A Low-Carbon Collaborative Optimization Operation Method for a Two-Layer Dynamic Community Integrated Energy System

Abstract

The traditional centralized optimization method encounters challenges in representing the interaction among multi-agents and cannot consider the interests of each agent. In traditional low-carbon scheduling, the fixed carbon quota trading price can easily cause arbitrage behavior of the trading subject, and the carbon reduction effect is poor. This paper proposes a two-layer dynamic community integrated energy system (CIES) low-carbon collaborative optimization operation method. Firstly, a multi-agent stage feedback carbon trading model is proposed, which calculates carbon trading costs in stages and introduces feedback factors to reduce carbon emissions indirectly. Secondly, a two-layer CIES low-carbon optimal scheduling model is constructed. The upper energy seller (ES) sets energy prices. The lower layer is the combined cooling, heating, and power (CCHP) system and load aggregator (LA), which is responsible for energy output and consumption. The energy supply and consumption are determined according to the ES energy price strategy, which reversely affects the energy quotation. Then, the non-dominated sorting genetic algorithm embedded with quadratic programming is utilized to solve the established scheduling model, which reduces the difficulty and improves the solving efficiency. Finally, the simulation results under the actual CIES example show that compared with the traditional centralized scheduling method, the total carbon emission of the proposed method is reduced by 16.34%, which can improve the income of each subject and make the energy supply lower carbon economy.

1. Introduction

Because of the continuous increase of greenhouse gas emissions, traditional production and lifestyles must be changed to meet the needs of low-carbon energy transformation [1]. In this context, the integrated energy system (IES) has become an important form of efficient energy use [2]. Analyzing the traits of the power–gas–heat network, carbon measurement methods, market mechanism, and scheduling strategy to improve the economy and low carbon of IES is greatly meaningful [3]. The community integrated energy system (CIES), which takes the coordination of various links of source, grid, and load as the main feature, helps promote the large-scale development of new energy [4,5]. The CIES schedules and optimizes the generation, transmission, conversion, consumption, and trading of various energy sources [6]. The CIES has many new characteristics, such as multi-energy flow coupling and a multi-time scale, which complicates its operation scheduling [7].

Currently, the centralized optimization operation strategy of the CIES is the main content of the research. Studies [8,9,10] investigated the multi-objective optimal operation strategy of IES with different structures. Another study [11] compared and analyzed the economy of two modes of independent operation and the multi-network coordinated operation of the combined cooling, heating, and power (CCHP) micro-energy network. However, these studies only optimized the energy supply side and ignored the load side. IES carbon emissions are usually used as part of the optimization goal or as a constraint condition to reduce carbon emissions [12]. Under the constraint of the carbon emission reduction index, reference [13] proposed a carbon capture power plant scheduling strategy to achieve emission reduction. Some studies have verified that introducing a carbon trading mechanism can reduce IES carbon emissions [14,15,16]. From the perspective of promoting the consumption of renewable energy and reducing carbon emissions, an optimization scheduling strategy to stabilize the fluctuation in loads and increase the wind power consumption of the IES is proposed in references [17,18]. However, the above studies all adopted the fixed carbon quota price trading method, without considering the non-performance penalty measures in the actual carbon emission process. The carbon reduction effect of a single carbon trading price is not obvious, and the enthusiasm of each subject to participate in the carbon trading market is low. With the development and reform of the CIES, the interactive coupling between source and load is changing from the traditional vertical integration structure to the interactive competition structure [19]. A park IES based on the master–slave game method was proposed in [20], aiming at maximizing the interests of each subject and achieving game equilibrium. This method needs to discuss the change in carbon emissions in the system and ensure the low-carbon economic operation of IES. Reference [21] proposed a maximum power point tracking scheme based on an artificial neural network algorithm to maximize photovoltaic power generation. The resulting strategy reduced electricity costs without affecting consumer satisfaction and promoted environmental friendliness by reducing carbon dioxide emissions. The traditional centralized scheduling strategy cannot demonstrate the interaction between energy prices and user demand. Moreover, CIES optimization scheduling has the characteristics of multiple participating entities, wide data dimensions, and complex calculations. Traditional centralized scheduling strategies have low solving efficiency and cannot achieve balanced decision-making among various entities. Therefore, the study of CIES distributed optimization is a more appropriate choice.

In view of the problems existing in the above research, the research questions, main contributions, and expected results of this paper are as follows:

(1)

A multi-agent stage feedback carbon trading model is proposed to calculate the carbon trading cost in stages. At the same time, a feedback factor is introduced to carry out cost feedback according to the actual carbon emissions of the CIES, so as to reduce carbon emissions indirectly.

(2)

A two-layer dynamic CIES low-carbon collaborative optimization operation scheduling model is constructed. The upper layer is responsible for setting energy prices for the energy seller (ES). The lower layer is a CCHP system and load aggregator (LA), which are responsible for energy output and energy consumption, respectively. The energy supply and consumption are determined by the upper ES energy price strategy and affect the ES energy quotation in the opposite direction.

(3)

The non-dominated sorting genetic algorithm embedded with quadratic programming with continuous decision-making ability is used to solve the established bi-level optimal scheduling model. The low-carbon economy of the proposed method is verified by simulation under the actual CIES example.

2. Community Integrated Energy System Architecture

2.1. CIES Architecture

The agents in the CIES can be divided into two layers, as shown in Figure 1. The upper-level entity is the ES, the optimization objective is maximizing revenue, and the output is real-time energy prices. The lower-level entities include CCHP and the LA. The optimization goal of CCHP is to maximize revenue by outputting energy, such as power and heat, while also generating carbon emissions and carbon trading fees. As an energy-consuming group, the LA’s optimization goal is to maximize consumer surplus, with variables including movable power load and reducible heat and gas load.

The CCHP system combines new energy power generation with traditional fossil fuel power generation to optimize the operation status of each piece of equipment and meet users’ needs for different energy sources at different times. The structure diagram is shown in Figure 2. In this paper, new energy includes wind turbine (WT), photovoltaic (PV), and battery (BT), and it adopts the principle of maximizing consumption. The controllable unit includes an internal combustion generator (ICG), gas boiler (GB), and power-to-gas (P2G) facilities.

Considering the low power level of CIES users, the direct participation of many users will increase the operational regulation pressure of the energy market. In this article, the LA is used to aggregate small- and medium-sized users together for representation. The LA participates in market transactions and is subject to regulation.

2.2. Energy Trading Process

The energy trading process of CIES is divided into two stages as follows:

(1)

ES formulates energy prices based on market conditions and provides price information to CCHP and the LA.

(2)

After receiving energy price information, CCHP adjusts its energy output, and the LA adjusts its energy consumption mode. At this stage, energy information is used to counteract the ES and obtain the final energy pricing plan.

3. Multi-Agent Stage Feedback Carbon Trading Mode

The multi-agent stage feedback carbon trading model consists of three parts. Firstly, the initial carbon quota of the multi-agent in the community integrated energy system is calculated, which is mainly distributed freely according to the rated capacity of the unit. The multi-agent includes the following three parts: coal-fired unit (CFU), CCHP system, and GB. Secondly, the actual carbon emissions are calculated. The actual carbon emissions of the IES include the CFU $E_{\mathrm{e}}^{\mathrm{r}}$, CCHP system $E_{\mathrm{cchp}}^{\mathrm{r}}$, carbon emissions $E_{\mathrm{p}2\mathrm{g}}^{\mathrm{r}}$ of P2G, and carbon emissions $E_{\mathrm{pcu}}^{\mathrm{r}}$ of the purification compression unit (PCU). Finally, a carbon trading cost model is established, and a multi-agent stage feedback carbon trading model is proposed. The carbon trading cost is calculated in stages, and the feedback factor is introduced. The cost feedback is based on the actual carbon emissions of IES to reduce carbon emissions indirectly.

3.1. Calculation of the Initial Carbon Quota

In the CIES, the initial carbon quota is mainly allocated freely according to the rated capacity of the unit, which mainly includes the following three parts: the CFU, CCHP system, and GB, which can be determined by the following formula:

$$\left\{\begin{array}{l}{E}_{\mathrm{e},\mathrm{gt}}={\displaystyle \sum {\mu }_{\mathrm{e},\mathrm{q}}{P}_{\mathrm{coal}}}\hfill \\ E_{\mathrm{e},\mathrm{buy}}={\displaystyle \sum {\mu }_{\mathrm{e},\mathrm{q}}{P}_{\mathrm{buy}}}\hfill \\ E_{\mathrm{cchp}}={\displaystyle \sum {\mu }_{\mathrm{h},\mathrm{q}}(\epsilon P_{\mathrm{gt}}^t+H_{\mathrm{whb}}^t+H_{\mathrm{gb}}^t+G_{\mathrm{ar}}^t+G_{\mathrm{ac}}^t)}\hfill \end{array}\right.$$

(1)

$$E_{\mathrm{q}}=E_{\mathrm{e},\mathrm{gt}}+E_{\mathrm{e},\mathrm{buy}}+E_{\mathrm{cchp}}$$

(2)

where $E_{\mathrm{e},\mathrm{gt}}$, $E_{\mathrm{e},\mathrm{buy}}$, and $E_{\mathrm{cchp}}$ represent the initial free carbon emission allocation quota of the CFU, power purchase from the power grid, and the CCHP system, respectively. ${\mu }_{\mathrm{e},\mathrm{q}}$ and ${\mu }_{\mathrm{h},\mathrm{q}}$ represent the initial quota of carbon emissions per unit of electricity/heat, 0.728 t/MWh and 0.102 t/GJ, respectively. $P_{\mathrm{coal}}$ and $P_{\mathrm{buy}}$ represent the power generation of the CFU and the purchase of electricity from the power grid by integrated energy traders, respectively. At time t, $H_{\mathrm{gb}}^t$, $G_{\mathrm{ac}}^t$, $P_{\mathrm{gt}}^t$, $H_{\mathrm{whb}}^t$, and $G_{\mathrm{ar}}^t$ represent the heat generation of the GB, the cooling capacity of ice storage air conditioning, the output power of gas turbine (GT), the heat energy generated by the waste heat boiler and the cooling capacity of absorption chiller, respectively. ε represents the conversion coefficient of electric power to thermal energy. E_q is the total carbon emission quota of the CIES.

3.2. Calculation of Actual Carbon Emissions

Because of the differences in the type, conversion efficiency, and fuel quality of different types of energy equipment, there will be deviations between the measured data and the theoretical data. In order to weaken this effect, the carbon emission intensity of energy equipment is modeled. The proposed carbon trading model calculates the carbon emissions according to different energy consumption patterns. The actual carbon emissions of the CIES include the CFU $E_{\mathrm{e}}^{\mathrm{r}}$, CCHP system $E_{\mathrm{cchp}}^{\mathrm{r}}$, carbon emissions of P2G $E_{\mathrm{p}2\mathrm{g}}^{\mathrm{r}}$, and PCU $E_{\mathrm{pcu}}^{\mathrm{r}}$.

$$\left\{\begin{array}{l}{E}_{\mathrm{e}}^{\mathrm{r}}={\displaystyle \sum _t^T{\mu }_{\mathrm{e},\mathrm{r}}{P}_{\mathrm{e},\mathrm{g}}^t}\hfill \\ E_{\mathrm{cchp}}^{\mathrm{r}}={\displaystyle \sum _t^T{\mu }_{\mathrm{g},\mathrm{r}}({\epsilon }_{\mathrm{g},\mathrm{gb}}{H}_{\mathrm{gb}}^t+{\epsilon }_{\mathrm{e},\mathrm{cchp}}{P}_{\mathrm{e},\mathrm{cchp}}^t+{\epsilon }_{\mathrm{g},\mathrm{cchp}}{H}_{\mathrm{g},\mathrm{cchp}}^t)}\hfill \\ E_{\mathrm{p}2\mathrm{g}}^{\mathrm{r}}={\displaystyle \sum _t^T{\mu }_{\mathrm{p}2\mathrm{g}}{P}_{\mathrm{p}2\mathrm{g}}^t}\hfill \\ E_{\mathrm{pcu}}^{\mathrm{r}}={\displaystyle \sum _t^T{\mu }_{\mathrm{pcu}}{\eta }_{\mathrm{pcu}}{P}_{\mathrm{e},\mathrm{g}}^t}\hfill \end{array}\right.$$

(3)

where $P_{\mathrm{e},\mathrm{g}}^t$, $P_{\mathrm{e},\mathrm{cchp}}^t$, and $P_{\mathrm{p}2\mathrm{g}}^t$ represent the output power values of the CFU, CCHP systems, and P2G equipment at time t, respectively. $H_{\mathrm{gb}}^t$ and $H_{\mathrm{g},\mathrm{cchp}}^t$ represent the output thermal power value of the GB and CCHP system at time t, respectively. ${\epsilon }_{\mathrm{g},\mathrm{gb}}$ represents the gas/heat conversion coefficient of the GB and ${\epsilon }_{\mathrm{e},\mathrm{cchp}}$ and ${\epsilon }_{\mathrm{g},\mathrm{cchp}}$ represent the gas/power and gas/heat conversion coefficients of the CCHP system, respectively. ${\eta }_{\mathrm{pcu}}$ represents the carbon capture rate of the PCU. ${\mu }_{\mathrm{e},\mathrm{r}}$, ${\mu }_{\mathrm{g},\mathrm{r}}$, ${\mu }_{\mathrm{p}2\mathrm{g}}$, and ${\mu }_{\mathrm{pcu}}$ represent the actual carbon emission coefficients of the CFU, CCHP systems, P2G equipment, and PCU devices, respectively, which can be expressed by the following formula:

$$\left\{\begin{array}{l}{\mu }_{\mathrm{ue}}=K_{\mathrm{ue}}{L}_{\mathrm{ue}}\\ {\mu }_{\mathrm{ug}}=(1+{\alpha }_{\mathrm{he}})L_{\mathrm{cchp}}+L_{\mathrm{gb}}\end{array}\right.$$

(4)

$$\left\{\begin{array}{c}{\mu }_{\mathrm{e}}={\mu }_{\mathrm{ue}}+{\mu }_{\mathrm{ce}}\\ {\mu }_{\mathrm{g}}={\mu }_{\mathrm{ug}}+{\mu }_{\mathrm{cg}}\end{array}\right.$$

(5)

In the energy cycle process, ${\mu }_{\mathrm{ue}}$ represents the carbon emission intensity of the power generation of the CFU, $K_{\mathrm{ue}}$ represents the unit coal consumption value of generators, $L_{\mathrm{ue}}$ represents the carbon emission intensity of greenhouse gases of the CFU, ${\mu }_{\mathrm{ug}}$ represents the carbon emission intensity per unit of power generation of the gas-fired units, $L_{\mathrm{cchp}}$ represents the carbon emission intensity per unit of power generation of the GT and GB, $L_{\mathrm{gb}}$ represents the carbon emission intensity per unit of heat production of the GB, and ${\alpha }_{\mathrm{he}}$ represents the conversion coefficient value between heat energy and power energy. During the power plant cycle, ${\mu }_{\mathrm{ce}}$ and ${\mu }_{\mathrm{cg}}$ represent the carbon emission coefficient per unit power generation of the CFU and gas-fired units, respectively. ${\mu }_{\mathrm{e}}$ and ${\mu }_{\mathrm{g}}$ represent the total carbon emission coefficient of the unit power generation of the CFU and gas-fired units, respectively.

Using Formulas (3)–(6), the actual carbon emission $E_{{\mathrm{co}}_2}$ of IES can be obtained as:

$$E_{{\mathrm{co}}_2}=E_{\mathrm{e}}^{\mathrm{r}}+E_{\mathrm{g}}^{\mathrm{r}}+E_{\mathrm{p}2\mathrm{g}}^{\mathrm{r}}-E_{\mathrm{pcu}}^{\mathrm{r}}$$

(6)

3.3. Carbon Trading Cost Model

Based on the traditional carbon trading model, a multi-agent stage feedback carbon trading model is proposed. The carbon trading cost is calculated in stages, and the feedback factor is introduced. The cost feedback is based on the actual carbon emissions of the CIES to reduce carbon emissions indirectly. The specific carbon trading cost model is as follows:

$$C_{\mathrm{tc}}=\left\{\begin{array}{l}-p_{{\mathrm{co}}_2}(1+2{\delta }_{\mathrm{a}})(E_{{\mathrm{co}}_2}-s-E_{\mathrm{q}}),E_{\mathrm{q}}\le E_{{\mathrm{co}}_2}-s\hfill \\ -p_{{\mathrm{co}}_2}s(1+2{\delta }_{\mathrm{a}})-p_{{\mathrm{co}}_2}(1+{\delta }_{\mathrm{a}})(E_{{\mathrm{co}}_2}-E_{\mathrm{q}}),E_{{\mathrm{co}}_2}-s<E_{\mathrm{q}}\le E_{{\mathrm{co}}_2}\hfill \\ p_{{\mathrm{co}}_2}(E_{{\mathrm{co}}_2}-E_{\mathrm{q}}),E_{{\mathrm{co}}_2}<E_{\mathrm{q}}\le E_{{\mathrm{co}}_2}+s\hfill \\ p_{{\mathrm{co}}_2}s+p_{{\mathrm{co}}_2}(1+{\delta }_{\mathrm{p}})(E_{\mathrm{q}}-s-E_{{\mathrm{co}}_2}),E_{{\mathrm{co}}_2}+s<E_{\mathrm{q}}\le E_{{\mathrm{co}}_2}+2s\hfill \\ p_{{\mathrm{co}}_2}s(2+{\delta }_{\mathrm{p}})+p_{{\mathrm{co}}_2}(1+2{\delta }_{\mathrm{p}})(E_{\mathrm{q}}-2s-E_{{\mathrm{co}}_2}),E_{{\mathrm{co}}_2}+2s<E_{\mathrm{q}}\le E_{{\mathrm{co}}_2}+3s\hfill \\ p_{{\mathrm{co}}_2}s(3+{\delta }_{\mathrm{p}})+p_{{\mathrm{co}}_2}(1+3{\delta }_{\mathrm{p}})(E_{\mathrm{q}}-3s-E_{{\mathrm{co}}_2}),E_{{\mathrm{co}}_2}+3s<E_{\mathrm{q}}\hfill \end{array}\right.$$

(7)

where $C_{\mathrm{tc}}$ represents the total cost of carbon trading, $p_{{\mathrm{co}}_2}$ represents the transaction price of carbon emissions, ${\delta }_{\mathrm{a}}$ and ${\delta }_{\mathrm{p}}$ represent positive feedback factors and negative feedback factors, respectively, and $s$ represents the range of carbon emissions.

The proposed carbon emission trading model divides the actual carbon emissions into multiple interval scales, and the unit carbon trading price increases with the increase in actual carbon emissions. Meanwhile, reward and penalty factors are introduced. When the actual carbon emissions of the trading agent exceed the set threshold, the penalty fee is levied on it; on the contrary, when the carbon emissions of the trading entity are lower than the set threshold, a reward is given. This avoids the problem of the transaction cost of the excessive emission agent being the same as that of the compliance agent and ensures the fairness of the multi-transaction agent.

4. Community Integrated Energy System Model

4.1. CIES Model

After comprehensively evaluating the output plan of the CCHP and the load demand of the LA, the ES formulates a price strategy. The optimal target function $F\mathrm{es}$ maximizes the income, including energy sales income, energy purchase cost, power grid side purchase cost, energy supply interruption penalty cost, and carbon transaction cost.

$$\begin{array}{ll}\max F\mathrm{es}& ={\displaystyle \sum _t^T(P_{\mathrm{ue}}^t{c}_{\mathrm{e},\mathrm{s}}^t+H_{\mathrm{uh}}^t{c}_{\mathrm{h},\mathrm{s}}^t)\Delta t}-{\displaystyle \sum _t^T(P_{\mathrm{oe}}^t{c}_{\mathrm{e},\mathrm{b}}^t+H_{\mathrm{oh}}^t{c}_{\mathrm{h},\mathrm{b}}^t)\Delta t}\\ & -{\displaystyle \sum _t^T[\max (P_{\mathrm{ue}}^t-P_{\mathrm{oe}}^t, 0)c_{\mathrm{g},\mathrm{s}}^t+\min (P_{\mathrm{ue}}^t-P_{\mathrm{oe}}^t, 0)c_{\mathrm{g},\mathrm{c}}^t]\Delta t}\\ & -{\displaystyle \sum _t^T\max (H_{\mathrm{uh}}^t-H_{\mathrm{oh}}^t, 0)\delta \mathrm{p}\Delta t}\end{array}$$

(8)

where T represents the optimization period (24 h). $P_{\mathrm{ue}}^t$ and $H_{\mathrm{uh}}^t$ represent the power and heat load of the LA at time t, respectively. $P_{\mathrm{oe}}^t$ and $H_{\mathrm{oh}}^t$ represent the power and heat output of the CCHP at time t, respectively. $c_{\mathrm{e},\mathrm{s}}^t$ and $c_{\mathrm{h},\mathrm{s}}^t$ represent the price of power and heat sold to the LA at time t, respectively. $c_{\mathrm{e},\mathrm{b}}^t$ and $c_{\mathrm{h},\mathrm{b}}^t$ represent the price of power and heat purchased from the CCHP side at time t, respectively. $c_{\mathrm{g},\mathrm{s}}^t$ and $c_{\mathrm{g},\mathrm{c}}^t$ represent the grid electricity sales and feed-in tariffs, respectively. Δ_p represents the penalty cost coefficient of interruption of heating.

4.2. CCHP System Considering Carbon Capture

The CCHP system optimizes the energy output according to the power and heat purchase price set by the ES and considers the carbon transaction cost. The optimization goal is to obtain the maximum benefit.

$$\max F\mathrm{cchp}=C_{\mathrm{buy}}^t-C_{\mathrm{cchp}}^t-C_{\mathrm{tc}}$$

(9)

where $C_{\mathrm{cchp}}^t$ represents the fuel cost, which is represented by the quadratic function of the output power and the fuel price by the variable condition efficiency characteristics of the ICG and GB.

$$C_{\mathrm{cchp}}^t={\displaystyle \sum _t^T[a\mathrm{e},\mathrm{ice}{(P_{\mathrm{ice}}^t)}^2+b\mathrm{e},\mathrm{ice}{P}_{\mathrm{ice}}^t+c\mathrm{e},\mathrm{ice}+a\mathrm{h},\mathrm{bt}{(H_{\mathrm{gb}}^t)}^2+b\mathrm{h},\mathrm{bt}{H}_{\mathrm{gb}}^t+c\mathrm{h},\mathrm{bt}]\Delta t}$$

(10)

where $P_{\mathrm{ice}}^t$ and $H_{\mathrm{gb}}^t$ are the output power and heat of the ICG and GB, respectively. A_e, b_e, and c_e (a_h, b_h, and c_h) are the cost coefficients of the ICG (GB).

The clean energy (WT, PV) and auxiliary devices such as P2G and the heat storage tank (HST) in the CCHP system are considered to have zero fuel cost. At time t, the power and heat output of the CCHP can be expressed as:

$$\left\{\begin{array}{c}{P}_{\mathrm{oe}}^t=P_{\mathrm{wt}}^t+P_{\mathrm{pv}}^t+P_{\mathrm{ice}}^t\\ H_{\mathrm{oe}}^t=(H_{\mathrm{re}}^t+H_{\mathrm{gb}}^t)·{\eta }_{\mathrm{h}/\mathrm{f}}\end{array}\right.$$

(11)

where $P_{\mathrm{wt}}^t$ and $P_{\mathrm{pv}}^t$ are the output of WT and PV at time t, respectively. $H_{\mathrm{re}}^t$ and $H_{\mathrm{gb}}^t$ are the output heat of the waste heat absorption device (WHAD) and the GB at time t, respectively. ${\eta }_{\mathrm{h}/\mathrm{f}}$ represents the heat conversion efficiency.

The heat energy other than the output power of the ICG will be recovered by the WHAD. The relationship between the two can be expressed as follows:

$$H_{\mathrm{re}}^t={\displaystyle \frac{P_{\mathrm{ice}}^t·(1-{\eta }_{\mathrm{ice}})}{{\eta }_{\mathrm{ice}}}}·{\eta }_{\mathrm{re}}$$

(12)

where $H_{\mathrm{re}}^t$ is the recovery of heat energy, ${\eta }_{\mathrm{ice}}$ is the power efficiency of the ICG, and ${\eta }_{\mathrm{re}}$ is the heat absorption efficiency of the WHAD.

ICG $P_{\mathrm{ice}}^t$ and GB $H_{\mathrm{gb}}^t$ need to meet the following constraints:

$$\left\{\begin{array}{c}0\le P_{\mathrm{ice}}^t\le P_{\mathrm{ice}}^{\mathrm{rat}}\\ 0\le H_{\mathrm{gb}}^t\le H_{\mathrm{gb}}^{\mathrm{rat}}\end{array}\right.$$

(13)

where $P_{\mathrm{ice}}^{\mathrm{rat}}$ is the rated power generation capacity of the ICG, and $H_{\mathrm{gb}}^{\mathrm{rat}}$ is the rated heating capacity of the GB.

The operating constraints of the BT are as follows:

$$\left\{\begin{array}{c}{M}_{\mathrm{bt},\mathrm{c}}{P}_{\mathrm{bt},\mathrm{c}}^{\min }\le P_{\mathrm{bt},\mathrm{c}}\le M_{\mathrm{bt},\mathrm{c}}{P}_{\mathrm{bt},\mathrm{c}}^{\max }\\ M_{\mathrm{bt},\mathrm{d}}{P}_{\mathrm{bt},\mathrm{d}}^{\min }\le P_{\mathrm{bt},\mathrm{d}}\le M_{\mathrm{bt},\mathrm{d}}{P}_{\mathrm{bt},\mathrm{d}}^{\max }\\ S_{\mathrm{bt}}^{\min }\le S_{\mathrm{bt}}\le S_{\mathrm{bt}}^{\max }\\ \Delta P_{\mathrm{bt},\mathrm{c}}^{\min }\le \Delta P_{\mathrm{bt},\mathrm{c}}\le \Delta P_{\mathrm{bt},\mathrm{c}}^{\max }\\ \Delta P_{\mathrm{bt},\mathrm{d}}^{\min }\le \Delta P_{\mathrm{bt},\mathrm{d}}\le \Delta P_{\mathrm{bt},\mathrm{d}}^{\max }\end{array}\right.$$

(14)

where $P_{\mathrm{bt},\mathrm{c}}$ ($P_{\mathrm{bt},\mathrm{d}}$) is the charging (discharging) power of the BT. $P_{\mathrm{bt},\mathrm{c}}^{\min }$($P_{\mathrm{bt},\mathrm{d}}^{\min }$) and $P_{\mathrm{bt},\mathrm{c}}^{\max }$($P_{\mathrm{bt},\mathrm{d}}^{\max }$) are the minimum and maximum values of BT charging (discharging) power. $M_{\mathrm{bt},\mathrm{c}}$($M_{\mathrm{bt},\mathrm{d}}$) is the BT charge (discharge) state marker. $S_{\mathrm{bt}}$ is the state of charge of the BT. $S_{\mathrm{bt}}^{\max }$ and $S_{\mathrm{bt}}^{\min }$ are the upper and lower limits of charge and discharge power. $\Delta P_{\mathrm{bt},\mathrm{c}}$($\Delta P_{\mathrm{bt},\mathrm{d}}$) is the charge (discharge) increment. $\Delta P_{\mathrm{bt},\mathrm{c}}^{\max }$ ($\Delta P_{\mathrm{bt},\mathrm{d}}^{\max }$) and $\Delta P_{\mathrm{bt},\mathrm{c}}^{\min }$ ($\Delta P_{\mathrm{bt},\mathrm{d}}^{\min }$) represent the upper and lower limits of ramping power in the state of charge (discharge).

The operation constraints of the HST are as follows:

$$\left\{\begin{array}{c}{M}_{\mathrm{hst},\mathrm{c}}{H}_{\mathrm{hst},\mathrm{c}}^{\min }\le H_{\mathrm{hst},\mathrm{c}}\le M_{\mathrm{hst},\mathrm{c}}{H}_{\mathrm{hst},\mathrm{c}}^{\max }\\ M_{\mathrm{hst},\mathrm{d}}{H}_{\mathrm{hst},\mathrm{d}}^{\min }\le H_{\mathrm{hst},\mathrm{d}}\le M_{\mathrm{hst},\mathrm{d}}{H}_{\mathrm{hst},\mathrm{d}}^{\max }\\ S_{\mathrm{hst}}^{\min }\le S_{\mathrm{hst}}\le S_{\mathrm{hst}}^{\max }\\ \Delta H_{\mathrm{hst},\mathrm{c}}^{\min }\le \Delta H_{\mathrm{hst},\mathrm{c}}\le \Delta H_{\mathrm{hst},\mathrm{c}}^{\max }\\ \Delta H_{\mathrm{hst},\mathrm{d}}^{\min }\le \Delta H_{\mathrm{hst},\mathrm{d}}\le \Delta H_{\mathrm{hst},\mathrm{d}}^{\max }\end{array}\right.$$

(15)

where $H_{\mathrm{hst},\mathrm{c}}$ ($H_{\mathrm{hst},\mathrm{d}}$) is the heat storage (discharge) power of the HST. $H_{\mathrm{hst},\mathrm{c}}^{\min }$ ($H_{\mathrm{hst},\mathrm{d}}^{\min }$) and $H_{\mathrm{hst},\mathrm{c}}^{\max }$ ($H_{\mathrm{hst},\mathrm{d}}^{\max }$) are the minimum and maximum heat storage (discharge) power of the HST. $M_{\mathrm{hst},\mathrm{c}}$ ($M_{\mathrm{hst},\mathrm{d}}$) is the heat storage (release) state mark bit of the HST. $S_{\mathrm{hst}}$ is the continuous heat of the HST. $S_{\mathrm{hst}}^{\max }$ and $S_{\mathrm{hst}}^{\min }$ are the upper and lower limits of heat storage capacity of the HST. $\Delta H_{\mathrm{hst},\mathrm{c}}$ ($\Delta H_{\mathrm{hst},\mathrm{d}}$) is the heat storage (discharge) increment. $\Delta H_{\mathrm{hst},\mathrm{c}}^{\max }$ ($\Delta H_{\mathrm{hst},\mathrm{d}}^{\max }$) and $\Delta H_{\mathrm{hst},\mathrm{c}}^{\min }$ ($\Delta H_{\mathrm{hst},\mathrm{d}}^{\min }$) represent the upper and lower limits of climbing power in the heat storage (release) state.

4.3. Load Model

Under the condition of energy price given by the ES, the energy-consuming group achieves the optimization goal by adjusting the shiftable load and reducible load, that is, maximizing consumer surplus. Maximizing consumer surplus can be expressed by the difference between user utility function and energy cost.

$$\max F_{\mathrm{la}}=f_{\mathrm{u}}^t-R_{\mathrm{sell}}^t$$

(16)

where $f_{\mathrm{u}}^t$ indicates the satisfaction degree of users, which can be expressed by quadratic function.

$$f_{\mathrm{u}}^t={\displaystyle \sum _{t=1}^T[{\gamma }_{\mathrm{e}}{P}_{\mathrm{ue}}^t-\frac{{\lambda }_{\mathrm{e}}}{2}{(P_{\mathrm{ue}}^t)}^2+{\gamma }_{\mathrm{h}}{H}_{\mathrm{uh}}^t-\frac{{\lambda }_{\mathrm{h}}}{2}{(H_{\mathrm{ue}}^t)}^2]}\Delta t$$

(17)

where ${\gamma }_{\mathrm{e}}$, ${\lambda }_{\mathrm{e}}$, and ${\gamma }_{\mathrm{h}}$, ${\lambda }_{\mathrm{h}}$ are the user’s preference coefficient for different energy use, which determines the LA’s demand for power and heat energy.

The power load $P_{\mathrm{ue}}^t$ of the energy-using side is determined by the fixed load $P_{\mathrm{fix}}^t$ and the shiftable load $P_{\mathrm{tra}}^t$.

$$P_{\mathrm{ue}}^t=P_{\mathrm{fix}}^t+P_{\mathrm{tra}}^t$$

(18)

where $P_{\mathrm{ue}}^t$ is relatively fixed in power consumption and has high requirements for power reliability, half of which is used for life, production, and other activities. $P_{\mathrm{tra}}^t$, the power consumption time, is relatively flexible, and it is determined according to the change in electricity price, such as charging load. The constraint condition is:

$$\left\{\begin{array}{l}0\le P_{\mathrm{tra}}^t\le P_{\mathrm{tra},\max }^t\hfill \\ {\displaystyle \sum _t^T{P}_{\mathrm{tra}}^t=Z_{\mathrm{tra}}}\hfill \end{array}\right.$$

(19)

where $P_{\mathrm{tra},\max }^t$ is the maximum value of the shiftable load power. $Z_{\mathrm{tra}}$ represents the total amount of translational load power in period T. The $Z_{\mathrm{tra}}$ value is constant before and after the demand side response.

The heat load power of the LA also includes two parts.

$$H_{\mathrm{uh}}^t=H_{\mathrm{fix}}^t-H_{\mathrm{tra}}^t$$

(20)

where $H_{\mathrm{fix}}^t$ is the minimum heat demand. $H_{\mathrm{tra}}^t$ represents the heat power that can be reduced, which is used to adjust and reduce the required heat power according to the satisfaction degree of heat use. The constraints that need to be met are

$$0\le H_{\mathrm{tra}}^t\le H_{\mathrm{tra},\max }^t$$

(21)

where $H_{\mathrm{tra},\max }^t$ denotes the maximum heat power that can be dissipated at time t.

4.4. Solving Algorithm

The two-layer model of the low-carbon CIES proposed in this paper is a continuous action space. The state space and action space of the model are discretized, and the problem of dimension disaster occurs. Meanwhile, discretizing the action space leads to insufficient energy transaction information.

Therefore, this paper uses a non-dominated sorting genetic algorithm embedded in quadratic programming (NSGA-QP) with continuous decision-making ability to solve the optimal scheduling problem of the low-carbon CIES. The NSGA-QP is used to solve the multi-objective optimization problem established by the above two-layer dynamic CIES low-carbon collaborative optimization method. The specific steps are as follows:

• Step 1: Determine the population size N and initialize the population.
• Step 2: Establish the ideal point, normalize the target values of all individuals, calculate the extreme point, construct the hyperplane, and determine the reference point.
• Step 3: Complete the non-dominated sorting of the population.
• Step 4: Operate the population with the genetic operator to obtain a sub-population size N.
• Step 5: Merge two populations to obtain a population of 2 N and perform fast non-dominated sorting to determine the non-dominated hierarchy.
• Step 6: According to the order of the non-dominated hierarchy from small to large, add individuals to the next generation until the population size is N. The non-dominated hierarchy at this time is L.
• Step 7: Select a part of the individuals in the L layer because, in most cases, the individuals in the L layer cannot be all added to the reference point. Firstly, associate the individuals in the 1~L layer with the reference point and then find the reference point with the least individuals in the 1~L−1 layer. Finally, select an individual associated with the reference point from the L layer to join, and repeat the step until the population size is N, and replace the original population with the new population.
• Step 8: Repeat Step 4~Step 8 until the set number of iterations is completed, and finally, obtain the Pareto optimal solution.

The specific implementation process of a low-carbon collaborative optimization operation method for a two-layer dynamic CIES is shown in Figure 3.

5. Community Integrated Energy System Model

5.1. Parameter Setting

Taking a community in North China as an example, the simulation analysis of the CIES distributed collaborative optimization operation strategy proposed in this paper is carried out. The translatable power load and the reducible heat load of the CIES are set no higher than 30% of the total load, and the translatable power load is not higher than 400 kW. The detailed parameters of the CIES are shown in

Table 1. The specific parameters of the system.

Parameter	Value	Parameter	Value
${\mu }_{\mathrm{e},\mathrm{q}}$	0.728 t/(MW·h)	${\gamma }_{\mathrm{e}}$	2100 CNY/MW·h
${\mu }_{\mathrm{h},\mathrm{q}}$	0.102 t/GJ	${\lambda }_{\mathrm{e}}$	0.9 CNY/(MW·h)2
${\mu }_{\mathrm{e},\mathrm{r}}$	0.924	${\gamma }_{\mathrm{h}}$	1100 CNY/MW·h
${\mu }_{\mathrm{g},\mathrm{r}}$	0.488	${\lambda }_{\mathrm{h}}$	1.2 CNY/(MW·h)2
${\mu }_{\mathrm{p}2\mathrm{g}}$	0.118	${\eta }_{\mathrm{re}}$	0.85
${\mu }_{\mathrm{pcu}}$	0.144	${\eta }_{\mathrm{ice}}$	0.39
$a_{\mathrm{e},\mathrm{iec}}$	0.0013	$c_{\mathrm{h},\mathrm{bt}}$	0.05
$b_{\mathrm{e},\mathrm{iec}}$	0.16	$P_{\mathrm{bt},\mathrm{c}}^{\max }$	350 kW
$c_{\mathrm{e},\mathrm{iec}}$	0	$P_{\mathrm{bt},\mathrm{d}}^{\max }$	350 kW
$b_{\mathrm{h},\mathrm{bt}}$	0.005	$H_{\mathrm{hst},\mathrm{c}}^{\max }$	200 kW
$b_{\mathrm{h},bt}$	0.11	$H_{\mathrm{hst},\mathrm{d}}^{\max }$	150 kW

.

5.2. Analysis of Optimal Scheduling Results

In order to verify the effectiveness of the proposed two-layer dynamic CIES low-carbon collaborative optimization operation scheduling model, as shown in

Table 2. The CIES simulation scenario settings.

Scenario	Carbon Trading Model	Scheduling Strategy
1	No	Centralized scheduling
2	Traditional fixed carbon trading price	Centralized scheduling
3	The proposed multi-agent stage feedback carbon trading mode	Centralized scheduling
4	The proposed multi-agent stage feedback carbon trading mode	The proposed two-layer dynamic distributed scheduling

, four different scenarios are set up. The scheduling results of CIES are shown in

Table 3. Comparison of CIER scheduling results in each scenario.

Scenario	ES Earnings	CCHP Earnings	LA Consumer Surplus	Carbon Emissions
1	CNY 6034	CNY 8872	CNY 9419	1006.7 t
2	CNY 5904	CNY 8415	CNY 8973	994.3 t
3	CNY 6072	CNY 8781	CNY 9532	914.6 t
4	CNY 7468	CNY 9637	CNY 10624	841.3 t

.

Comparing scenario 3 and scenario 1, the system’s carbon emissions are reduced by 92.1 t in each scheduling cycle after using the proposed carbon trading model. Compared with the traditional fixed carbon trading price model, the proposed carbon trading model reduces carbon emissions by 8.02%. Compared with the traditional scheduling method (scenario 1), the ES revenue, CCHP revenue, and LA consumer surplus in the scheduling results of the proposed method (scenario 4) increase by 23.77%, 8.62%, and 12.79%, respectively, and the carbon emission decreases by 16.34%. Therefore, the proposed two-layer dynamic low-carbon collaborative optimization scheduling model can reduce the system’s carbon emissions and ensure its economical operation.

The pricing strategy of the upper ES in the proposed optimal scheduling model is shown in Figure 4. In Figure 4a, the ES formulates a price strategy within the envelope of time-of-use electricity price and on-grid electricity price to provide a better price for both the CCHP and the LA than the power grid. The fluctuation trend in the hourly price of the ES is similar to the time-of-use price of the power grid, and the purchase price is similar to the load change trend. There are two peaks at 12:00–14:00 and 20:00–22:00. This is to encourage new energy CCHP power generation, decrease the amount of electricity purchased, and increase income. The change rule of the heat price curve is the same as that of the electricity price in Figure 4b.

The electrical and thermal load curves before and after the demand response on the LA side are shown in Figure 5. Figure 5a shows that under the incentive of reducing electricity costs, there is a peak load shift in the power load curve before and after the demand response. The peak of LA’s original power load occurs between 10:00–14:00 and 18:00–19:00. Currently, the electricity price is relatively high. After LA optimization, the peak load rapidly decreased. By transitioning to the lower-priced load valley stage between 2:00–8:00 and 22:00–24:00, the fluctuation in the electricity load curve is significantly reduced. From Figure 5b, it can be seen that the overall heat load decreased, but during the period of 13:00–15:00, the original demand was lower. In order to ensure user comfort, the reduction in the heat load also decreases synchronously.

The optimal scheduling results of the power and heat of the new energy CCHP system on typical days are shown in Figure 6. Considering the environmental protection of new energy, photovoltaic and wind power output will be preferentially sold to the ES, and the gas generator of the CCHP system will be used as a supplement to make up for the lack of new energy. At the valley value of electricity consumption after the demand response, the gas generator has more output in order to obtain higher income, resulting in oversupply and excess power grid connected through the ES. However, at the peak of electricity consumption, the missing electricity needs to be purchased from the grid by the ES. As shown in Figure 6b, the GT and GB jointly provide heat energy, and the waste heat of the GT is directly related to the amount of power generated. To ensure uninterrupted heat supply and reduce penalty costs, the ES adjusts the purchase price of heat to maintain the supply–demand balance, thereby scheduling GB and GT production.

6. Conclusions

This paper proposes a low-carbon collaborative optimization operation scheduling model for a two-level dynamic community integrated energy system. The ES is used as the upper layer, and new energy CCHP operators and load aggregators are used as the lower layer to solve their equilibrium interaction strategies to achieve multi-agent distributed collaborative optimization operation. A multi-agent stage feedback carbon trading model is proposed to calculate carbon trading costs at stages. At the same time, feedback factors are introduced to conduct cost feedback based on the actual carbon emissions of the system, so as to reduce carbon emissions indirectly. Finally, the validity of the model is verified by a practical example. The following conclusions are obtained:

• The proposed low-carbon collaborative optimization operation scheduling model of the two-layer dynamic community integrated energy system can ensure the optimal interests of each differentiated subject and reduce the carbon emissions of the system. The NSGA-QP distributed method is used to solve the problem, which reduces the difficulty of solving, improves the efficiency of solving, and avoids falling into the local optimal solution.
• The simulation results show that compared with the traditional scheduling method, the ES revenue, CCHP revenue, and LA consumer surplus in the scheduling results of the proposed method increased by 23.77%, 8.62%, and 12.79%, respectively, and the carbon emission decreased 16.34%. Therefore, the proposed two-layer dynamic low-carbon collaborative optimization scheduling model can reduce the system’s carbon emissions and ensure its economical operation.
• Using the price signal to guide the new energy CCHP output and adjust the LA’s energy consumption plan can improve the energy supply side income, reduce the energy cost under the premise of ensuring the satisfaction of energy consumption, stabilize the load fluctuation, and make the energy supply lower carbon economy and more reasonable.

The model proposed in this paper describes the interaction behavior among agents from the vertical dimension but does not consider the modeling of the horizontal dimension. In future research, various coupling relationships among agents, such as master–slave relationships, non-cooperative games, etc., will be considered. The model proposed in this paper will be extended to adapt to the CIES with more complex participants and more intensive information interactions.