Provincial Electricity–Heat Integrated Energy System Optimal Dispatching Model for Time-Series Production Simulation

Abstract

This paper focuses on the provincial integrated energy system in northern China, which is characterized by the large-scale integration of renewable energy, thorough coupling of electricity and heat, and interactive operation of sources, loads, and storages. When conducting time-series production simulation with the daily rolling optimization dispatching method, the embedded daily optimal dispatching model fails to effectively charge and discharge electric and thermal energy storages across days to accommodate the curtailed electricity from renewable energy. Thus, a new embedded daily optimal dispatching model is proposed. The new model adopts a strategy of converting the stored energy of electric and thermal energy storages at the end of the dispatching day into equivalent coal consumption, respectively, and deducting it from the objective function of the optimal dispatching model. Through theoretical analysis, the reasonable range of the conversion coefficient is determined, enabling the model to use electric and thermal energy storages to store the curtailed electricity during surplus power generation in a dispatching day and accommodate it in subsequent days. A case study based on a provincial electricity–heat integrated energy system in northern China shows that the curtailment of renewable energy with the suggested strategy is much less than that with the traditional strategy, verifying the effectiveness of the proposed model.

1. Introduction

Thermal power plants are being retrofitted for electricity–heat decoupling [1], the deployment of grid-side energy storage [2], and the rapid development of new P2X loads such as power to gas and power to hydrogen [3]. The energy system in northern China is gradually evolving into a provincial-level integrated energy system characterized by thorough electricity–heat coupling and multi-dimensional interaction among sources, loads, and energy storage.

Conducting a time-series production simulation for the energy system for 8760 h throughout the year is an important way to obtain the future operational status of an energy system with a high proportion of renewable energy [4]. However, when carrying out long-term time-series production simulation for the above-mentioned energy system, challenges related to the huge scale of model variables and the complex representation of the multi-energy balance mechanism can occur.

To date, a substantial body of literature has been dedicated to the research on this issue. For example, reference [5] highlights that the development of integrated energy systems relies on the support of integrated energy simulation and planning platforms, and compares and introduces the simulation-planning functions, energy service types, and platform characteristics of 10 representative simulation-planning platforms. Reference [6] emphasizes that selecting appropriate energy tools is crucial for analyzing the integration of renewable energy into diverse energy systems under different objectives. It also evaluates 37 energy tools in this regard.

In these studies, the time-series production simulation of energy systems can be categorized into two technical approaches. The first is the heuristic time-series production simulation method, which first aggregates similar devices and then achieves hourly calculations by pre-setting coordination and operation rules among devices to obtain balanced results. Typical platforms such as EnergyPLAN [7,8,9] have been widely used in the production simulation and analysis of national-level energy systems in Europe [10,11] and South America [12], as well as provincial-level integrated energy systems in China [13,14,15,16], including countries and regions such as Denmark, Norway, Colombia, the Beijing–Tianjin–Hebei region, Inner Mongolia, Sichuan, and Jiangsu. The advantages of this method lie in its simple and transparent principle, clear device operation rules, and fast calculation speed. Its main drawback is that with the advancement of coal power flexibility transformation, the configuration of diversified energy storage, and the development of multiple types of P2X, the structural complexity of the source–load–storage system has significantly increased, making it difficult to design coordination and balance strategies among different energy sources and device types.

The other category is the time-series production simulation method based on optimal dispatching. This kind of method only requires the reasonable setting of the objective function and constraint conditions of the optimization model to achieve the coordinated operation of various devices, avoiding the flaw of heuristic methods where complex device coordination operation strategies need to be set in advance. Therefore, it can be applied to more complex operation scenarios. A typical example is the Balmorel platform [17], which can conduct hourly time-series production simulation throughout the year and obtain the interactive operation status of electrical and thermal devices within the system. For example, reference [18] uses the Balmorel model based on a linear programming algorithm and mixed-integer programming algorithm to carry out research on wind power accommodation; reference [19] employs the open-source energy modeling framework Balmorel to analyze the decarbonization pathways for space heating and domestic hot water beyond the centralized power generation sector. Reference [20] constructed a time-series production simulation model similar to the optimal dispatching idea of Balmorel and incorporated it into the system planning model, achieving the optimized calculation of the system’s production simulation for 8760 h throughout the year. The advantages of this type of method include that it is easy to show the multi-dimensional coordination and balance mechanism of electricity–heat and sources–loads–storages through the optimal dispatching model. The disadvantage is that with the increase in the structural complexity of the energy system, there are a huge number of variables and complex constraints similar to the start-stop of units and the coupling of energy storage, making the model solution increasingly difficult.

In order to improve the efficiency of the optimization solution, the Balmorel platform and Reference [20] have, respectively, adopted the methods of integrating typical periods week by week and aggregating typical scenarios month by month to achieve the dimensionality reduction and simplification of the optimization problem in the time scale, thus improving the solution speed. However, scenario aggregation will reduce the representation of the volatility of wind power, resulting in relatively large precision loss and making the production simulation results less accurate. Therefore, the method of rolling day by day in time is often adopted to simplify the solution of the time-series production simulation model, such as in reference [21], which establishes a critical time-section selection strategy based on the iterative method to improve the solution efficiency of the time-series production simulation model. Due to the low computational complexity of the problem, Reference [22] directly adopts time-by-time production simulation to obtain the unit output for each time period. Reference [23] adopts a hierarchical time-series production simulation method. Reference [24] presents an interior point method to accelerate the convergence speed of solving the optimal power flow problem. Additionally, Reference [25] proposes a daily rolling balance calculation method.

In a system with a high proportion of both wind power and energy storage, since a single fluctuation process in wind power often lasts for several days [26,27,28], there is a high probability of overall power generation surplus on windy days, while on light-wind days, a power shortage is shown [29]. For electrical energy storage, during actual dispatching, it is necessary to store curtailed wind power on windy days for use on subsequent light-wind days, thus realizing the cross-cycle charging and discharging of electrical energy storage. As for thermal energy storage, in order to discharge on windy days to accommodate wind power, it is necessary to make full use of the combined heat and power generation opportunities on light-wind days before the arrival of windy days to store heat as much as possible in advance, which also requires realizing cross-dispatching cycle charging and discharging. However, the existing methods that currently conduct rolling optimization with a daily dispatching cycle and impose constraints on the stored energy of electrical and thermal energy storage at the end of the day have a new problem: that the energy storage devices cannot accommodate wind power across the dispatching cycle [30]. Moreover, expanding the dispatching decision-making cycle will lead to other problems, such as difficulty in determining the decision-making cycle due to the instability of the wind power cycle and the nonlinear increase in computational complexity [20,31].

To address the issue that the existing embedded daily optimal dispatching model fails to effectively charge and discharge electric and thermal energy storages across days to accommodate the curtailed electricity from renewable energy during the daily rolling optimal dispatching in the time-series production simulation, a new daily optimal dispatching model is proposed. The new dispatching model adopts the strategy of converting the stored energy of electric and thermal energy storages at the end of the dispatching day into equivalent coal consumption, respectively, and deducting it from the objective function of the optimal dispatching model. Through theoretical analysis, the reasonable range of the conversion coefficient is determined, enabling the model to store the curtailed electricity with electric and thermal energy storages during the surplus power generation in a dispatching day and accommodate it in subsequent dispatching days.

2. Provincial Energy System Structure and Production Simulation Ideas

2.1. Energy System Structure

Taking the energy system in northern China as the object, the system not only includes traditional power sources such as wind power, photovoltaics, hydropower, nuclear power, coal power, and AC and DC transmission lines, as well as heat sources such as coal-fired cogeneration, nuclear power cogeneration, and coal-fired boilers, it also includes diversified electric energy storage, thermal energy storage, electric heating, and flexible power loads. The system structure is shown in Figure 1.

In this system, wind power, photovoltaics, hydropower, nuclear power, coal-fired power, and electric energy storage provide electric energy for the power grid. Centralized electric boilers, cogeneration units, coal-fired boilers, nuclear power, and thermal energy storage supply heat for the heating network. Together, they form an integrated energy system with thermoelectric coupling.

2.2. Ideas for Time-Series Production Simulation Based on Daily Rolling Optimal Dispatching

When conducting a time-series production simulation for the above-mentioned provincial electricity–heat integrated energy system, the daily rolling optimal dispatching method is usually adopted. One day is taken as a dispatching decision-making cycle, and the annual production simulation results are obtained through daily rolling dispatching calculations.

For a certain day, the main process of production simulation is as follows:

(1) Obtain the parameters of various source, load, and storage units participating in the production simulation on that day, and aggregate them by considering factors such as whether to supply heat or not to form an aggregated system, as shown in Figure 1.

(2) For the aggregated system, construct a daily optimal dispatching model of the electricity–heat integrated energy system, as described in Section 3, below.

(3) Solve this optimal dispatching model to obtain results such as the time-series operating power of the source, load, and storage units on that day.

(4) Take the stored energy of the electrical and thermal energy storages on that day as the inter-day coupling parameter and pass it to the next day as an input to conduct the production simulation of the next day, thus realizing the daily rolling calculation.

(5) Based on the results of the daily rolling calculation, the time-series operating curves of various source, load, and storage devices within the year can be obtained in the assessment year. Furthermore, various indicators can be statistically obtained.

The flow chart of time-series production simulation is as shown in Figure 2. Based on this flowchart, a production simulation tool was built using MATLAB (Version R2023b). The core of this tool is the solution module for the daily optimization dispatching model, which is solved by the CPLEX commercial solver.

2.3. Energy System Aggregation Strategy

The core of the above time-series production simulation method based on daily rolling optimal dispatching lies in the construction of the optimal dispatching model for the electricity–heat integrated energy system on a single day. With the improvement of the flexibility retrofit of coal-fired power generation, the configuration of diversified energy storage, and the development of flexible loads, the structure of the provincial electricity–heat coupling system has become increasingly complex. Even with a cycle of one day or multiple days, the computational scale for solving this production simulation problem remains extremely large. Therefore, considering that production simulation mainly focuses on the results of macroscopic balance rather than the operating conditions of individual devices, this paper refers to the methods in References [7,9] and aggregates similar devices before conducting the daily optimal dispatching calculation. The structure of the aggregated system is as shown in Figure 1, as mentioned above. Reference [9] shows through analysis that by carefully setting the aggregation method and aggregation parameters, the output range, consumption characteristics, and operating efficiency of the aggregated units can be very similar to those before aggregation, and this will have little impact on the accuracy of the macroscopic balance results.

During the aggregation process, considering that whether the units supply heat or not will change dynamically on different dates during the heating period, for each decision-making day, it is necessary to dynamically determine whether the units are in the heating state according to the heat load and the relevant operation mode documents released by the energy regulatory authorities, and then determine the capacities of the condensing units and the heating units in Figure 1.

Regarding energy storage, considering that the power grids in northern China mainly use electro-chemical energy storage and pumped storage, this paper aggregates the existing energy storage into two types of electrical energy storage with time scales of short (2 h) and medium (8 h) according to the time scale [32].

3. A Daily Optimal Dispatching Model Realizing Cross-Day Charging and Discharging of Energy Storage

Aiming at the aggregated provincial electricity–heat integrated energy system shown in Figure 1, this section constructs its daily optimal dispatching model. The model takes minimizing the coal consumption as the main objective, and realizes the cross-day charging and discharging of energy storage by converting the energy stored at the end of the day in both electrical and thermal energy storage devices into equivalent coal consumption and deducting it from the objective function.

3.1. Objective Function

The objective function of the daily dispatching model consists of five parts, as shown in Formula (1). In the formula, $Z_1$ is the operating coal consumption of coal-fired power and coal-fired boilers, $Z_2$ is the starting coal consumption of condensing coal-fired power to increase the starting capacity on this day, $Z_3$ is the coal consumption converted by load loss penalty, $Z_4$ is the equivalent coal consumption converted from the compensation for the demand response call of flexible loads, and $Z_5$ is used to guide the electric and thermal energy storage to achieve cross-day charging and discharging according to the dispatching strategy to accommodate curtailed renewable energy.

$$Z=\min (Z_1+Z_2+Z_3+Z_4-Z_5)$$

(1)

3.1.1. Power and Heat Source Coal Consumption Model

(1) The operation coal consumption of the coal-fired power and coal-fired boiler is as follows:

$$\left\{\begin{array}{l}{Z}_1={\displaystyle \sum _{\mathrm{t}=1}^T(F_{\mathrm{CON}}^t+F_{\mathrm{CHP}}^t+}{F}_{\mathrm{BO}}^t)\\ F_{\mathrm{CON}}^t=a_{\mathrm{CON}}{(P_{\mathrm{CON}}^t)}^2+b_{\mathrm{CON}}{P}_{\mathrm{CON}}^t+c_{\mathrm{CON}}\\ F_{\mathrm{CHP}}^t=a_{\mathrm{CHP}}{(P_{\mathrm{CHP}}^t+{\mathrm{c}}_v{Q}_{\mathrm{CHP}}^t)}^2+b_{\mathrm{CHP}}(P_{\mathrm{CHP}}^t+{\mathrm{c}}_v{Q}_{\mathrm{CHP}}^t)+c_{\mathrm{CHP}}\\ F_{\mathrm{BO}}^t=a_{\mathrm{BO}}{(Q_{\mathrm{BO}}^t)}^2+b_{\mathrm{BO}}{Q}_{\mathrm{BO}}^t+c_{\mathrm{BO}}\end{array}\right.$$

(2)

In the formula, $t$ is the serial number of the period, $T$ is the total number of time periods in the day; the subscripts CON, CHP and BO denote aggregated condensing coal-fired power, aggregated cogeneration coal-fired power and aggregated coal-fired boilers, respectively; $P_{\mathrm{CON}}^t$ and $P_{\mathrm{CHP}}^t$ are the generation power of aggregated condensing and cogeneration coal-fired power, respectively; $Q_{\mathrm{CHP}}^t$ and $Q_{\mathrm{BO}}^t$ are the heating power of aggregated cogeneration coal-fired power and aggregated coal-fired boiler, respectively; $F_{\mathrm{CON}}^t$, $F_{\mathrm{CHP}}^t$ and $F_{\mathrm{BO}}^t$ are the operating coal consumption of aggregated three types units in time period $t$, respectively; and $a_{\mathrm{CON}}$, $b_{\mathrm{CON}}$, $c_{\mathrm{CON}}$, $a_{\mathrm{CHP}}$, $b_{\mathrm{CHP}}$, $c_{\mathrm{CHP}}$, $a_{\mathrm{BO}}$, $b_{\mathrm{BO}}$, and $c_{\mathrm{BO}}$ are the coefficients of the coal consumption function for the three types of units, respectively. $c_{\mathrm{v}}$ is the loss coefficient of the power generation caused by the extraction of steam heating in the aggregated cogeneration unit [9].

When aggregating units, in order to ensure that the coal consumption rate after aggregation is basically the same as that before aggregation, the coefficient of the coal consumption function of the three types of units can be set by Formula (3), based on the parameters of the mainstream units within the system.

$$\left\{\begin{array}{l}{a}_{\mathrm{CON}}={\displaystyle \frac{a_{\mathrm{CON}\_\mathrm{com}}{C}_{\mathrm{CON}\_\mathrm{com}}}{C_{\mathrm{CON},\mathrm{on}}}},b_{\mathrm{CON}}=b_{\mathrm{CON}\_\mathrm{com}},c_{\mathrm{CON}}={\displaystyle \frac{C_{\mathrm{CON},\mathrm{on}}}{C_{\mathrm{CON}\_\mathrm{com}}}}{c}_{\mathrm{CON}\_\mathrm{com}}\\ a_{\mathrm{CHP}}={\displaystyle \frac{a_{\mathrm{CHP}\_\mathrm{com}}{C}_{\mathrm{CHP}\_\mathrm{com}}}{C_{\mathrm{CHP},\mathrm{on}}}},b_{\mathrm{CHP}}=b_{\mathrm{CHP}\_\mathrm{com}},c_{\mathrm{CHP}}={\displaystyle \frac{C_{\mathrm{CHP},\mathrm{on}}}{C_{\mathrm{CHP}\_\mathrm{com}}}}{c}_{\mathrm{CHP}\_\mathrm{com}}\\ a_{\mathrm{BO}}={\displaystyle \frac{a_{\mathrm{BO}\_\mathrm{com}}{C}_{\mathrm{BO}\_\mathrm{com}}}{C_{\mathrm{BO},\mathrm{on}}}},b_{\mathrm{BO}}=b_{\mathrm{BO}\_\mathrm{com}},c_{\mathrm{BO}}={\displaystyle \frac{C_{\mathrm{BO},\mathrm{on}}}{C_{\mathrm{BO}\_\mathrm{com}}}}{c}_{\mathrm{BO}\_\mathrm{com}}\end{array}\right.$$

(3)

In the formula, $a_{\mathrm{CON}\_\mathrm{com}}$, $b_{\mathrm{CON}\_\mathrm{com}}$, $c_{\mathrm{CON}\_\mathrm{com}}$, $a_{\mathrm{CHP}\_\mathrm{com}}$, $b_{\mathrm{CHP}\_\mathrm{com}}$, $c_{\mathrm{CHP}\_\mathrm{com}}$, $a_{\mathrm{BO}\_\mathrm{com}}$, $b_{\mathrm{BO}\_\mathrm{com}}$, and $c_{\mathrm{BO}\_\mathrm{com}}$ are the coefficients of the coal consumption function of a typical single condensing coal-fired power unit, combined heat and power coal-fired power unit, and coal-fired boiler, respectively. $C_{\mathrm{CON},\mathrm{on}}$, $C_{\mathrm{CHP},\mathrm{on}}$, and $C_{\mathrm{BO},\mathrm{on}}$ are the operating capacities of the three types of units within the dispatching day; $C_{\mathrm{CON}\_\mathrm{com}}$, $C_{\mathrm{CHP}\_\mathrm{com}}$, and $C_{\mathrm{BO}\_\mathrm{com}}$ are the typical single-unit capacities of the three types of units.

The operating capacity of the condensing unit within the dispatching day is shown in Formula (4).

$$C_{\mathrm{CON},\mathrm{on}}=C_{\min ,\mathrm{CON},\mathrm{on}}+\Delta C_{\mathrm{slt},\mathrm{CON}}$$

(4)

In the formula, slt denotes the optional opening unit; $C_{\min ,\mathrm{CON},\mathrm{on}}$ is the must-open condensing coal-fired power opening capacity of the dispatching day, which is set by the minimum operation mode of the system; and $\Delta C_{\mathrm{slt},\mathrm{CON}}$ is the actual opening capacity of the optional opening condensing coal-fired power.

(2) Start-up coal consumption for increased start-up capacity of condensing coal power units:

$$Z_2=e_{\mathrm{CON}\_\mathrm{com},\mathrm{up}}\cdot {\displaystyle \frac{(C_{\mathrm{CON},\mathrm{on}}-C_{\mathrm{CON},\mathrm{on}}^{\mathrm{ytd}})}{C_{\mathrm{CON}\_\mathrm{com}}}},C_{\mathrm{CON},\mathrm{on}}^{\mathrm{ytd}}\le C_{\mathrm{CON},\mathrm{on}}$$

(5)

where ytd is the last dispatching day index and ${\mathrm{e}}_{\mathrm{CON}\_\mathrm{com},\mathrm{up}}$ is the start-up coal consumption of a single mainstream condensing coal-fired power unit. Considering that the current large-scale condensing coal-fired power does not perform intra-day startup and shutdown peaking, it is assumed that the capacity of aggregated condensing coal power units started up in each time period in the same dispatching day is equal.

3.1.2. Coal Consumption Converted from Load Loss Penalty and Demand Response Model

(1) The coal consumption converted from the penalty for load loss is as follows:

$$Z_3=e_{\mathrm{lack}}\cdot {\displaystyle \sum _{\mathrm{t}=1}^T{P}_{\mathrm{lack}}^t}$$

(6)

where $P_{\mathrm{lack}}^t$ is the load loss power of the system t period; $e_{\mathrm{lack}}$ is the coal consumption coefficient converted by the load loss penalty.

(2) The coal consumption converted from the compensation for the invocation of load demand response is as follows:

$$Z_4=e_{\mathrm{drp}1}\cdot {\displaystyle \sum _{\mathrm{t}=1}^T{P}_{\mathrm{drp}\_\mathrm{out}}^t}+e_{\mathrm{drp}2}\cdot {\displaystyle \sum _{\mathrm{t}=1}^T{P}_{\mathrm{drp}\_\mathrm{cut}}^t}$$

(7)

where $P_{\mathrm{drp}\_\mathrm{out}}^t$ and $P_{\mathrm{drp}\_\mathrm{cut}}^t$ are the transferable and interruptible electric power of the demand response at time t; ${\mathrm{e}}_{\mathrm{drp}1}$ and ${\mathrm{e}}_{\mathrm{drp}2}$ are the compensation coefficients (converted to coal consumption rate) for calling the power of this type of demand response, respectively. Since the transferable demand response has to be equal in terms of transfer-in and transfer-out power in the dispatching day, it is sufficient to compensate only the transfer-out power in the objective function.

3.1.3. Equivalent Consumption Model of Electrical and Thermal Energy Storage

In order to realize the cross-day charging and discharging of electric and thermal energy storage according to the demand of wind and solar accommodation in the production simulation based on daily rolling optimization dispatching, considering that the charge of electricity storage is to replace the subsequent condensing coal-fired power generation and the charge of heat storage is to replace the subsequent cogeneration heat discharge, this paper proposes a strategy of converting the stored energy of electric and thermal energy storage in this day into equivalent coal consumption and then deducting it in the objective function. The equivalent coal consumption is shown in Formula (8).

$$Z_5=\alpha \cdot {\displaystyle \sum _{i=1}^3{\eta }_{\mathrm{es},i}\cdot (H_{\mathrm{es},i}^{\mathrm{T}}-H_{\mathrm{es},i}^0)+\beta \cdot {\eta }_{\mathrm{hs}}\cdot (H_{\mathrm{hs}}^{\mathrm{T}}-H_{\mathrm{hs}}^0)}$$

(8)

where $\mathrm{es}$ denotes electrical storage, $\mathrm{hs}$ denotes thermal storage, $i$ is the index of the type of electric energy storage, and the serial numbers 1 and 2 denote hourly regulated energy storage (electro-chemical energy storage) and daily regulated energy storage (pumped storage), respectively. $\alpha$ and $\beta$ are the equivalent coal consumption rates of electric storage and heat storage, respectively, in kg/MWh. $H_{\mathrm{es},i}^0$, $H_{\mathrm{es},i}^{\mathrm{T}}$, $H_{\mathrm{hs}}^0$, and $H_{\mathrm{hs}}^{\mathrm{T}}$ are the energy stored of the electric and heat energy storage in the first and last periods of the dispatching day, respectively; ${\eta }_{\mathrm{es},\mathrm{i}}$ and ${\eta }_{\mathrm{hs}}$ are the operating efficiencies of electric and thermal energy storage, respectively. By deducting the equivalent coal consumption as shown in (8) from the objective function (1), the electric energy storage can be guided to store electricity during the power curtailment period or converted curtailed electricity to heat energy for storage for the next dispatching cycle.

3.2. Analysis of Equivalent Coal Consumption Conversion Coefficient of Electric and Thermal Energy Storage

In the above model, the conversion coefficients of the equivalent coal consumption rates for electrical and thermal energy storage are key parameters of the optimization model, which guide the coordinated operation of the two types of energy storage and prevent the occurrence of unreasonable charging and discharging behaviors.

(1) Analysis of the Values of the Conversion Coefficient of the Equivalent Coal Consumption for Electrical Energy Storage

The conversion coefficient rate of the equivalent coal consumption for electrical energy storage should theoretically be equal to the marginal coal consumption rate of the power generation of the condensing units that will be replaced in the future. However, when the adopted conversion coefficient is higher than the marginal coal consumption rate of the power generation of the condensing units within this cycle, the objective function will guide the electrical energy storage to store the power generated by the condensing units within this cycle. To avoid this situation, this paper takes the conversion coefficient as the minimum marginal coal consumption of power generation of the aggregated condensing units in this cycle; that is, the value of $\alpha$ should satisfy Formula (9).

$$\alpha \le \min ({\displaystyle \frac{d{F}_{\mathrm{CON}}^t}{d{P}_{\mathrm{CON}}^t}})$$

(9)

(2) Analysis of the Values of the Conversion Coefficient of the Equivalent Coal Consumption Rate for Thermal Energy Storage

In order to guide the combined heat and power (CHP) units to utilize the power generation opportunities for combined heating during the non-curtailment periods of this cycle for subsequent deep peak shaving, the deducted coal consumption should be greater than or equal to the maximum marginal coal consumption rate for heating of the aggregated extraction condensing generating units. Therefore, the value of $\beta$ should satisfy the following formula.

$$\beta \ge \max \left\{{\displaystyle \frac{d{F}_{\mathrm{CHP}}^t}{d{Q}_{\mathrm{CHP}}^t}}\right\}$$

(10)

When an extraction-condensing unit is equipped with an electric boiler, the coordination between the unit and the electric boiler can achieve an effect similar to that of direct heating by the unit’s boiler [33]. The principle is shown in Figure 3. In the figure, the area enclosed by ABCD is the operating range of the extraction-condensing heat and power generation unit. The line segment BC is the back-pressure operating condition line when the low-pressure turbine of the unit is at the minimum steam inlet volume. $P_{\mathrm{CHP},\mathrm{pp},\min }$ is the condensing power generation capacity corresponding to the minimum steam inlet volume of the low-pressure turbine of the extraction-condensing unit; $Q_{\mathrm{F}}$ is the heating capacity corresponding to the minimum power generation capacity of the unit; ${\mathrm{c}}_m$ is the electric-to-heat ratio of the extraction-condensing unit under the back-pressure operating condition; and ${\eta }_{\mathrm{eb}}$ is the electric-to-heat conversion efficiency of the electric boiler. When the unit operates at point M, the unit can simultaneously increase power generation and heating generation along its back-pressure line (such as at point N), and use the electric boiler to convert the increased electric energy into heat energy (equivalent to operating at point K in the figure). In this way, it is possible to increase the heating amount $(1+{\mathrm{c}}_m{\eta }_{\mathrm{eb}})\Delta P$ while the power generation remains unchanged. If the efficiency loss is ignored, the above method will be equivalent to direct heating by the boiler steam [33].

At this time, if the value of the conversion coefficient rate of the equivalent coal consumption is greater than the heating coal consumption rate under the above operating mode, it will lead to the storage of the direct heat supply because the deducted coal consumption rate for heat storage in the objective function will be higher than the coal consumption rate of the direct heat supply by the boiler. In order to avoid this situation, the value of $\beta$ should satisfy the following formula:

$$\beta <\min \left\{{\displaystyle \frac{F_{\mathrm{CHP}}^t(P_{\mathrm{CHP}}^t+{\mathrm{c}}_m,Q_{\mathrm{CHP}}^t+1)-F_{\mathrm{CHP}}^t(P_{\mathrm{CHP}}^t,Q_{\mathrm{CHP}}^t)}{1+{\mathrm{c}}_m\cdot {\eta }_{\mathrm{eb}}}}\right\}$$

(11)

(3) Analysis of the values of conversion coefficients for the coordinated operation of electrical and thermal energy storage

When both electrical energy storage and thermal energy storage exist in the system, if the conversion coefficients of the two types of energy storage are too large, this will also guide the heating units to simultaneously increase power generation and heat generation along the back-pressure line (line CB), as shown in Figure 3, and store the electricity and heat in the electrical energy storage and thermal energy storage devices, respectively. In order to prevent this situation from occurring, the values of the conversion coefficients of the equivalent coal consumption of the two types of energy storage should also meet the constraint that the deducted coal consumption in this mode is less than the production coal consumption; that is, the combined values of $\alpha$ and $\beta$ should satisfy the following formula:

$$\alpha {\mathrm{c}}_m+\beta <\min \{F_{\mathrm{CHP}}^t(P_{\mathrm{CHP}}^t+{\mathrm{c}}_m,Q_{\mathrm{CHP}}^t+1)-F_{\mathrm{CHP}}^t(P_{\mathrm{CHP}}^t,Q_{\mathrm{CHP}}^t)\}$$

(12)

At the same time, it should be considered that the electricity stored replaces the power generation of condensing units in subsequent dispatching cycles, while the heat stored replaces the combined heat and power unit’s heating generation. Therefore, the energy-saving benefit of electricity storage is much greater than that of heat storage. Thus, the values of $\alpha$ and $\beta$ should satisfy the following formula:

$$\alpha >\beta$$

(13)

3.3. Constraint Condition

The constraints in the optimal dispatching model include the power-feasible region constraints of wind power, photovoltaics, hydropower, nuclear power, condensing coal-fired power, CHP coal-fired power, coal-fired boilers, electric boilers, and other power and heat sources; energy-feasible region constraints for energy storage devices such as electrochemical storage, pumped storage, hydrogen storage, and thermal energy storage; and interruptible and transferrable demand response capability constraints and system constraints such as system capacity balance, power balance, heat balance, and other system constraints. In a single decision-making cycle, the following constraints are imposed on each time period t.

(1) Aggregated wind and photovoltaic output boundary constraints:

Wind and PV output should be less than their maximum generating power:

$$\left\{\begin{array}{l}{P}_{\mathrm{wind}}^t\le C_{\mathrm{wind},\mathrm{fore}}\cdot {\lambda }_{\mathrm{wind},\mathrm{pu}}^t\\ P_{\mathrm{solar}}^t\le C_{\mathrm{solar},\mathrm{fore}}\cdot {\lambda }_{\mathrm{solar},\mathrm{pu}}^t\end{array}\right.$$

(14)

where wind and solar denote wind power and photovoltaics, respectively; fore and pu denote forecast and pu unit values, respectively; $P_{\mathrm{wind}}^t$ and $P_{\mathrm{solar}}^t$ are the system t time period for wind power and photovoltaic power generation; and the value is obtained through the assessment of the level of annual installed capacity of wind power and photovoltaics, $C_{\mathrm{wind},\mathrm{fore}}$, $C_{\mathrm{solar},\mathrm{fore}}$, multiplied by the historical hourly standard generation curve ${\lambda }_{\mathrm{wind},\mathrm{pu}}^t$, ${\lambda }_{\mathrm{solar},\mathrm{pu}}^t$.

(2) Aggregated hydropower operational boundary constraints:

$$\left\{\begin{array}{l}0\le P_{\mathrm{hyd}}^t\le C_{\mathrm{hyd}}\\ {\displaystyle \sum _{t=1}^T{P}_{\mathrm{hyd}}^t}=W_{\mathrm{hyd}}\end{array}\right.$$

(15)

where hyd denotes hydropower, $C_{\mathrm{hyd}}$ is the maximum available capacity for hydropower generation (usually less than the installed capacity), $W_{\mathrm{hyd}}$ is the total hydropower generation in the cycle, and $P_{\mathrm{hyd}}^t$ is the generation power of aggregated hydropower in time period t.

(3) Aggregated condensing coal-fired power operation boundary constraints:

$${\partial }_{\min ,\mathrm{CON}}{C}_{\mathrm{CON},\mathrm{on}}\le P_{\mathrm{CON}}^t\le C_{\mathrm{CON},\mathrm{on}}$$

(16)

where CON denotes aggregated condensing coal-fired power; ${\partial }_{\min ,\mathrm{CON}}$ is the minimum output rate of condensing coal-fired power; $P_{\mathrm{CON}}^t$ is the generation power of condensing coal-fired power in time period t; and $C_{\mathrm{CON}}$ is the total installed capacity of condensing coal-fired power. Since in this paper the heating units that do not operate with heat loads are also regarded as condensing units, the value of $C_{\mathrm{CON}}$ is dynamically changed and is closely related to the intra-annual period in which the cycle is located.

(4) Aggregated CHP coal-fired power operation boundary constraints:

$$\left\{\begin{array}{l}{P}_{\mathrm{CHP}}^t\ge P_{\mathrm{CHP},\mathrm{pp},\min }+c_{\mathrm{m}}{Q}_{\mathrm{CHP}}^t\\ P_{\mathrm{CHP}}^t\ge P_{\mathrm{CHP},\mathrm{pp},\min }+c_{\mathrm{m}}{Q}_{\mathrm{CHP}}^t-(c_{\mathrm{v}}+c_{\mathrm{m}})(Q_{\mathrm{CHP}}^t-Q_{\mathrm{F}})\\ P_{\mathrm{CHP}}^t\le C_{\mathrm{CHP},\mathrm{on}}-c_{\mathrm{v}}{Q}_{\mathrm{CHP}}^t\\ Q_{\mathrm{CHP}}^t\ge 0\end{array}\right.$$

(17)

Equation (17) describes the feasible region of the aggregated extraction-condensing unit shown in Figure 2.

(5) Aggregated nuclear power operational constraints

$$P_{\mathrm{nuc}}^t=C_{\mathrm{nuc},\mathrm{fore}}-c_{\mathrm{v}\_\mathrm{nuc}}\cdot Q_{\mathrm{nuc}}^t$$

(18)

Nuclear power mainly bears a base load, and generally only in the maintenance period to reduce the output power. In the production simulation, it can be considered that the maintenance status of the nuclear power unit is known, so the power, heat balance, and the start-up capacity of nuclear power $C_{\mathrm{nuc},\mathrm{fore}}$ is known for each dispatching day in the assessment year.

Nuclear power units are also supplied with heat by means of steam extraction, which has an impact on power generation. Considering that nuclear power heat supply is currently in the small-scale pilot stage and the proportion of the supplied heat load is not large, this paper treats the nuclear power heating output $Q_{\mathrm{nuc}}^t$ as a fixed-value output and sets its impact on power generation in a way that takes into account the energy loss coefficients $c_{\mathrm{v}\_\mathrm{nuc}}$ of fixed pumped-steam heating on power generation.

(6) Aggregated coal-fired boiler operating boundary constraints

$$0\le Q_{\mathrm{BO}}^t\le C_{\mathrm{BO},\mathrm{on}}$$

(19)

(7) Aggregated electric boiler operating boundary constraints

$$\left\{\begin{array}{l}0\le P_{\mathrm{eb}}^t\le C_{\mathrm{eb}}\\ Q_{\mathrm{eb}}^t=P_{\mathrm{eb}}^t{\eta }_{\mathrm{eb}}\end{array}\right.$$

(20)

$P_{\mathrm{eb}}^t$, $Q_{\mathrm{eb}}^t$ are the electricity and heating power used by the aggregated electric boiler at time t; $C_{\mathrm{eb}}$ is the aggregated capacity of the electric boiler.

(8) Aggregated out-of-province AC/DC transmission line constraints:

In this paper, the DC and AC tie lines outside the province are considered according to the fixed curve transmission, and their power values, $P_{DC}^t$ and $P_{AC}^t$, are given as planned, following the following constraints:

$$\left\{\begin{array}{l}{P}_{DC}^t={\lambda }_{\mathrm{DC}}^t\cdot C_{DC}\\ P_{AC}^t={\lambda }_{\mathrm{AC}}^t\cdot C_{AC}\end{array}\right.$$

(21)

where ${\lambda }_{\mathrm{DC}}^t$, ${\lambda }_{\mathrm{AC}}^t$ are the historical levels of the year t time period of such out-of-province DC, AC transmission line power pu values (can also be adjusted according to the planning of the coefficient curve); $C_{DC}$ and $C_{AC}$ are the total capacities of DC and AC tie lines in the whole province in the assessment year.

(9) Aggregated electrical storage operation constraints

$$\left\{\begin{array}{l}-C_{\mathrm{es},i}\le P_{\mathrm{es},i}^t\le C_{\mathrm{es},i}\\ 0\le H_{\mathrm{es},i}^t\le H_{\mathrm{es},i,\max }\\ H_{\mathrm{es},i}^{t+1}=H_{\mathrm{es},i}^t-{\displaystyle \frac{\max \left(P_{\mathrm{es},i}^t,0\right)\Delta t}{{\eta }_{\mathrm{es},i}}}+\max \left(-P_{\mathrm{es},i}^t,0\right){\eta }_{\mathrm{es},i}\Delta t\\ H_{\mathrm{es},i}^0=H_{\mathrm{es},i}^{\mathrm{yst},\mathrm{T}},i\in \{1,2\}\end{array}\right.$$

(22)

where $\Delta t$ is the length of the time period, and $P_{\mathrm{es},i}^t$ is the charging and discharging power of the type i electric energy storage in the t period of the dispatching day (the discharge is positive and the charging is negative). $H_{\mathrm{es},i}^t$ and $H_{\mathrm{es},i,\max }$ are the storage energy and the maximum storage energy of class i electric energy storage in time period t, respectively; the third line indicates the coupling relationship of the storage energy of the electric storage of subsequent time periods in the dispatching day, and the fourth line of the formula takes the end value of energy storage $H_{\mathrm{es},i}^{\mathrm{yst},\mathrm{T}}$ of the three types of electrical storage in the last cycle as the initial value of energy storage $H_{\mathrm{es},i}^0$ in the current cycle, thus realizing the cross-cycle transfer of energy.

(10) Aggregated thermal energy storage operational constraints

$$\left\{\begin{array}{l}-Q_{\mathrm{hs},\mathrm{in}}\le Q_{\mathrm{hs}}^t\le Q_{\mathrm{hs},\mathrm{out}}\\ 0\le H_{\mathrm{hs}}^t\le H_{\mathrm{hs},\max }\\ H_{\mathrm{hs}}^{t+1}=H_{\mathrm{hs}}^t-{\displaystyle \frac{\max \left(Q_{\mathrm{hs}}^t,0\right)}{{\eta }_{\mathrm{hs}}}}\Delta t-\min \left(Q_{\mathrm{hs}}^t,0\right){\eta }_{\mathrm{hs}}\Delta t\\ H_{\mathrm{hs}}^0=H_{\mathrm{hs}}^{\mathrm{yst},T}\end{array}\right.$$

(23)

In the formula, $Q_{\mathrm{hs}}^t$ is the heating power of the heat storage equipment in time period t (heat charging is negative, heat release is positive); $Q_{\mathrm{hs},\mathrm{in}}$ and $Q_{\mathrm{hs},\mathrm{out}}$ denote the maximum heat charging and releasing power of the heat storage; and $H_{\mathrm{hs}}^t$ is the amount of heat stored in the heat storage in time period t. The fourth line of the formula takes the end value of heat storage $H_{\mathrm{hs}}^{\mathrm{yst},T}$ in the last cycle as the initial value of heat storage $H_{\mathrm{hs}}^0$ in the current cycle, thus realizing the cross-cycle transfer of heat energy.

(11) Aggregated flexibility load demand response capacity constraints

The demand response capabilities of flexible loads can be divided into two categories: transferable and interruptible [3]. The constraints on their demand response capabilities are shown in Formulas (24) and (25):

$$\left\{\begin{array}{l}{P}_{\mathrm{drp}\_\mathrm{in}}^t\le P_{\mathrm{drp}\_\mathrm{in},\max }^t\\ P_{\mathrm{drp}\_\mathrm{out}}^t\le P_{\mathrm{drp}\_\mathrm{out},\max }^t\\ {\displaystyle \sum _{\mathrm{t}=1}^T{P}_{\mathrm{drp}\_\mathrm{in}}^t}={\displaystyle \sum _{\mathrm{t}=1}^T{P}_{\mathrm{drp}\_\mathrm{out}}^t}\end{array}\right.$$

(24)

where $P_{\mathrm{drp}\_\mathrm{in}}^t$ and $P_{\mathrm{drp}\_\mathrm{out}}^t$ denote the actual transferred-in and transferred-out power of flexibility loads in time period t; $P_{\mathrm{drp}\_\mathrm{in},\max }^t$ and $P_{\mathrm{drp}\_\mathrm{out},\max }^t$ are the upper limits of the capabilities for the transfer-in and transfer-out of flexible loads. The first two lines of the formula are the constraints on the upper limits of the transfer-out and transfer-in powers of flexible transferable loads, aiming to ensure that the demand response transfer-out and transfer-in loads of all flexible loads in any time period t do not exceed their maximum response potential. The third line of the formula is the balance constraint of flexible transferred electricity quantity, aiming to ensure that the cumulative transfer-out and transfer-in loads of the daily flexible demand response are equal.

$$P_{\mathrm{drp}\_\mathrm{cut}}^t\le P_{\mathrm{drp}\_\mathrm{cut},\max }^t$$

(25)

where $P_{\mathrm{drp}\_\mathrm{cut}}^t$ and $P_{\mathrm{drp}\_\mathrm{cut},\max }^t$ are the actual interruptible power and the maximum allowable interruptible power of the flexibility interruptible load at time t, respectively.

(12) System power balance constraint

$$P_{\mathrm{wind}}^t+P_{\mathrm{solar}}^t+P_{\mathrm{hyd}}^t+P_{\mathrm{CHP}}^t+P_{\mathrm{CON}}^t+P_{\mathrm{nuclear}}^t+P_{DC}^t+P_{AC}^t-P_{\mathrm{eb}}^t+{\displaystyle \sum _{i=1}^3{P}_{\mathrm{es}}^t}=P_{\mathrm{ld}}^t-P_{\mathrm{lack}}^t-P_{\mathrm{drp}\_\mathrm{out}}^t+P_{\mathrm{drp}\_\mathrm{in}}^t-P_{\mathrm{drp}\_\mathrm{cut}}^t$$

(26)

$P_{\mathrm{ld}}^t$ is the electrical load of the system at time t.

(13) Power heat balance constraints

$$Q_{\mathrm{ld}}^t=Q_{\mathrm{CHP}}^t+Q_{\mathrm{eb}}^t+Q_{\mathrm{hs}}^t+Q_{\mathrm{bo}}^t+Q_{\mathrm{nuc}}^t$$

(27)

$Q_{\mathrm{ld}}^t$ is the heat load of the system at time t.

(14) Adequacy of System Power Source Capacity Constraint

$$\left\{\begin{array}{l}{R}_{\mathrm{G}}^t+{\displaystyle \sum _{i=1}^3{R}_{\mathrm{es},\mathrm{i}}^t}+R_{\mathrm{drp}}^t\ge (1+r_{ld})(P_{\mathrm{ld}}^t-P_{\mathrm{lack}}^t)+R_{\mathrm{em}}^t\\ R_{\mathrm{G}}^t=R_{\mathrm{wind}}^t+R_{\mathrm{solar}}^t+R_{\mathrm{hyd}}^t+R_{\mathrm{CHP}}^t+R_{\mathrm{CON}}^t+R_{\mathrm{nuclear}}^t+R_{\mathrm{DC}}^t+R_{\mathrm{AC}}^t\\ R_{\mathrm{em}}^t=C_{\mathrm{fire},\max }^t+P_{\mathrm{DC},\max }^t\end{array}\right.$$

(28)

where $R_{\mathrm{G}}^t$ is the available capacity of all types of power sources in time period t, including wind power, photovoltaics, hydropower, CHP coal-fired power, condensing coal-fired power, nuclear power and out-of-province DC/AC transmission lines, respectively, as $R_{\mathrm{wind}}^t$, $R_{\mathrm{solar}}^t$, $R_{\mathrm{hyd}}^t$, $R_{\mathrm{CHP}}^t$, $R_{\mathrm{CON}}^t$, $R_{\mathrm{nuc}}^t$, $R_{\mathrm{DC}}^t$, and $R_{\mathrm{AC}}^t$. The reserve capacities provided by type i electric storage and demand response are $R_{\mathrm{es},\mathrm{i}}^t$ and $R_{\mathrm{drp}}^t$, respectively; $r_{ld}$ is the load reserve rate of the system; and $R_{\mathrm{em}}^t$ is the available capacity requirement for accidental reserve, which is set by taking the sum of the maximum capacity $C_{\mathrm{fire},\max }^t$ of the largest single coal-fired generating unit in the province and the power shortfall $P_{\mathrm{DC},\max }^t$ of the bipolar blocking of the largest single DC transmission line.

The available capacity provided by each type of power source, energy storage, and demand response can be determined by (29), as follows:

$$\left\{\begin{array}{l}{R}_{\mathrm{wind}}^t={\partial }_{\mathrm{wind}}{P}_{\mathrm{wind}}^t\\ R_{\mathrm{solar}}^t={\partial }_{\mathrm{solar}}{P}_{\mathrm{solar}}^t\\ R_{\mathrm{hyd}}^t=\min \left(C_{\mathrm{hyd}},({\displaystyle \frac{W_{\mathrm{hyd}}}{\Delta t}}-{\displaystyle \sum _{n=1}^{t-1}{P}_{\mathrm{hyd}}^n})\right)\\ R_{\mathrm{CHP}}^t=C_{\mathrm{CHP},\mathrm{on}}-{\mathrm{c}}_{\mathrm{v}}{Q}_{\mathrm{CHP}}^t\\ R_{\mathrm{CON}}^t=C_{\mathrm{CON},\mathrm{on}}\\ R_{\mathrm{nuc}}^t=P_{\mathrm{nuc}}^t\\ R_{\mathrm{DC}}^t=P_{\mathrm{DC}}^t\\ R_{\mathrm{AC}}^t=P_{\mathrm{AC}}^t\\ R_{\mathrm{drp}}^t=P_{\mathrm{drp}\_\mathrm{out},\max }^t+P_{\mathrm{drp}\_\mathrm{cut},\max }^t\\ R_{\mathrm{es},\mathrm{i}}^t=\min \left(C_{\mathrm{es},\mathrm{i}},{\displaystyle \frac{H_{\mathrm{es},\mathrm{i}}^t}{\Delta t}}\right)\end{array}\right.$$

(29)

In the formula, the available capacity of wind power and photovoltaic is its minimum guaranteed output within the dispatching day, ${\partial }_{\mathrm{wind}}$ and ${\partial }_{\mathrm{solar}}$ are the credible coefficients of wind power and photovoltaic output, respectively, and the available capacity of hydropower in time period t is the lesser value between the remaining power in that time period and the maximum available capacity in that day. The available capacity for power generation provided by extraction-condensing units during the heating period takes into account the impact of heating blocked; in addition, the available capacity for condensing-fired coal power is its start-up capacity; the available capacity for nuclear power and AC/DC transmission lines is the planned power in their cycle; the available capacity for demand response is the sum of the maximum transferable and maximum interruptible load capacity at time t; and the available capacity for type i energy storage is the lesser value of the equivalent generating power of the storage surplus and the installed generating capacity at the current time period.

3.4. Model Solution Method

The objective function of the daily dispatching model of the electricity–heat integrated energy system constructed above is a quadratic function. The constraints are all linear constraints and contain integer variables, making it a mixed-integer quadratic programming model, which can be solved by using the ILOG CPLEX commercial optimization solver. Through the daily rolling calculation according to the process described in Section 2.2, the system can obtain the time-series operation curves of the daily start-up capacity of condensing coal-fired power and various sources, loads, and energy storage devices within the assessment year. Furthermore, various indexes can be obtained through statistical calculation.

4. Case Analysis

4.1. Basic Data

4.1.1. Case System

In this paper, an example of a provincial electric–heat integrated energy system in northern China is analyzed. The installed capacity data of the electric and heat sources of the example system are shown in Figure 4 and Figure 5, respectively. The total installed capacity is 154.57 GW and 37.65 GW, respectively. The annual power and heat load time series per unit curve of the system (the length of the time period is 1 h) is shown in Figure 6. The annual maximum power and heat loads are 90.58 GW and 26.37 GW, respectively. In the example system, the proportion of wind and solar power generation to the annual load power is 26.66% without considering the curtailed wind and solar power.

4.1.2. Production Dispatching Model Parameter Setting

The example takes one day as a dispatching day for rolling calculation. The day is divided into 24 periods, and the length of each period is 1 h. The system load reserve rate is 4%, and the emergency reserve capacity is 4%. The credibility coefficient of wind and solar power generation is 10%.

4.1.3. Comparison of Scene Settings

The example sets the following four scenarios for calculation and comparative analysis. The factors considered in each scenario are shown in

Table 1. Considerations for each scenario.

Scenario	Electric Storage	Heat Storage	Electric Boiler	Demand Response	Heating Relationship Between Power Plant and Boiler Station	Operation Strategy
Scenario A	no	no	no	no	independent	suggested
Scenario B	yes	yes	yes	no	independent	suggested
Scenario C	yes	yes	yes	yes	independent	suggested
Scenario D	yes	yes	yes	yes	combined	suggested
Scenario E	yes	yes	yes	no	independent	traditional

(note: ‘yes’ means that such factors are considered; ‘no’ means that such factors are not considered).

4.2. Effectiveness Analysis of Suggested Optimal Dispatching Model

4.2.1. Rationality Analysis of a Typical Day’s Power Balance and Heating Balance

Taking January 18, a typical winter day, as an example, Figure 7 and Figure 8 show the balance of the power system and heating system in each period of time under Scenario C by means of a stacking diagram.

It can be seen that hydropower is arranged to generate electricity during the peak period of electric load. The electric energy storage is charged in the period of 1–6 when the renewable energy has a lot of power generation and cannot be accommodated, and discharges in the peak period of 11–13 and 15–22; the extraction condensing unit reduces the power output and heat output to accommodate the renewable energy in the period of a lot of renewable energy power generation, and the lack of heating is supplemented by heat storage and an electric boiler. In the period with less renewable energy power generation, the power and heat output are increased, and the thermal energy storage equipment is stored. The transferable load increases the demand for electricity during the period in which the renewable energy generation is large, and the interruptible load does not operate because there is no shortage of electricity; the renewable energy has curtailed power when the power generation is large and the system generation regulation capability is insufficient. The above operational results are in full compliance with the dispatching operation rules of the electric and thermal systems and the preset strategies of this paper, verifying the effectiveness of the constructed daily optimal dispatching model in simulating intra-day dispatching.

4.2.2. Effectiveness Analysis of the Cross-Day Coordinated Accommodation of Curtailed Electricity by Electric and Thermal Energy Storage

Figure 9 takes the week from 6 January to 12 January in winter as an example, and gives the action timing curves of electric thermal energy storage and electric boilers under Scenario B, and gives the curtailment curve under Scenario A in the diagram. It can be seen that under Scenario A, when each flexible resource is not put to use, the week produces power curtailment during periods 1–7, 27–31, 50–55, 68–80, 92–104, and 120–127, and the duration of each power curtailment is different. Among them, the longest power curtailment process reached 12 h, and spanned the third, fourth, and fifth days, respectively.

At the same time, it can be seen that in the Scenario B production simulation results, using the strategy proposed in this paper, the thermal energy storage makes full use of the coal-fired generation opportunities to carry out cogeneration heating in each period of small wind power generation and no power curtailment, and realizes cross-day storage so as to provide heat for the subsequent power curtailment period to replace cogeneration heating by heat discharge, thereby reducing the minimum power output of cogeneration to accommodate wind power. The electric energy storage also realizes cross-day storage according to the power curtailment situation, such as the power curtailment storage at the end of the third day and the beginning of the fourth day.

4.2.3. Effectiveness Analysis of the Annual Production Simulation Calculation

In this paper, four scenarios of Table 1 are simulated on an AMD Ryzen 7 7840 H CPU and 32.0 G memory computer throughout the year. The statistical results are shown in

Table 2. Annual production simulation results under five different scenarios.

Scenario	Coal Power Utilization Hours (h)	Curtailed Renewable Energy Generation (GWh)	Curtailed Power	CO2 Emission (Mt)
Scenario A	3494	23,206	20.07%	23,116
Scenario B	3395	12,866	11.13%	22,475
Scenario C	3380	11,848	10.25%	22,384
Scenario D	3374	11,443	9.90%	21,775
Scenario E	3410	13,676	11.83%	22,564

. Among them, Scenario C adds the consideration of demand response on the basis of Scenario B, assuming that 5% of the electricity load can be transferred within a day. On the basis of Scenario C, Scenario D assumes that the current thermal power plant and centralized boiler station are changed from independent heating mode to combined interactive heating mode.

At the same time, it also can be seen from Table 2 that compared with Scenario B, Scenario C after considering demand response has a lower curtailment rate, and a response ability of 5% reduces the curtailment rate of renewable energy by 0.88%. Scenario D shows that through the complementary heating between the thermal power plant and the boiler station, and by supplementing the heating supply with the boiler station during the power curtailment period to decouple the constraint of ordering power output by heat output of the cogeneration units, the renewable energy accommodation capacity of the system can be effectively improved. At the same time, in the renewable energy non-curtailed power period, cogeneration heating is fully utilized to replace boiler station heating, as shown in Figure 10, thereby saving the overall coal consumption.

The solution times for the annual production simulations under various scenarios are shown in

Table 3. Solving time of yearly time-series production simulation.

Scheme	Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
Time	106.3 s	203.1 s	186.7 s	203.4 s	174.7 s

. It can be seen that the production simulation method proposed in this paper is able to complete the annual time-series production simulation of a provincial-scale electricity–thermal integrated energy system within a few minutes, which can meet the needs of daily calculation and analysis.

4.3. Comparing the Analysis of the Suggested Strategy and Traditional Strategy for Electrical and Thermal Energy Storage

Scenario E also takes the week from 6 January to 12 January in winter as an example; however, it uses the constraint that the energy storage of electric and thermal energy in the last hour is equal to the energy in the first hour. Figure 11 gives the action timing curves of electric and thermal energy storage and electric boilers under Scenario E, and the curtailment curve under Scenario A.

In Figure 11, it can be seen that the traditional strategy realizes the complete accommodation of the original curtailed electricity on the 2nd, 5th, and 6th days when the amount of curtailed electricity is relatively small, the daily power generation is not surplus, and the curtailed electricity period is ahead of the day. However, on the fourth day, when wind power is large and the generation in a whole day is surplus, the accommodation of the curtailment of renewable energy is much lower than in Scenario B because of the constraint that the energy storage of electric and thermal energy storage in the last hour in the dispatching day has to be equal to the energy in the first hour. Compared with Scenario E, in Scenario B, more heat is stored in advance to accommodate subsequent curtailed power and more curtailed power is stored in the electric energy storage through cross-day continuous charging.

5. Conclusions

This paper takes the provincial electricity–heat integrated energy system in northern China as the research target, in which the coal-fired power generation on the source side is highly flexible, the energy storage capacity is rapidly increasing, and the flexible loads on the load side are continuously developing. An embedded daily optimal dispatching model for time-series production simulation is constructed, which can realize the cross-day charging and discharging of electric energy storage and thermal energy storage to accommodate the curtailed renewable energy power by converting the net stored energy of electric and thermal energy storage at the end of the cycle into equivalent coal consumption and deduct it from the objective function.

Theoretical analysis and calculation results of the case show that adopting the modeling strategy proposed in this paper, the cross-day charging and discharging of electric and thermal energy storage can be realized to effectively accommodate the wind power, which can make the production simulation results more consistent with the actual situation.

The model proposed in this paper can provide an effective tool for the production simulation of the provincial electricity–thermal integrated energy system in most cold regions in China because of the generalizability of the model.

In future, the model will be improved by adding network constraints in order to apply the multi-provincial system and by adding a consideration of decarbonization retrofitting for coal power plants.