The data center server is the main device for processing task requests. The task requests in data centers can be divided into two types: delay sensitive and delay tolerant. Among them, delay-tolerant task requests have lower execution time requirements and only need to be executed within the delay limit, which has good time transfer potential. The execution order of delay-tolerant task requests can be reasonably arranged based on the current energy supply situation of the integrated energy system.

The total power consumption of data center servers is related to active servers and task requests processed by servers, which can be expressed as (Yang T. et al., 2022) P s r v , n , s , t = m n , s , t P n + P p − P n v n , s , t / m n , s , t F . (1)

Here, P _srv,n,s,t is the total power consumption of the server at time t under scenario s in the nth year; m _n,s,t is the number of active servers at time t under scenario s in the nth year; P _n is the idle power consumption of the server; P _p is the full power consumption of the server; v _n,s,t is the total number of tasks processed by all active servers at time t under scenario s in the nth year; and F is the maximum number of tasks processed by a single server.

The aforementioned formula is simplified and converted into a linear function of active servers and task requests: P s r v , s , t = c 1 m s , t + c 2 ν s , t , (2) c 1 = P n , (3) c 2 = P p − P n / F . (4)

Here, c ₁ and c ₂ are server performance-related parameters.

Some task requests are delay tolerant and can be adjusted in execution time. v n , s , t = v n , s , t a j + v n , s , t u n a j − v − , n , s , t a j + v + , n , s , t a j , (5) ∑ t T − v − , s , t a j + v + , s , t a j = 0 , (6) v − , s , t a j , v + , s , t a j ≥ 0 . (7)

Here, v ^aj _n,s,t is the number of delay-tolerant task requests at time t under scenario s in the nth year. v ^unaj _n,s,t is the number of delay-sensitive task requests at time t under scenario s in the nth year. v ^aj _-,n,s,t is the number of delay-tolerant task requests reduced in execution at time t under scenario s in the nth year. v ^aj _+,n,s,t is the number of delay-tolerant task requests increased in execution at time t under scenario s in the nth year.

The linear relationship between the overall power consumption of data centers and server power consumption can be expressed as P d c , n , s , t = P U E ⋅ P s r v , n , s , t . (8)

Here, P _dc,n,s,t are the power consumption at time t under scenario s in the nth year of the data center and PUE is the energy efficiency coefficient of the data center.

The server generates a certain amount of thermal energy when processing computing tasks. In order to ensure the normal operation of the data center servers, the temperature of the data center computer room needs to be maintained within a certain range, so the data center needs to be equipped with sufficient electric refrigerators. At each moment, the data center server generates a certain amount of thermal energy, while the electric refrigerator provides a certain amount of cooling capacity. Therefore, based on the first-order equivalent thermal parameter model, the temperature variation relationship between the beginning and end of the time period can be obtained as follows (Ding et al., 2018): T i n , n , t + 1 , s = T o u t , n , t , s − Q n , s , t R − T o u t , n , t , s − Q n , s , t R − T i n , n , t , s e − Δ t R C , (9) Q n , s , t = Q c o , n , s , t − ς P s r v , n , s , t , (10) T t e m p min ≤ T i n , n , t , s ≤ T t e m p max . (11)

Here, T _in,n,t,s is the indoor temperature of the computer room at time t under scenario s in the nth year. T _out,n,t,s is the outdoor temperature at time t under scenario s in the nth year. R and C are the equivalent thermal resistance and equivalent thermal capacity of the electric refrigerator load, respectively. Q _n,s,t is the cooling capacity of the computer room at time t under scenario s in the nth year. Q _co,n,s,t is the cooling capacity of the electric refrigerator at time t under scenario s in the nth year. Ϛ is the ratio of server thermal energy to power consumption. T ^max _temp and T ^min _temp are the upper and lower limits of the computer room temperature, respectively, to ensure the normal operation of the data center. This article stipulates that the temperature of the computer room must be maintained between 18°C and 24°C (ASHRAE, 2021; Wu et al., 2023).

Considering that the electric refrigerator in the computer room is a variable-frequency air conditioner, the relationship between air conditioning power consumption and air conditioning cooling capacity is P c o , n , s , t = k 1 k 2 Q c o , n , s , t + k 2 l 1 − k 1 l 2 k 2 , (12) 0 ⩽ P c o , n , s , t ⩽ P c o max . (13)

Here, k ₁, k ₂, l ₁, and l ₂ are a constant coefficient; P _co,n,s,t is the air conditioning power consumption of the computer room at time t under scenario s in the nth year. P _co ^max is the rated power consumption of the computer room air conditioner.

Therefore, while ensuring the temperature of the data center computer room, the cooling capacity of the air conditioning can be adjusted by adjusting the power consumption of the air conditioning to achieve load time transfer.

The economic benefits of the integrated energy system in the day-ahead electricity market conclude the benefits of the day-ahead electricity market and the day-ahead auxiliary frequency regulation market. In the day-ahead electricity market, integrated energy systems can purchase and sell electricity. In the frequency regulation market, the integrated energy system obtains economic benefits by providing frequency modulation capacity through the demand side response. The integrated energy system reports adjustable capacity, tracks the frequency modulation signal of the dispatching center, and finally, settles the frequency modulation capacity and frequency modulation mileage according to market rules (Liu et al., 2021). The revenue model of the day-ahead electricity market and frequency regulation market can be expressed as C 1 , n = ∑ s = 1 S ∑ t = 1 T e n , s , t P e , s e l l , n , s , t − e n , s , t P e , b u y , n , s , t , (14) C 2 , n = ∑ s = 1 S ∑ t = 1 T C A P n , s , t λ c p , n , s , t + λ m p , n , s , t R m i l e a g e A , (15) C D A , n = C 1 , n + C 2 , n , (16) where C_1,n and C_2,n represent the economic benefits of the day-ahead electricity market and the frequency regulation market in the nth year, respectively. e _n,s,t represents the electricity price at time t of the sth typical scenario in the nth year. p _e,sell,n,s,t represents the power sold to the superior power grid at time t of the sth typical scenario in the nth year. P _e,buy,n,s,t represents the power purchased from the superior power grid at time t of the sth typical scenario in the nth year. CAP _n,s,t represents the bid winning capacity of the frequency regulation market at time t of the sth typical scenario in the nth year. λ _cp,n,s,t is the capacity price at time t of the sth typical scenario in the nth year. λ _mp,n,s,t is the mileage price at time t of the sth typical scenario in the nth year. R ^mileage is the mileage coefficient. A is the demand side response performance coefficient.

A certain capacity of P2G equipment has been built in the integrated energy system. On one hand, it can convert carbon dioxide generated into methane, effectively reducing carbon emissions. On the other hand, P2G equipment can play a role in energy storage. During the peak period of renewable energy generation, the energy generated from renewable energy that cannot be consumed is converted into chemical energy for storage, which effectively improves the renewable energy consumption rate of the integrated energy system. The integrated energy system can sell excess carbon quotas in the carbon market for profit (Zhou et al., 2023).

The equipment for planning in this article includes photovoltaics, wind turbines, CHP units, electrical energy storage, and thermal energy storage. With the goal of minimizing multi-stage integrated costs, a planning model for the integrated energy system is constructed. The integrated cost includes construction cost, operating cost, day-ahead market revenue, and carbon market revenue (Zhou et al., 2023): min ∑ k = 1 K R A k C c o n s t r , k + ∑ n = 1 N R n C o p e , n − C D A , n − C C O 2 , n − R N L R V , (21) R n = 1 + r − n , (22) C c o n s t r , k = ∑ m ∈ M C m , k X m , k N m , k , (23) C o p e , n = ∑ s ∈ S ∑ t ∈ T F g r i d , n , s , t c g , n , s , t + ∑ m ∈ M c o p e , m P m , n , s , t , (24) L R V = ∑ j = 1 M x c c o n s t r , j − T j c d e p , j , (25) c d e p , j = c c o n s t r , j 1 − δ j N j , (26) where C _constr,k is the equipment construction cost for the kth planning stage. C _ope,n , C _DA,n , and C _CO2,n represent the operating cost of the integrated energy system in the nth year, the daily market revenue, and the carbon market revenue, respectively. R _Ak , R _n , and R _N represent the discount coefficients for the A _k th planning year, the nth planning year, and the Nth planning year, respectively. A _k is the starting year of the kth planning stage. N is the total planning years. m is the type of equipment. M is the type of equipment, M = {PV, MT, CHP, GB, ESS, HS}. C _m,k is the cost per unit capacity of m equipment construction. X _m,k is a 0–1 variable, representing whether m equipment is constructed. N _m,k is the capacity of m equipment construction. L _RV is the residual value of the equipment at the end of the planning period. M _x is the remaining equipment at the end of the planning period. c _constr,j represents the construction cost of j equipment. T _j is the number of years in use of the jth equipment among M _x at the end of the planning period. c _dep,j is the annual depreciation cost of the jth equipment.

(1) Energy equipment quantity constraints

Due to factors such as construction cost, there is an upper limit on the number of energy equipment to be planned for the integrated energy station in the station: 0 ≤ N m , k ≤ N m , k max , (27) where N ^max _m,k is the maximum capacity of m-type energy equipment in the kth planning stage of the integrated energy system.

(2) Energy purchase constraints

Due to capacity limitations of gas and electricity stations, there are capacity limits for the purchased electricity and gas: 0 ≤ P e , b u y , n , s , t ≤ P g r i d max , (29) 0 ≤ P g , b u y , n , s , t ≤ P g , b u y max . (30)

(3) Energy and heat storage constraints

According to the method proposed by Zhang et al. (2022) this article linearizes the tiered carbon trading price of Eq. 20. The integrated energy multi-stage planning model is a mixed-integer linear programming problem. This article uses PyCharm 2019.1.1 x 64 to call Gurobi 9.1.2 to solve the aforementioned model.

The integrated energy system includes electricity, thermal, and cooling loads. The cooling power balance is relatively simple. Therefore, this article selects scheme 6 to analyze the electricity and thermal power balance for the summer of 25 years.

It can be observed from Figure 3 that the electrical load of the integrated energy system is mainly met by photovoltaic power generation and wind power generation. Among these, photovoltaic power generation has a significant peak valley difference, but it can fill the power generation gap in the morning and evening when there is no light. At the same time, the peak period of photovoltaic power generation is at noon, and the peak period of wind power generation is in the morning and evening. The combination of photovoltaic power generation and wind power generation can reduce the peak valley difference of renewable energy power generation so as to better match the load curve. The power generated by CHP is relatively stable due to the poor regulation performance and high regulation cost of the CHP unit, which generally bears the basic load. The adjustable load of the data center includes electric refrigerators and servers. After the demand response, the difference between the peak and valley of the load power of the data center is significantly reduced. Energy storage provides flexible regulation capabilities for integrated energy systems, charging during periods of high renewable energy generation and discharging during periods of low renewable energy generation, thereby avoiding the phenomenon of wind and light abandonment. The power transmission of the power grid mainly plays a role in suppressing the load and mismatching the power curve. It serves as the main source of power supply during periods when renewable energy is scarce, ensuring the balance of power in the integrated energy system.

It can be observed in Figure 4 that the heat load is mainly borne by gas boilers and CHP units, with a bimodal thermal load pattern and peak periods of 7–9 and 17–20. Due to the poor regulation performance of gas boilers and CHP units, the regulation speed and range are limited, and the thermal generation power cannot change rapidly. Heat storage plays a role in suppressing the fluctuation of thermal load and can, to some extent, reduce the peak valley difference of thermal load.

As shown in Figure 5, the difference between the peak and valley of adjusted server power is smaller, and demand response shifts the load from 8–17 and 19–22 to 1–5, 16–18, and 22–24, realizing load peak shaving and valley filling. The electric refrigerator ensures that the temperature of the machine room is between 19°C and 24°C. Data center demand response can effectively improve the load curve of the comprehensive energy system, thereby making the load curve more consistent with the energy supply curve.

Figure 6 shows that scheme 6 is planned in five stages. In the starting year of each stage, renewable energy increases significantly and carbon emissions decrease significantly. This is because photovoltaic and wind power are invested in the starting year of each stage. As the years increase, the load constantly increases, with non-renewable energy sources and carbon emissions slightly increasing. In the 30^th year, the carbon emission of the integrated energy system is 0, achieving the goal of carbon neutrality.

The carbon emissions of the integrated energy system depend on the energy structure and the emission coefficients of various pieces of energy equipment. Carbon emission targets are one of the most important factors that influence the energy structure of integrated energy planning. This article sets different carbon emission targets and analyzes the impact of different carbon emission constraints on the results of integrated energy system planning.

1) Carbon-free emission target: no carbon emission constraints

Using scheme 6 for multi-stage planning, the planning results can be obtained (see Table 3):

(1) The carbon emission target affects the total cost. From the scheme of carbon target 1, if carbon emission constraints are not considered, the integrated energy system will greatly reduce the construction capacity of photovoltaic and wind power. Therefore, the power balance mainly relies on CHP units and external power grids. At the same time, the capacity of energy storage and P2G equipment construction in the integrated energy system was also greatly reduced. This is because the capacity of renewable energy decreased, which leads to integrated energy system reduction in the demand for flexible resources to handle load and renewable energy fluctuation.

From Figure 7, it can be observed that without carbon emission constraints, such as carbon target 1, as the load continues to increase, the carbon emissions of the integrated energy system continue to increase, which clearly does not comply with the concept of low-carbon development. For carbon target 2, the carbon peak target is achieved at the beginning of the second stage, and the carbon emissions in the subsequent planning stages are lower than those in carbon target 1. Carbon targets 3 and 4 have both achieved the carbon-neutrality goal, while carbon goal 4 is relatively early, which achieves in the fourth planning stage.