Coordinated Spatio-Temporal Operation of Wind–Solar–Storage-Powered Data Centers Considering Building Thermal Inertia

Abstract

In the context of the booming digital economy, the energy consumption of data centers (DC) is experiencing exponential growth, and achieving green transformation has become a crucial issue. This paper presents a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia. Firstly, based on users’ differentiated needs, the spatio-temporal flexibility of data loads is deeply explored to lower DC’s operation costs through load shifting. Secondly, a DC mathematical model considering building thermal inertia is established, revealing the quantitative relationship among air-conditioning power, data load rate, and building parameters. Finally, a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia is proposed to promote renewable energy consumption and realize the green transformation of DC. The case study results show that the proposed strategy reduces the DC operation cost by 37.92% and significantly increases the renewable energy-consumption ratio.

1. Introduction

With the full arrival of the digital economy, global DC energy consumption has shown an exponential rise. According to the International Energy Agency (IEA), DCs already account for 2.5% of the world’s total electricity consumption in 2022 and are growing at an average annual rate of more than 15% [1]. The problem of high energy consumption in DC is becoming more and more serious, and how to achieve green and low-carbon transformation through multi-dimensional synergistic optimization has become the core proposition for the sustainable development of DC.

Numerous scholars have conducted research on energy management in DC. Empirical studies reveal that information technology (IT) equipment contributes significantly to DC energy profiles, representing nearly half of aggregate power consumption [2], which is primarily utilized for computing and task processing. Consequently, it is imperative to explore methods to enhance energy efficiency by leveraging the regulatory potential of the load, both temporally and spatially. Reference [3] exploited spatial regulation of energy usage in DC so that geographically distributed multiple DCs can dynamically share physical resources. Reference [4] exploited the temporal regulation of energy usage in DC to reduce the total energy cost of DC operators. Reference [5] exploited the spatial and temporal regulation of energy use in DC and proposed a coupled DC load modeling approach that considered multiple regulation methods to facilitate demand response in DC.

At the same time, about 37% of the energy consumption of the DCs comes from the air-conditioning system [2], which leads to a certain lag in the indoor temperature change due to the good cooling storage capacity of the materials constituting the DC envelope [6]. Therefore, DC building energy use will show certain energy storage characteristics and flexibility. By fully exploiting the building thermal inertia of the DC, the economic flexibility of DC operation can be significantly improved. Reference [7] has demonstrated that the energy consumption of air-conditioning systems can be reduced by adjusting the operating parameters based on the thermal inertia of the DC building. Reference [8] has employed thermal inertia to regulate indoor temperature fluctuations in DC, thereby facilitating energy savings. While the aforementioned studies have made significant contributions, the present research primarily focuses on management optimization, neglecting to leverage synergies with renewable energy and energy storage (ES). This hinders the realization of a green and low-carbon transition through multi-dimensional synergies.

In the context of the global emphasis on sustainable development, the role of renewable energy sources, such as solar and wind, in transforming the energy structure is paramount due to their clean and inexhaustible characteristics [9]. ES has been identified as a pivotal solution to meet the challenges of the intermittency and volatility of renewable energy generation, enabling the flexible storage and deployment of energy [10]. In the context of DC, a synergistic approach entails the integration of wind, solar, and ES with the energy management of DC, thereby facilitating the establishment of an efficient and low-carbon energy supply system [11]. Through a systematic planning process, solar and wind are integrated with the DC, enabling the direct provision of green power. Conversely, ES ensures the stability of the power supply by storing power when there is an excess of renewable energy generation and releasing power [12]. Through the DC and WF, PV and ES’ coupling synergy can realize the dynamic balance of energy supply and demand and multi-energy complementary optimization, significantly enhancing the local consumption rate of renewable energy and system energy efficiency level. Reference [13] used ES to reduce the energy consumption of DCs and improve the operating economy. Reference [14] proposed the use of a water–wind–solar complementary power generation system, which effectively reduces the cost of electricity in DCs. Reference [15] considered the integration of co-located solar power and battery storage to improve renewable energy utilization for DC operations. However, research on the synergistic integration of renewable energy systems with building thermal inertia and spatio-temporal load regulation in DCs remains underdeveloped. Existing studies have largely treated these elements in isolation, neglecting their combined potential to enhance energy flexibility.

As demonstrated in the preceding analysis, this paper puts forward a coordinated spatio-temporal operation strategy of wind–solar–storage-powered DCs considering building thermal inertia, with the following main contributions:

(1)

Based on the differentiated needs of users, the spatio-temporal flexibility of data loads is deeply explored, which enables DC to reduce the operation cost by leveling and transferring the data loads;

(2)

Considering the building thermal inertia of the DC, a mathematical model of the DC taking into account the building thermal inertia is established, and the quantitative mathematical relationship between air-conditioning power, data load rate, and building parameters is given;

(3)

We propose a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia, which improves the consumption of renewable energy and realizes the green transformation.

2. Problem Description

The operation framework of the DC integrated with wind, solar, and ES is shown in Figure 1. Energy consumption in a DC is mainly driven by IT equipment, air conditioning, power distribution, and lighting. Based on the difference in real-time demand, IT equipment carries two types of loads: interactive loads and batch loads. Interactive loads are delay-sensitive and do not have the ability to regulate time, but their data load transmission speed is extremely fast, so they can be flexibly deployed on a spatial scale. Batch loads are delay-tolerant and have the ability to migrate in time sequence, showing a high degree of flexibility in regulating both time and space scales [16] since a large proportion of the electricity consumed by IT equipment is converted into heat. Thus, air-conditioning systems consume a large amount of electricity for cooling.

By deploying a wind farm (WF), a photovoltaic power plant (PV), and ES devices within the DC, the DC is able to capture energy from this source. At the same time, ES can store the surplus energy to be used in case of an emergency. In addition, DC can also purchase power from the grid.

3. Mathematical Formulation

3.1. Objective Function

In this paper, with the objective of economic optimization, the total cost C includes the cost of purchasing electricity for the DC $C_{buy}$, as well as the cost of operation and maintenance $C_{op}$.

$$\min C=C_{buy}+C_{op}$$

(1)

$$C_{buy}={\displaystyle \sum _{t=1}^T(P_{buy,t}^{DC,A}}+P_{buy,t}^{DC,B})c_t^e$$

(2)

$$C_{op}={\omega }_{PV}(P_{PV,t}^{DC,A}+P_{PV,t}^{DC,B})+{\omega }_{WT}(P_{WT,t}^{DC,A}+P_{WT,t}^{DC,B})+{\omega }_{ES}(P_{ES,ch,t}^{DC,A}+P_{ES,ch,t}^{DC,B}+P_{ES,dis,t}^{DC,A}+P_{ES,dis,t}^{DC,B})$$

(3)

3.2. DC Energy-Consumption Model

$$P_t^{DC}=P_t^{IT}+P_t^{AC}+P_t^L$$

(4)

$$P_t^L=P_0^L+\chi P_t^{IT}$$

(5)

3.2.1. IT Equipment Model

$$P_t^{IT}=\underset{m\in M}{\Sigma }\underset{s\in S}{\Sigma }{P}_{m,s,t}$$

(6)

$$P_{m,s,t}=P_{m,st}+P_{m,dy,t}$$

(7)

$$P_{m,dy,t}=k_m{f}_m^3$$

(8)

3.2.2. Air-Conditioning System Model

Based on the building’s thermal inertia, the heat balance equation of the building is obtained based on the conservation of energy as follows:

$$\Delta Q=\rho CV{\displaystyle \frac{\mathrm{d}{T}_t^{in}}{\mathrm{d}t}}$$

(9)

$$k_{wall}{F}_{wall}(T_t^{out}-T_t^{in})+k_{win}{F}_{win}(T_t^{out}-T_t^{in})+I{F}_{win}SC+Q_t^{IT}-Q_t^{AC}=\rho CV{\displaystyle \frac{\mathrm{d}{T}_t^{in}}{\mathrm{d}t}}$$

(10)

where ρ = 1.225 kg/m³ according to reference [17], and C = 1.005 kJ/(kg·K) according to reference [18].

The power expression for an air-conditioning system is shown below:

$$P_t^{AC}=Q_t^{AC}/E_{EER}$$

(11)

3.2.3. PV Model

The light intensity of PV obeys a Beta distribution, and the density function that represents its probability is as follows:

$$f_{PV}(r)={\displaystyle \frac{\Gamma (a+b)}{\Gamma (a)\Gamma (b)}}{r}^{a-1}{(1-r)}^{b-1}$$

(12)

The output power of PV with the intensity of sunlight, temperature, and other uncertainties.

$$P_t^{PV}=P_{STC}{\displaystyle \frac{G_t}{G_{STC}}}(1+k(T_t-T_{STC}))$$

(13)

3.2.4. WF Model

In the WF model, the output power $P_t^{WT}$ is calculated using the following equation:

$$P_t^{WT}=\left\{\begin{array}{cc}0& \hspace{1em}\nu <{\nu }_i\\ 0.5\rho \pi R^2{\nu }^3& \hspace{1em}{\nu }_i<\nu <{\nu }_n\\ P_n& \hspace{1em}{\nu }_n<\nu <{\nu }_0\\ 0& \hspace{1em}\nu >{\nu }_0\end{array}\right.$$

(14)

3.2.5. ES Model

The ES is modeled based on the law of conservation of energy and battery operation constraints as follows [19]:

$$E_t^{ES}=(1-\tau )E_{t-1}^{ES}+[{\eta }_{\mathrm{ch}}{P}_{ES,t}^{ch}-{\displaystyle \frac{1}{{\eta }_{\mathrm{dis}}}}{P}_{ES,t}^{dis}]\Delta t$$

(15)

$$P_{ES,t}^{ch}=\max \{0,-P_t^{ES}\}$$

(16)

$$P_{ES,t}^{dis}=\max \{0,P_t^{ES}\}$$

(17)

$$10\%E_{ES}^{\max }\le E_t^{ES}\le 90\%E_{ES}^{\max }$$

(18)

$$E_0^{ES}=20\%E_{ES}^{\max }$$

(19)

$$E_0^{ES}=E_T^{ES}$$

(20)

3.3. Constraints

3.3.1. Data Load Rate Constraints

The data load rate is the amount of cloud subscriber load per unit of time allocated to a DC. The sum of the data load rates of the N DC at time t ${\lambda }_t$ can be expressed as

$${\lambda }_t={\lambda }_t^{itr}+{\lambda }_t^{batch}$$

(21)

Accordingly, the data load rate of the nth DC ${\lambda }_{n,t}$ can be expressed as

$${\lambda }_{n,t}={\lambda }_{n,t}^{itr}+{\lambda }_{n,t}^{batch}$$

(22)

3.3.2. Aggregate Service Rate Constraints

The sum of the service rates of the N DC in terms of server types ${\mu }_t$ is represented as

$${\mu }_t={\displaystyle \sum _{i=1}^N{\displaystyle \sum _{m\in M}{\displaystyle \sum _{s\in S}{\mu }_{t,i}^{m,s}}}}$$

(23)

From the point of view of the user’s real-time requirements, it can also be expressed as follows:

$${\mu }_t={\mu }_t^{itr}+{\mu }_t^{batch}$$

(24)

Interactive loads have spatial adjustment capabilities, as shown below:

$${\displaystyle \sum _{n=1}^N{u}_{n,t}^{itr}=}{\displaystyle \sum _{n=1}^N{\widehat{u}}_{n,t}^{itr}}$$

(25)

The batch load has the flexibility to be regulated in both time and space; it can be represented as

$${\displaystyle \sum _{n=1}^N{\displaystyle \sum _{t=1}^{N_T}{u}_{n,t}^{batch}}}={\displaystyle \sum _{n=1}^N{\displaystyle \sum _{t=1}^{N_T}{\widehat{u}}_{n,t}^{batch}}}$$

(26)

3.3.3. Maximum Response Time Constraints

The maximum response time of an interactive load satisfies the following constraints:

$$t_{w,t}\le D_{itr}-d_{itr}$$

(27)

The maximum response time for batch loads satisfies the following constraints:

$${\displaystyle \sum _{t=1}^{T_{batch}}{\mu }_t^{batch}}={\displaystyle \sum _{t=1}^{T_{batch}}{\lambda }_t^{batch}}$$

(28)

3.3.4. Indoor Temperature Requirements

The indoor temperature during normal operation of the DC servers should be within a certain interval range, which meets the following constraints:

$$T_{\min }^{in}\le T_t^{in}\le T_{\max }^{in}$$

(29)

3.3.5. Maximum Data Load Rate Constraint

DC servers should process data within the maximum data load they can handle, meeting the following constraints:

$$0\le {\lambda }_{n,t}\le {\lambda }_{n,\max }$$

(30)

3.3.6. Server Operating Frequency and Service Rate Constraints

In order to adjust the CPU frequency and service rate in real time according to the load demand, the server processors considered in this paper are equipped with discrete operating frequencies and service rate steps that correspond to each other:

$$f_t\in \left\{f_1,f_2,\dots f_h\dots ,f_H\right\}$$

(31)

$${\mu }_t\in \left\{{\mu }_1,{\mu }_2,\dots {\mu }_h\dots ,{\mu }_H\right\}$$

(32)

The CPU operating frequency f_t and service rate μ_t at time period t are specifically described as

$$f_t={\mathit{f}}_H{\mathit{x}}_t^H=[f_1,f_2,\cdots f_h\cdots ,f_H]\left[\begin{array}{l}{x}_t^1\\ x_t^2\\ \cdots \\ x_t^h\\ \cdots \\ x_t^H\end{array}\right]$$

(33)

$${\mu }_t={\mathit{\mu }}_H{\mathit{x}}_t^H=[{\mu }_1,{\mu }_2,\cdots {\mu }_h\cdots ,{\mu }_H]\left[\begin{array}{l}{x}_t^1\\ x_t^2\\ \cdots \\ x_t^h\\ \cdots \\ x_t^H\end{array}\right]$$

(34)

$${\displaystyle \sum _{f_h}{x}_t^h}=1$$

(35)

$$x_t^h\in \left\{0,1\right\}$$

(36)

3.3.7. Air-Conditioning Operational Constraints

$$0\le P_t^{AC}\le P_{\max }^{AC}$$

(37)

3.3.8. Renewable Energy Capacity Constraints

$$0\le P_t^{PV}\le P_{\max }^{PV}$$

(38)

$$0\le P_t^{WT}\le P_{\max }^{WT}$$

(39)

3.3.9. ES Multiplier Constraints

$$E_{ES}^{\max }=\beta P_{ES}^{\max }$$

(40)

where $\beta$ is the energy multiplier of the ES.

3.3.10. Power Balance Constraints

$$P_t^{DC}=P_t^{PV}+P_t^{WT}+P_t^{ES}+P_{buy,t}^{DC}$$

(41)

4. Case Studies

4.1. Basic Data

Table 1. Parameters of DC, PV, WF, and ES.

DC A		DC B
Parameters	Values	Parameters	Values
CPU type	ADM EPYC 7003	CPU type	ADM EPYC 7002
ft (GHz)	{2.0, 2.5, 3.0, 3.5, 4.0}	ft (GHz)	{1.8, 2.3, 2.7, 3.1, 3.3}
μt (Bar/s)	{15, 20, 25, 30, 35}	μt (Bar/s)	{14, 18, 22, 27, 31}
Pm,st (W)	80	Pm,st (W)	78
Pm,dy,t (W/GHz3)	8.0	Pm,dy,t (W/GHz3)	7.8
ωPV (CNY/kWh)	0.05	ωPV (CNY/kWh)	0.05
ωWT (CNY/kWh)	0.07	ωWT (CNY/kWh)	0.07
ωES (CNY/kWh)	0.05	ωES (CNY/kWh)	0.05

shows the relevant parameters of DC, PV, WF, and ES [20,21]. The upper limit of the response time for batch loads is set to 24 h; the optimization period of the model is 24 h, and the indoor temperature range of the servers is 18–27 °C [22].

4.2. Results Analysis

Table 2. Cost comparison of different cases.

Cases	Cost (CNY)
Case 1	31,126.72
Case 2	26,470.46
Case 3	19,324.39

provides the cost of the following three cases:

Case1: DCs are not configured with WF, PV, and ES, and the spatio-temporal regulation characteristics of the load and thermal inertia of DCs are not considered;

Case2: DCs are not configured with WF, PV, and ES, but the spatio-temporal regulation characteristics of the load and thermal inertia of DCs are considered;

Case3: DCs are configured with WF, PV, and ES, and the spatio-temporal regulation characteristics of the load and thermal inertia of DCs are considered.

Figure 2 illustrates the raw load arrival rate and the electricity price for each DC. Figure 3 demonstrates the data load arrival rate as well as the electricity price for each DC. In consideration of the temporal and spatial adjustment properties of DC, it is anticipated that each DC will level batch loads from periods of high tariffs to periods of low tariffs. Furthermore, it is expected that the DCA will shift both types of loads to DCB processing with the aim of reducing operating costs.

Figure 4 and Figure 5 demonstrate the air-conditioning power and room temperature for each DC. Due to the temporal and spatial flexibility of the data load, the power of the air-conditioning system also exhibits temporal and spatial adjustment characteristics. When the air-conditioning power is high, the temperature of the server room is higher at this time in order to reduce the operating cost, while when the air-conditioning power is low, the temperature of the server room is more utilized for the operation of the IT equipment.

Figure 6 and Figure 7 demonstrate ES charging from WF and PV. Figure 8 demonstrates DC’s power purchase from the grid. In order to effectively promote the green transformation of DC and reduce its operating costs, the power generated by PV and WF is prioritized to meet the power demand of DC. When the combined output of PV and WF exceeds the power demand of the DC, the surplus power generated will be stored in the ES. And when the sum of PV and WF output cannot satisfy the DC’s power demand, the ES will start the discharge mode, and at the same time, the DC will purchase the required power from the grid to ensure its normal operation.

5. Conclusions

This paper proposes a coordinated spatio-temporal operation of wind–solar–storage-powered DCs considering building thermal inertia. Through the case studies, the following conclusions and outlook were drawn [23,24,25]:

(1)

By digging deeper into the temporal and spatial flexibility of loads, each DC can be enabled to significantly reduce DC operating costs by rationally migrating loads from periods of high tariffs to periods of low tariffs and by optimizing the distribution of loads between different DC;

(2)

It is vital to fully take into account the building thermal inertia of DC, as this will significantly reduce the energy consumption of air-conditioning systems while guaranteeing the normal operating ambient temperature of servers in DC;

(3)

The proposed strategy of DC integrated with wind, solar, and ES can reduce the operation cost of the DC by 37.92% and improve the level of renewable energy consumption.

In future research, we will focus on two key areas:

(1)

Conduct significance tests and sensitivity analyses, define error margins, and evaluate the strategy’s robustness under complex conditions to ensure reliable and generalizable results;

(2)

Explore limitations related to renewable energy availability, scalability, and real-world constraints to enhance the practical applicability of the research.