Optimal Scheduling of Cogeneration System with Heat Storage Device Based on Artificial Bee Colony Algorithm

Abstract

The rigid constraint of using heat in determining electricity for thermal power units is eliminated to improve the absorption capacity of wind power. In this study, heat storage devices and electric boilers are added to the cogeneration system to alleviate the wind curtailment phenomenon. First, the main reasons for wind curtailment are analyzed according to the structural characteristics of the power supply in the northern part of China. Second, a scheduling model of a cogeneration system, including a heat storage device and an electric boiler, is constructed. An improved artificial bee colony algorithm program is also designed and compiled based on MATLAB. Finally, the feasibility of the proposed scheme is verified by simulation examples, and an economic analysis of wind power consumption is performed. Results show that adding electric boilers lessens coal consumption costs and improves economic benefits.

1. Introduction and Background

1.1. Literature Review

The continuous use of traditional energy results in the continued increase in the global temperature, causing irreversible damage to the originally beautiful natural environment. The proposal of the dual-carbon strategy promotes human beings to move gradually from industrial civilization to ecological civilization. People have begun to solve the contradiction between social progress and environmental protection by vigorously developing renewable energy to ensure the sustainable development of human civilization and the ecological environment. In recent years, aggressive clean energy development has begun in China. Among many new energy sources, wind energy has developed rapidly with its advantages of advancement and stability [1]. Wind energy reserves are highly abundant in the three northern parts of China. However, these areas also face the challenges of wind curtailment [2]. The wind curtailment volume and wind curtailment rate are shown in Figure 1 and Figure 2, respectively. Electric power workers have proposed various measures to improve the capacity of wind power consumption; among these measures, energy storage technology has received extensive attention [3].

Scholars have made many improvements in the system structure to improve the wind power consumption capacity of the cogeneration system. Literature [4] proposed solutions for electric heating, such as heat pumps and electric boilers. Literature [5,6,7] proposed a heat storage device on the side of the cogeneration unit for the decoupling of the rigid constraints of using heat to determine electricity and improve the grid capacity of wind power. Literature [8] showed that heat storage can improve the regulation ability of thermal power units. The authors of [9] used the gas-to-heat system of natural gas to alleviate the output of the thermal power unit. Various energy storage technologies, such as heat pump technology [10], pumped water storage [11], and mechanical energy storage [12], have been widely used. The literature in [13,14,15] proposed an electric boiler in load measurement through the electric heating conversion of the electric boiler and the use of abandoned wind for heating to improve wind power utilization.

Similarly, scholars have done considerable research on optimization solutions. The authors of [16] studied the mixed-integer optimization scheduling problem of the community-scale combined heat and power system. An optimized scheduling model was also established to optimize minimum energy consumption. In addition, a genetic algorithm was selected as the solution to the scheduling problem, and the genetic method was verified through specific examples. Literatures [17,18] established a multi-objective function to lessen system power loss, total power cost, and minimum total pollutants from fuel cells and substation busbars. Literature [19] established an optimal dispatch model for a combined heat and power system, including fans. The authors of [20] studied the optimal dispatching problem of microgrids, including various distributed power sources, such as wind power, photovoltaic cells, and energy storage batteries. In addition, a genetic algorithm was used to solve the problem. In [21], scholars analyzed the combined thermoelectric system of distributed power sources, such as photovoltaic cells and fuel cells. The literature in [22] proposed a particle swarm algorithm to solve the model, and the algorithm was improved [23]. The literature in [24] showed that the improved particle swarm self-tuning optimization algorithm is computationally efficient. The literature in [25] proposed a weight initialization method based on a neural network. The state of the art of the combined heat and power system is shown in

Table 1. The state of the art of the combined heat and power system.

Ref.	Optimal Object	Optimization Structure(s)	Solving Method(s)
[4]	System revenue maximization	Heat pumps and electric boilers	Particle swarm algorithm
[5,6,7,8]	Minimum system operating cost	A heat storage device decouple the rigid constraints of using heat	The mixed-integer optimization
[9]	The unit consumes the least coal	The gas-to-heat system of natural gas alleviate the output of the thermal power unit	The improved particle swarm algorithm
[10]	System profit maximization	Heat pump technology	Genetic algorithm
[11]	System revenue maximization	Heat water storage	Nonlinear programming
[12]	Minimum system operating cost	Mechanical energy storage	Immune genetic algorithm
[13,14,15]	The unit consumes the least coal	Electric boiler consummate wind power for heating	Genetic algorithm
[16]	System revenue maximization	Heat water storage	The mixed-integer optimization
[17,18]	The unit consumes the least coal	Thermal storage device and electric boilers	Multi objective function optimization
[19]	System revenue maximization	Thermal storage tank	Genetic algorithm
[20]	The unit consumes the least coal	Electric boilers	Genetic algorithm
[21]	Minimum system operating cost	The heat pump and the heat storage unit coordinate heating	A particle swarm algorithm
[22,23,24,25]	System revenue maximization	Battery energy storage	The improved particle swarm algorithm

.

As a swarm intelligence model, the artificial bee colony algorithm has been successfully applied to problem optimization in many fields because of its excellent performance in convergence and optimization performance. In [26], the artificial bee colony algorithm and fuzzy theory were applied to the real-time control of the joint manipulator. The traditional artificial bee colony algorithm easily falls into the local extremum problem in the later stage. Literature [27] introduced the chaotic sequence into the initialization process, expanded the search range of the solution, and established the optimized adaptive step size in the neighborhood search to accelerate the convergence speed of the algorithm. Literature [28] proposed an adaptive variable difference artificial bee colony algorithm for antenna optimization design, which can adaptively determine the number of decision variables to be mutated in each iteration, accelerate the convergence speed, and improve the efficiency of the algorithm. In [29], the artificial bee colony algorithm was applied to extract the optimal power points of the multistring topology of a photovoltaic power station. Literature [30] combined the artificial neural network with the artificial bee colony algorithm to improve the performance of short-term load forecasting. In [31], the artificial bee colony algorithm was applied to the load monitoring of a smart home. The artificial bee colony algorithm was applied to the energy storage scheduling of microgrids with a self-healing function in [32]. In [33], a hybrid artificial bee colony algorithm was proposed to solve the distributed flow job problem with deteriorating jobs. In summary, the artificial bee colony algorithm has a wide range of applications, which can be improved according to the specific characteristics of different problems. The artificial bee colony algorithm can also be integrated with other intelligent algorithms to improve the optimization efficiency of specific problems.

1.2. Novelty of The Present Study

The previous research is mostly improved from two aspects by reviewing the literature related to the optimal scheduling of cogeneration. These aspects include the system structure and the solving algorithm. In the aspect of system structure, single components such as the heat storage tank, the heat pump and the electric boiler are added to the system to realize the decoupling between power generation and heating. Few studies have used the heat storage device and electric boiler to improve the ability of wind power consumption. In the aspect of the solving algorithm, the scheduling objective function of the cogeneration system is usually high-order nonlinear, and the solving process of the mathematical method is complex. Thus, the exact solution to the scheduling problem is difficult to obtain. However, the intelligent algorithm shows excellent performance in solving.

In the present study, the output of thermal power units is relieved, and the space for wind power grid connection is increased by adding electric boilers and heat storage devices to coordinate heat supply. Based on the existing research, most of the algorithms for solving the day-ahead scheduling model use a particle swarm algorithm and a neural network algorithm. The present study uses an improved artificial bee colony algorithm to solve the model. It also compares the advantages and disadvantages of several algorithms through the simulation results, thereby providing a certain reference value for the problem of day-ahead scheduling.

The remainder of this article is organized as follows. In Section 2, the addition of a heat storage device and electric boiler to the system is proposed to increase the utilization rate of wind. In Section 3, the optimal scheduling model is established, with the power generation cost as the objective function. Moreover, a global-guided artificial bee colony solution algorithm is designed based on cross-operation. Section 4 discusses the economics of wind power consumption. As discussed in Section 5, an example simulation is conducted, and the simulation results are analyzed.

2. Problem Description

In the three northern parts of China, the weather is cold during winter, and much heat is needed to meet the heat load demand. Most of the units in this area are thermal power units that can generate electricity and heat. Exhaust gas units have been extensively developed because of their efficient energy utilization. This type of unit solves the contradiction between the power supply and heat supply of the backpressure-type unit. Therefore, the thermal power units mentioned in this article are all exhaust-type thermal power units.

2.1. Model of a Traditional Thermal Power Unit

According to their different electric heating characteristics, common heat and power units can be divided into exhaust-type units and backpressure-type units. This study uses the most common exhaust-type thermoelectric units in China. The pumped-air unit possesses various advantages, including the use of steam from high-pressure cylinders for electricity generation to meet the user’s electrical load and the extraction of steam from middle- and low-pressure cylinders for heating. Therefore, the heating task is achieved, and the electric load can decouple the thermoelectric coupling relationship of the unit to a certain extent. The structure diagram is shown in Figure 3.

This study analyzes the change of the electric heating characteristic curve of the unit after the heat storage device is added. As shown in Figure 4, the shaded part represents the feasible region for unit operation, and its characteristic curve expression is as follows.

$$\{\begin{array}{l}\max \left\{P^{\mathrm{E},\min }-\gamma P,\alpha P+\beta \right\}\le P_h\le P^{\mathrm{E},\max }-\gamma P\\ 0\le P_h\le P^{\mathrm{H},\max }\end{array},$$

(1)

where $P^{\mathrm{E},\max }$ and $P^{\mathrm{E},\min }$ represent the maximum and minimum outputs of the unit under pure condensing conditions, respectively, MW; $\alpha$ represents the coefficient of elasticity of the thermal power unit; $\gamma$ represents the reduction in the amount of electricity generated under the condition that the amount of air intake is constant and the unit of heat is extracted; $\beta$ is a constant; $P^{\mathrm{H},\max }$ indicates the maximum heat supply that the unit can provide, MW.

The electric heating characteristic curve of the unit indicates that when the amount of heat required at night increases, the output of the unit increases, thereby increasing the forced electric output and reducing the peak regulation capacity of the unit. When the heating power of the unit is $P^{\mathrm{H}}$, the adjustment range of the electric power is $P^{\mathrm{E}}-P^{\mathrm{F}}$ and the peak regulation capacity is limited.

2.2. Model of Thermal Power Unit after the Addition of Heat Storage Device and Electric Boiler

Wind turbine output depends mainly on thermal turbine output. Given the characteristics of the real-time balance of electrical energy, the increase in the output of cogeneration units compresses the grid space of wind power, resulting in the wind abandonment phenomenon. This phenomenon can be effectively solved after the addition of a heat storage device and an electric boiler. The system structure is shown in Figure 5.

The working principle can be described as follows. During the daytime of the heating season, the wind power output is small, the electricity load is large, and the heat load is small. The wind abandonment phenomenon rarely occurs in this period, and the electric boiler does not work. The cogeneration unit can increase the power output to meet the demand of the power supply load. The thermal output of the unit also increases because of the electrothermal coupling characteristics of the cogeneration unit itself. Moreover, the heat storage device stores excess heat. During the nighttime of the heating season, the wind power output is large, the electricity load is small, and the heat load is large. During this period, cogeneration units produce a large number of forced power outputs to meet the demand for heating. These outputs occupy the Internet space of wind power, resulting in a wastage of wind power. At this time, the heat stored in the heat storage device during the day can be released to reduce the output of cogeneration units, creating opportunities for wind power to be connected to the grid. If abandoned wind exists, then the electric boiler is started to convert excess abandoned air into heat and participate in heating.

The adjustment range of the electric power is extensive when the heat provided by the units is P^H because of the heat released by the heat storage device. Therefore, the AB section of the curve shifts to the right of the GI section, and the CD section shifts to the left of the LK section in the same manner. The electric heating unit works at a low power output level when wind abandonment occurs. In this scenario, the space for the wind power Internet connection increases. However, excess wind abandonment may occur after the addition of the heat storage device. An electric boiler is added to absorb wind abandonment further, and its electric heating principle is used to improve the utilization rate of wind power. Figure 6 shows that the electric heating characteristic curve of the unit changes after the addition of the heat storage device.

Wind abandonment generally occurs at night, when the heat load is most needed. During this period, the heat storage device should release heat to reduce the output of the thermal power unit, allowing the wind power to go online. When wind energy is particularly sufficient, wind abandonment may occur after the addition of the heat storage device. At this time, an electric boiler is added to the system to absorb the abandonment further. In the morning and noon, nearly no wind abandonment occurs. During this period, the output of the thermal power unit is increased. Thus, the excess heat is stored in the heat storage device.

Operating Conditions of Heat Storage Device and Electric Boiler

During winter, wind abandonment mainly occurs because of the need for heating at night. The thermal power unit generates a large amount of forced electricity to compress the grid space of wind power. The operation signs of heat storage devices and electric boilers are assessed based on whether wind abandonment is present. The abandonment zone is highly important. If the thermal power unit works in the BC section, then it needs much heat at night, and the thermal power is maintained at a high level. The electric output of the thermal power unit should be minimized. This implication is also in line with the actual scenario. The thermoelectric characteristic expression formula of the unit’s working area is as follows:

$$P=\alpha P_h+\beta .$$

(2)

The sign of wind abandonment is

$$J_t^{\mathrm{flag}}=\{\begin{array}{l}1,{\displaystyle \sum _{i=1}^N{P}_t^{\mathrm{Huo}}+{\displaystyle \sum _{i=1}^N(\alpha P_h+\beta )+P_t^{\mathrm{Max}}>P_t^{\mathrm{L}}}}\\ 0,{\displaystyle \sum _{i=1}^N{P}_t^{\mathrm{Huo}}+{\displaystyle \sum _{i=1}^N(\alpha P_h+\beta )+P_t^{\mathrm{Max}}\le P_t^{\mathrm{L}}}}\end{array},$$

(3)

where $P_t^{\mathrm{Huo}}$ represents the electrical output of the thermal power unit, MW; $\alpha P_h+\beta$ represents the electrical output of the thermal power unit; $P_t^{\mathrm{Max}}$ represents the maximum fan output, MW.

The heat storage device and the electric boiler work simultaneously when $J_t^{\mathrm{flag}}$= 1. The heat storage device works, but the electric boiler does not work when $J_t^{\mathrm{flag}}$ = 0.

3. Mathematical Model of the Cogeneration Unit

3.1. Objective Function

This study considers the minimum coal consumption F of the entire system unit as the objective function [34,35]. The cost of wind power generation is minimal and can be ignored.

$$\{\begin{array}{l}\min F=F1+F2\\ F1={\alpha }_i{\left(P_{i,t}^{\mathrm{E}}\right)}^2+b_i{P}_{i,t}^{\mathrm{E}}+c_i\\ F2={\alpha }_i(P_{i,t}^{\mathrm{E}}+c_v{P}^{\mathrm{H}})+b_i(P_{i,t}^{\mathrm{E}}+c_v{P}^{\mathrm{H}})+c_i\end{array},$$

(4)

where F1 and F2 are the coal consumption of thermal power units, ten thousand yuan; ${\alpha }_i,b_i,c_i$ denote the coal consumption coefficient of the ith unit; $P_{i,t}^{\mathrm{E}}$ represents the electric power of the ith unit at time t; $P^{\mathrm{H}}$ denotes the thermal power of the unit, MW.

3.2. Constraints

Real-time balance constraint of electric load

Given that the electrical energy cannot be stored, the power system must meet real-time power balance, that is, the amount of electrical energy emitted by the system must be equal to the size of the load.

$${\displaystyle \sum _{i=1}^N{P}_{\mathrm{i},t}^{\mathrm{E}}+P_t^{\mathrm{W}}=P_t^{\mathrm{L}}+\theta P_t^{\mathrm{EB}}},$$

(5)

where ${\displaystyle \sum _{i=1}^N{P}_{\mathrm{i},t}^{\mathrm{E}}}$ represents the sum of the electrical output of all units at time t; $P_t^{\mathrm{L}}$ represents the electrical load value of the system at time t; $P_t^{\mathrm{EB}}$ represents the electrical power of the electric boiler, MW. When the electric boiler is working, $\theta$ = 1; otherwise, $\theta$ = 0.

Balance constraints of thermal load

The system requires the heat load to maintain the indoor temperature in a feasible range because the heating network has a certain thermal inertia. The heat supply of the system should be equal to the heat load.

$${\displaystyle \sum _{i=1}^N{P}_t^{\mathrm{H}}+\omega P_t^{\mathrm{F}}+\theta P_t^{\mathrm{EB}}=P_t^{\mathrm{L}}}+(1-\omega )P_t^{\mathrm{C}}.$$

(6)

When $\omega$ = 1, the heat storage device releases energy; when $\omega$ = 0, the heat storage device stores energy.

Upper and lower limits of unit output

In the power generation by power plant units, high-temperature and high-pressure steam enters the steam turbine to drive the coaxial generator to generate electricity. Moreover, the amount of air intake determines the amount of power generation. Each unit has a steam valve to control the unit output by changing the air intake. Therefore, the unit output must meet the maximum and minimum outputs.

$$P^{\mathrm{E},\min }\le P_{i,t}^{\mathrm{E}}+C_{i,t}^{\mathrm{V}}\le P^{\mathrm{E},\max }.$$

(7)

The upper and lower limits of the unit’s climbing rate

The ramp rate of a unit refers to the change in unit power per unit time. This measurement is essential in maintaining power system stability. If the change in unit power is excessively large or extremely small, then system stability is seriously affected. Therefore, controlling the ramp rate of the unit is a prerequisite to ensure that the electrical energy has good quality.

$$\{\begin{array}{l}{P}_{t-1,i}^{\mathrm{E}}-P_{t,i}^{\mathrm{E}}\le P_i^{\mathrm{down}}\\ P_{t,i}^{\mathrm{E}}-P_{t-1,i}^{\mathrm{E}}\le P_i^{\mathrm{up}}\end{array}.$$

(8)

Restriction of fan output

Wind turbine output should not exceed the maximum value predicted by the wind because of the characteristics of wind volatility and instability.

$$0\le P_t^{\mathrm{W}}\le P_t^{\mathrm{W},\max }.$$

(9)

Constraints on electric boiler output

Electric boiler output should not exceed its maximum power because of the limitation of the maximum power of the design parameters.

$$0\le P_t^{\mathrm{EB}}\le P_t^{\mathrm{EB},\max }.$$

(10)

Constraints on the heat storage and heat release power of heat storage devices

$$\{\begin{array}{l}0\le P_t^{\mathrm{F}}\le P^{\mathrm{F},\max }\\ 0\le P_t^{\mathrm{C}}\le P^{\mathrm{C},\max }\\ 0\le S_t^{\mathrm{C}}\le S^{\mathrm{C},\max }\end{array},$$

(11)

where $P^{\mathrm{F},\max }$ and $P^{\mathrm{C},\max }$ represent the maximum heat release power and maximum heat storage power of the heat storage device, respectively; $S^{\mathrm{C},\max }$ represents the maximum heat storage capacity of the heat storage device, MW.

The following are the decision variables: electric output of the thermoelectric unit, output of thermal power units, power of the electric boiler at each moment, and heat change value of the heat storage device.

3.3. Design of the Artificial Bee Colony Algorithm

The objective function is a high-order nonlinear function. Thus, solving it using mathematical methods is difficult. In this study, two swarm intelligence algorithms are used to solve the problem, and their advantages and disadvantages are compared.

3.3.1. Basic Artificial Bee Colony Algorithm

The artificial bee colony algorithm is based on the honey-collecting mechanism of bees. The bees are mainly divided into three types: collecting bees, observing bees, and reconnaissance bees. The solution to the problem is obtained through the repeated searches of these three types of bees. A type of bee can be converted to another type under different conditions, as shown in Figure 7. The bee colony constantly changes its position according to the principle of greed to find the best nectar source (optimal solution). The search formula is as follows [36]:

$$\mathrm{new}\_X_i=X_i+\mathrm{rand}\left(0,1\right)\left(X_i-X_k\right).$$

(12)

The solution process of the basic artificial bee colony algorithm can be described below.

At the initial moment, N feasible solutions $(X_1,X_2,\dots ,X_N)$ are randomly generated, and the specific randomly generated feasible solutions are as follows:

$$X_i=X^{\min }+\mathrm{rand}\left(0,1\right)\left(X^{\max }-X^{\min }\right).$$

(13)

After discovering the nectar source, the collecting bee attracts the observation bee to collect the nectar.

$$P_i=\frac{fitnes{s}_i}{{\displaystyle \sum _{n=1}^{N}fitnes{s}_n}}.$$

(14)

In the new position vector ($\mathrm{new}\_X_i$) and the original position vector ($X_i$) searched by bees, the greedy selection operator selects the one with enhanced fitness and keeps it for the next generation population, denoted as Ts: $S\to S^2$. Its probability distribution is as follows [37]:

$$P\left\{T_s\left(X_i,\mathrm{new}\_X_i\right)=\mathrm{new}\_X_i\right\}=\{\begin{array}{l}1, f\left(\mathrm{new}\_X_i\right)\ge f\left(X_i\right)\\ 0, f\left(\mathrm{new}\_X_i\right)<f\left(X_i\right)\end{array}.$$

(15)

Table 2. Correspondence between honey collection behavior and optimization problem.

Nectar-Collecting Behavior of Bees	Optimization Problem
Location of the nectar	Feasible solution to optimization problem
Nectar amount of nectar source	Quality of feasible solutions
Maximum amount of nectar	Optimal solution of optimization problem

shows the corresponding relationship between the honey-collecting behavior of the bees and the function optimization problem in the artificial bee colony.

When artificial bee colonies solve various problems, the iterative process generally has five types of operations: employed bee phase, nectar source evaluation, onlooker bee phase, recorded nectar source, and bee detection stage. Each iteration simulates the honey-collecting behavior of a bee colony, as shown in Figure 8.

3.3.2. Global Artificial Bee Colony (GABC)

This study refers to the particle swarm algorithm and proposes an artificial bee colony algorithm guided by the global optimal solution (i.e., GABC) [38]. The search formula is shown below.

$$\mathrm{new}\_X_i=X_i+\mathrm{rand}\left(0,1\right)\left(X_i-X_k\right)+\beta \left(X^{\mathrm{Global}}-X_i\right),$$

(16)

where $\beta$ is the adjustment factor, which is generally a random number between 0 and 1.5. The adjusted value $\beta$ is used to balance the exploration and development capabilities of the algorithm. After the global optimal solution $X^{\mathrm{Global}}$ is added to the search formula, the search range of the algorithm is increased to a certain extent to avoid falling into the local optimal solution.

3.3.3. GABC Algorithm Based on Cross Operation

The GABC algorithm based on the crossover operation combines the basic artificial bee colony algorithm with the crossover operation in the genetic algorithm. In the crossover operation, the two selected individuals are taken as the parent individuals, and the part of the code values of the two is exchanged by bit. The experiment has two eight-bit individuals, P1 and P2, as shown in Figure 9.

A number four between one and seven is randomly generated using the crossover operation to exchange the last four digits of P1 and P2, and a new individual can be obtained. The exchange process is shown in Figure 10.

Figure 11 shows the operation steps of the cross section based on the improved GABC algorithm.

For binomial crossover, a uniformly distributed random value rand between 0 and 1 is generated for each component. If rand < cr, the scout bee randomly finds a new nectar source near the nectar source; otherwise, the current nectar source is kept. The bee performs a cross operation with the global optimal value after the neighborhood search, as shown in the following formula.

$$\mathrm{new}\_X_i=\{\begin{array}{ll}{X}_i,& \mathrm{rand}<cr\\ X^{\mathrm{Global}}+\beta \left(X^{\mathrm{Global}}-X_i\right),& \mathrm{other}\end{array}$$

(17)

The program flowchart of the algorithm is shown in Figure 12.

The pseudocode of the artificial bee colony algorithm based on the cross operation is designed and written to enhance the Algorithm 1, as shown in the following table.

Algorithm 1: Artificial bee colony solving method based on cross operation.

4. Economic Analysis of Wind Elimination Plan

This study installs an electric boiler in the combined heat and power system, thereby increasing the cost of system operation and maintenance and reducing heating profits. Therefore, the practicality of this method is studied from the economic point of view.

4.1. System Benefits

The total revenue of the combined heat and power system includes heating benefit and power supply benefit.

Power supply revenue:

$$R^{\mathrm{E}}={\displaystyle \sum _{t=1}^T\left({\rho }_t^{\mathrm{CHP}}{E}_t^{\mathrm{CHP}}+{\rho }_t^{\mathrm{CON}}{E}_t^{\mathrm{CON}}+{\rho }^{\mathrm{Wind}}{E}^{\mathrm{Wind}}\right)},$$

(18)

where $R^{\mathrm{E}}$ denotes system electricity sales benefit, ten thousand yuan; ${\rho }_t^{\mathrm{CHP}}$ and ${\rho }_t^{\mathrm{CON}}$ denotes the unit electricity costs of thermal power plants and thermal power plants at time t, ten thousand yuan/MWh; ${\rho }^{\mathrm{Wind}}$ denotes the on-grid tariff for wind power, ten thousand yuan/MWh; $E_t^{\mathrm{CHP}}$ and $E_t^{\mathrm{CON}}$ denote total on-grid power of thermal power plants and thermal power plants at time t, and $E^{\mathrm{Wind}}$ denotes the total on-grid power of wind farms in a dispatch period, MW.

Heating income:

$$R^{\mathrm{H}}={\rho }^{\mathrm{H}}{Q}^{\mathrm{CHP}},$$

(19)

where $R^{\mathrm{H}}$ denotes the heating income of thermal power plants, ten thousand yuan; ${\rho }^{\mathrm{H}}$ denotes the unit price of heat sold in thermal power plant, ten thousand yuan; and $Q^{\mathrm{CHP}}$ denotes the total heat supply of all thermal power units in a dispatch period, MW.

4.2. System Cost

The operating cost of the system refers to the system cost under the premise of meeting the demand for the electric heating load when the regular operation of the combined heat and power system is being ensured. In the traditional mode, the cost of the thermal power system only includes fuel purchase cost. In the scheme proposed in this study, maintenance cost, purchase of coal, electric power required for the electric boiler, and depreciation cost constitute the cost of the combined thermal power system.

Coal cost:

$$R^{\mathrm{F}}={\rho }^{\mathrm{F}}\left(F^{\mathrm{CHP}}+F^{\mathrm{CON}}\right),$$

(20)

where $R^{\mathrm{F}}$ denotes coal cost, ten thousand yuan; ${\rho }^{\mathrm{F}}$ denotes the unit price of coal, ten thousand yuan/t; $F^{\mathrm{CHP}}$ denotes the total coal consumption of thermal power plants in the dispatch period, t; and $F^{\mathrm{CON}}$ denotes the total coal consumption of thermal power plants in the dispatch period, t.

Operating cost of electric boiler:

$$R^{\mathrm{ope}}={\displaystyle \sum _{t=1}^T\left({\rho }_t^{\mathrm{ope}}\times {\displaystyle \sum _{i=1}^N{P}_{i,t}^{\mathrm{EB}}}\right)},$$

(21)

where $R^{\mathrm{ope}}$ denotes electric boiler operating cost, ten thousand yuan; ${\rho }_t^{\mathrm{ope}}$ denotes the unit price of electricity sold by the grid at time t, ten thousand yuan/MWh; and $P_{i,t}^{\mathrm{EB}}$ denotes the electric power consumed by electric boiler i at time t, MW.

The cost and depreciation expenses of electric boilers are calculated according to the following formula:

$$R^{\mathrm{dep}}=\left[\frac{I{(1+I)}^n}{{(1+I)}^n-1}\right]V^{\mathrm{E}}$$

(22)

$$V^{\mathrm{E}}=C\times {\displaystyle \sum _{i=1}^N{V}_i^{\mathrm{P}}}$$

(23)

$$V_i^{\mathrm{P}}=k_i{Q}^{\mathrm{Max}}/3.6$$

(24)

where $R^{\mathrm{dep}}$ denotes the cost of depreciation, $V^{\mathrm{E}}$ denotes the installation cost of electric boiler, I denotes working capital interest, n denotes the maximum service life of the electric boiler, $V_i^{\mathrm{P}}$ denotes electric boiler power, C denotes the unit power investment cost of electric boiler, $k_i$ denotes the peak shaving coefficient of electric boiler, and $Q^{\mathrm{Max}}$ denotes the maximum predicted value of heat load.

Maintenance cost of electric boiler:

$$R^{\mathrm{main}}=\beta C\times P_{i,t}^{\mathrm{EB}},$$

(25)

where $R^{\mathrm{main}}$ denotes the maintenance cost of the electric boiler, ten thousand yuan; and $\beta$ indicates the percentage of maintenance cost.

4.3. System Profit

The total system revenue minus the system cost is the system profit. According to Formulas (20)–(25), the system profit R after adding the electric boiler can be obtained.

$$R=R^{\mathrm{E}}+R^{\mathrm{H}}-R^{\mathrm{F}}-(R^{\mathrm{dep}}+R^{\mathrm{main}})T/T_{\alpha }-R^{\mathrm{ope}},$$

(26)

where $T_{\alpha }$ denotes the time for apportioning the total cost of the electric boiler.

The total profit of the system before the addition of the electric boiler is as follows:

$$R^{\prime }={R^{\prime }}^{\mathrm{E}}+{R^{\prime }}^{\mathrm{H}}-{R^{\prime }}^{\mathrm{F}}.$$

(27)

4.4. Impact of Time-of-Use Electricity Price on Program Economy

Peak–valley time-of-use electricity price is an effective demand-side management method at this stage. It is also conducive to peak shaving and valley filling. Its effect depends on scientific peak–valley time division and appropriate time-of-use electricity price. This study uses the membership function to divide the peak and valley moments. Figure 13 shows that the partially small semi-trapezoidal membership function is used to determine the probability that each point on the load curve is in the valley period. Figure 14 shows that the overlarge semi-trapezoidal membership function is used to determine the probability that each point on the load curve is in the peak period.

The peak and trough tariffs on the load side are based on the flat section and adjusted by a 50% increase and decrease, respectively.

$${\rho }^{\mathrm{U}}=1.5{\rho }^{\mathrm{P}},$$

(28)

$${\rho }^{\mathrm{D}}=0.5{\rho }^{\mathrm{P}},$$

(29)

where ${\rho }^{\mathrm{D}}$ denotes user-side electricity price during the low period, ${\rho }^{\mathrm{P}}$ denotes user-side electricity price during the flat period, and ${\rho }^{\mathrm{U}}$ denotes customer-side electricity prices during the peak period.

The electricity price of the Internet (RMB), coal price (RMB/t), and unit price of the heat sold (RMB/MW) issued by the generating set are shown in

Table 3. Electricity price of the Internet, coal price, and price of the heat sold.

Coefficient	Price
${\rho }_t^{\mathrm{CHP}}$	380
${\rho }_t^{\mathrm{CON}}$	400
${\rho }^{\mathrm{Wind}}$	600
${\rho }^{\mathrm{F}}$	700
${\rho }^{\mathrm{H}}$	30
${\rho }^{\mathrm{U}}$	600

.

The improved artificial bee colony algorithm can calculate the optimization results of the two operation modes before and after addition of the electric boiler in a dispatch period. The operating cost and the depreciation cost of the electric boiler are not considered for the time being when the scheme profit is calculated. The optimization results of the scheme and the comparison of the scheme income after the addition of the electric boiler are shown in

Table 4. Optimization results without or with electric boiler.

Operation Mode	Thermal Power Plant (MW)	Pure Thermal Power Unit (MW)	Electric Boiler (MW)	Fan Output (MW)	Heat Supply (MW)	Coal Consumption (t)	System Benefits (Wan Yuan)
Before the addition of electric boiler	32,819	11,862	0	3325	1800	17,404	602.450
After the addition of electric boiler	29,958	12,185	1592	5863	1800	17,040	688.222

.

5. Example Simulation

5.1. Original Data

The calculation example in this study adopts the actual power structure of China’s northern power grid to test the construction feasibility of the model. The power load of the system and the predicted wind power are shown in

Table 5. Wind power forecast and electric load forecast.

Time	Electric Load/MW	Wind Power/MW	Time	Electric Load/MW	Wind Power/MW
09:00	2130	255	21:00	1915	268
10:10	2208	233	22:00	1860	270
11:00	2296	194	23:00	1800	269
12:00	2254	186	24:00	1782	250
13:00	2112	202	01:00	1702	241
14:00	2140	190	02:00	1696	258
15:00	2262	181	03:00	1694	268
16:00	2400	217	04:00	1716	278
17:00	2350	223	05:00	1770	288
18:00	2182	235	06:00	1792	300
19:00	2098	255	07:00	1864	280
20:00	2038	260	08:00	1946	262

. The installed capacity of the grid is shown in

Table 6. Installed capacity and type.

Unit Type	Installed Capacity (MW)	Proportion (%)
Pure thermal power unit	700	25
Thermoelectric unit	1800	64.3
Wind unit	300	10.7

, and the unit parameters are shown in

Table 7. Unit parameters.

Units	Maximum Power Generation/MW	Minimum Power Generation/MW	Maximum Heating Power/MW	ai	bi	ci	Up Rate /MW	Down Rate /MW
1	200	100	250	0.000171	0.2705	11.537	50	50
2	350	175	450	0.000072	0.2292	14.618	70	70
3	350	175	450	0.000072	0.2292	14.618	70	70
4	300	150	400	0.000076	0.2716	18.822	80	80
5	300	150	400	0.000076	0.2716	18.822	80	80
6	300	150	400	0.000076	0.2716	18.822	80	80
7	200	80	0	0.000171	0.2705	11.537	50	50
8	500	200	0	0.000038	0.2716	37.645	130	130

[39].

The power structure of the example in this study includes six thermal power units, two pure condensing units, and one wind power unit. Thermal power units 1, 2, and 3 belong to thermal power plant 1, and thermal power units 4, 5, and 6 belong to thermal power plant 2. Thermal power plants 1 and 2 supply heat to areas 1 and 2, respectively, assuming that the heat supply is 900 MW at the same time.

In the calculation example in this study, the scheduling time is 1 day (24 h), the scheduling step is 1 h, and t = 1, 2, 3,…, 24. The proposed improved artificial bee colony algorithm program is designed and compiled based on MATLAB. The constructed model is simulated and solved, and the simulation results are analyzed and compared.

The MATLAB 2015b platform is used under an Intel i7 processor, 8 GB memory, and the Windows 10 operating system to test the effect of the algorithm in the optimal scheduling of cogeneration. In the selection of the artificial bee colony algorithm parameters, the number of bees is 50, the maximum number of iterations is 1000, and the crossover probability is 0.6. In the selection of the parameters of the particle swarm algorithm, the number of particles is 50, the maximum number of iterations is 1000, and the learning factor is 0.6. The parameters of the memetic algorithm (MA) are as follows: the population size is 50, the number of iterations is 1000, the crossover probability is 0.8, and the mutation probability is 0.15.

5.2. Analysis of Simulation Results

Figure 15 and Figure 16 show the simulation results without and with heat storage, respectively. The simulation results indicate that before the addition of the heat storage device, a large amount of wind abandonment occurs from 18:00 to 8:00. Moreover, nearly no wind abandonment occurs from 9:00 to 18:00.

The scheduling strategy in this study involves increasing the thermal power generator output during the non-wind abandonment period and storing heat in the heat storage device. During the wind abandonment period, the heat storage device releases heat to reduce the output of the thermal power generation unit, thereby increasing the grid space of wind power. This dispatching plan does not change the thermal power generation of the thermal power unit, and the total output of the unit in a day does not change considerably. However, the output range of the unit changes. The increased wind power from the grid replaces the output of the traditional thermal power unit.

Figure 16 shows that the output of conventional units and wind turbines changes correspondingly after the addition of the heat storage device. Figure 16 also shows that the addition of heat storage capacity considerably eliminates wind abandonment, thereby reducing the output of thermal power units. Therefore, power generation costs are considerably reduced, and the effect of clean energy on environmental improvements becomes evident.

The output distribution of each unit and fan before the addition of the heat storage device and electric boiler is shown in Figure 17. At night, the power generation of the fan is almost zero, and a large amount of clean energy cannot be effectively used.

The wind power output of the reference mode and heat storage mode is shown in Figure 18. In the reference mode, the wind abandonment during the low-load period (18:00–8:00) is severe, and wind power has nearly no opportunity to go online. The wind turbine output is consistent with the wind power forecast curve after the heat storage device is added. Moreover, the wind abandonment is solved, thereby improving the utilization rate of wind power.

The electric boiler output is shown in Figure 19, and the heat change of the heat storage device is shown in Figure 20.

The daily power generation of each method with the heat storage device and with no heat storage device is shown in

Table 8. Comparison of various power generation methods.

Operation Mode	Condensing Steam Power Generation (MW)	Thermal Power Generation (MW)	Wind Power Consumption (MW)	Coal Consumption (t)
No heat storage	11,074	32,400	4533	17,426.607
With heat storage	10,087	32,400	5520	17,138.990

.

After the addition of the heat storage device, the wind power consumption increases by 987 MW, and the coal saving of 287.617 t is achieved. However, the thermal power generation of the system does not decrease, and only the condensing steam power generation decreases. This observation indicates that the power generation replaced by the curtailed wind power is the condensing steam power generation. The reason is that the heat storage device changes only the heat production time, but not the heat production. Thus, the thermal power generation does not change.

In this study, the capacity of the electric boiler is 200 MW, and its electric-heat conversion efficiency is taken as 1. The reference, heat storage, and electric boiler modes are simulated. The results of coal consumption, wind power consumption, and power generation of various types of thermal power units are shown in

Table 9. Scheduling results of different operating modes.

Operation Mode	Coal Consumption (t)	Wind Power Consumption (MW)	Thermal Power Generation (MW)	Solution Time (s)
Reference	17,426.61	4533	11,074	1.1
Heat storage	17,040.08	5863	9749	1.7
Electric boiler	17,214.96	5863	11,074	1.9

.

Validation of the Algorithm

Given that the intelligent algorithm has a certain degree of randomness, this study performs 50 iterations and saves the data to make a box plot and verify the effectiveness of the algorithm. The interval of unit output operation is shown in Figure 21.

The yellow part indicates that the unit power range is 25–75%. The range between two lines indicates the minimum power to the maximum power. The red line indicates the power median line.

According to the trend of the box diagram, the unit maintains an increased output during the peak load (non-wind abandonment period), whereas the unit output at night is considerably reduced because the heat storage device is added to reduce the output. The space for the wind power Internet connection is increased with the output of thermal power units. This finding is consistent with the expected results.

This study uses particle swarm algorithm, artificial bee colony algorithm, improved GABC, and MA for solving. The MA is a bionic intelligence algorithm proposed by Australian scholars Moscato and Norman in 1992; this algorithm is a mixture of the global search algorithm and local heuristic search [40].

The number of iterations is compared with convergence speed. Figure 22 indicates that the improved artificial bee colony algorithm has fast convergence speed and enhanced convergence. In addition, a particular theoretical basis is provided to select the method for solving the optimal dispatching model of the power system.

Running time is also an important criterion for the quality evaluation of the algorithm. In this study, the artificial bee colony algorithm and the particle swarm algorithm are timed to solve the calculation examples under the same conditions. The average of 10 running times is taken as the comparison criterion to avoid contingency, as shown in

Table 10. Simulation run time.

Number of Operations	Artificial Bee Colony Algorithm Operation Hours (s)	Particle Swarm Algorithm Operation Hours (s)
1	0.884280	3.449543
2	0.890126	3.753758
3	0.900890	3.525356
4	0.889605	3.233461
5	0.900808	3.468850
6	0.873453	3.292744
7	0.850203	3.367196
8	0.918579	3.375366
9	0.874527	3.201665
10	0.855253	3.267189
Average value	0.883772	3.395513

. The operating results indicate that the artificial bee colony algorithm has better convergence and faster convergence speed than the particle swarm algorithm.

Under the premise of the same original data, the average solution time of [31] is 7.6 s, and the solution time of the algorithm used in this study is 0.88 s. Artificial bee colonies have good performance indicators in terms of solution speed and convergence.

In this study, the mutation method is compared with the following five methods to test the performance of the presented method: PSO, ABC, MA, and GABC. We implemented the above four algorithms to explore the same objective function. These four mutation methods were operated on the same computer. The four methods were independently operated 10 times for every instance. The relative percentage increase (RPI) is calculated for the replication. The compared results are shown in

Table 11. RPI values obtained by different algorithms.

Number of Runs	PSO	ABC	MA	GABC
1	13.051	11.454	6.887	0.756
2	13.044	11.175	7.394	0.705
3	12.896	11.046	7.423	0.680
4	12.655	10.867	7.527	0.541
5	12.598	10.206	7.598	0.123
6	12.505	9.131	7.601	0.075
7	10.650	9.0179	7.781	0.073
8	10.646	8.827	7.982	0.017
9	10.471	8.501	8.360	0.008
10	9.702	6.894	5.344	0
Mean	11.822	9.712	7.389	0.298

. The RPI is given to measure the performance, which is shown by the following:

$$RPI\left(f\right)=\frac{\left(f-f^{*}\right)}{f^{*}}\times 100,$$

(30)

where $f$ represents the solution created by the algorithm, and $f^{*}$ represents the best solution found by any of the algorithms in the comparison.

A “multifactor analysis of variance” is performed where the type of algorithm is defined as factors to verify the observed differences in the statistics from Table 11. The results are presented in Figure 23 at a 95% confidence level. The GABC algorithm reflects significantly better performance.

Meanwhile, the binomial crossover is used as a different behavior. All of these changes should be evaluated individually to demonstrate their impact on the behavior of the algorithm as a whole. The RPI values obtained under different behaviors are shown in

Table 12. RPI values obtained by different behaviors.

Number of Runs	ABC	GABC	Only Considering Crossover Operations	Only Considering the Global
1	12.296	1.236	6.125	8.739
2	11.228	0	6.561	8.067
3	11.020	1.160	6.669	8.333
4	10.525	1.417	6.805	7.761
5	9.866	0.604	7.591	7.104
6	8.795	0.557	7.662	7.215
7	8.681	0.950	6.795	7.496
8	8.492	1.289	7.053	8.385
9	8.166	2.071	6.844	7.377
10	6.565	1.272	7.239	6.606
Mean	9.563	1.056	6.934	7.708

.

Table 12 establishes that the scheduling results solved by the improved algorithm are obviously excellent.

6. Conclusions

In this study, heat storage devices and electric boilers are based on the traditional model. The artificial bee colony algorithm in the new swarm intelligence algorithm is used to solve the problem. Simulation examples verify the effectiveness of the proposed method, and the following conclusions can be obtained.

(1)

Compared with the reference mode, the cogeneration operation mode involving the addition of heat storage devices and electric boilers increases wind energy to generate power, reduces the occurrence of wind abandonment, nearly doubles the wind power generation, and improves the utilization rate of wind energy.

(2)

After the addition of an electrical energy storage device, the gap between the peak and valley of the electric load is considerably reduced, the system stability is increased, and the safe operation of the power system is beneficial.

(3)

The simulation results show that when the electric boiler and the heat storage device provide heat in coordination, all wind energy can be consumed, thereby achieving the best economic efficiency.

(4)

The addition of electric boilers reduces the coal consumption of the system and saves approximately 1000 tons of coal. The revenue of the system is also increased by approximately 10%. These results are valuable to the concept of sustainable development.

In summary, the scheme in this study can improve the utilization rate of wind power and reduce power generation costs. It also provides a theoretical basis for the day-ahead dispatch method of the power system. However, this study does not consider the heat loss of the heat storage device, which should be further analyzed and discussed in practical applications.