# Coordinated Control Strategy of Electricity-Heat-Gas Integrated Energy System Considering Renewable Energy Uncertainty and Multi-Agent Mixed Game Yan Jing, et al.

Jun 23, 2022

## 1 Introduction

With the trend of low-carbon, cleanness and sustainability of electric industry going further, the energy structure of all countries in the world is gradually realizing electric energy substitution and clean energy substitution. China’s “carbon peaking and carbon neutrality (dual carbon)” goals are also important to the international community (Ali et al., 2021). Effective response to green and low-carbon development. The Integrated Energy System (IES) runs through the coordinated operation of electric and thermal energy, which can effectively improve energy utilization, and is of great significance for promoting the consumption of renewable energy and achieving the “dual carbon” goal (Mohamed, 2022). On the energy side, wind power, photovoltaic, natural gas and other clean energy access the grid and will increase the uncertainty of power supply, heating and other aspects (Rezaei et al., 2021; Xia et al., 2021). Meanwhile, on the load side, new types of loads such as electric vehicles, smart homes and other forms of energy loads can deeply participate in energy interactions and also increase new uncertainties in the demand side (Al-Ghussain et al., 2021; Lan et al., 2021). Moreover, the integrated energy system integrates coal, oil, natural gas, electricity, heat and other energy sources in the region (Tan et al., 2022). At the same time, the existing market investment body is increasing. This means that in the existing market environment in China, grid companies have changed from being the dominant player in the construction of energy networks to being an important player in the construction of energy networks (Sun et al., 2015; Ma et al., 2021). Unlike the traditional integrated energy synergy from the overall perspective of decision-making, the integrated energy system is oriented to multiple competing subjects, and there is a significant game relationship between different subjects (Weinstein, 2010). In this background, it is important to study and propose an integrated energy system control strategy that takes into account the game relationship of diverse investment agents.

The problem of integrated energy system regulation has been studied by scholars in China and abroad and certain results have been achieved (Abdelaziz Mohamed and Eltamaly, 2018a). In order to solve the energy station-grid configuration problem, Huang Wei et al. (Huang and Liu, 2020) proposed an integrated energy station-grid double-layer planning optimization model for parks considering the multi-energy complementary characteristics of energy stations. The model effectively alleviates the problem of under-supply or over-supply caused by zonal supply and peak-to-valley demand. The authors in (Yao and Wang, 2020) propose a two-level collaborative optimal allocation method for integrated energy systems considering wind and solar uncertainty. The approach improves both total annualized system cost and average annual equipment utilization. The article verifies the effectiveness and economy of the proposed method. Walter et al. (2020) proposed the integration of thermal energy systems into microgrid energy management systems. He builds models based on consideration of fuel costs, thermal comfort and other factors. Moreover, its economic efficiency is fully considered the optimal solution to achieve the purpose of reducing the cost of electricity and heating. All of the above literature uses a game theory and traditional centralized method approach to regulate aspects such as power system generation, and grid structure. The disadvantage of above approach is that it is difficult to allocate the power system dynamically and also having the problem of solving quickly.

It is worth noting the close coupling of different energy networks such as electricity and natural gas in the integrated energy system (Abdelaziz Mohamed and Eltamaly, 2018b). The problem of solving control strategies for integrated energy systems is a nonlinear, non-convex optimization problem. Therefore, it is difficult to solve the problem by relying only on traditional mathematical modeling methods (Mohamed et al., 2020).

Aiming at the difficulty solving problem of the traditional modelling methods are difficult to solve the problem, this paper model the multi-agent game process, applies DRL to the multi-agent game process of IES, and simulates the multi-agent systemization based on the MADRL algorithm, which at the same time, may contribute to further reduce the cost of the Integrated Energy System, optimize the energy efficiency and meet the daily load. To be specific, considering the game relationship of diversified investment entities in the IES, this article takes the electric-heat-gas integrated energy system as the object and constructs a multi-agent strategy model based on DRL. The main contributions of this article are as follows:

(1) Considering different kinds of energy equipment and their coupling relations in the integrated energy system, the mathematical model of the integrated energy system is constructed;

(2) Based on the theory of DRL, the dynamic game process and decision model of interests multi-energy players of electricity, heat and gas are constructed according to the decisions of different players and their respective benefits;

(3) A two-layer model is established. The lower layer decides the output of electricity, heat and gas networks, and the upper layer model calculates the equilibrium output of the Integrated Energy System based on the output decision of the lower layer and the constraints of multi-power flow;

(4) The reliability and validity of the proposed model is proved by the analysis of calculation examples.

The rest of this paper is organized as follows. Section 2 introduced the structure of Integrated Energy System and multi-agent game theory; In Section 3, mathematical model of Integrated Energy System is discussed in detail, including the constraints. In Section 4, the two-lavel model is introduced and proposed the setting method to a DRL model; Section 5 presents the numerical simulation results. Finally, conclusions and suggestions for future work are drawn in Section 5

## 2 Integrated Energy System Structure and Multi-Agent Game

FIGURE 1. Integrated energy system.

### 2.1 Integrated Energy System Structure

In this integrated energy park system, electricity and natural gas can be purchased from external sources; Conversion between electricity and gas can be done by combined heat and power units and gas turbines; Conversion between electricity and heat through combined heat and power units and electric boilers; Conversion between heat and gas via combined heat and power units and gas boilers.

On this basis, this paper takes the three networks that exist in the system as different subjects of interest. The structure divides IES into three investment entities: electricity (main grid, renewable energy, combined heat and power units), heat (gas boilers, electric boilers) and natural gas.

### 2.2 Multi-Agent Game Model

This section analyzes the control problem of multi-energy synergy within an integrated energy system and constructs a hybrid game Markov process for electrical and thermal multi-subjects. The structure can fully consider the interests of different subjects and avoids the dimensional catastrophe in the state and action space that arises when deep reinforcement learning is applied.

In this paper, the Nash equilibrium point of solving the game between multiple agents is used as a control strategy for integrated energy systems. Its target expression is

Where,

$G$

is the equilibrium point reached by the game between multiple agents;

$g(·)$

is the game function between multiple agents;

$Ng$

is the set of behaviors of the agents involved in the game. It is expressed as the operating action of each type of equipment in this article;

$ug$

is the set of utilities of the agents participating in the game. It is represented the economic interests of the respective agents in this paper.

## 3 Mathematical Model of Integrated Energy System Control Strategy

The three investment entities included in the actual IES: electricity, natural gas and heat. These three investment entities will consider their interests more in the operation process. Traditional optimization methods are difficult to solve optimally for the game relationship between the three entities and to minimize the operating cost of the system. Therefore, this section considers the return of the investment subject based on the intelligent body division method proposed in Section 2. And the control strategy revenue model of electric, natural gas and thermal energy investment entities is constructed.

### 3.1 Objective Function

$F=max∑t=1TI(t)−C(t)s.t. I(t)=∑n=1Nie(t)+ih(t)+ig(t)C(t)=∑n=1Nccos⁡t(t)(2)$

Where,

$I(t)$

is the profit of the system at time

$t$

;

$C(t)$

is the operating cost of the system at time t;

$ccos⁡t(t)$

is the cost of purchased energy. The specific expression for the cost of purchased energy is as follows.

#### 3.1.1 Sales of Electricity, Heat and Gas Revenue

Where,

$cse$

,

$csh$

and

$csg$

are the sold prices of electricity, heat and natural gas, respectively;

$Pgridsell(t)$

is the electrical power delivered to the consumer by subject n at time period t;

$Hsell(t)$

is the thermal power to supply heat to the customer in time period t;

$Vsell(t)$

is the volume of natural gas required by the customer in time period t.

#### 3.1.2 Cost of Purchased Electricity, Heat and Gas

$ccos⁡t(t)=(cbePbuy(t)+cbgVbuy(t))(6)$

Where,

$cbe$

and

$cbg$

are the buying prices of electricity and natural gas, respectively;

$Pbuy(t)$

is the electric power delivered from the grid to the IES system at moment t;

$Vbuy(t)$

is the amount of natural gas delivered from the natural gas network to the IES system at time t.

For heat networks, their power generation is delivered internally by the integrated energy system and is not purchased from outside. Heat network costs have been partially converted from gas source power output and electric power output.

### 3.2 Equipment Model

The input-output relationship of CHP, GT, EB and GB are introduced as follow. These equipment can convert energy from one form to another.

#### 3.2.1 Combined Heat and Power Unit Model

For the CHP unit, there is a coupling between its output electric power and thermal power. Depending on whether the CHP unit electric heat ratio varies or not, there are two types: fixed heat and power ratio and variable heat and power ratio. In this paper, a fixed heat and power ratio is set, denoted by variable

$ηCHP$

.

Where,

$hCHP(t)$

represents the thermal power of the CHP unit at moment t;

$pCHP(t)$

is the electrical power of the CHP unit at moment t. In addition, the natural gas volume consumed by CHP unit is:

$Vg=pCHP(t)·ΔtQLHV·ηG_E(8)$

Where,

$ηG_E$

represents the gas-to-power efficiency of CHP unit; Natural gas low calorific value

$QLHV$

is 9.7kwh/m3.

#### 3.2.2 Gas Turbine Model

A gas turbine generates electricity by burning natural gas and has the following equation

Where,

$pGT(t)$

represents the electrical power of the gas turbine unit at time t;

$ηGT$

is the gas-electric conversion factor of the gas turbine.

#### 3.2.3 Electric Boiler Model

The electric boiler is connected to the grid as a load, and its mathematical model is shown in the following equation

Where,

$hEB(t)$

represents the thermal power emitted by the electric boiler unit at time t;

$pEB(t)$

is the electrical power consumed by the EB unit at time t.

#### 3.2.4 Gas Boiler Model

The gas boiler is connected to the gas network in the form of a load, and its mathematical model is shown in the following equation:

$VGB(t)=hGB(t)ηG_H/QLHV(11)$

Where,

$hGB(t)$

represents the thermal power emitted by the gas boiler unit at time t;

$VGB(t)$

is the amount of natural gas consumed by the gas boiler at time t;

$ηG_H$

is the gas-to-heat efficiency of the gas boiler.

### 3.3 Constraint Condition

The constraints of the integrated energy system control problem include power balance constraints, external energy supply constraints, and equipment operation constraints.

#### 3.3.1 Power Constraints

At moment t, the electric power balance constraint and the thermal power balance constraint can be expressed respectively as:

$pgrid(t)+pRES(t)+pGT(t)pCHP(t)−pEB(t)=pload(t)(12)$
$hCHP(t)+hGB(t)+hEB(t)=hload(t)(13)$

Where,

$pgrid(t)$

is the power exchanged between the system and the main grid at time t. A positive power indicates that the system purchases power from the main grid, and a negative power indicates that the system carries out surplus power to the grid;

$pRES(t)$

is the output power of renewable energy;

$pload(t)$

is the electrical load for time period t;

$hload(t)$

is the heat load for time slot t.

#### 3.3.2 Equipment Operating Constraints

The devices in the IES system have an upper and lower operating limit range. There are requirements for the electric power output of CHP units, the thermal power output of gas boilers and electric boilers.

$PCHPmin⩽pCHP(t)⩽PCHPmax(14)$
$PGTmin⩽pGT(t)⩽PGTmax(15)$
$HGBmin⩽hGB(t)⩽HGBmax(16)$
$HEBmin⩽hEB(t)⩽HEBmax(17)$

Where,

$PCHPmax$

and

$PCHPmin$

are the upper and lower limits of the output power of the CHP unit;

$PGTmax$

and

$PGTmin$

are the upper and lower limits of the electrical power output of the CHP unit;

$HGBmax$

and

$HGBmin$

are the upper and lower limits of the thermal power output of the gas boiler;

$HEBmax$

and

$HEBmin$

are the upper and lower limits of the thermal power output of electric boiler respectively.

### 3.3.3 Energy Conversion Equipment Constraint

The energy conversion equipment of IES must meet the constraints shown in 711.

## 4 Two-Level Decision Model

IES control problems have complex constraints and are difficult to converge. To address this problem, this paper proposes a two-level model to achieve efficient model learning and effective control of IES. The upper layer DRL agent is responsible for learning strategies to make decisions for the output of the integrated energy system. The lower layer model receives the actions of the upper layer and performs energy flow calculations to verify the security of the model. When the action of the upper RL model has a tide crossing the line, energy flow imbalance, etc., add an appropriate penalty to the reward. The reward design complexity when the upper output action violates the constraint is reduced by a two-level model design. Meanwhile, the model avoids the problem of the difficult convergence of currents.

### 4.1 Upper Layer DRL Model Design

In RL, there are two interactive objects: agent and environment. The agents sense the external state and obtain reward. After that, the agent learns and makes decisions. The environment will be affected by the action of the agent and change its state, and give feedback to the agent to get the reward in response. DRL has the general intelligence to solve complex problems to a certain extent and has achieved great success in many tasks. A Markov decision process (MDP) is a sequence of random variables with Markov properties, in which the state of the next moment depends only on the current state. If an action is added to the Markov process, the state at the next moment is related to action and the current state.

The upper layer of the two-level model is the DRL agent. In the paper, IES is the environment of the intelligent, which makes optimal control strategy decisions by regulating the device output in the system.

#### 4.1.1 Reward Function Design

When designing the reward function, setting the scaling factor facilitates the agent to learn the gains of different subjects more equally. This helps to balance the weight of the contribution of each agent. Therefore, the reward function for the upper layer DRL agents is designed as follows:

$r=(−c−cos⁡tγplscpls−rpun)(18)$

Where,

$γpls$

is the line loss penalty factor, taken as 0.5;

$rpun$

is the line crossing penalty, taken as 200.

#### 4.1.2 State-Space Design

The DRL status should contain sufficient information to make decisions, including electric load demand, thermal load demand, gas load demand and renewable generation power, as well as real-time electricity sales prices. It can be expressed as follows:

$st={pload(t),hload(t),Vload(t),pRES(t),ce_sell(t),cg_buy(t)}(19)$

#### 4.1.3 Action Space Design

At time slot t, the action in IES can be indicated by the output of the device. In this paper, the multi-agent body consists of three parts, grid agent body, heat network agent body and gas network agent body. The intelligent body action can be represented as follows:

$At={aet,aht}s.t. aet={pCHP(t)}aht={hGB(t)}agt={pGT(t)}(20)$

Where,

$At$

is the total set of multi-agent actions;

$aet$

represents grid agent actions;

$aht$

represents thermal network agent actions;

$agt$

represents thermal network agent actions.

### 4.2 Lower Layer Model Design

The objective of the lower layer model is to verify the security of the grid through power flow calculations after the upper layer has made decisions on the output of the grid and the heat network. Meanwhile, its interactive power with the superior grid is obtained. Gas network to minimize operating costs to optimize autonomous costs. Gas source treatment of the gas network by flow calculation calibration. The results are returned to the upper DRL model to calculate the operating costs of the IES system.

#### 4.2.1 Power Flow Calculation

The electric output of CHP units, electric boiler heat output, and gas boiler heat output are delivered to the lower model in multi-intelligent planning. By power flow calculation, the exchange power and line losses with the main network are derived. The specific calculations are as follows:

#### 4.2.2 Gas Network Flow Calculation

The calculation process is aimed at minimizing the cost of the gas network. Electric output of CHP units, heat output of electric boilers, and heat output of gas boilers are passed into the gas network flow model through the upper layer agent planning. At the same time, the calculation considers the constraints of the gas network and constructs the gas network flow model. The details are as follows:

$wj,t+∑ij∈Z(j)wij,t=∑jk∈v(j)wjk,t(23)$
$wij,t=Cij|ψi,t2−ψj,t2|(26)$
$ψmin≤ψi,t≤ψmax(27)$
$wij,min≤wij,t≤wij,max(28)$

Where,

$wij,t$

is the gas flow transmitted from pipe node

$i$

to node

$j$

;

$wj,twell$

and

$wj,tpgu$

are the source point injection gas flow and the gas consumption of the CHP unit or gas boiler at the node

$j$

, respectively;

$wj,tload$

is the node

$j$

$Z(j)$

and

$v(j)$

are the set of pipes with node

$j$

as the last node and node

$j$

as the first node, respectively;

$ψi,t$

is the gas pressure at node

$i$

;

$wij,max$

and

$wij,min$

are the upper and lower node gas pressure limits;

$Cij$

is the constant of pipe

$ij$

constant. The constant is related to the pipe length, direct, operating temperature and the gas pressure difference between the nodes.

### 4.3 Model Training and Decision Algorithms

TABLE 1. Algorithm of MADDPG.

At moment t, the upper layer DRL agents observe the state of the environment. The upper layer DRL selects the action of the multi-intelligent according to the strategy and transmits this action to the lower layer. The lower layer uses the solver to calculate the flow of the grid and the gas network. The lower layer returns the upper grid output and the treatment of gas sources in the gas network and returns to the DRL model to calculate the reward. Finally, the state

$st$

at this moment, the state

$st+1$

at the next moment, and the action

$At$

are stored in the experience pool for the DRL model to train and use. The specific process is shown in Figure 2.

FIGURE 2. The Two-level model.

## 5 Experimental Verifications

### 5.1 Example Setting

In this section, arithmetic examples will be designed to verify the advantages and effectiveness of the proposed MADDPG algorithm-based two-level strategy model for integrated energy system dynamic game strategy. The code of chemical learning and trend calculation model is solved based on python programming.

Figure 3 shows the electric-thermal-gas coupling system. The system consists of a 33-node electrical system, and a 20-node natural gas system. The heat network is converted to electrical load form connected to the grid. The power system includes 2 CHP power supplies, 2 wind power supplies and 1 PV power supply. The heating system includes 4 heat sources (1 electric boiler, 3 gas boilers). A natural gas system with 6 gas sources. The system scheduling time is 24 h and the interval between 2 adjacent periods is 1 h. The operating parameters of the components in the integrated energy system are shown in Tables 2, 3.

FIGURE 3. Coupling network.

TABLE 2. Equipment parameters.

TABLE 3. Price of electricity/gas/heat.

### 5.2 Result Analysis

This section tests the ability of the proposed model to cope with system uncertainty. The model needs to consider the electrical, thermal and gas loads in the IES as well as the renewable energy output. The existence of uncertainty leads to a large number of different scenarios for IES control. This example puts 1 year of renewable energy data (wind turbine and photovoltaic), electrical load data, thermal load data and gas load data into the model to validate the strategy results. The search time step is 24 and sets for 50,000 rounds.

The results shown in Figure 4 show the effectiveness of the control of the integrated energy system using the two-level model. Initially, due to the incomplete exploration of the action strategies of the agents, the agents choose to sacrifice profits to ensure the operational constraints. Therefore, this decision results in a low value of the reward function. At a later period, through extensive learning, the agents can make effective decisions for different scenarios. Thus, the reward function increases until it converges at about 26,000 steps. In addition, the loss functions of Figures 5, 6 show that the loss functions corresponding to the three agents show oscillations at the initial stage. This is due to the failure to find a better action to guarantee the function when the agent is making decisions in the early stages. However, the loss function of the agents smoothed out by continuously sampling and learning from the experience pool and adding noise to ensure data diversity.

FIGURE 4. Reward function curve.

FIGURE 5. Evaluation loss function curve.

FIGURE 6. Strategy loss function curve.

In order to verify the convergence and strategy effectiveness under multiple scenarios, the operation of the grid, heat and gas networks for one of the days are shown in Figures 7, 8, and 9, respectively.

FIGURE 7. Grid operation.

FIGURE 8. Operation of heat network.

From the results in Figures 79, it can be seen that the full consumption of renewable energy is achieved within the integrated energy system. The heat load in the heat network can be met by the equipment in the integrated energy system. In addition, due to the limited power supply equipment in the integrated energy system, most of the electricity is satisfied by the grid exchange power. This also makes the operational efficiency of the integrated energy system more related to the exchange of power. As can be seen from Figure 10, the higher demand for cooling equipment in summer leads to an increase in power consumption. The resulting increase in interactive power with the grid increases the cost of integrated energy and leads to reduced benefits. In winter, the benefits of the integrated energy system are increased by the abundance of heating equipment within the system to meet the thermal energy demand.

FIGURE 9. Operation of the gas network.

FIGURE 10. Operational benefits of the integrated energy system.

## 6 Conclusion

For the game relationship between different subjects in IES and the complex energy coupling relationship, this paper establishes a two-level DRL model of an integrated energy system containing three subjects: electricity, heat and gas. The upper layer of the model uses the reinforcement learning MADDPG algorithm to determine the power output of each device for electricity and heat. The lower layer calculates the interactive power with the grid that satisfies the power flow and the output power of the gas source node of the gas network. The proposed two-level model in this paper can simplify the design of reward functions for multi-intelligent reinforcement learning. The model can strengthen action constraints and effectively improve the training speed of reinforcement learning. The analysis shows that the proposed model can effectively improve the energy utilization efficiency of the integrated energy system with the full consideration of the dynamic game of electricity, heat and gas. In addition, the model combines a data-driven multi-agent reinforcement learning approach with traditional trending algorithms. This allows the model to be solved with higher efficiency, realizing the collaborative control strategies for IES, meeting the needs of various energy sources while reducing the cost and energy consumption of the integrated energy system.

In future research, on the one hand, we will further consider the coupling network with more constraints and energy storage devices to the multi-agent economy influence, on the other hand, consider the load demand of different level, such as the reducible and non-reducible loads, and improve the control strategy, to reduce the cost of the integrated energy system and increase energy efficiency.

## Data Availability Statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

## Author Contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

## Funding

The work is supported by the technology project of SGCC (State Grid Corporation of China) under Grant SGTYHT/19-JS-215.

## Conflict of Interest

YJ and ZB were employed by the company State Grid Hubei Electric Power Co., Ltd. DZ and WY were employed by the company State Grid Hubei Electric Power Co., Ltd. Economic and Technological Research Institute.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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