A Review of Research on Dynamic and Static Economic Dispatching of Hybrid Wind–Thermal Power Microgrids

Abstract

As fossil energy is increasingly depleted, promoting the integration of renewable energy into the grid and improving its utilization rate has become an irresistible development trend in China’s power industry. However, the volatility of wind power increases the difficulty of economic dispatch in power systems. With the rising participation of wind power in the system, the complexity of traditional microgrid dynamic scheduling problems has increased, transforming into a dynamic economic scheduling problem for wind power thermal power hybrid microgrids. Starting from the concept and research significance of economic dispatch, this article analyzes the current research status of microgrid economic dispatch as well as the impact and influencing factors of wind energy grid connection on it. It summarizes the research performed by scholars in two aspects: scheduling models and solving algorithms in static dispatch, as well as how to deal with wind power randomness in dynamic dispatch and how to balance environmental protection while ensuring economic maximization. Finally, the existing problems in current research were summarized and future development directions were prospected. This research has important application prospects in improving the economy of the system and protecting the ecological environment.

1. Introduction

Due to continuous population growth, economic development, and the improvement of living standards, people become more dependent on energy, especially fossil fuels, and non-renewable energy is increasingly being exhausted due to excessive exploitation [1,2]. Regarding non-renewable energy, while in the short term coal in the power supply of energy is difficult to change the important position, the position of thermal power generation is currently unbreakable. However, the progressive increase in power demand worsens the consumption of fossil energy, leading to a significant increase in the emission of air pollutants such as dust particles, carbon monoxide, and nitrogen oxides generated by energy combustion, which seriously affect the life and health of the people, and also leads to global environmental problems such as continuous global warming, a sharp rise in the number of haze days in local areas, acid rain, and photochemical smog pollution [3]. Safety, economy, and low pollution are the requests of countries in terms of power industry development in the current times. As for the pollutants produced by thermal power generation, people generally increase the use of renewable energy or improve thermal power generation technology to reduce pollution emissions. Renewable energy is clean and environmentally friendly. Its development and utilization processes do not increase pollutant emission and it is relatively easy to obtain renewable energy [4]. The wind energy resources on Earth are very abundant, and compared to traditional fossil fuels, wind power generation has a significant impact on improving the environment. Meanwhile, the microgrid system is a micropower system that integrates the power generation system, energy storage system, energy conversion system, and load monitoring and protection system, including the traditional thermal power generation and new energy power generation [5]. The existence of a microgrid system can reduce the disturbance of new energy to the power system and ensure the maximum economy and stability of the system [6].

As wind power accounts for an increasing proportion of installed capacity in microgrids, its impact on the economic dispatch of microgrids has attracted great attention. However, due to its stochastic variability, the power quality and stability of the microgrid face significant challenges. For example, when the wind is strong excess electricity is generated by wind power and it is necessary to store and dispatch the electricity to ensure that it is not wasted and meets the demand for electricity. When the wind is weak or absent, alternative energy sources such as thermal power are needed to ensure the stability of the microgrid’s power supply. Meanwhile, the models that need to be established are increasingly complex, and in the process of model solving, improving system reliability and reducing operating costs has become a conflicting issue. To achieve one aspect, sacrifices must be made in the other. Therefore, how to accurately and reasonably achieve economic dispatch in microgrids while ensuring safe and stable system operation and obtaining more economic benefits has become a difficult problem that scholars at home and abroad are constantly exploring.

This review will combine the advantages and characteristics of microgrid and economic dispatch, investigate the current situation of domestic and foreign dynamic and static economic dispatch of microgrids, as well as the research status of economic dispatch of wind energy grid connection at home and abroad. It will introduce and discuss the existing economic dispatch models and solutions, and discuss how to solve the problem of wind power fluctuation, and analyze the advantages and disadvantages. Finally, a comprehensive analysis and outlook is made on the problems and future research directions in the economic dispatch of wind–thermal power hybrid energy microgrid. The research results of this paper will help to deepen the understanding of the economic dispatch mechanism and implementation methods of wind power and thermal power hybrid microgrids, providing a scientific basis and reference for future research and practice in related fields. It can effectively improve the operational efficiency and economy of its power system, reduce its energy and operating costs, and enhance its market competitiveness.

This study can better address the uncertainty of microgrids after wind power grid integration can provide new solutions for the economic dispatch problem of new energy grid integration. This study has important application prospects in improving the economic efficiency of system operation and protecting the ecological environment.

2. The Significance of Wind Power Grid Connection

2.1. The Development of Thermal Power Generation

Among the proven reserves of non-renewable energy in China, coal reserves account for about 94% and the share of primary energy consumption accounted for by coal reached over 57% [7]. The carbon dioxide released by burning stored natural gas is much lower than coal, but at present, our dependency on natural gas externally is too high, up to 40% above, so the replacement of coal in the power supply energy by natural gas is not favorable to control the economic lifeline of our country [8]. Taking power supply as an example, at present the electric power capacity of coal in our country accounts for less than 50%, but electricity generated mainly by coal is close to 60% of the total electricity production capacity and supports more than 70% of peak load demand, so coal is still the main energy of the power supply of our country [9]. However, coal-fired power generation results in the emission of soot particles, sulfur dioxide, and nitrogen oxides of more than 3.8 million tons, 13.22 million tons, and 11.08 million tons, respectively, and the carbon emissions account for 44% of the total pollution emissions. There is still a big gap between the clean, efficient, and sustainable development goals proposed for the development of China’s electric power industry in the new era [10].

2.2. Development of Renewable Energy Power Generation

In recent years, China’s energy front has unswervingly promoted the energy revolution, built a diversified and clean energy supply system, given full credit to the role of scientific and technological innovation as the primary driving force, and made new strides in high-quality energy development. China’s energy consumption has continued to accelerate its clean and low-carbon transformation. Data show that since 2014, China has reduced energy consumption per unit of GDP by a cumulative 20%, supporting 6.2% national economic growth with an annual average energy consumption growth of about 2.9%. In the past decade, the proportion of coal consumption has decreased by about 10%, while the proportion of new energy consumption has increased by about 10%. The proportion of new energy consumption such as solar energy and wind energy is increasing, now accounting for more than half of the total energy consumption. By the end of 2022, data provided by China’s Energy Administration showed that China’s total installed power capacity from renewable energy sources reached 1.213 billion kW, accounting for 47.3 percent of the total, an increase of 2.5 percentage points over 2021. The specific installed capacity information of renewable energy in 2022 is shown in

Table 1. Information of the installed capacity of renewable energy.

Types of Energy	Installed Capacity (Gigawatts)	Proportion (%)	Newly Installed Capacity (Million kW)	Proportion (%)
Hydroelectric power Generation	4.13	16.1	2387	11.9
Wind power Generation	3.65	14.2	3763	18.8
Photovoltaic power	3.93	15.3	8741	43.7
biomass power generation Generation	0.41	1.6	334	1.67
total	12.13	47.3	15225	76.2

.

2.3. Development of Wind Power Generation

The earth is very rich in wind energy resources; compared to the allocation of disposable energy, wind power generation to improve the environment is very obvious. According to data released by the International Energy Agency (IEA) in 2021, the installed wind power capacity worldwide has exceeded 700 gigawatts, accounting for approximately 6% of the total installed capacity worldwide. In addition, in some countries and regions such as Denmark, Germany, Spain, etc., wind power has become one of the main sources of clean energy, with penetration rates even exceeding 30%. By the end of 2022, China will have installed 365 million kW of wind power, including 334 million kW of onshore wind power and 30.51 million kW of offshore wind power. In 2022, China added 48.8 million kW of wind power connected to the grid, including 43.6 million kW onshore and 5.2 million kW offshore. From the present information, the onshore wind power technology has tended to mature and the service market is close to full. The balance of newly installed wind power capacity will in the future be inclined to sea wind power, especially the far-reaching sea breeze power project, and there will be huge development potential due to our country’s continuous advancement. The regional distribution information of national wind power installed capacity in China is shown in

Table 2. Regional distribution of national wind power installed capacity.

Area	Installed Capacity (Gigawatts)	Proportion (%)	Newly Installed Capacity (Million kW)	Proportion (%)
Onshore wind power	3.34	91.5	4360	89.3
Offshore wind power	0.31	8.5	520	10.7
total	3.65	100	4880	100

.

2.4. Development of A Microgrid

A microgrid is a small-scale power system that consists of various energy resources and energy storage devices, as shown in Figure 1, which can operate independently or be interconnected with the main grid. Microgrids typically include various types of energy resources, such as renewable energy sources including solar PV, wind energy, biomass, and small hydro and conventional sources such as thermal power, gas, etc. Microgrids can autonomously adjust the distribution and utilization of energy based on actual conditions, thereby achieving more efficient energy utilization and lower carbon emissions. Microgrids can be classified into two types: independent and interconnected. Independent microgrids refer to microgrid systems that operate completely independently of the main grid and are typically used in remote areas, islands, battlefields, etc. Interconnected microgrids are those that are connected to the main grid and are typically used in urban areas, industrial parks, hospitals, schools, etc. They can achieve bidirectional power supply and energy exchange with the main grid.

According to the 2021 China Microgrid Development Report, microgrids in China are mainly distributed in the eastern, central, and southwestern regions. Among them, the scale of microgrids in the eastern region is the largest, accounting for more than 50%; the scale of microgrids in the central region is moderate, accounting for about 30%; and the scale of microgrids in the southwestern region is relatively small, accounting for less than 20%. The main application areas of microgrids in China include urban areas, industrial parks, rural areas, transportation, military, etc. Among them, urban areas and industrial parks are the main application areas, accounting for 35.5% and 26.7%, respectively. The rural microgrid is also developing rapidly, accounting for 15.3%. The microgrids in transportation and military fields account for 11.6% and 11.1%, respectively. The energy types of microgrids in China include solar PV, wind energy, gas, energy storage, etc. Among them, solar PV and wind energy are the main renewable energy sources in microgrids, accounting for about 44.5% and 26.9%, respectively. Gas and energy storage account for 18.3% and 10.3%, respectively. The development of microgrids in China presents the characteristics of uneven regional distribution, diverse application areas, interconnection type as the main type, and solar PV and wind energy as the main energy types. In the future, with the continuous promotion of policies and the continuous development of technology, the scale and application areas of microgrids in China will further expand and deepen.

3. Concept and Research Significance of Economic Dispatching

3.1. Concept of Economic Dispatching

The goal of the economic dispatch of microgrids is to rationalize the generation capacity of each generating unit in a power plant according to the load demand of users, while minimizing the system’s operating costs [11]. The basic idea of the economic dispatching problem of microgrids is to optimize the economic benefits of the system under the premise of power system technology and safety constraints by rationally dispatching and arranging the operation mode of power supply and fully meeting the load demand. The traditional economic dispatch problem is to determine the active output of each thermal power generation unit while meeting the power balance and unit power boundary so as to minimize the total fuel consumption (power generation cost). As the uncertainty of new energy outputs increases, the constraints of the system become more complex and uncertain. At present, the economic dispatching problem of microgrids is classified into two aspects: static economic dispatching and dynamic economic dispatching. Static economic dispatching refers to the rational distribution of generating unit outputs with the goal of minimizing cost under the condition that the system’s supply and needs balance is satisfied within a certain period of time. Unlike static economic dispatching, dynamic economic dispatching is equivalent to static economic dispatching in several time periods (mostly 1 h). Moreover, it is more complicated than static economic dispatching to minimize the system’s pollution emissions while considering the minimization of the system operation cost.

3.2. Research Significance and the Direction of Economic Dispatching

No matter the static economic dispatching or dynamic economic dispatching, there are many different limiting factors that need to be controlled reasonably in the generating process of the generator set, which is also a very complicated task. These factors include: the power demand changes of users, power loss of system transmission lines, valve point effect of generator set during operation, different power generation limits of each generator set, and power change limits of increasing or decreasing unit output in each period [12]. Improper consideration of these constraints will lead to potential increases in operating costs and pollution emissions during power distribution in microgrid systems, so it is critical that the power output of these generating sets is correctly allocated. Meanwhile, the indeterminacy of renewable energy output has brought challenges to the market pricing mechanism, and realizing the balanced distribution of benefits among market participants has become a critical issue that needs to be addressed.

In recent years, grid system operators have focused on researching and developing renewable energy, among which wind and solar energy are the most concerned. Although renewable energy has a positive impact on the environment, it is greatly affected by weather conditions and it is not easy to accurately predict its output power. Therefore, system operators are not mature enough in controlling technologies of new energy such as wind energy [13]. Therefore, new energy is usually used in combination with traditional energy (such as thermal power generation) to meet the balance between user demand and power supply. However, improper operation of thermal generating units will result in high operating costs and excessive pollution emissions. In addition, due to the volatility of the output of renewable energy (especially wind energy), the double uncertainty of power generation and demand has increased [14]. The decision-makers of the power sector should use optimal power dispatching to meet the balance between user demand and power supply of the system under the stochastic condition of wind power generation and further reduce the operating costs and emissions of the system. Moreover, when conducting dynamic economic dispatching, due to the dynamic characteristics of current load demand, it is necessary to dispatch the output of the generator set based on the changes of power demand. In order to achieve the above tasks, economic dispatching of microgrids including wind energy has become a key problem faced by system operators.

3.3. The Economic Dispatch Calculation Method

3.3.1. Calculation Methods and the Steps for Static Economic Dispatch

(1)

Determine the objective function. Usually, minimizing costs is used as the objective function or multiple indicators such as cost and emissions are considered simultaneously;

(2)

Establish a power system model. Establish a feasible mathematical model of the power system. This model typically includes load equations, unit generation equations, transmission loss equations, and constraint conditions;

(3)

Perform optimization solution. Substitute the objective function into the power system model and use mathematical optimization methods to obtain the optimal solution, which is to achieve economic dispatch;

3.3.2. Calculation Methods and the Steps for Dynamic Economic Dispatch

(1)

Predicting load and power output. For short-term dynamic economic scheduling, it is necessary to predict the load and power output for a period of time in the future. Time series analysis and other methods can be used for prediction;

(2)

Dynamic programming. Input the current state and prediction information in a future period of time into the dynamic programming model and obtain a group of optimal solutions by optimizing the decision of each time step, that is, to achieve dynamic economic scheduling;

(3)

Model predictive control. Using the predicted results of load and power output as inputs for dynamic economic scheduling, economic scheduling is achieved through two steps: prediction and control. Among them, prediction uses algorithms such as ARIMA and LSTM, while control uses optimization algorithms for decision making.

4. Current Status of Static Economic Dispatch Research on Wind–Thermal Power Hybrid Microgrids

The static economic dispatching problem of microgrids is an optimization problem that considers a sequence of equality constraints and inequality constraints and aims to minimize the system operation cost in the solving process [15]. Static economic dispatch mainly involves generator output dispatch, battery pack charging and discharging dispatch, power grid purchase and sales decision making, etc. When establishing the static economic dispatch model of microgrids, attention should be paid to the objective function of economic dispatch and the operational constraints of generator units. Currently, the economic dispatch objective function in the research is mostly based on the system operating cost, while the model has numerous constraints, such as basic power balance equality constraints, generator capacity constraints, slope constraints between different time periods, and prohibited operation area constraints [16]. The complexity of objective function and constraint conditions directly affects the difficulty of solving the static economic dispatching problem of microgrids. Therefore, this chapter mainly focuses on two aspects of economic dispatch models and solving methods.

4.1. Static Economic Scheduling Model

(1)

Objective function

Static economic dispatch refers to the optimal allocation of electricity resources through reasonable planning and scheduling within a certain period of time, including optimizing electricity production, adjusting electricity load, and allocating electricity reasonably. The economic dispatch model of microgrids directly affects the feasibility and rationality of microgrid operation plans and is the core content of microgrid economic dispatch research. The objective function of the basic static scheduling model in microgrids can be described as follows:

$$\min (F(P_i(t)))$$

(1)

$$F(P_i(t))=C_{grid}^t+{\displaystyle \sum _{i=1}^N(C_{fuel}(P_i(t))+C_{OM}(P_i(t)))}$$

(2)

$$C_{grid}^t=C_{ph}^t{P}_b^t-C_{se}^t{P}_s^t$$

(3)

$$C_{OM}(P_i(t))=K_{O\mathrm{M}}{\mathrm{P}}_i(t)$$

(4)

$$\begin{array}{l}{C}_{fuel}(P_i(t))=\\ \left\{\begin{array}{l}{C}_{nl}\times \frac{1}{LHV}\times \frac{P_i(t)}{{\eta }_i(t)},P_i(t)=P_{MT,i}(t),P_{FC,i}(t)\\ a_i+b_i{P}_i(t)+c_i{P}_i^2(t),P_i(t)=P_{DC,i}(t)\end{array}\right.\end{array}$$

(5)

where $F(P_i(t))$ is the total cost of the microgrid operation in period t and $P_i(t)$ is the output of controllable micropower sources in period t. The micropower sources here are generally micro gas turbines (MT), fuel cells (FC), and diesel generators (DG). $N$ is the total number of micropower supplies; and $C_{grid}^t$ is the cost of purchasing and selling electricity between the microgrid and the main grid during period t. $C_{ph}^t$ and $C_{se}^t$, respectively, represent the purchasing and selling prices of the microgrid during period t. $P_b^t$ and $P_s^t$, respectively, represent the purchasing and selling electricity of the microgrid during period $t$. $C_{OM}$ represents the operating and maintenance costs of each micropower source; $K_{O\mathrm{M}}$ is the operation and maintenance coefficient of the micropower supply; $C_{fuel}$ is the fuel cost of micropower sources; $C_{nl}$ is the price of natural gas; low calorific value of natural gas; $LHV$ is the low calorific value of natural gas; ${\eta }_i(t)$ is the power generation efficiency of the MT or FC; $a_i$ $b_i$ $c_i$ is the fuel factor of the first diesel generator.

In the establishment of a wind–thermal power hybrid microgrid static economic scheduling model, to make the static economic scheduling model closer to the actual operation of the system generator set, many constraints of the system generator are important factors that cannot be ignored, such as the power balance equation, generating capacity constraints, prohibited operation area constraints, and so on.

• Power balance equation constraint

The power balance equation constraint is of the utmost importance in microgrid system operation as it directly affects the system’s reliability. This constraint involves ensuring that the total output power of the thermal power unit and wind farm equals the sum of the microgrid system’s load and transmission loss. In mathematical terms, the power balance equation constraint can be expressed as the following function:

$${\displaystyle \sum _{i=1}^N{P}_i(t)}+{\displaystyle \sum _{j=1}^M{P}_{k,j}(t)+P_b^t-P_s^t=P_{boad}^t}$$

(6)

where k refers to the fan driven generator (WT). Due to the strong fluctuation and randomness of WT outputs, it is an uncontrollable micropower source that usually generates electricity according to actual weather conditions. $M$ refers to the number of WT units and $P_{boad}^t$ is the total electricity load demand during the time period $t$.

B.

Power generation capacity constraints

The generation capacity constraint refers to the total generation capacity of various generators in the microgrid which cannot exceed the load demand of the microgrid, that is, the total generation power cannot be greater than the total load power. In the process of the static economic dispatch of microgrids, it is necessary to optimize the output of each generator to meet the load demand of the microgrid while avoiding overcapacity or insufficient capacity. Therefore, for each generator, it is necessary to determine its maximum output power and its output power curve under different loads to meet the requirements of the generation capacity constraint.

$$P_i^{\min }\le P_i(t)\le P_i^{\max }$$

(7)

where $P_i^{\min }$ and $P_i^{\max }$ are the upper and lower limits of the output of the $i$-th generator set, respectively.

C.

Slope rate constraint

The change in power output of a generator set within a time interval is limited, that is, the increase in output power of the generator set cannot exceed the upper limit of the threshold and the decrease in output power cannot exceed the lower limit of the threshold because when the change in power output of the unit exceeds the upper and lower limit of the threshold, the boiler and combustion equipment in the unit will be damaged. The equation of the slope rate constraint is:

$$\left\{\begin{array}{l}{P}_{gi}-P_{gi}^0\le P_{gi}^{UR}\\ P_{gi}^0-P_{gi}\le P_{gi}^{DR}\end{array}\right.$$

(8)

where $P_{gi}$ represents the output power of the $i$-th generator unit; $P_{gi}^0$ represents the output power of the $i$-th generator set at the previous moment; $P_{gi}^{DR}$ represents the lower limit of the output power fluctuation of the $i$-th generator set; and $P_{gi}^{UR}$ represents the upper limit of the output power fluctuation of the $i$-th generator set.

D.

The constraint of prohibited operating zone of the unit

There are several prohibited operating zones on the cost curve of the generator unit which will cause the operation cost curve to have discontinuities. However, in consideration of the safe operation of the system generator unit, the introduction of the constraint of a prohibited operating zone is necessary. The function expression of the constraint of a prohibited operating zone is:

$$\left\{\begin{array}{l}{P}_{gi}^{\min }\le P_{gi}\le P_{gi,1}^l\\ P_{gi,j-1}^u\le P_{gi}\le P_{gi,j}^l\\ P_{gi,m}^u\le P_{gi}\le P_{gi}^{\max }\end{array}\right.$$

(9)

where $P_{gi}$ represents the output power of the i generator unit; m represents the number of prohibited operation areas of the generator unit, j = 2,3, …, m; $P_{gi}^{\max }$ and $P_{gi,m}^u$ are, respectively, the upper and lower limits of the output power of the $i$ thermal power unit of the microgrid system; $P_{gi,1}^l$ and $P_{gi,1}^u$ are the upper and lower limits of the $j$ prohibited operation areas of the $i$ generator unit.

Current research suggests that introducing constraint conditions into static economic dispatch models can make dispatch plans more compliant with the limitations and requirements of actual operations, thereby improving the dispatch and economic efficiency. However, the introduction of constraint conditions also brings new problems and challenges, such as the complexity of constraint conditions, computational efficiency issues, and the coordination between constraint conditions and economic objectives. Gaing et al. [17] took constraints such as the unit’s forbidden operation area, climbing rate limit, and unit output limit into the model and used an optimization algorithm to solve the model. However, the optimization ability, solving speed, and stability of this method need to be improved. Bulbul et al. [18] proposed a heuristic algorithm combining the krill swarm algorithm with the opposition learning method. This method mainly considers the forbidden operation constraint, ramp rate constraint, and transmission loss when solving economic load allocation. According to the data obtained from the two test systems, this method has achieved a slight cost improvement compared with the traditional method and the improvement ratio is 0.55% and 0.57%, respectively. Therefore, we know that this method does not play a great role in reducing the operating cost of the system. Chen et al. [19] proposed a two-stage strategy based on the artificial bee colony algorithm to handle the equality constraints in economic scheduling problems. In the first stage, two groups of bees were used to search for feasible solutions that satisfy the conditions and in the second stage, a new search strategy was introduced to make feasible solutions have dynamic boundaries. However, this method is not comprehensive enough in terms of the inequality constraint and has some limitations. Li et al. [20] put forward a new constraint mechanism for the economic scheduling problem with the valve point effect, which consists of a virtual generator set and power distribution scheme. A differential evolution algorithm was used to solve the economic scheduling problem and the effectiveness of the proposed method was verified on three different unit systems. To further research and improve the constraints in the static economic dispatch of wind–thermal hybrid microgrids, more studies are needed. For example, combining advanced optimization algorithms to model and solve the constraints in a more precise manner; designing reasonable economic objective functions to achieve coordination between the constraints and economic objectives; and considering practical operational restrictions and requirements to integrate theoretical research with practical applications and ensure the effective operation of static economic dispatch.

For the dispatch model in the solving process, simpler research mainly uses linear programming methods. Various parts of the microgrid are abstracted into mathematical models, and constraints such as the cost and power balance are added to the model. Then, the optimal solution is obtained through optimization. This type of model often uses linear programming methods to allocate and dispatch power in the microgrid to achieve goals such as minimizing costs or maximizing profits. This method is simple and intuitive but cannot handle nonlinear problems such as the variation of the generation cost of wind and thermal power with load.

As microgrids scale up and operating conditions become more complex, researchers have begun to introduce mixed-integer programming methods into static economic dispatch models of microgrids to better address nonlinear problems. Arun Kumar V et al. [21] used a mixed-integer nonlinear programming model in a hybrid generation system consisting of wind–solar units and fuel-based generators to minimize the operating cost of the system and to flatten the cost of electricity by 25% compared to other similar works. This method also considered discrete decision problems such as the start-up, shutdown, and switching of generator units but the difficulty and computational complexity of solving mixed-integer programming problems remain significant.

With the continuous development of computer technology and mathematical optimization algorithms, researchers have begun to explore models based on metaheuristic algorithms. These models use algorithms based on experience and rules to search and iterate through the solution space to find the optimal or near-optimal solution. These algorithms usually do not depend on specific mathematical models of the problem but attempt to simulate natural processes such as biological evolution, physical simulation, etc., to obtain optimized solutions. Compared to mixed integer programming methods, this approach is more flexible, faster, and better at handling complex constraints in practical situations, thus improving the feasibility and reliability of the model.

In recent years, with the development of machine learning technology, researchers have begun to explore the application of machine learning methods in the static economic dispatch model of microgrids. This approach can learn the rules and parameters of the model through a large amount of data which can better solve the nonlinear problems in microgrids. Meanwhile, machine learning methods can also be combined with metaheuristic algorithms to further improve the efficiency of the solution. Among them, deep learning models have attracted great attention due to their real-time decision making and continuous feedback correction features. The biggest advantage of deep learning models is their ability to learn autonomously from historical experience, adaptively learn scheduling strategies, and make real-time decisions, avoiding the complex modeling process and coping with higher uncertainty and complexity in a data-driven way. In recent years, more and more researchers have started to explore the use of deep learning models to solve static economic dispatch problems. For example, Fermín Rodríguez et al. [22] used long-short term memory (LSTM) neural network models and convolutional neural network (CNN) models to model and predict meteorological parameters such as temperature, radiation, and humidity and combined wind speed data with different machine learning algorithms after time–frequency domain decomposition to analyze the improvement in wind speed prediction accuracy under different algorithms. This method achieved good prediction results in two practical application scenarios in Germany and Spain, with prediction errors of 3.4% and 4.0%, respectively. This indicates that the method can provide more reliable and effective decision support for the control and scheduling of intelligent power grids.

Indeed, the economic dispatch model in microgrids is highly complex due to the presence of multiple types of energy resources, as well as the complex topology and energy interconnection characteristics of the microgrid. This requires researchers to balance the optimization performance and feasibility of the algorithms when building dispatch models in order to ensure both the practicality and feasibility of implementation.

4.2. Solution Method of Static Economic Scheduling

When solving the economic dispatch problem in microgrids, the model composed of multiple constraints of generating units and dispatch objective functions is complex, which is a multi-dimensional and non-differentiable optimization problem. It cannot be solved by human labor alone, so researchers use mathematical methods to solve this problem [11]. The traditional mathematical methods include the gradient method [23], quadratic programming method [24], linear programming method [25], Lagrange relaxation method [26], mixed integer programming method [27], etc. These methods can handle simple optimization problems and a small number of constraints, but as the number of generators and loads increases, the dimensions of the optimization problem and the types of constraints also increase. Traditional mathematical methods are no longer sufficient to meet the requirements of accuracy and convergence speed in solving these problems. With the development of science and technology, researchers have discovered the advantages of intelligent algorithms and gradually applied them to economic dispatch. Intelligent algorithms have played a crucial role in solving multidimensional and non-differentiable optimization problems due to their excellent solving accuracy and convergence speed [28]. Therefore, using intelligent algorithms or their improved algorithms to solve economic dispatch problems is a promising research direction. Researchers usually optimize the algorithm’s performance from two aspects: solving accuracy and convergence speed.

In terms of the solving accuracy aspect, compared to original statistical analysis methods, scholars prefer machine learning methods that have more accurate solutions. Selvakumar et al. [29] put forward a new particle swarm optimization algorithm which combined the cognitive behavior splitting method and local random search method with the traditional particle swarm optimization algorithm to make the algorithm more effective to explore the search space. A series of experiments have verified the effectiveness of this method in solving non-convex economic scheduling problems. However, the convergence rate of this method is not high. Pothiya et al. [30] adopted an improved tabu search algorithm for economic scheduling optimization which introduced initialization, adaptive search, multiple search, crossover, restart, etc., but the stability and convergence speed of this method were not ideal. Xiong et al. [31] proposed a hybrid algorithm based on gradient descent and meta-heuristic optimization. This algorithm combines the Shuffled Frog Leaping Algorithm and the traditional Back Propagation (BP) algorithm which is superior to the BP algorithm in terms of accuracy, stability, and efficiency, while retaining the advantage of the BP algorithm in quickly obtaining high-quality random initial parameters. However, the convergence speed and prediction performance of this method still need to be improved. Fermín Rodríguez et al. [32] proposed a mixed hourly prediction model which decomposes wind speed data in the time and frequency domain and combines it with different machine learning algorithms. It analyzed the degree of improvement in the accuracy of wind speed prediction in the next 1 h under different algorithms. This method has achieved good prediction results in two practical application scenarios in Germany and Spain, with prediction errors of 3.4% and 4.0%, respectively. This indicates that this method can more accurately predict the output range of wind power generation in the next hour, providing more reliable and effective decision support for the control and scheduling of smart grids. However, the combination of multiple technologies makes predictions more complex. The static economic dispatch problem of microgrids is relatively simple compared to dynamic problems, so it can usually achieve high solution accuracy.

In terms of the convergence rate, Nawaz et al. [33] proposed a Nelder–Mead algorithm with global constraints. Variance variable probability was applied to the method to optimize the economic load allocation problem which made the method have local and global search characteristics. Experimental comparisons were conducted on an IEEE 30-node testing system and the results showed that compared to traditional genetic algorithms this method achieved significant improvements in terms of both the total cost and convergence speed. The total cost was reduced from 2810 $/h to 2788 $/h and the convergence speed was reduced from 3.58 s to 1.09 s. The convergence speed of this algorithm is obviously improved, as is the accuracy, which can solve the network limited static and dynamic economic scheduling problems more efficiently and has high research value and application prospects. Xu et al. [34] proposed a new grey wolf optimization algorithm for economic load allocation problems with constraints such as slope rate restrictions and forbidden operation area constraints. The grey wolf algorithm was improved by introducing an independent local search strategy and a non-inferior solution neighborhood and the convergence speed and search capability of the algorithm were verified by arithmetic examples. Through numerical examples, it was verified that compared to other algorithms and methods, this method achieved lower economic scheduling costs and had a faster convergence speed. For the IEEE 30 node testing system, the cost improvement ratio of this method is 0.72%. For the IEEE 118 node testing system, the cost improvement ratio is 4.79%. However, the stability and solution accuracy of the method are not high. Guo et al. [35] proposed an accelerated distributed gradient algorithm; this method introduced a momentum term containing a customized acceleration gain into the local update and improved the convergence rate of the algorithm by giving the step size and acceleration gain. Different meta-heuristic algorithms have different effects in solving economic scheduling problems but it shows the superiority of meta-heuristic algorithms in this aspect.

The model and algorithms for static economic dispatch in wind power and thermal power hybrid microgrids are constantly improving: from traditional mathematical optimization models to heuristic algorithms to deep learning and artificial intelligence algorithms now, thus continuously improving the accuracy and robustness of the model. However, due to the interdependence of multiple energy sources such as wind power and thermal power in microgrids, the relationship between energy generation and consumption is quite complex. Therefore, in future models and algorithms, it is necessary to conduct in-depth research on their collaborative effects.

5. Current Status of Dynamic Economic Dispatch Research on Wind–Thermal Power Hybrid Microgrids

Dynamic economic dispatch refers to the process of dynamically adjusting the utilization of various resources during the operation of the power grid to achieve the optimal power grid operation goals, including reducing energy consumption, reducing costs, and improving efficiency. The difference between dynamic economic dispatch and static economic dispatch is that dynamic economic dispatch searches for the output power distribution solution of generator units during a 24-h dynamic process.

5.1. Dynamic Economic Scheduling Model and Algorithm

The basic dynamic economic dispatching model in the microgrid can be described as follows:

(1)

Objective function

$$\min (F(P_i(t)))$$

(10)

$$F(P_i(t))={\displaystyle \sum _{t=1}^T[C_{grid}^t+{\displaystyle \sum _{i=1}^N(C_{fuei}(P_i(t))+C_{OM}(P_i(t)))}]}$$

(11)

where $T$ is the total number of scheduling periods, generally taken to be 24, and $P_i(t)$ contained energy storage equipment, such as batteries. The other parameters are the same Formulas (1)–(5).

(2)

Constraint condition

The battery output is added to the equation constraint to become:

$${\displaystyle \sum _{i=1}^N{P}_i(t)}+{\displaystyle \sum _{j=1}^M{P}_{k,j}(t)+P_{BT}(t)+P_{ph}^t-P_{se}^t=P_{Load}^t}$$

(12)

where $P_{BT}(t)$ is the charging and discharging power of the battery in the t period, negative values indicate charge and positive values indicate discharge.

Furthermore, in addition to the constraints included in the first static economic scheduling, it should be added:

• Climbing constraint of controllable unit:

  $$R_i^d\le P_i(t)-P_i(t-1)\le R_i^u$$

  (13)

  where $R_i^d$ and $R_i^u$ are the upward and downward climbing rates of the generator set, respectively.
• Energy storage equipment operation constraints, here to the battery (BT) as the representative.

  $$\begin{array}{l}{P}_{BT}^{\min }\le P_{BT}(t)\le R_{BT}^{\max }\\ {\displaystyle \sum _{t=1}^T{P}_{BT}}(t)=0\\ W_{BT,\min }\le W_{injt}-{\displaystyle \sum _{t=1}^n{P}_{BT}(t)}\le W_{BT,\max },n=1,2,\cdots T\end{array}$$

  (14)

  where $P_{BT}^{\min }$ and $R_{BT}^{\max }$ are the minimum and maximum charging and discharging powers of the battery, respectively; $W_{BT,\min }$ and $W_{BT,\max }$ are the minimum and maximum stored energy of the battery, respectively; $W_{injt}$ is the initial energy storage of the battery.
• Considering the utilization rate of wind power, the grid-connected power and wind abandon power need to be met:

  $$P_t^w+P_t^{wc}\le {\mathrm{\Lambda }}_t^w$$

  (15)

  where ${\mathrm{\Lambda }}_t^w$ is the actual generating power (MW) of the wind farm, $P_t^{wc}$ is the wind abandon power (MW), and $P_t^w$ is the grid-connected power (MW) of the wind power generation.

For 24-h dynamic economic dispatch, the generator constraints are more complex compared to static economic dispatch. Therefore, in terms of scheduling models, a power system dispatch model based on the wind power prediction model can be established and the wind power prediction results can be incorporated into the dispatch model for system optimization dispatch. Prediction models can use machine learning methods to predict wind power for a future period of time based on factors such as historical wind speed and weather data to optimize the real-time operation of the system. Li et al. [36] proposed an IES optimal daily dispatch model that takes into account the uncertainty of source load power prediction, with the aim of minimizing system operating costs. Different processing strategies were used for the model at the day-ahead and intraday time scales and, based on the operating costs presented in scenarios 1 and 2 in

Table 3. Operating costs in different scenarios.

Scenario	Total Cost (Yuan)	Electricity Purchase Cost (Yuan)	Gas Purchase Cost (Yuan)
1	2,380,977.356	308,359.0327	1,700,017.44
2	2,221,565.65	287,023.3357	1,572,484.016

, the total cost, power purchasing cost, and natural gas purchasing cost of the day-ahead dispatch model under this model were all reduced.

Scholars have different objectives when using different scheduling models, resulting in diverse outcomes. In the research of dynamic economic dispatch, with the increase of generator units, the scheduling model becomes more complex, which requires more stringent requirements for problem-solving methods. Therefore, scholars have optimized metaheuristic algorithms to improve search efficiency. Metaheuristic algorithms can provide a feasible solution to a problem by simulating natural and human intelligence within an acceptable time and space cost. These algorithms are usually used to solve global optimization problems and are flexible and gradient-free methods. Metaheuristic algorithms include animal-inspired algorithms such as the ant colony algorithm, fish swarm algorithm, bee colony algorithm, plant-inspired algorithms such as the phototaxis algorithm, weed optimization algorithm, human-inspired algorithms such as the genetic algorithm, neural network, and other widely used algorithms such as the taboo search algorithm, simulated annealing algorithm, etc. Metaheuristic optimization algorithms can be mainly divided into four categories: evolution-based algorithms, swarm intelligence-based algorithms, human-based algorithms, and physics and chemistry-based algorithms. Davide et al. [37] tested five different metaheuristics and concluded that Variable Neighborhood Search has the strongest global search ability, and taboo search is the second highest performance. They also described a construction heuristic called Sweep which can find initial high-quality solutions in a very short computational time. Li et al. [38] proposed an enhanced and acoustic search algorithm which is improved in two aspects to improve its competitiveness in the search ability. At the same time, important factors such as transmission loss and slope rate constraints were effectively solved under this algorithm, but the issue of convergence speed was ignored. Vijay, R. et al. [39] proposed a Quorum Sensing Driven Bacterial Swarm algorithm to solve the dynamic economic scheduling problem and verify that the method can minimize the economic cost of power generation. The study for the bacterial group optimization algorithm to solve the problem of the economic scheduling valve effect provides a new train of thought. Song et al. [40] put forward an improved adaptive cuckoo search algorithm that combines parameter dynamic adjustment mechanism and uses a shared parallel computing platform to accelerate the algorithm, reducing the difficulty of solving dynamic economic scheduling models. Due to the instability and load constraints of renewable resources, the optimization results of the meta-heuristic algorithm are good and bad in solving the problem of dynamic economic scheduling, but it shows the effectiveness of the meta-heuristic algorithm in this field. However, in the existing scheduling processes, some optimization algorithms consider the scheduling output priority of each participating unit at the same level, which results in the output of the scheduled units being arranged randomly within the optimization algorithm. This not only fails to achieve the goal of economic optimality, but in actual operation it will cause low efficiency and high energy consumption units to generate more power, increasing operating costs. To solve this problem, it is possible to introduce information on the characteristics and operating costs of the units, such as the cost of power generation, start-up and shutdown costs, and the ability and constraints of load adjustment, into the optimization algorithm to enable more precise scheduling decisions. Due to the instability of renewable resources and load constraints, metaheuristic algorithms have varying degrees of success in solving dynamic economic dispatch problems, but this demonstrates their effectiveness in this field. Therefore, how to improve the computational capabilities of metaheuristic algorithms will become a key direction for future researchers.

5.2. The Random Volatility of Wind Energy

As a widely used renewable energy source, wind power has been developed to a mature stage and is highly appreciated. Although increasing the permeability of wind energy is conducive to energy saving and emission reduction, the intermittency and uncertainty of wind power add difficulties to the system economic scheduling [41]. When wind energy is used in economic dispatch, some inevitable problems arise. Economic dispatch after wind power grid connection is a large-scale, highly constrained, multi-dimensional, and nonlinear optimization problem. The stochastic nature of wind power poses a major challenge to economic dispatch problems. Therefore, scholars have adopted two types of methods to deal with the stochastic nature of wind power.

The first method is to establish a deterministic model which takes the power generated by wind energy as a fixed value and combines it with the economic dispatch model. In the model, a portion of the load demand is directly shared by the power generated by wind energy, and the remaining load demand is allocated by thermal power generation units. The positive and negative rotational reserve constraints can be described as follows:

$$\left\{\begin{array}{l}{S}_{u,t}={\displaystyle \sum _{g\in N_G}{S}_{u,gt}\ge {\displaystyle \sum _{w\in N_W}\left(P_{wt}\times w_u\%\right)}}\\ S_{d,t}={\displaystyle \sum _{g\in N_G}{S}_{d,gt}}\ge {\displaystyle \sum _{w\in N_W}\left(\overline{P_{wt}}-P_{wt}\right)\times w_d\%}\end{array}\right.$$

(16)

where $S_{u,t}$ and $S_{d,t}$ are the positive and negative rotation reserve capacity of the system at time interval $t$; $\overline{P_{wt}}$ is the collection success rate of the wind farm $w$ and $P_{wt}$ is the actual dispatching output power of wind farm $w$; $w_u\%$ and $w_d\%$ are the wind power integration demand coefficient of positive and negative rotation reserve, respectively.

The rotation standby constraints provided by each cell during the response time can be described as follows:

$$\left\{\begin{array}{l}0\le s_{u,gt}\le \min (P_{g\max }-P_{gt},r_{u,g}\times {\mathrm{T}}_{10})\\ 0\le s_{d,gt}\le \min (P_{gt}-P_{g\min },r_{d,g}\times {\mathrm{T}}_{10})\end{array}\right.$$

(17)

where $s_{u,gt}$ and $s_{d,gt}$ are, respectively, the positive and negative rotation spare capacity of cell $g$ at time intervals $t$ and ${\mathrm{T}}_{10}$ is the period between any two adjacent time intervals, 10 min.

Zhou et al. [42] established a dynamic economic dispatch model including wind farms which fully grid the wind power and dynamically dispatch the power generation units based on this. In response to the non-differentiability and multi peak characteristics in the model, this study used a particle swarm optimization algorithm optimized by smooth processing technology to solve, verifying the practical value of the method. This type of method has significant limitations as the power generated by wind energy cannot be a constant value in practical situations.

The second approach is to establish a stochastic model where wind power is not seen as a constant value but rather as a random variable shared with conventional power plants to meet the electricity demand. In an actual wind farm, the power captured by each wind turbine can be considered as a function of wind speed and a typical conversion relationship can be calculated using the following segment function:

$$\left\{\begin{array}{l}w=0,v<v_{in} or v>v_{out}\\ w=w_r\frac{v-v_{in}}{v_r-v_{in}},v_{in}\le v\le v_r\\ w=w_r,v_r\le v\le v_{out}\end{array}\right.$$

(18)

where $v_{in}$, $v_{out}$, and $v_r$ are the cut in, cutting out, and rated wind speed of the fan, respectively, m/s and $w_r$ is the rated power of the fan, MW.

The randomness model includes the robust optimization model, the probability scenario model, and the probability density distribution model. Liu et al. [43] established a two-stage robust optimization model to adjust the conservative level of the solution by introducing a parameter of uncertainty budget. The model aims at reducing the cost of electrical energy and considers the coordination of constraints in the operation of renewable energy uncertainties, generators, and energy storage equipment. Talari et al. [44] proposed a stochastic model for economic scheduling of microgrid mixed energy system. Their model generated a variety of scenarios based on Monte Carlo simulation and considered the uncertainty of some decision variables such as random variables, namely the output power of wind power. Ye et al. [45] established an equivalent wind speed model which considered the geographical distribution of wind turbines and the spatio-temporal distribution of wind speed. Based on this model, the wind speed relationship between upstream and downstream fans was established to determine the wind speed of downstream fans. Matevosyan et al. [46] studied the optimization scheduling method of simulating the output characteristics of wind turbines to make wind power models more suitable for power systems in the context of large-scale wind power integration systems. Hu et al. [47] proposed a dynamic economic dispatching model based on robust optimization and two-layer programming. Aiming at the randomness of wind power output, the sequential method was adopted to model it and relaxation variables were introduced into the model to ensure the safety of the power system. The modeling methods for such problems mainly focus on the opportunity constrained programming scenario method and fuzzy modeling. At present, there is no modeling method that takes into account the accuracy of the objective function, calculation speed, and the adaptability of conventional unit output to the randomness of wind power. Therefore, further research is needed on modeling methods in the future to better adapt to the randomness of wind power while balancing the accuracy and speed of the calculation model.

In the stochastic model, the exact probability distribution model is also a good choice to deal with the randomness of wind power generation, such as Laplacian distribution [48], Universal distribution [49], Weibull distribution [50], and Beta distribution [51]. The statistical analysis of wind speed is typically performed using the average wind speed over a time interval Δt, with a typical time limit of 1 h. The two-parameter Weibull distribution can fit the distribution characteristics of wind speed well and the cumulative distribution function of wind speed for each time interval can be given by the following equation:

$$F_{V_t}(v_t)=1-\exp [-{(\frac{v_t}{c_t})}^{k_t}]$$

(19)

Then, the corresponding probability density function $f_{V_t}(v_t)$ from the cumulative distribution function is:

$$f_{V_t}(v_t)=\frac{k_t}{c_t}{\left(\frac{v_t}{c_t}\right)}^{k_t-1}\exp \left(-{\left(\frac{v_t}{c_t}\right)}^{k_t}\right)$$

(20)

where $k_t$ and $c_t$ are the shape parameters and scale parameters of the Weibull distribution model in t period which need to be estimated by the parameter estimation method. If the shape parameter $k_t$ is taken as 2, then the distribution function is called the Rayleigh distribution.

Based on the probability theory of Formulas (18) and (20), the probability density function of wind power random variable w_t at [v_in, v_r] wind speed is:

$$f_{W_t}(w_t)=\frac{k_{t}h{v}_{in}}{w_r{c}_t}{\left[(1+h{v}_{in})\frac{v_{in}}{c_t}\right]}^{k_t-1}\times \exp \left\{-{\left[(1+\frac{h{w}_t}{w_r})\frac{v_{in}}{c_t}\right]}^{k_t}\right\}$$

(21)

In the equation, $h=\left(v_r/v_{in}\right)-1$, the probability of w_t = 0 and w_t = w_r is:

$$\begin{array}{l}{P}_{W_t}\left\{w_t=0\right\}=1-\exp \left(-{\left(\frac{v_{in}}{c_t}\right)}^{k_t}\right)+\exp \left(-{\left(\frac{v_{out}}{c_t}\right)}^{k_t}\right)\\ P_{W_t}\left\{w_t=w_r\right\}=\exp \left(-{\left(\frac{v_r}{c_t}\right)}^{k_t}\right)-\exp \left(-{\left(\frac{v_{out}}{c_t}\right)}^{k_t}\right)\end{array}$$

(22)

Finally, the cumulative probability distribution function of wind power w_t can be obtained:

$$\begin{array}{l}{F}_{W_t}(w_t)=P(W_t\le w_t)\\ =\left\{\begin{array}{l}0; (w_t<0)\\ 1-\exp \left\{-{\left[(1+\frac{h{w}_t}{w_r})\frac{v_{in}}{c_t}\right]}^{k_t}\right\}+\exp \left(-{\left(\frac{v_{out}}{c_t}\right)}^{k_t}\right)\\ 1. (w_t\ge w_r)\end{array}\right.; (0\le w_t\le w_r)\end{array}$$

(23)

In order to simplify the model without considering the wake effect of the wind farm and the wind farm unit scheduling, the Formulas (21) and (23) can be extended to the whole wind farm. That is, the probability density function and cumulative distribution function of the whole wind farm output are obtained. At this time, $w_r$ is the installed wind power capacity w_max (w_max = w_r × N, where N is the number of wind turbines).

Increasing the penetration rate of wind energy in the power system can significantly reduce carbon emissions and the use of fossil fuels. However, due to the intermittency and uncertainty of wind energy, the large-scale integration of this energy will also pose challenges to the economic dispatch and operation of the power system [52]. To overcome these challenges, researchers have proposed various methods. Yang et al. [53] put forward a new modeling method for the conditional probability distribution of wind power forecast error. They used the clustering algorithm to cluster multi-dimensional influencing factors such as weather and wind energy, used general distribution to simulate the probability distribution of wind power forecast error which solved the problem of how to give consideration to the instability of weather and wind energy in the probability distribution modeling of wind power prediction, and effectively improved the permeability of wind energy. Zhang et al. [54] put forward a multi-target based on the adaptive grid differential evolution algorithm with different scenarios to simulate each that may be generated by wind power in different situations of random dynamic economic emissions scheduling model. Moreover, they reduced the mechanism to reduce the number of covariance relationship for the practical application of wind power instability to provide a valuable solution. Wang et al. [55] developed a hybrid Markovian and interval approach which uses Lagrangian relaxation and branch cutting to correlate the power generation of the unit with local wind conditions, solving the uncertainty of how to reduce wind power in situations without battery storage. Chiodo et al. [56] put forward the Compound Inverse Rayleigh distribution model which uses a new Bayesian method to estimate the probability distribution of wind speed extreme values. A large number of examples show that the method has good performance in terms of the feasibility, efficiency, and accuracy.

Deterministic models and stochastic models both have their own scope and limitations. Therefore, suitable models should be chosen based on specific circumstances to analyze and optimize wind power system operations. Deterministic models can be used to accurately calculate the behavior and performance of a system when input data are highly predictable, reliable, and accurate. They have fast solution speed, high reliability of results, low calculation costs, and clear assumptions and parameter requirements for input data, making them easy to interpret and verify. However, the limitation of deterministic models is that they cannot consider the stochastic volatility and uncertainty of input data. Therefore, in the case of input data that have uncertainty and stochastic volatility, the calculated results of deterministic models may have significant biases with respect to the actual situation. In this case, stochastic models are needed to solve the problem. Stochastic models can comprehensively consider the probability of different possibilities and risks, reflect more features and behavior of actual systems, and better reflect uncertainty with a wider scope of application and lower requirements for input data. However, stochastic models usually require a large amount of input data, have high computational complexity, and different assumptions and parameter choices can lead to different results, making the interpretation and verification of results more difficult.

5.3. Dynamic Economic Scheduling of Environmental Benefit Objectives

The traditional economic dispatch is centered around thermal power generation, which consumes a large amount of fossil energy that produces waste gas and poses a huge threat to the environment. In this context, the environmental benefits of microgrids have received widespread attention and attention. Many scholars have incorporated environmental benefits into the economic operation research of microgrids in order to comprehensively analyze the overall benefits of microgrids.

The microgrid economic dispatch model that considers environmental factors is based on the basic dispatch model with the addition of emission costs for micropower sources. There are two main formulas for calculating emission costs:

$$\begin{array}{l}E(P_i)={\displaystyle \sum _{i=1}^N{V}_w(P_i)}{\mu }_w\\ E(P_i)={\displaystyle \sum _{i=1}^N{10}^{-2}}({\alpha }_{w,j}+{\beta }_{w,i}{P}_i+{\gamma }_{w,i}{P}_i^2)+{\zeta }_{w,i}\exp ({\lambda }_i{P}_i)\end{array}$$

(24)

where $E(P_i)$ is the emission cost of the microgrid system; $w$ is the emission gas generally CO₂, SO₂, and NO_x; $V_w$ is the volume of the w gas emitted by the micropower source; ${\mu }_w$ is the emission penalty price of w gas; $\alpha ,\beta ,\gamma ,\zeta ,\lambda$ are the fuel cost coefficients of the micropower supply.

Dynamic economic dispatching is a multi-objective optimization problem that combines two contradictory goals of reducing the system operating cost and reducing the pollution emission amount [57,58]. Its form can be expressed as follows:

$$F=\min (F(P_i(t))+F(P_i(t)))$$

(25)

where $F(P_i(t))$ and $F(P_i(t))$ represent the power generation cost and emission cost, respectively.

Scholars have two treatment methods for such problems. The first method treats [59] as the target of dynamic economic scheduling and it is difficult to determine the trade-off between the two. The second method is to combine the operating cost of the system and the generated pollution emissions to transform the multi-objective optimization problem into a single-target optimization problem [60]. A series of Pareto solution sets can be obtained when scholars use intelligent algorithms to solve hybrid dynamic economic scheduling problems and the solution satisfying decision makers can be obtained by processing Pareto solution sets with the satisfaction function method [61]. Qu et al. [62] proposed the multi-objective differential evolution with an ensemble of selection methods (MODE-EMS), which is an evolution of differential evolution in solving multi-objective optimization problems. Simulation tests show that the MODE-EMS algorithm has significant effects on dynamic economic emission distribution problems.

Renewable energy sources such as wind energy have been widely studied by scholars due to their pollution-free, easy-to-collect, and diverse styles. In response to the high requirements for environmental pollution and energy utilization, scholars have conducted research on the economic scheduling problem of microgrid systems combined with wind energy [63]. Ding et al. [64] established a mathematical model of the EEMD-LSTM-SVR algorithm and a comprehensive low-carbon economic scheduling model and verified through simulation that the total cost of this method was relatively reduced by 6.70%, carbon emissions were relatively reduced by 18.64%, and wind power waste was relatively reduced by 38.02%. While achieving low-carbon emissions, the system’s wind power absorption capacity and operational efficiency were improved. Narimani et al. [65] proposed a hybrid shuffling jumping frog algorithm to solve the problem of economic dispatching by considering power generation cost and environmental pollution, as well as constraints such as the valve point effect and forbidden operation constraints. The experimental results show that compared with the traditional wind power or thermal power system, the cost of the system is reduced by 35.5% and the carbon emissions are reduced by 44.6%. Boudab et al. [66] explored a dynamic neural network model for handling highly complex joint economic emission scheduling problems. This model was solved quickly and with low complexity, but the study did not consider the slope rate constraint, which is essential in dynamic scheduling.

5.4. Optimization of Bidding Strategy of Wind Power Suppliers and the Improvement of Wind Power Absorption Capacity

With the large-scale incorporation of wind energy into the grid, existing wind power supplier bidding strategies have limitations in potential cooperation, bidding behavior of other competitors, network losses, uncertainty in wind power production, and balancing market prices. In order to address these issues, Zhang et al. [67] proposed a Hybrid Particle Swarm Optimization and Improved Firefly Algorithm. This algorithm has the characteristics of periodicity, randomness, and regularity and can enhance local searches to avoid local minima. However, the algorithm does not consider the bidding demand and accuracy on the demand side. Zhang et al. [68] proposed a wind power consumption model for the connection between bidding and dispatching. As China’s electricity market is dominated by medium and long-term transactions, this model conducts long-term scale planning for wind power consumption, divides monthly power generation into days, and effectively reduces wind power abandonment while improving the dynamic economic dispatch of microgrids simultaneously. The model reduced the total cost of thermal power from 121,600 yuan to 56,900 yuan and the improvement ratio of the total cost of thermal power was 53.21%.

In addition, increasing wind power integration capacity has also become one of the important methods to improve economic dispatch. The uncontrollable nature of wind power makes it highly volatile, posing challenges to the stability of power systems. If the wind power integration capacity is insufficient, it may lead to load imbalance in the power system, thereby affecting the safe and stable operation of the power system. Chu et al. [69] considered the advantages of load scheduling and operating boundaries, analyzed the adaptability of wind power consumption scheduling demands at different time scales, established a multi-time-scale optimization scheduling mechanism, and based on this, developed day-ahead, intra-day, and real-time optimization scheduling models. They proposed a control strategy for wind turbines to reduce load operation under full wind conditions based on the overspeed control and pitch angle control methods of variable-speed wind turbines. Cheng et al. [70] proposed an adaptive robust model to solve the optimal scheduling problem including wind energy storage (ES) and study the dynamic multistage ES. Furthermore, the generator scheduling mode is optimized and the existence of energy storage can effectively alleviate the problem of wind and realize the wind power given but the model ignores the wind power prediction value and the actual error and the robust model cannot consider the uncertainty of the wind network system power balance and the whole scenario line tide safety double constraints. Chinnadurrai et al. [71] put forward a hybrid dynamic economic emissions dispatch model incorporating demand side management to cope with the variability of wind energy by controlling load through demand side management and modifying the electricity consumption pattern according to different tariffs during low, peak, and off-peak hours, but the stochasticity of wind energy was not addressed. However, due to the complexity of the mathematical model for wind power consumption capacity evaluation, which includes numerous constraints, conventional algorithms struggle to achieve precise solutions. Therefore, developing an intelligent algorithm with good search performance and strong solving ability is a future research challenge.

6. Application Prospect

The hybrid microgrid of wind and thermal power is an emerging power system that has received widespread attention and research due to its environmentally friendly and high energy utilization efficiency. This system can organically combine stable thermal power and highly volatile wind power to achieve an economic and efficient energy supply. Therefore, the economic dispatch problem has become an important research direction.

In terms of dynamic economic dispatch, the wind power thermal power hybrid microgrid can start, stop, and distribute power of generator units according to the current load situation and market price so as to achieve maximum economic benefits. At the same time, the system can also use energy storage devices such as batteries to regulate peak and valley electricity, further optimizing power generation costs.

In terms of static economic dispatch, wind power thermal power hybrid microgrids can be planned and optimized for system operation and maintenance by establishing appropriate mathematical models. These models can consider many factors, such as weather, market price, network topology, etc., to achieve the optimal energy allocation and supply scheme.

In addition, research on the dynamic and static economic dispatch of wind and thermal hybrid microgrids can help promote sustainable energy development. The hybrid microgrid of wind power and thermal power is a clean energy system that can effectively reduce pollutant emissions and carbon emissions and promote sustainable energy development. This is by improving its operational efficiency and economy, promoting its application in the power system, achieving effective utilization of clean energy, and improving energy efficiency, reducing pollution and carbon emissions, and promoting the popularization and application of clean energy. For example, Alameda County in the San Francisco Bay Area has established a wind power thermal power hybrid microgrid to provide a clean and reliable energy supply for local residents and enterprises. Abu Dhabi Power Company has developed a wind thermal hybrid microgrid demonstration project in the United Arab Emirates, which includes 10 MW of wind power, 6 MW of solar energy, and 2 MW of lithium ion energy storage system. By adopting an intelligent monitoring system and predictive model, the project achieved dynamic scheduling, optimized control of the system, and successfully increased the proportion of clean energy to 90%.

7. Summary and Outlook

By the end of 2022, China’s installed coal power capacity was 1.33 billion kW, an increase of 2.7% year-on-year, while wind power capacity was 370 million kW, an increase of 11.2% year-on-year. Although the position of thermal power is still unshakable, the government has begun to gradually reduce its reliance on coal and accelerate the development of renewable energy. The application of wind–thermal power hybrid microgrids will inevitably become more widespread in the future, and its economic dispatch problem will also become a key research topic for scholars. This article introduces the static and dynamic economic dispatch problems of wind–thermal power hybrid microgrids and explains the research status and challenges in terms of models and algorithm principles for static economic dispatch. In terms of dynamic economic dispatch problems, research and predictions are conducted from the aspects of environmental protection and wind power uncertainty factors. Although scholars have conducted a lot of research in these areas, there are still many issues that need to be addressed.

General economic dispatch optimization methods often require a series of assumptions to be made about the system and also struggle to cope with the challenges of dynamic changes in systems containing wind power. Traditional optimization algorithms such as random optimization, robust optimization, distributed robust optimization, and heuristic optimization algorithms have been used to solve the uncertainty problem of wind power thermal power hybrid microgrids. However, they all rely on accurate prediction and are difficult to cope with the changing scenarios of new energy output and load demand. Stochastic optimization often transforms uncertain problems into deterministic problems by sampling, chance constraint generation, and other methods, but the complexity of the algorithm increases with the increase of the scene. Robust optimization solves uncertainty by providing an uncertain set, but usually the optimization results it provides are only oriented towards the worst-case scenario and are too conservative. Heuristic optimization algorithms, such as genetic algorithms and particle swarm optimization, etc., are prone to falling into local optima and the increase in action complexity brings serious dimensionality problems to heuristic optimization algorithms, making it difficult to converge stably. Therefore, in order to better solve the economic dispatch problem of wind power thermal power hybrid microgrids, further in-depth research is needed in the following aspects.

(1)

A good algorithm can provide the technical basis for solving the dynamic and static economic dispatching model of wind–thermal power hybrid microgrids and provide methods for solving the problems of high complexity and high dimension in economic dispatching. Some existing algorithms such as the basic sailfish optimization algorithm (SFO), the particle swarm optimization algorithm (PSO), and the multiverse algorithm (MVO) can be applied to many simple optimization problems in science and engineering due to their flexibility and simplicity. However, with the increase in problem complexity and data dimension, there will be some problems in the process of data processing of these algorithms, such as low solving accuracy and slow convergence speed. Therefore, some improvements should be made to the original algorithm when solving problems. The algorithm can be improved from the three aspects of solving ability, exploration diversity, and convergence speed. Three methods, namely weight inertia, global search factor, and population diversity maintenance strategy, were used, respectively;

(2)

To solve the static economic dispatching problem of wind–thermal power hybrid microgrids, we can start with the establishment of its optimization mathematical model, reduce the impact of its volatility on system stability by limiting the grid-connected capacity of wind energy, and take the low cost of wind energy into account so as to further guarantee the economy of microgrid system dispatching. At the same time, more constraints should be considered in future research of hybrid dynamic and static economic scheduling models so that the solution of the model can be closer to the actual operation of the system;

(3)

The non-stationary characteristics of wind energy should be taken into account when establishing the dynamic economic dispatching model of wind–thermal power hybrid microgrids so as to make the power output estimation of the microgrid system more realistic and make full use of wind energy, in order to ensure the economy and environmental protection of microgrid dispatching;

(4)

At present, research on the static economic dispatch of wind power thermal power hybrid microgrids lacks a global and refined evaluation of system economy and environmental protection. Based on the comparison and demonstration of previous operation plans, it can be seen that proposing methods and indicators that can finely evaluate the long-term operating cost, energy consumption, and efficiency of the system are urgently needed for future research.