be called a global search and a local search. In the exploration phase, the swarms try to detect the global optimum solution, and candidates converge in the exploitation phase. One of the limitations of these algorithms is that they often tend to converge quickly and become stuck in the local optima. However, if it becomes stuck in the local optima, it cannot determine the best optimal solution globally. Metaheuristic algorithms do not guarantee finding the global optimum solution for a given optimization problem. They are used as an approximation method to determine good solutions, and not necessarily the best possible solutions.

Metaheuristics are a class of optimization algorithms that are used to determine approximate solutions to difficult problems that cannot be solved using traditional optimization methods. They are based on the idea of simulating natural processes, such as the behavior of animals, to determine good solutions. Because of this, they can often provide solutions that are close to the global optimum, but they may not always offer the exact global optimum.

Therefore, the global optimality of a solution depends on the specific algorithm, the problem, and the stopping criterion. Some metaheuristics methods might be more likely to produce the global optima than others, but it depends on many factors such as the problem structure and the parameter tuning. That is where parameter-less hybrid metaheuristic algorithm comes into play. Sometimes, due to many search spaces, design varies when multiple constraints such as generator limits, ramp rate limit, spinning reserve, and security constraints are put in place.

In such systems, hybrid parameter-less metaheuristics algorithms can overcome such challenges. Advantages of hybrid parameter-less algorithms are listed as below.

Compared to conventional optimization methods, hybrid metaheuristic algorithms for economic load dispatch provide a number of benefits. These consist of:

• Global search capability: Unlike traditional approaches, which are prone to becoming stuck in local minima, hybrid metaheuristic algorithms are able to traverse the whole search space.
• Flexibility: Hybrid metaheuristic algorithms can be quickly adjusted to add new constraints or objectives and can be easily adaptable to other sorts of economic load dispatch situations.
• Robustness: Large-scale, non-convex, and non-smooth optimization problems can be handled by hybrid metaheuristic algorithms.
• Solutions of high quality: Hybrid metaheuristic algorithms are capable of finding solutions of high quality with a high level of accuracy and precision.
• Efficiency: Hybrid metaheuristic algorithms are capable of solving complex problems quickly and are computationally efficient.
• Handling uncertainty: Hybrid metaheuristics can handle the system’s uncertainty, such as the output of the random generator, the speed of the wind, etc.

It is recommended to use parameter-less hybrid metaheuristic algorithms in such a scenario as they can manage ample search space, many design variables, parameters, and computational costs. Moreover, it will help to determine the best cost as it is not prone to becoming stuck in the local optima.

9. Conclusions

The contribution of this paper is divided into two parts. The first part presents a comprehensive review of various optimization techniques and recent algorithms for economic load dispatch, as well as combined economic load dispatch. For optimal generation, it is necessary to take into account both cost and emissions to achieve the best possible outcome. Based on the nature of the optimization problem, these techniques were classified into three major categories: conventional, metaheuristic, and hybrid. An in-depth table summarizing the advantages and disadvantages of prominent recent algorithms was included. When summarizing the strengths and weaknesses of these algorithms, various power constraints and integrated sources were also taken into account. Through close observation, it was determined that hybrid algorithms performed better for grid optimization through economic load dispatch with integrated renewable sources as they combine the merits of two or more algorithms to reach global optima faster and more efficiently. The latter half of the paper addresses the problems and solutions associated with integrating large-scale renewables into the existing power system. From a technical point of view, the grid integration discussed in the latter half of the paper highlights the fact that the operational problems of the power system are associated with major factors such as spinning and non-spinning reserve, unit commitment, and load following mechanisms. For large-scale PV integration, custom-made operational dispatch is necessary. Inverter technology for PV systems can play a significant role by injecting reactive power, controlling the ramp rate, and providing solutions to anti-islanding problems. The fluctuations in PV output power can be minimized by using BESS techniques along with inverters. Batteries connected in parallel with PV systems can compensate for power fluctuations through ramping rate limit control. In future work, researchers will investigate novel hybrid algorithms and further explore newly launched optimization modeling languages and constraint optimization tools to solve the economic load dispatch problem.