Dynamic Pricing and System Optimization of Integrated Energy
System in Industrial Parks Based on Carbon Tax
Yuanyuan Deng, Masahiro Mae, Ryuji Matsuhashi
Department of Electrical Engineering and Information Systems Graduate School of Engineering
The University of Tokyo
Tokyo, Japan{deng,mae,matu}@enesys.t.u-tokyo.ac.jp
Abstract—Aiming to improve the efficiency of the industry park's
integrated energy system and reduce carbon emissions, this paper
adopts dynamic pricing and carbon tax mechanisms. Utilizing
game theory, a leader-follower game framework is constructedwith the energy system operator (ESO) as the leader and building
users as followers. Through the integration of dynamic pricing
and carbon tax model, the paper demonstrates notable
improvements in economic and low-carbon performance within
the energy system. Consequently, in this paper, it provides
valuable support for sustainable energy development andeconomic operations in a low-carbon economy. The findings
underscore the potential of dynamic pricing and carbon tax
mechanisms as integral contributors to achieving a moresustainable and economically efficient energy landscape.
Index Terms--Carbon Tax, Demand Response, Differential
Evolution Algorithm, Dynamic Electricity Prices, Leaderfollower Game

I. INTRODUCTION
Energy plays a pivotal role in driving modern societal
development, offering avenues for enhancing efficiency,
reducing costs, and fostering the adoption of clean energy
solutions through comprehensive energy systems [1]-[3]. As
urbanization accelerates and environmental concerns takecenter stage, park-level comprehensive energy systems haveemerged as a focal point for efficient energy supply andmanagement [4]. However, traditional dynamic pricing
mechanisms within these systems face challenges such as pricefluctuations and limited adaptability [5]-[7], necessitating
exploration into innovative approaches like game theory toenhance their effectiveness.
Scholars have extensively researched optimal planningschemes for comprehensive energy systems, focusing on
economic efficiency, reliability, and the promotion ofrenewable energy consumption. Among these efforts, demand
response (DR) has gained traction as a solution for smart grid
utilization. Integrated Demand Response (IDR) strategies
leverage demand-side resources for flexible adjustments.
Reference [8] developed optimization and scheduling models
for comprehensive energy systems with carbon capturesystems, employing a leader-follower game framework.
References [9]-[10] proposed low-carbon optimization
strategies for integrated energy systems, incorporating tiered979-8-3503-8174-0/24/$31.00 ©2024 IEEE

carbon trading mechanisms and comprehensive demand
response strategies. Reference [11] introduced a Stackelberg
leader-follower game model to optimize industrial park
comprehensive energy systems, integrating economic operation
and auxiliary services. Reference [12] established a leaderfollower game model for optimizing power company park
integrated energy systems (PIES), addressing equilibrium
strategy problems between PIES, power companies, and users.
Reference [13] proposed a multi-party energy management
framework for combined heat and power (CHP) systems,
incorporating power and thermal demand response.
Carbon trading and carbon taxes are recognized as effectivemeans to promote low-carbon operations [14]. Research [15]presents optimization models incorporating carbon taxes,
showing improved performance compared to reference
systems. Research [16]-[17] determines optimal renewableenergy subsidies and establishes energy-carbon prices,enhancing low-carbon operation. Research [18] introduces a
hybrid carbon tax in an operator-user game model, reducing
system emissions and user energy costs. Additionally, research[19] proposes coordinated optimization strategies considering
carbon quotas and integrated demand response, offering dual
incentives for comprehensive energy systems.
However, while these studies have delved into various
aspects of comprehensive energy systems optimization, there isa notable gap in understanding the integration of carbon tax
mechanisms into integrated energy systems. In this context, thispaper aims to explore the potential of integrating carbon tax
mechanisms into park-level integrated energy systems to
improve energy utilization efficiency and reduce carbon
emissions. By leveraging insights from game theory andbuilding upon existing literature on energy system
optimization, this paper seeks to develop more flexible andefficient pricing mechanisms that integrate carbon tax, thereby
contributing to both theoretical understanding and practicalimplementation in energy system management.
II. MODEL CONSTRUCTION
A. Energy Trading Framework
In the electricity market, the energy system operator (ESO)and PIES play pivotal roles, and their autonomous decisionmaking profoundly impacts each other and the market.

𝐶𝑃𝐼𝐸𝑆 (𝑡) = ∑𝑛𝑖=1 𝐴𝑖,𝑏 (𝑡)𝜋𝑏𝑒 (𝑡)(6)𝐶𝑚𝑡 (𝑡) = 𝑃𝑚𝑡 (𝑡) ∗ 𝐾𝑀𝑇(7)

𝐶𝑝𝑣 (𝑡) = 𝑃𝑝𝑣 (𝑡) ∗ 𝐾𝑃𝑉(8)𝐶𝑤𝑡 (𝑡) = 𝑃𝑤𝑡 (𝑡) ∗ 𝐾𝑃𝑊(9)Where 𝜋𝑒𝑠 (𝑡)，𝜋𝑠𝑤 (𝑡) is the price at which ESO sells
and purchases electricity from users at time t;𝜋𝑓𝑠 (𝑡), 𝜋𝑠𝑤 (𝑡) is
time-of-use electricity price and the on-grid electricity price ofthe power grid at time t; 𝐴𝑖.𝑠 (𝑡) is the amount of electricity soldby ESO to users at time t.

𝐶𝑔𝑟𝑖𝑑 (𝑡), 𝐶𝑃𝐼𝐸𝑆 (𝑡)is the cost of purchasing energy fromthe superior power grid and park by ESO at time t; Asw (t)Asw (t) is the amount of electricity purchased and sold by ESO
from the superior power grid at time t; 𝐴𝑖,𝑏 (𝑡) is the amount of

Figure 1. Energy trading framework

ESO, as the leader, sets time-based electricity pricing andgrid access fees, aiming to maximize economic interests byconsidering electricity purchase demands and carbon
emissions. ESO profits through transactions with the grid andindustry parks.
Users, as followers, respond to ESO's pricing strategy,
factoring in variables like carbon tax prices. Their decisions
influence ESO, which adjusts its strategies to meet market
demands and optimize profitability.
This dynamic interaction forms a leader-follower gameframework with ESO as the leader and users as followers in
Fig.1. They mutually influence each other, shaping theelectricity market's operation. The complexity of thisframework requires adaptability to evolving market dynamics
and demands.
B. Profit Model of ESO
The objective function is a critical component of thesystem's dynamic pricing model based on leader-follower gametheory, playing a significant role in the study. This paper aims
to achieve the efficient utilization of PIES and a reduction incarbon emissions through this model. Therefore, in setting theobjective function, it is necessary to consider three aspects:
supply-demand equilibrium, energy efficiency, and carbon
emission control.
max 𝐹𝐸𝑆𝑂 = ∑𝑇𝑡=1(𝐼𝑠𝑒𝑙𝑙 (𝑡) − 𝐶𝑏𝑢𝑦 (𝑡) − 𝐶𝑅𝑚 (𝑡)) − 𝛾(∑𝑖=1 𝐶𝑖,𝑃𝐼𝐸𝑆 − 𝐶̅ )electricity purchased by ESO from the i-th user at time t.

𝐶𝑅𝑚 (𝑡) is the operation and maintenance cost. 𝐶𝑀𝑇 (𝑡),𝐶𝑃𝑉 (𝑡) , 𝐶𝑃𝑊 (𝑡) represents the operation and maintenancecosts of gas turbines, photovoltaic motors, and wind turbines;
𝑃𝑚𝑡 (𝑡), 𝑃𝑝𝑣 (𝑡), 𝑃𝑤𝑡 (𝑡) represents the operating power of gas
turbines, photovoltaic motors, and wind turbines; 𝐾𝑀𝑇 , 𝐾𝑃𝑉
𝐾𝑃𝑊 is the operation and maintenance constant for gas turbines,
photovoltaic motors, and wind turbines.
C. Constraint Condition
1) Restrictions on Purchasing and Selling Electricity
To ensure that each entity does not directly engage intransactions across operators or with the outside world,
restrictions should be placed on the seller's quotation to ensurethat the buying and selling prices are within the market pricerange of electric thermal energy, expressed as:(3)

𝐶𝑅𝑚 (𝑡) = 𝐶𝑚𝑡 (𝑡) + 𝐶𝑝𝑣 (𝑡) + 𝐶𝑤𝑡 (𝑡)

(4)
(5)

𝑃𝑔𝑟𝑖𝑑𝑚𝑖𝑛 ≤ 𝑃𝑔𝑟𝑖𝑑_𝑠𝑒𝑙𝑙 (𝑡) ≤ 0(12)Electric energy storage constraints:
𝑆𝑂𝐶𝑒 (𝑡) = 𝑆𝑂𝐶𝑒 (𝑡 − 1) + (𝑃𝑐ℎ (𝑡) ∗ 𝑒𝑐ℎ−𝑃𝑑𝑖𝑠𝑐ℎ (𝑡)/𝑒𝑑𝑖𝑠𝑐ℎ /𝐸𝑠𝑡𝑜_𝑚𝑎𝑥 )(13)

𝑆𝑂𝐶𝑒,𝑚𝑖𝑛 ≤ 𝑆𝑂𝐶𝑒 (𝑡) ≤ 𝑆𝑂𝐶𝑒,𝑚𝑎𝑥(14)Power constraint:
0 ≤ 𝑃𝑐ℎ (𝑡) ≤ 𝛾𝑐ℎ 𝑃𝑐ℎ,𝑚𝑎𝑥(15)0 ≤ 𝑃𝑑𝑖𝑠𝑐ℎ (𝑡) ≤ 𝛾𝑑𝑖𝑠𝑐ℎ 𝑃𝑑𝑖𝑠𝑐ℎ,𝑚𝑎𝑥(16)State constraint:
𝑃𝑐ℎ_𝑏𝑖𝑛 (𝑡) + 𝑃𝑑𝑖𝑠𝑐ℎ_𝑏𝑖𝑛 (𝑡) = 1

Where in:
𝐶𝑔𝑟𝑖𝑑 (𝑡) = 𝐴𝑓𝑠 (𝑡)𝜋𝑓𝑠 (𝑡)(11)2) Energy Storage Constraints

represents the sales electricity revenue of ESO at time t;
𝐶𝑏𝑢𝑦 (𝑡) is the energy purchase cost of ESO at time t; 𝐶𝑅𝑚 (𝑡)represents the operating cost of ESO at time t. 𝐶𝑖,𝑃𝐼𝐸𝑆 is theactual carbon energy emissions of the i-th user. γ is the carbon
penalty coefficient. 𝐶̅ is the carbon emission threshold set by
the government, and if it exceeds, a certain penalty will be
imposed.

𝐶𝑏𝑢𝑦 (𝑡) = 𝐶𝑔𝑟𝑖𝑑 (𝑡) + 𝐶𝑃𝐼𝐸𝑆 (𝑡)0 ≤ 𝑃𝑔𝑟𝑖𝑑_𝑏𝑢𝑦 (𝑡) ≤ 𝑃𝑔𝑟𝑖𝑑𝑚𝑎𝑥

which the seller purchases and sells electricity, respectively
𝑃𝑔𝑟𝑖𝑑𝑚𝑖𝑛 and 𝑃𝑔𝑟𝑖𝑑𝑚𝑎𝑥 are the time of use electricity price andgrid electricity price of the power grid, respectively.

(1)

(2)

(10)

Where 𝑃𝑔𝑟𝑖𝑑_𝑏𝑢𝑦 (𝑡) and 𝑃𝑔𝑟𝑖𝑑_𝑠𝑒𝑙𝑙 (𝑡) are the prices at

Where 𝐹𝐸𝑆𝑂 represents the total profit of ESO; 𝐼𝑠𝑒𝑙𝑙 (𝑡)𝐼𝑠𝑒𝑙𝑙 (𝑡) = ∑𝑛𝑖=1 𝐴𝑖.𝑠 (𝑡) 𝜋𝑠𝑒 (𝑡) + 𝐴𝑠𝑤 (𝑡)𝜋𝑠𝑤 (𝑡)𝑃𝑔𝑟𝑖𝑑𝑚𝑖𝑛 ≤ 𝑃𝑔𝑟𝑖𝑑 (𝑡) ≤ 𝑃𝑔𝑟𝑖𝑑𝑚𝑎𝑥

𝑒𝑐ℎ

(17)

Where 𝑆𝑂𝐶𝑒 (𝑡) is real-time storage capacity at time t;
and 𝑒𝑑𝑖𝑠𝑐ℎ represent the charging and discharging

efficiency of electrical energy; 𝑆𝑂𝐶𝑒,𝑚𝑖𝑛 , 𝑆𝑂𝐶𝑒,𝑚𝑎𝑥
represents the minimum and maximum storage capacity,respectively; 𝑃𝑐ℎ,𝑚𝑎𝑥 and 𝑃𝑑𝑖𝑠𝑐ℎ,𝑚𝑎𝑥 are the maximum
charging and discharging power;𝑃𝑐ℎ_𝑏𝑖𝑛 (𝑡) and 𝑃𝑑𝑖𝑠𝑐ℎ_𝑏𝑖𝑛 (𝑡)is a binary variable that ensures that the charging anddischarging processes do not occur at the same time.
3) Gas Turbine Constraints
Micro gas turbines recover the waste heat from hightemperature flue gas and provide heating power. The
operational constraints of micro gas turbines mainly include theupper and lower limits of output. Only the upper and lower
limits of output and climbing speed of micro gas turbines are
considered.
Gas turbine fuel cost:
𝐹𝑀𝑇 (𝑡) = 𝑎𝑀𝑇 (𝑡)𝑃𝑀𝑇 (𝑡) + 𝑏𝑀𝑇(18)

Climbing constraints for gas turbines:
𝛾𝜁,𝑚𝑖𝑛 ≤ 𝑃𝑀𝑇 (𝑡) − 𝑃𝑀𝑇 (𝑡 − 1) ≤ 𝛾𝜇,𝑚𝑖𝑛(19)

Gas turbine upper and lower limits:
𝑃𝑀𝑇,𝑚𝑖𝑛 ≤ 𝑃𝑀𝑇 (𝑡) ≤ 𝑃𝑀𝑇,𝑚𝑎𝑥(20)

Where 𝑃𝑀𝑇,𝑚𝑖𝑛 and 𝑃𝑀𝑇,𝑚𝑎𝑥 is the lower limit and upper
limit of active output for gas turbine units; 𝑃𝑀𝑇 (𝑡) is the active
output of the gas turbine during the time period; 𝛾𝜁,𝑚𝑖𝑛 and
𝛾𝜇,𝑚𝑖𝑛 are the uphill and downhill power limits of the gas
turbine; 𝑎𝑀𝑇 (𝑡) is a coefficient that represents the impact of
𝑃𝑀𝑇 (𝑡) that is the degree of impact of 𝑃𝑀𝑇 (𝑡) ; 𝑏𝑀𝑇 is aconstant term that represents other factors that affect fuel costs
besides active output such as fixed costs equipment costs.
4) Power Balance Constraints
In the operation, the total power generation and power load
must be balanced, as shown in the equation. The user load must
be balanced with the output of distributed energy.
𝑃𝑤𝑡 (𝑡) + 𝑃𝑝𝑣 (𝑡) + 𝑃𝑔𝑟𝑖𝑑 (𝑡) + 𝑃𝑀𝑇 (𝑡) + 𝑃𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 (𝑡)= 𝑒𝑙𝑜𝑎𝑑 (𝑡) + 𝑃𝑐ℎ𝑎𝑟𝑔𝑒 (𝑡)(21)Where 𝑒𝑙𝑜𝑎𝑑 (𝑡) is the electrical load reported by the user.
5) Power Generation Constraints of Wind and Solar
Power Generation𝑠
0 ≤ 𝑃𝑤𝑡 (𝑡) ≤ 𝑃𝑤𝑡
(𝑡)

(22)

𝑠
0 ≤ 𝑃𝑝𝑣 (𝑡) ≤ 𝑃𝑝𝑣
(𝑡)

(23)

𝑠
Where 𝑃𝑤𝑡 (𝑡) 𝑃𝑤𝑡(𝑡) represents the actual and predicted𝑠output of wind power during the time period; 𝑃𝑝𝑣 (𝑡) 𝑃𝑝𝑣(𝑡) isthe actual and predicted output of the photovoltaic system
during the time period.

D. Profit Model of the Building Users
The cost of an individual user consists of utility profit
expenditures of purchasing electricity/heat and comfortable
degree for thermal dissatisfaction which could be defined as:
𝐹𝑃𝐼𝐸𝑆 (𝑡) = 𝑘𝑖 ∗ ln(1 + 𝑒𝑙𝑜𝑎𝑑 (𝑡)) − 𝑝𝑠𝑒𝑙𝑙 ∗ 𝑒𝑙𝑜𝑎𝑑 (𝑡) (24)

Where 𝑘𝑖 ∗ ln(1 + 𝑒𝑙𝑖ℎ ) is the utility that the building
users i achieve from consuming energy 𝑒𝑙𝑖ℎ ; 𝑘𝑖 is thepreference parameter. Normally the building users’
comfortable degree will be reduced by adjusting their door
temperatures under DR. However for the economic reason aslong as the discomfort could be counterbalanced by economic
benefits the users would be willing to participate in the DR. In
this paper the value of 𝑘𝑖 is 100.
E. Carbon Tax Model
1) Traditional Carbon Tax Model
Carbon tax is a tax measure implemented by thegovernment on carbon emissions aiming to internalize theexternal costs of carbon emissions on the environment andsociety. This tax is typically based on energy production
consumption or emissions and is levied on a unit of carbon
emissions. By taxing carbon emissions the government cancreate economic incentives to encourage businesses andindividuals to take measures to reduce carbon emissions andpromote the development and application of clean energy andlow-carbon technologies. The carbon surcharge is seen as aneffective economic tool.
The calculation criteria for ordinary carbon taxes areusually based on the carbon content of emissions and the tax
rate. Generally speaking the calculation formula can be
expressed as:
𝐶𝐶𝑂2 = 𝑐(𝐸𝑝 − 𝐸𝑐 )(25)

Where 𝐶𝐶𝑂2 is the carbon tax cost; 𝑐 is the carbon tax
price of the current year's carbon tax; 𝐸𝑐 is initial free carbon
emission quota; 𝐸𝑝 is the total carbon emissions of the system.
Therefore in the actual carbon emission model theabsorbed CO2 is treated and the specific conversion process ofthe carbon emission model is shown in the equation:
𝐶𝐶𝑂2 = 𝐶𝑏𝑢𝑦 + 𝐶𝐺𝑇 + 𝐶𝐺𝐵(26)

𝐶𝑏𝑢𝑦 = 𝑋𝑒 ∑𝑇𝑡=1 𝑃𝑖,𝑠 (𝑡)(27)

𝐶𝐺𝑇 = 𝑋ℎ ∑𝑇𝑡=1(𝜆𝑃𝑖,𝐺𝑇 (𝑡) + 𝐻𝑖,𝐺𝑇 (𝑡))𝐶𝐺𝐵 = 𝑋ℎ ∑𝑇𝑡=1 𝐻𝑖,𝐺𝐵 (𝑡)

(28)
(29)

Where 𝐶𝑏𝑢𝑦 𝐶𝐺𝑇 𝐶𝐺𝐵 respectively are the actual carbon
emissions of users purchasing electricity from ESO gas
turbines and gas boilers; 𝑋ℎ . 𝑋𝑒 is the actual carbon emission
coefficient of the unit electric power produced by coal-fired
units and the unit thermal power produced by natural gas units.
2) Tiered Carbon Tax Model
Tiered Carbon Tax is a variant that sets different tax rates
according to different levels of carbon emissions usually basedon the tiered classification of emissions. In a laddered carbon
tax multiple emission ladders are usually set with each laddercorresponding to a different tax rate. The specific carbon
emission cost range can be divided as follows:−𝑐(1 + 2𝜆)(𝐸𝑐 − 𝜈 − 𝐸𝑝 ),−𝑐(1 + 2𝜆)𝜈 − 𝑐(1 + 𝜆)(𝐸𝑐 − 𝐸𝑝 ),𝑐(𝐸𝑐 − 𝐸𝑝 ),𝐶𝐶𝑂2 = 𝑐𝜈 + 𝑐(1 + 𝛼)(𝐸𝑝 − 𝐸𝑐 − 𝜈),𝑐(2 + 𝛼)𝜈 + 𝑐(1 + 2𝛼)(𝐸𝑝 − 𝐸𝑐 − 2𝜈),𝑐(3 + 𝛼)𝜈 + 𝑐(1 + 3𝛼)(𝐸𝑝 − 𝐸𝑐 − 3𝜈),{ 𝑐(4 + 𝛼)𝜈 + 𝑐(1 + 4𝛼)(𝐸𝑝 − 𝐸𝑐 − 4𝜈),

TABLE I.

𝐸𝑝 ≤ 𝐸𝑐 − 𝜈𝐸𝑐 − 𝜈 ≤ 𝐸𝑝 ≤ 𝐸𝑐
𝐸𝑐 ≤ 𝐸𝑝 ≤ 𝐸𝑐 + 𝜈
𝐸𝑐 + 𝜈 ≤ 𝐸𝑝 ≤ 𝐸𝑐 + 2𝜈𝐸𝑐 + 2𝜈 ≤ 𝐸𝑝 ≤ 𝐸𝑐 + 3𝜈𝐸𝑐 + 3𝜈 ≤ 𝐸𝑝 ≤ 𝐸𝑐 + 4𝜈𝐸𝑐 + 4𝜈 ≤ 𝐸𝑝

(30)

Where 𝜈 represents the length of the carbon emissioninterval; 𝜆 𝛼 is the reward coefficient and punishment
coefficient.

III. ALGORITHM FRAMEWORK
A. The Leader-follower Game Framework
In the interaction process of the game, there are two main
entities: ESO and PIES. The internal connection between themis established through the price information released by ESO to
PIES and the optimization results within PIES. As the leader,
ESO first sets the electricity purchase and sale prices, thecarbon trading base price, and the rate of price increase, thencommunicates this information to the follower, PIES. PIES
optimizes its equipment output and performs demand response
based on the received price information, and then sends thepurchase and sale volume information back to the leader. Sincecarbon emissions cannot be predicted in advance, this paper
does not consider dynamic changes to the interval length. The
leader, ESO, continuously optimizes the price strategy based on
the information provided by the follower, PIES. Due to thesequential decision-making of ESO and PIES, a leader-follower
game framework is formed, with ESO as the leader and PIES
as the follower. This leader-follower game model can be
represented as:𝑒 𝑒𝑠 , 𝜋𝑏 , 𝐴𝑖,𝑠 , 𝐴𝑖,𝑏 }𝐺 = {{𝐸𝑆𝑂,𝑃𝐼𝐸𝑆};{𝜋}{𝑚𝑎𝑥𝐹𝐸𝑆𝑂 ,𝑚𝑖𝑛𝐹𝑃𝐼𝐸𝑆 }(31)

The model comprises the participants of the game,specifically ESO and PIES; the strategy sets of both parties,
which include the electricity purchase and sale prices 𝜋𝑠𝑒 and𝜋𝑏𝑒 determined by the leader ESO; the purchase and sale
electricity volumes 𝐴𝑖,𝑠 and 𝐴𝑖,𝑏 provided by i-th PIES to ESO;
and the utilities of both parties, represented by their respective
objective functions. The proof of the existence and uniquenessof the game equilibrium is shown in Appendix A.
B. Game Solving Algorithms
This article is based on the MATLAB platform tosimulate and implement a comprehensive energy system in
the industrial park and uses differential evolution algorithm
combined with CPLEX solver to solve the established multiagent leader-follower game model. The solution flow chart isshown in Appendix B Fig.B1.
IV. EXAMPLE ANALYSIS
A. Basic Data
Taking an industrial park in northern China as a calculation
example, the PIES optimization operation strategy proposed inthis article is simulated and analyzed, the operation period is 24
hours, and the scheduling interval is an hour. There are twogenerators and one gas distribution station.

TOTAL EXPENDITURE AND CARBON EMISSIONS
Case 1Case 2

Case 3

Case 4

Total Cost (CNY)15716.44

14391.814295.18

14727.77

Maintenance Cost (CNY)1975.82

1975.82

1874.72

1821.14Natural Gas Cost (CNY)3767.453767.453558.743455.86

Electricity Selling Cost (CNY)0-521.44-286.74-224.02

Electricity Purchase Cost (CNY)6314.145510.945694.565731.5

Carbon Emission Cost (CNY)1920.23

1920.23

1805.82

1983.29

MT Unit Carbon Emission Cost
(CNY)

1738.81738.81648.081960

Total Carbon Emissions (kg)26114.04

24905.3

24642.46

24586.42

The park service providers include CHP, photovoltaic
power generation systems, and wind turbines. The typical day
wind power and photovoltaic prediction curves are shown in
Fig.C1. The daily electric load curves of these buildings areshown in Fig.C2. The proportion of maximum shiftable electricloads is set to nearly 20%.
The prices of electricity and gas purchased from the power
grid and gas grid are shown in Table II. The basic parametersof the gas turbine are shown in Table III. Other specificparameters are set in [20].
B. Scheme Designs
Based on the above data, the incomplete information gameand mixed integer nonlinear model solver are used to solve theoptimal dispatching results of the multi-energy collection
system. In order to illustrate the rationality of the optimizedscheduling model built, this article will compare and analyze
the scheduling results of the four models:Case 1: Without considering dynamic electricity prices andcarbon tax.
Case 2: Considering dynamic electricity prices, but do notconsider carbon tax.
Case 3: Considering dynamic electricity prices and use thetraditional carbon tax mechanisms.
Case 4: Considering dynamic electricity prices and use thetiered carbon tax mechanism.
Taking each model as one-time as an example for analysis,
the scheduling results are as TABLE I.
Based on TABLE I, we conducted an analysis of thescheduling results for each scenario. Firstly, in Case 1, the total
cost is the highest and the carbon emissions are the largest. This
is attributed to the absence of considerations for dynamic
electricity prices and carbon tax. In contrast, Case 2, which
considers dynamic electricity prices, exhibits reduced total costand carbon emissions, at 14391.8 CNY and 24905.3 kg,
respectively. In Case 3, the incorporation of dynamic electricity
prices and traditional carbon tax mechanisms further decreases
the total cost and carbon emissions to 14295.18 CNY and
24642.46 kg, respectively which reduce 262.84kg CO2.
Specifically, the use of the traditional carbon tax mechanism
reduces carbon tax costs to 1805.82 CNY, compared to Case 1.
Lastly, Case 4 integrates dynamic electricity prices with tiered
carbon tax mechanisms, resulting in a slightly higher total costof 14727.77 CNY but the lowest

environmental impacts to select the optimal schedulingstrategy, which may involve further optimization of carbon tax
strategies or adjustments to energy usage plans based on Case
4.

8200
7700

ESO Profit (CNY)

7200
6700
6200

In conclusion, the leader-follower game scenario
involving demand response and carbon tax mechanism withdynamic parameters benefits ESO and reduces costs for the
PIES. It also achieves lower total carbon emissions, showing
superior economic and low-carbon performance.

5700
5200
4700
4200

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
Number of iterations

Power (kW)Figure 2.

C. Analysis of Optimization Results

Changes in ESO revenue for Case 3

The optimization iteration process of ESO is shown in
Fig.2. At the 30th iteration, the results have converged. It canbe seen from the figure that the method used in this paper has agood convergence effect. When the Stackelberg equilibrium isreached, its strategy no longer changes, which means that under
this strategy, no player can obtain more benefits byindependently changing his strategy.

2000
1800
1600
1400
1200
1000
800
600
400
200
0

The results in Fig.3 indicate that new energy power
generation has been fully utilized, improving the justification
rate of new energy power generation.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (Hour)

Power Purchase

Gas Turbine Output

Gas Turbine Output

The user energy consumption strategy formulated by thefollower based on the energy sales strategy and equipment
operating status of the leader ESO and the load curve before
and after optimization are shown in Fig.4. Under the incentiveof electricity prices, in order to reduce energy expenditures,users reduce electricity consumption and interrupt part of theelectricity load during the peak periods of 9:00-11:00 and
20:00-22:00 due to high electricity prices. The peak value ofelectricity load decreases; during the trough period from 00:00
to 06:00, due to low electricity prices, as shown in Fig.5, users
use battery charging to increase electricity consumption, andthe user load valley value increases. Before and after
optimization, the user's electric load curve shows obvious "peakshaving and valley filling" characteristics, which shows that theoperation strategy proposed can effectively reduce the user's
energy cost.

Photovoltaic Output

Figure 3. Power load scheduling results for Case 3
2000

Original Eload

New Eload

Electric Price

1800

Electric Load (kW)

1600
1400
1200
1000
800
600
400

1

3

5

7

9

11 13 15
Time (Hour)

17

19

21

23

Figure 4. Electric load curve before and after dispatch for Case 31

1.5State of Charge

1

0.6
0.4

0.5

0.2
0

SOC
1

3

5

7

Price
9

11 13 15
Time (Hour)

17

19

21

23

Electric Price (CNY)

0.8

0Figure 5. Charging and discharging situation of the battery varies with theelectricity price for Case 3

carbon emissions of 24586.42kg, which reduce 56.04kg carbon
emission compared with Case 3.
The specific data analysis demonstrates the effectivenessof considering dynamic electricity prices and carbon tax inreducing total costs and carbon emissions. In practicalapplications, it is crucial to consider both economic costs and

The simulation results show that the proposed gameinteraction model has good convergence, and ESO can better
adjust the operation of its distributed energy equipment andpurchase energy at a lower cost through game interaction withthe user side.
V. CONCLUSION
This paper explores dynamic pricing in park integrated
energy systems, integrating it with carbon tax. A
comprehensive overview of these systems and game theory
concepts is provided. The introduced dynamic pricing
mechanism demonstrates notable advantages in improving
energy efficiency and reducing carbon emissions. Combining
carbon tax and stepped carbon tax further enhances carbon
reduction and sustains energy system sustainability. Overall,this integrated approach offers a promising pathway forachieving sustainable energy development and a low-carbon
economy.

VI. APPENDIX

B. The Solving Process of Leader-Follower gameA. The Existence and Uniqueness of Game Equilibrium
The reference [21] for proving the existence and uniquenessof game equilibrium is as follows:
Theorem 1: When the master-slave game model satisfies
the following conditions, there is a unique Stackelberg
equilibrium:
1) The utility function of game participants is a non-empty,
continuous function about the game strategy set.
2)The follower utility function is a continuous concave/
convex function with respect to the respective game strategy
set.
According to the model proposed in this article, it can beseen that the strategy set needs to satisfy the constraints (10)(23). Therefore, the strategy sets of both the leader and theparticipant are non-empty and continuous. Calculate thesecond-order partial derivatives of a and b respectively for the
PIES objective function (24):

𝜕2 𝐹𝑃𝐼𝐸𝑆
𝜕2 𝐴𝑖,𝑏 (𝑡)2

=0

(A1)

=0

(A2)

It can be seen from the above formula that the PIES
objective function formula is a linear function about its policy
set Ai,s (t) and Ai,b (t). According to the definition of concavity,
the linear function is both a concave function and a convex
function.
In the game, when neither the leader nor the follower canachieve greater benefits by altering their own strategies, thegame reaches a Stackelberg equilibrium, which can be defined
as follows:
∗

∗

∗

∗

∗

𝑒∗

𝑒∗

𝑒∗

Figure B1. Flow chart of Stackelberg game solution

C. Basic Data
0.2
0.18
0.16
0.14

Power (kW)𝜕2 𝐹𝑃𝐼𝐸𝑆
𝜕2 𝐴𝑖,𝑠 (𝑡)2

0.12

0.1

0.08
0.06

∗

𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ ) ≥ 𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ )0.04

𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ ) ≥ 𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ )

0.02
0

𝑒∗

𝐹𝐸𝑆𝑂 (𝜋𝑠 , 𝜋𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ ) ≥ 𝐹𝐸𝑆𝑂 (𝜋𝑠 , 𝜋𝑏 , 𝑃𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ )

1

3

5

∗
∗
∗
∗
𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ ) ≥ 𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃𝑀𝑇 , 𝐷𝑅∗ )
∗

∗

∗

7

9

11 13 15
Time (Hour)Wind Turbine Output

17

19

21

23

Photovoltaic Output∗

𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅∗ ) ≥ 𝐹𝐸𝑆𝑂 (𝜋𝑒𝑠 , 𝜋𝑒𝑏 , 𝑃∗𝐶𝐻𝑃 , 𝑃∗𝑀𝑇 , 𝐷𝑅)

Figure C1. Wind and solar output prediction(A3)

Where the superscript * indicates the optimal equilibrium
solution.

2000

In the game process, when no interested subject canunilaterally change the strategy of the equilibrium solution to
obtain benefits, it means that the game reaches the Stackelberg
equilibrium and satisfies the conditions of equation (A3), thenit is the equilibrium of the Stackelberg game.

1400

1800

Electric Load (kW)

1600
1200
1000
800
600
400
200
0

1

3

5

7
user1

9

11

13

Time (Hour)
user2

15

17

19

user3

Figure C2. Daily load curves of users

21

23
eload

TABLE II.

PARAMETERS OF RENEWABLE CHP SYSTEM
Parameters of CHP system

Boiler Capacity (kW)300

Gas turbine capacity (kW)800

Generator Electrical Efficiency

0.2

Preheat Recovery Efficiency

0.4

TABLE III.

ELECTRICITY PRICE AND GAS PRICE
Data (CNY/kWh)Time (Hour)

Grid Price

Gas Price

23:00-06:00

0.25

3.075

06:00-13:00

0.8

2.355

13:00-19:00

0.53

3.075

19:00-23:00

0.8

2.355

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