Hybrid Control Strategy for 5G Base Station Virtual Battery-Assisted Power Grid Peak Shaving

Abstract

With the rapid development of the digital new infrastructure industry, the energy demand for communication base stations in smart grid systems is escalating daily. The country is vigorously promoting the communication energy storage industry. However, the energy storage capacity of base stations is limited and widely distributed, making it difficult to effectively participate in power grid auxiliary services by only implementing the centralized control of base stations. Aiming at this issue, an interactive hybrid control mode between energy storage and the power system under the base station sleep control strategy is delved into in this paper. Grounded in the spatiotemporal traits of chemical energy storage and thermal energy storage, a virtual battery model for base stations is established and the scheduling potential of battery clusters in multiple scenarios is explored. Then, based on the time of use electricity price and user fitness indicators, with the maximum transmission signal and minimum operating cost as objective functions, a decentralized control device is used to locally and quickly regulate the communication system. Furthermore, a multi-objective joint peak shaving model for base stations is established, centrally controlling the energy storage system of the base station through a virtual battery management system. Finally, a simulation analysis was conducted on data from different types of base stations in the region, designing two distinct scheduling schemes for four regional categories. The analysis results demonstrate that the proposed model can effectively reduce the power consumption of base stations while mitigating the fluctuation of the power grid load.

1. Introduction

With the extensive integration of renewable energy sources into the power grid, the power system is increasingly reliant on flexible energy storage solutions to optimize scheduling and alleviate the burden of peak load electricity consumption. The construction of new power energy storage equipment undoubtedly increases the economic strain on the power system [1,2]. Meanwhile, communication base stations often configure battery energy storage as a backup power source to maintain the normal operation of communication equipment [3,4]. Given the rapid proliferation of 5G base stations in recent years, the significance of communication energy storage has grown exponentially [5,6]. Therefore, the focus of research should be directed towards developing novel strategies that not only maximize the utilization of idle base station energy storage resources in power system auxiliary peak shaving work, but also motivate users to the maximum extent while ensuring communication quality and the normal operation of the base station equipment, to achieve a mutually beneficial outcome for both power grid companies and communication operators.

With regards to the aggregation of communication energy storage, scholars are increasingly and flexibly utilizing dispersed resources through information technology. The literature [7,8] has constructed a dynamic economic dispatch (DED) combination model that integrates the power system and 5G communication network. This model encompasses numerous energy-consuming 5G base stations (gNBs) and their backup energy storage systems (BESSs) in a virtual power plant to provide power support and obtain economic incentives, and develop virtual power plant management functions within the 5G core network to minimize control costs. In [9], a dual-layer optimization model for energy storage operation is introduced, with the goal of maximizing the collective benefits of base station energy storage investors and operators. The research focuses on a multi-base station collaborative system to achieve the highest net profit throughout the entire lifecycle of energy storage. Reference [10] presents a communication and power coordination planning model, where the communication quality serves as a fundamental parameter and is crucial for ensuring reliable energy sharing among market participants. Meanwhile, reference [11] proposes a 5G and distribution system expansion planning model that considers source–network–load–storage coordination. This model leverages the synergy of cloud computing and edge computing to enable the flexible distribution of data loads, reformulating the original expansion planning model as a mixed integer linear programming problem. Lastly, reference [12] evaluates the differences in the schedulable capacity of base station backup batteries under different distribution networks and communication load levels.

In terms of coupling with renewable energy sources, reference [13] has investigated the potential of utilizing grid-connected solar cell BS in Kuwait. Reference [14] has achieved green energy conservation by aligning the electricity consumption of base stations with the output of renewable energy. References [15,16] have capitalized on the idle space of base station energy storage to stabilize the photovoltaic output, and established a microgrid and 5G base station cooperation mode for photovoltaic energy storage systems. In addition, reference [17] has proposed a novel energy microgrid architecture for small base station clusters, maximizing the utilization of sustainable energy through intra- and inter-microgrid cooperation. This approach is complemented by an on-demand resource allocation method for small base stations in sleep mode, coupled with energy cooperation to optimize the energy efficiency and technical feasibility of microgrids. In [18], an MOIO-based framework is proposed to enable the synergistic planning of 5G BS and REG in the context of low-carbon PDS. The model comprehensively captures the potential flexibility of 5G BSs, considering both communication and energy-related characteristics, while explicitly incorporating the impacts of system uncertainties through interval modeling. To solve the presented problem effectively, an evolutionary algorithm named CIMOEA/D is developed.

Given the significant increase in electricity consumption in 5G networks, which contradicts the concept of communication operators building green communication networks, the current research focus on 5G base stations is mainly on energy-saving measures and their integration with optimized power grid operation. Therefore, exploring efficient and feasible energy consumption reduction technologies for base stations has become a focus of industry attention. At present, the energy-saving strategies for 5G base stations are mainly divided into two categories: hardware and software. Compared to hardware energy-saving technology, its research and development, production, and application cycle is longer, while software energy-saving technology shows higher flexibility. In the field of software energy-saving, the key base station sleep control strategy has become an effective means to solve the problem of resource waste caused by a load imbalance [19]. This strategy flexibly adjusts the user connections of low-load base stations to put inefficient base stations into sleep mode, thereby improving base station utilization and reducing the overall system energy consumption [20,21]. The literature [22] built a multi-access edge computing network model by solving the problem of mobile network task unloading. By considering base station prices, IoT device base station selection, and job offloading mechanisms, the maximization of base station revenue and IoT device utility can be achieved. Reference [23] proposes a small-cell base stations (SBS) model with a dynamic sleep mechanism for small base stations to address the challenges of maintaining SBS service quality and reducing SBS energy consumption during passenger traffic fluctuations. Reference [24] proposed a 5G base station energy consumption optimization strategy that considers a variable threshold sleep mechanism, which makes sleep decisions more reasonable by considering interference between the base station and users. Reference [25] proposes a mobile sensing dual-level base station sleep control strategy based on cellular traffic prediction, which monitors the current network traffic and user mobility of the base station to meet the needs of reducing power consumption and improving service quality, thereby placing the base station in two different sleep states. Reference [26] dynamically changes the status (active/sleep) of small base stations based on load traffic requirements by handling the dynamic traffic demands of user devices (U).

At present, many scholars and experts have conducted in-depth discussions on the participation of base station energy storage technology in power grid scheduling [27]. However, there is still insufficient discussion on the potential impact of sudden energy consumption changes caused by dormant base stations on grid interaction, as well as how to optimize system performance by incentivizing users to adjust the communication service quality. In addition, multi-type base station aggregation regulation also involves more complex optimization algorithms and coordination mechanisms, which need to comprehensively consider multiple factors. Therefore, further research is needed on base station aggregation regulation in different scenarios, exploring more efficient and intelligent regulation strategies and methods to promote the application and development of base station energy storage technology in smart grid construction.

Based on the above issues, this article aims to maximize the utilization of idle energy storage resources in communication base stations, and designs a hybrid control peak shaving strategy for communication base stations considering user fitness under time of use electricity prices and spatiotemporal characteristics. Firstly, consider the spatiotemporal characteristics of the base station to establish a virtual battery model for the base station and explore its scheduling potential. Then, the user adaptability evaluation index is introduced, and the time of use electricity price is used to increase user participation and increase the potential of virtual battery scheduling. Through the autonomy of the decentralized control device and the fast response-ability to local base station load rate fluctuations, the communication system of the base station is subjected to decentralized sleep control. Finally, based on the multi-scenario interconnection strategy, virtual battery management is constructed, and a real-time peak shaving model for base station virtual batteries is designed using the ADMM algorithm to minimize the variance of the load curve and economic costs, achieving the maximum utilization of energy storage resources. The performance verification of the proposed control strategy was conducted through the simulation of two scheduling modes in four scenarios, and the impact of base station parameters on the peak shaving results was analyzed for different scales.

2. Virtual Battery Model for 5G Base Station

The 5G communication base station can be regarded as a power consumption system that integrates communication, power, and temperature coupling, which is composed of three major pieces of equipment: the communication system, energy storage system, and temperature control system. The energy consumption of the base station is closely related to the communication load it bears, while the temperature environment working conditions of the base station and the demand for energy storage and power reserves are inseparable from the real-time energy consumption of the base station. Firstly, this paper analyzes the energy consumption of the communication base station dynamically, and conducts a general battery capacity analysis of the temperature control system and energy storage system that can be managed for energy management, so as to establish a virtual battery model of the base station.

2.1. Communication System Model

In a given area, the communication base stations are represented as M = {1, 2, …, m} base stations, I = {1, 2, …, i} mobile users, and T = {1, 2, …, t} operating time slots of base stations. Figure 1 illustrates the distribution of communication base stations and users in the region.

This is the connection between a user and a base station at a certain moment.

(1) ${\Omega }_{i,m,t}$ is the connection between the user and the base station at a given moment in time, if ${\Omega }_{i,m,t}=1$ then user i is connected to base station m, if ${\Omega }_{i,m,t}=0$ then user i is unable to connect to base station m;

(2) ${\lambda }_{m,t}$ is the state of the base station m at moment t, if ${\lambda }_{m,t}=1$ then the base station is in normal operation, if ${\lambda }_{m,t}=0$ then the base station is in hibernation.

When the base station is dormant, users cannot connect to the base station; when the base station is working, at least one user connects to the base station.

The 5G network is the wireless terminal data; it first sends a signal to the wireless base station side, then sends via the base station to the core network equipment, and is ultimately sent to the destination receiving end. The deployment of communication systems for general transmission equipment solutions encompasses: the Packet Transport Network (PTN), Base Band Unite (BBU), and Active Antenna Unit (AAU). The network architecture is shown in Figure 2.

AAU generates 80% of the communication system’s power consumption [28], but this is not constant due to the power consumption. BBU is the second-largest energy consumer in the communication system, yet it is largely unaffected by the service volume and constant [29], since PTN and BBU equipment are installed in close proximity to each other and their power consumptions are relatively small. When supplying power to BBU, the power demand of PTN has been met, so PTN’s power supply demand is no longer considered separately.

$$P_{m,t}^{BSCO}=\left\{\begin{array}{c}{P}_{m,t}^{AAU}+P^{BBU}+\left|{\lambda }_{m,t-1}-{\lambda }_{m,t}\right|P^{CHA},{\lambda }_{m,t}=1\\ P^{SL},{\lambda }_{m,t}=0\end{array}\right.$$

(1)

The transmission power of the base station communication system can be described as Equation (1): $P_{m,t}^{BSCO}$ is the convey power consumption of a single base station at time t; ${\lambda }_{m,t}$ is the state of the base station m at moment t; $P_{m,t}^{AAU}$ is the power consumption of the AAU device of the base station m in time slot t; $P^{BBU}$ is the power consumption of the BBU device of the base station; $P^{CHA}$ is the power required for the switching state of the base station; and $P^{SL}$ is the dormant power of the base station.

$$P_{m,t}^{AAU}=P^{AAUBS}+P_{m,t}^{AAUWK}$$

(2)

where $P^{AAUBS}$ is the basic power consumption of AAU, no matter whether the base station is in the dormant state or working state, and the power consumption of this part is stable and unchanged; and $P_{m,t}^{AAUWK}$ is the variable power consumption of AAU, which is closely related to the service volume of the base station. The power consumption of the power amplifier module in the AAU equipment grows rapidly with the increase in the service volume of the base station, which belongs to the working power consumption of the AAU equipment, according to Shannon’s formula and the path fading model which can be obtained:

$$P_{i,m,t}^{AAUWK}=N_0(2^{{\displaystyle \frac{L_i}{B}}}-1)•{10}^{{\displaystyle \frac{A_{PL}\lg (d^{m,i})+B_{PL}}{10}}}$$

(3)

$$P_{m,t}^{AAUWK}={\displaystyle \sum _{i=1}^I{\Omega }_{i,m,t}}•P_{i,m,t}^{AAUWK}$$

(4)

where $P_{i,m,t}^{AAUWK}$ is the AAU variable power consumption generated by user i connected to base station m at time t; $N_0$ is the thermal noise and other signal interference coefficients of user i; $L_i$ is the user traffic demand; $A_{PL}$ and $B_{PL}$ are the channel fading coefficients; and $d^{m,i}$ is the distance between base station m and user i.

2.2. Base Stations Energy Storage System Modeling

The equipped capacity of the internal energy storage system of the communication base station is determined by the load current and the minimum backup time of the battery, and the rated capacity of the energy storage system $E_m^{ba}$:

$$E_m^{ba}={\displaystyle \frac{K^{ba}{I}_{\max }{U}_{BSES}\Delta t_{res}}{{\eta }^{ba}[1+{\omega }^{ba}(T_m^{out}-T^{\lim }]}}$$

(5)

where $K^{ba}=1.25$ is the safety constant coefficient, $I_{\max }$ is the maximum load current of the communication system, $U_{BSES}$ is the rated voltage of the energy storage system, $\Delta t_{res}$ is the general standardized backup time for large equipment, ${\eta }_{ba}$ is the discharge capacity coefficient, ${\omega }^{ba}=0.008$ is the battery temperature coefficient, $T_m^{out,\min }$ is the minimum outdoor temperature of the base station m, and $T^{\lim }$ is the set limit.

The energy storage system of the base station is different from the conventional energy storage power station, the minimum standby capacity is positively correlated with the business volume of the base station, and the change in the business volume changes at any time and in any space characteristics. In time, it needs the standby capacity to support the normal operation of the base station business of the next moment based on the general accident processing time; in space, it needs the standby capacity to support the probability of occurrence of accidents in the region and the importance of the communication degree of the basis for the BTS operation. In addition, the life of the battery pack also restricts the charging and discharging depth, in order to prolong the life of the battery pack in the energy storage system, and to avoid overcharging and overdischarging frequently when participating in grid scheduling. $S_m^{O\min }$ and $S_m^{O\max }$ are set as the upper and lower limits of the state of charge of the battery to avoid overcharging for the communication base station m to consider. Therefore, the upper and lower limits of the charging state of base station m at time t are:

$$\left\{\begin{array}{c}SO{C}_{m,t}^{\min }=\max \{S_{m,t}^{T\min },S_{m,t}^{P\min },S_m^{O\min }\}\\ SO{C}_{m,t}^{\max }=S_m^{O\max }\end{array}\right.$$

(6)

where $SO{C}_{m,t}^{\min }$ and $SO{C}_{m,t}^{\max }$ are the lower and upper limits of the charging state of the communication base station m at time t; $S_{m,t+1}^{T\min }$ is the minimum charging state of the communication base station m at time t after considering the user’s temporal characteristics of the power supply; and $S_{m,t+1}^{P\min }$ is the minimum charging state of the communication base station m at time t after considering the user’s spatial characteristics of the power supply.

$$\left\{\begin{array}{c}{S}_{m,t}^{T\min }={\displaystyle \frac{{\sigma }^{ba}{\beta }_{m,t+1}^{load}}{E_m^{ba}}}\\ S_{m,t}^{P\min }={\displaystyle \frac{{\displaystyle {\int }_t^{t+\Delta t_{m,res}}{P}_{m,t}^{BSCO}dt}}{E_m^{ba}}}\end{array}\right.$$

(7)

The minimum reserve SOC of the energy storage battery pack considering the spatiotemporal characteristics of the base station can be described as Formula (7): ${\sigma }^{ba}$ is the correlation coefficient between the load factor of the base station and the state of charge of the energy storage system, and $\Delta t_{m,res}$ is the base station power reserve time determined according to the spatial characteristics of the communication base station m.

$$\Delta t_{m,res}={\displaystyle \frac{{\gamma }_m^{ba}\Delta t_{m,pf}}{{\gamma }^{ba}\Delta t_{pf}}}\Delta t_{res}$$

(8)

where ${\gamma }_m^{ba}$ and ${\gamma }^{ba}$ are the average annual number of faults within the radiation range of base station m and the total dispatch range, respectively, and $\Delta t_{i,pf}$ and $\Delta t_{pf}$ are the average outage time of faults within the radiation range of base station m and the total dispatch range, respectively.

$${\mu }_{m,t}^{po}=\left\{\begin{array}{c}1,SO{C}_{m,t+1}>SO{C}_{m,t}^{\max }-S_{m,t}^{bach}\\ -1,SO{C}_{m,t+1}<SO{C}_{m,t}^{\min }+S_{m,t}^{badi}\\ 0,SO{C}_{m,t}^{\min }+S_{m,t}^{badi}\le SO{C}_{m,t}\le SO{C}_{m,t}^{\max }-S_{m,t}^{bach}\end{array}\right.$$

(9)

$$\left\{\begin{array}{c}{S}_{m,t}^{bach}={\displaystyle \frac{{\eta }^{ba}\times \Delta t\times P_{m,t}^{char}}{E_m}}\\ S_{m,t}^{badi}={\displaystyle \frac{{\eta }^{ba}\times \Delta t\times P_{m,t}^{diss}}{E_m}}\end{array}\right.$$

(10)

$$SO{C}_{m,t+1}=SO{C}_{m,t}-{\mu }_{m,t}^{re}{S}_{m,t}^{bach}+(1-{\mu }_{m,t}^{re})S_{m,t}^{badi}$$

(11)

$$P_{m,t}^{es}=\left\{\begin{array}{c}{P}_{m,t}^{char},{\mu }_{m,t}^{re}=-1\\ P_{m,t}^{diss},{\mu }_{m,t}^{re}=1\\ 0,{\mu }_{m,t}^{re}=0\end{array}\right.$$

(12)

The selectable operating state of the battery pack of the energy storage system of the base station can be described as Equation (9): ${\mu }_{m,t}^{po}$ is the selectable operating state of the battery pack of the energy storage system of base station m at time t; $P_{m,t}^{es}$ is the power of the battery pack of the energy storage system of the base station; ${\mu }_{m,t}^{re}$ is the actual operating state of the battery pack of the energy storage system of base station m at time t; ${\eta }^{ba}$ is the charging/discharging efficiency of the battery; and $S_{m,t}^{bach}$ and $S_{m,t}^{badi}$ are the current charging capacity and discharging capacity of the battery, respectively. The charging and discharging capacity of the battery pack in the base station energy storage system can be described as Equation (10): $P_{m,t}^{char}$ and $P_{m,t}^{diss}$ are the current charging power and discharging power of the battery, respectively, and $\Delta t$ is an operating cycle. The charging and discharging capacity of the battery pack at the next moment can be described as Equation (11): $SO{C}_{m,t+1}$ is the charging state of the base station m for the next time period. When ${\mu }_{m,t}^{po}=1$, the storage battery only supports the discharge or idle operation; when ${\mu }_{m,t}^{po}=-1$, the storage battery only supports the charging operation; and when ${\mu }_{m,t}^{po}=0$, the storage battery supports both charging and discharging. The power of the base station energy storage battery pack can be described as Equation (11): ${\mu }_{m,t}^{re}=-1$ is the actual charging operation where, at this time, $P_{m,t}^{es}=P_{m,t}^{char}$; ${\mu }_{m,t}^{re}=1$ is the actual discharging operation where, at this time, $P_{m,t}^{es}=P_{m,t}^{diss}$ is the actual neither charging nor discharging operation; and ${\mu }_{m,t}^{re}=0$ is the actual neither charging nor discharging operation where, at this time, $P_{m,t}^{es}=0$ is the actual discharging operation.

2.3. Base Station Temperature Control System Modeling

The temperature control system model is constructed according to the equivalent thermal parameter model of the air conditioning unit as shown in Figure 3, and its differential equation can be obtained.

$${\displaystyle \frac{dT}{dt}}={\displaystyle \frac{(T_{m,t}^{out}-T_{m,t}^{in})/R-(Q_{m,t}^a-Q_m^k)}{C}}$$

(13)

where $T_{m,t}^{out}$ and $T_{m,t}^{in}$ are the outdoor temperature and indoor temperature of base station m at time t, respectively; $R$ is the equivalent thermal resistance, °C/kW; $C$ is the equivalent heat capacity, kJ/°C; $Q_{m,t}^a$ is the cooling capacity of the air conditioning unit of base station m at time t; and $Q_m^k$ is the heat dissipation of the other equipment of the base station.

The cooling capacity of the air conditioning unit is controlled by the electrical power of the unit, which can be obtained after simplification:

$$Q_{m,t}^a=k^{\mathrm{air}}{P}_{m,t}^a+l^{\mathrm{air}}$$

(14)

where $k^{\mathrm{air}}$ and $l^{\mathrm{air}}$ are air-conditioning system coefficients and air-conditioning constant coefficients, respectively; and $P_{m,t}^a$ is the air-conditioning power of the base station m at the moment t, $P_{m,t}^a\in \left[P^{\min },P^{\max }\right]$, where the temperature control system of the base station belongs to the inverter air-conditioning, its power varies with the frequency of the frequency converter, the upper and lower limits of the variation value are $P^{\max }$ and $P^{\min }$, and the speed of the compressor motor is altered according to the temperature difference between the room temperature and the set limit value of $T^{\lim }$ adjusting the power supply frequency.

$$\left\{\begin{array}{c}{T}_{m,t}^{\min }=T^{\lim }-T_{m,t}^{lendo}\\ T_{m,t}^{\max }=T^{\lim }+T_{m,t}^{lenup}\end{array}\right.$$

(15)

$$\left\{\begin{array}{c}{T}_{m,t}^{\min }\le T^{\min ba}\\ T_{m,t}^{\max }\le T^{\max ba}\end{array}\right.$$

(16)

where $T_{m,t+1}^{lenup}$ and $T_{m,t+1}^{lendo}$ are the upward adjustable temperature interval and the downward adjustable temperature interval of base station m at time t, respectively; $T_{m,t}^{\max }$ and $T_{m,t}^{\min }$ are the upper and lower indoor temperature limits of base station m at time t, which are not fixed values and are determined by the length of the temperature control interval; and $T^{\max ba}$ and $T^{\min ba}$ are the permissible upper and lower indoor temperature limits of the base station.

The phenomenon of self-discharge in the virtual thermal battery of the temperature control system differs from that of traditional batteries in that the loss relative to the battery’s storage capacity is negligible. This is because the virtual thermal battery is not a standalone entity, but rather a component of the building system, which is responsible for dissipating heat. Consequently, the self-discharge loss in the virtual thermal battery must be considered in the context of the overall heat dissipation brought about by the building system. The greater the load factor of the base station, the greater the power consumption, the more energy required to maintain room temperature, the more severe the self-discharge, and the higher the float power.

$$P_{m,t}^{ba}={\displaystyle \frac{T_{m,t}^{out}-T_{m,t}^{in}+{\mu }^{\mathrm{rad}}{\beta }_{m,t}^{load}R}{{\eta }^{air}R}}$$

(17)

where $P_{m,t}^{ba}$ is the floating power of the temperature-controlled battery of the base station m at moment t, ${\mu }^{\mathrm{rad}}$ is the heat generation coefficient, and ${\eta }^{air}$ is the rated electrical heat conversion efficiency of the air conditioner.

The room temperature limitation interval is primarily influenced by the grid price and the optimal room temperature for the base station. During periods of a peak grid load, operators of the base station may choose to relax the temperature limitation interval due to the elevated price of electricity. Conversely, the daily lives of individuals result in the production and living habits that influence the real-time business volume of the base station, which in turn affects the peak and valley of the daily load curve. This phenomenon is more pronounced in base stations with a high price range, which experience a greater volume of business and consequently require more heat dissipation. Consequently, the temperature control system is unable to regulate the temperature within the specified limits, resulting in an increase in the base station’s own heat dissipation. Furthermore, the adjustable potential of the temperature control system is reduced.

$$T_{m,t+1}^{lendo}=T^{lenbase}+k^{lendo}{\beta }_{m,t}^{load}(1-k^{cba})$$

(18)

$$T_{m,t+1}^{lenup}=T^{lenbase}+k^{lenup}(1-{\beta }_{m,t}^{load})k^{cba}$$

(19)

where $T^{lenbase}$ represents the base temperature limit length of the base station m at a given moment t; ${\beta }_{m,t}^{load}$ represents the load factor of base station m at a given moment t; $k^{cba}$ is the price incentive coefficient; and $k^{lendo}$ and $k^{lenup}$ are the downward and upward length coefficients, respectively:

$$k^{cha}={\displaystyle \frac{C_t^{BS}}{C^{BS\max }+C^{BS\min }}}$$

(20)

$$k^{lendo}={\displaystyle \frac{(T^{\lim }-T^{\min ba}-T^{lenbase})(C^{BS\max }+C^{BS\min })}{C^{BS\min }}}$$

(21)

$$k^{lenup}={\displaystyle \frac{(T^{\max ba}-T^{\lim }-T^{lenbase})(C^{BS\max }+C^{BS\min })}{C^{BS\max }}}$$

(22)

where $C_t^{BS}$ is the time-of-day tariff of the power company, and $C^{BS\max }$ and $C^{BS\min }$ are the upper and lower limits of the tariff.

The temperature control system draws power from the grid at a variable rate through the variable frequency air conditioner. The virtual energy storage capacity and rated capacity of the air conditioning control unit are as follows:

$$E_{m,t}^{airin}=C(T_{m,t}^{\max }-T_{m,t})/{\eta }^{air}$$

(23)

$$E_{m,t}^{airN}=C(T_{m,t}^{\max }-T_{m,t}^{\min })/{\eta }^{air}$$

(24)

where $E_{m,t}^{airin}$ is the virtual power storage of the air conditioner of base station m at time t and $E_m^{airN}$ is the rated power storage of the air conditioner of base station m.

The State of Virtual Charge (SOVC) of the temperature-controlled load is:

$$SOV{C}_{m,t}^{in}={\displaystyle \frac{T_{m,t}^{\max }-T_{m,t}}{T_{m,t}^{\max }-T_{m,t}^{\min }}}$$

(25)

where $SOV{C}_{m,t}^{in}$ is the virtual charging state of the temperature control system of the base station m at moment t. When the indoor temperature is at the lowest boundary value $T_{m,t}^{\min }$, the stored thermal energy is the highest; when the indoor temperature is at the lowest boundary value $T_{m,t}^{\max }$, it does not have energy storage. This can be obtained by discretely updating the above equation:

$$P_{m,t}^{adj}=P_{m,t}^a-P_{m,t}^{ba}$$

(26)

$$SOV{C}_{m,t+1}^{in}=e^{-{\displaystyle \frac{\Delta t}{RC}}}SOV{C}_{m,t}^{in}+({\displaystyle \frac{\eta R{P}_{m,t}^{adj}}{T_{m,t}^{\max }-T_{m,t}^{\min }}}+0.5)(1-e^{-{\displaystyle \frac{\Delta t}{RC}}})$$

(27)

$${\mu }_{m,t}^{air}=\left\{\begin{array}{c}-1,P_{m,t}^{adj}>0\\ 0,P_{m,t}^{adj}=0\\ 1,P_{m,t}^{adj}<0\end{array}\right.$$

(28)

where $P_{m,t}^{adj}$ is the air conditioning adjustable power of base station m at moment t. ${\mu }_{m,t}^{air}$ is the operating state of the temperature control system of base station m at time t. When the regional load is in the wave peak, it is necessary to reduce the power consumption of the temperature control system of the base station as the air-conditioning power is smaller than its floating power, and at this time, the adjustable power is negative, ${\mu }_{m,t}^{air}=1$, and the battery is discharged. When the regional load is in the wave valley, the air-conditioning adjustable power is increased, the air-conditioning power is larger than its floating power, ${\mu }_{m,t}^{air}=-1$, the adjustable power is positive, and the battery is charged. When ${\mu }_{m,t}^{air}=0$, it is equivalent to neither charging nor discharging the virtual battery.

In the event that the outdoor temperature is below the optimal operating temperature of the base station, the air conditioning unit is rendered inoperable, and the temperature control system becomes the primary consumer of the base station’s power. At this juncture, the temperature control system’s adjustable potential is set to zero, and the virtual energy storage of the base station is recalibrated.

$$E_{m,t}^{air}=\left\{\begin{array}{c}{\displaystyle \frac{C(T_{m,t}^{\max }-T_{m,t})}{{\eta }^{air}}}, T_{m,t}^{out}<T_{m,t}^{\lim }\\ {\displaystyle \frac{C(T_{m,t}^{\max }-T_{m,t})}{{\eta }^{air}}}, T_{m,t}^{\lim }\le T_{m,t}^{out}\le T_{m,t}^{\max }\\ 0, T_{m,t}^{out}>T_{m,t}^{\max }\end{array}\right.$$

(29)

where $E_{m,t}^{air}$ is the corrected air-conditioning capacity of the base station m at moment t.

$$SOV{C}_{m,t}=\left\{\begin{array}{c}{\displaystyle \frac{T_{m,t}^{\max }-T_{m,t}}{T_{m,t}^{\max }-T_{m,t}^{\min }}}, T_{m,t}^{out}<T_{m,t}^{\lim }\\ {\displaystyle \frac{T_{m,t}^{\max }-T_{m,t}}{T_{m,t}^{\max }-T_{m,t}^{\min }}}, T_{m,t}^{\lim }\le T_{m,t}^{out}\le T_{m,t}^{\max }\\ 0, T_{m,t}^{out}>T_{m,t}^{\max }\end{array}\right.$$

(30)

where $SOV{C}_{m,t}$ is the corrected charging state of the base station m at moment t.

3. Distributed Hibernation Control Model for Communication Systems

The network load in the region is typically shared by the base station clusters in the area. Due to the inevitable overlap between the base stations in the coverage area, a significant number of base stations repeatedly provide signals, resulting in a considerable burden on redundant mobile communication traffic and a high incidence of power loss. In order to reduce the energy loss of BTSs and to optimize the utilization of BTSs’ virtual battery storage, this paper controls the users’ acceptance of the dormant mechanism by setting two indicators, namely, a network fee incentive and Internet access delay, on the basis of the potential mining of the virtual battery model. The network fee incentive indicator is related to the time-sharing tariff. Subsequently, the optimal transmission signal of the BTS and the optimal operation cost of the operators are taken as the objective function in order to solve the decentralized BTS dormancy control strategy under a multi-objective.

3.1. Analysis of User Adaptation under the Influence of Spatio-Temporal Characteristics

The number of users is considerable. If the communication habits and load of each user are analyzed separately, the calculation of the operation status and connection of the base station is large, and the data results are complex and difficult to integrate. Furthermore, the frequent switching of the base station mode will reduce the user experience, cause certain loss to the hardware, and increase the operation and maintenance cost. Consequently, the temporal and spatial characteristics of users are clustered, whereby the time scale of base station scheduling is increased and the state of the base station is maintained for a brief period. Furthermore, the spatial scope of the user control is expanded and consistent user connectivity is ensured within a small geographical area.

3.1.1. Temporal Characterization

For users in the time of day, the communication signal is always present and regular. Over the course of a 24 h period, users will move regularly. The migration of users results in a greater volume of communication in office areas during working hours than in residential areas during non-working hours. This is analogous to the change in the regional load curve. This migration phenomenon of users can be explained by the concept of a typical “tidal effect”. Figure 4 illustrates the density of base station population connections in the residential area, which tends to be zero during the day and peaks during non-working hours. In contrast, the number of connections in the school area fluctuates more with the time of the school day and peaks at midday. The overall distribution of connections is similar in the commercial area and the office area, with the exception that the office area is more densely connected in the middle of the night due to overtime work.

3.1.2. Spatial User Clustering

It is necessary to consider the scheduling of the type of base station for a macro base station. In the working state of the signal, this type of base station transmits a positive hexagonal region for a base station radiation area. The scope of a single radiation area is divided to achieve the scope of the sub-control area of the range of the increase, that is, to complete a small range of user clustering. Figure 5 is the control range schematic diagram. Given that the radiation area is hexagonal in shape, it is divided into six triangular sub-areas, which are defined as sub-control ranges. The different colors in the Figure 5 represent the different radiation areas.The switching and transfer of users is realized in units of sub-control ranges.

When a user connection is switched, users within a sub-control area are given priority, and the user clustering method reduces the frequency of switching the user connection state, thereby improving user performance and reducing equipment loss.

3.2. Indicators of User Adaptation Based on Tariff Incentives

The signal switching caused by the BTS dormant control strategy affects the user’s sense of experience. Therefore, it is necessary to analyze the user’s adaptability in order to determine whether the user accepts switching the radiated BTS signals or not. The user’s adaptability directly affects their participation in the BTS dormant control. When the adaptability of user i is low, the user does not allow the BTS to switch the signals. Conversely, when the adaptability of user i is high, the user actively participates in the modulation and control of the BTS communication system strategy. The user’s adaptation is jointly affected by the service delay and the network cost. The service delay of base station m is influenced by its current service volume and the total capacity of the base station. The network cost is affected by the Time-of-Day tariff of the power system. Time-of-Day tariffs are designed to charge different rates according to the varying operating conditions of the system. This approach can encourage power users to shift their consumption patterns to align with peak and off-peak periods, thereby optimizing their overall energy usage. Additionally, the network costs associated with users also fluctuate in response to the impact of time-of-use tariffs on base stations. It means that the system scheduling demand and the network cost are inversely proportional to each other; when the scheduling demand is higher, the network cost will be lowered accordingly, and vice versa, the network cost will not be lowered to be maintained as the base price, which is relatively high. The user adaptation function is defined as:

$$fi{t}_{i,t}=C{H}_{\mathrm{t}}^{\mathrm{exc}}/D{L}_{i,t}$$

(31)

where $fi{t}_{i,t}$ is the adaptability of user i at the next moment; $D{L}_{i,t}$ is the service delay impact on user i at moment t; and $C{H}_t^{exc}$ is the network fee incentive for user i in the region at moment t. To enable the operator to incentivize the user to reduce the network demand standard to a greater extent through the network charge, the network charge incentive is set numerically according to the peak area of the planning potential of the virtual battery.

The user service delay is mainly considered as the ratio of the current service volume of the base station to its total capacity and the effect of the minimum demand transmission requirement.

$$D{L}_{i,t}={\displaystyle \frac{R_{i,t}^{BS\min }{\beta }_{m,t}^{load}Y}{B}}$$

(32)

where $R_{i,t}^{BS\min }$ is the minimum demand transmission requirement of user i at moment t. If the user adaptation at the next moment is less than the minimum user adaptation $fi{t}_{\min }$, i.e., $fi{t}_{i,t+1}<fi{t}_{\min }$, the user does not receive the signal switching service, i.e., the BTS does not participate in the hibernation control.

3.3. Base Station Dormancy Control Model Considering Optimal Cost of Communication System

The dormancy control strategy of the base station is mainly a question of considering the efficiency of signal transmission within the slice area, and radiating the most effective signals with the smallest total cost. Based on the analysis of the user’s adaptability in the previous section, it is firstly determined whether or not the user supports the signal switching, and then a multi-objective function is constructed with the maximum total transmission signal capacity of the base station and the minimum total cost of maintaining the base station operation; the multi-template function is normalized by the magnitude of the scale, and then it is unitarily processed by the ideal. After normalizing the multi-template function, the ideal value method is used to unify the process, and the final base station control hibernation control objective function is obtained.

3.3.1. Objective Function of Base Station Dormancy Control Model

To determine whether the users of the communication base station enter the dormant mode, the main consideration is whether the transmission efficiency can be maximized, i.e., to meet the maximum transmission capacity of the base station in the area during the day and the best user experience, and to meet the lowest single-day consumption price of electricity in the area, so as to realize the optimal operation of the communication system with the smallest cost.

• Maximize the Total Transmission Signal Capacity of the Base Station

The calculation of the signal-to-noise ratio (SNR) enables the assessment of the communication quality and the determination of whether the quality and reliability of the communication meet the required standards. The channel gain is directly proportional to the signal-to-noise ratio, and the distance between the base station and the user affects the numerical size of the channel gain.

$${\epsilon }_{i,m}=\left\{\begin{array}{c}{K}_{CG}^{BS}{({\displaystyle \frac{d^{m,i}}{d_{CG}^{BS}}})}^{-\delta }, d^{m,i}\ge d_{CG}^{BS}\\ K_{CG}^{BS}, d^{m,i}<d_{CG}^{BS}\end{array}\right.$$

(33)

where ${\epsilon }_{i,m}$ represents the channel gain of user i, which is connected to the base station m; $K_{CG}^{BS}$ and $\delta$ represent the loss-fixing parameter and loss-fixing index, respectively; and $d_{CG}^{BS}$ is the specified user base station spacing. When the spacing is less than the specified value, the channel gain value is independent of the other phases and is taken as a constant. Otherwise, it is attenuated according to the exponential attenuation. It can be seen that no situation exists where the spacing is less than zero.

The SNR is calculated based on the channel gain.

$$S_{i,m,t}={\displaystyle \frac{(P_{m,t}^{BBUWK}+P_{m,t}^{AAUWK}){\epsilon }_{i,m}}{P_{no}^{BA}+{\displaystyle \sum _{m=1}^M{\lambda }_{m,t}}(P^{AAUBS}+P^{BBUBS}){\epsilon }_{i,m}}}$$

(34)

where $S_{i,m,t}$ represents the SNR of user i connected to base station m at time t and $P_{no}^{BA}$ represents the power of the stationary noise.

It can be demonstrated that user i is connected to base station m at a specific point in time, designated as moment t, in accordance with the principles of Shannon’s theorem.

$$R_{i,m,t}^{BS}={\displaystyle \frac{B}{Y}}{\displaystyle \sum _{i=1}^I{\Omega }_{i,m,t}}{\log }_2(1+S_{i,m,t})$$

(35)

where $Y$ is the total number of resources available at the base station; $B$ is the channel bandwidth; and $R_{i,m,t}^{BS}$ is the network utility rate of user i connected to base station m at time t.

The maximum objective function of the signal capacity for base station communication transmission is:

$$\max F^{sig}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{m=1}^M{\displaystyle \sum _{i=1}^I{R}_{i,m,t}^{BS}{\Omega }_{i,m,t}}}}$$

(36)

where $F^{sig}$ represents the total capacity of the transmitted signal from all base stations in a given area during the day. The base station with the highest work utilization is that which operates at the maximum capacity for the total transmitted signal.

2.

Minimal Cost to Keep the Base Station Running

The operating costs of a base station need to be considered in terms of both the total intra-day electricity costs and the maintenance costs associated with switching states.

$$\min F^{BSCO}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{m=1}^M{C}_t^{CH}\left|{\lambda }_{m,t-1}-{\lambda }_{m,t}\right|}}+{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{m=1}^M{C}_t^{BS}{P}_{m,t}^{BS}}}+0.1{\displaystyle \sum _{t=1}^T(C{H}_t^{exc}-1)n_t}$$

(37)

where $F^{BSCO}$ is the cost of electricity for all base stations in the day area; $C_t^{CH}$ is the cost of each switching state; and $n_t$ is the number of users in the current scenario at time t.

3.3.2. Constraints of Base Station Dormancy Control Model

(1)

System Operational Constraints

In order to maximize base station utilization, there are operational constraints to ensure that a user only receives signals from one base station and that the default base station does not emit signals when it goes into sleep mode:

$$\left\{\begin{array}{c}1\le {\displaystyle \sum _{i=1}^I{\Omega }_{i,m,t}\le {\Omega }^{\max },{\lambda }_{m,t}=1}\\ {\displaystyle \sum _{i=1}^I{\Omega }_{i,m,t}=0,{\lambda }_{m,t}=0}\end{array}\right.$$

(38)

$${\lambda }_{m,t}\ge {\Omega }_{i,m,t}$$

(39)

where ${\Omega }^{\max }$ is the maximum number of serviceable users. The number of connections to the base station must not exceed the maximum number of serviceable users.

(2)

Transmission Quality Constraints

To ensure the user’s effectiveness, the base station’s transmission rate should be greater than the user’s minimum operational requirements:

$$R^{BS}\ge R_{i,t}^{BS\min }$$

(40)

where $R^{BS}$ is the default value of the base station’s transmission rate.

The transmitted traffic cannot exceed the upper limit of the traffic that can be handled by the base station:

$$L^{\max }\ge {\displaystyle \sum _{i=1}^I{\Omega }_{i,m,t}}{L}_{i,t}$$

(41)

where $L^{\max }$ is the upper limit of base station transmission traffic.

(3)

System Power Constraints

The base station must not be operated at more than its maximum power:

$$P_{m,t}^{BS}\le P_m^{BS\max }$$

(42)

where $P_m^{BS\max }$ is the maximum transmission power of the base station.

(4)

User Participation Constraints

Subsequent control may only be initiated when the user’s fitness level at the next moment is greater than or equal to the minimum user fitness $fi{t}_{\min }$:

$$fi{t}_{i,t+1}\ge fi{t}_{\min }$$

(43)

3.3.3. Model Solving of Base Station Dormancy Control Model

The dormancy control strategy that considers the optimal cost of the communication base station is a multi-objective optimization function, with constraints that are nonlinear. Firstly, the data are normalized, which can facilitate faster data processing by scaling the data and converting the expression to being dimensionless, thereby reducing its discretization. Consequently, the following can be stated:

$$F_{df}^{sig}={\displaystyle \frac{\max F^{sig}-F^{sig}}{\max F^{sig}-\min F^{sig}}}$$

(44)

$$F_{df}^{BSCO}={\displaystyle \frac{F^{BSCO}-\min F^{BSCO}}{\max F^{BSCO}-\min F^{BSCO}}}$$

(45)

where $F_{df}^{sig}$ and $F_{df}^{BSCO}$ are the normalized objective functions of maximizing the transmission signal capacity and minimizing the cost of operation, respectively; $F_{df}^{sig}$ is the negative correlation index; and $F_{df}^{BSCO}$ is the positive correlation index.

The optimal value method is employed to determine the maximum value of the transmitted signal capacity and the minimum value of the cost of operation. Subsequently, a new objective function is constructed, which is the sum of the squares of the differences between the individual objective functions and the optimal solution. The quadratic solution is then applied to the control strategy, and the final solution is obtained by calculating the minimum of the weighted sum of squares of the differences between the individual objective functions and the ideal value.

$$\begin{array}{l}\max F_{df}^{sig},\\ s.t.\left\{(38)~(43)\right\}\end{array}$$

(46)

$$\begin{array}{l}\min F_{df}^{BSCO},\\ s.t.\left\{(38)~(43)\right\}\end{array}$$

(47)

$$\begin{array}{l}\min F^{BSed}=(F_{df}^{sig}-F_{df\max }^{sig}{)}^2+(F_{df}^{BSCO}-F_{df\min }^{BSCO}{)}^2,\\ s.t.\left\{(38)~(43)\right\}\end{array}$$

(48)

where $F^{BSed}$ is the quadratic single-objective function of the base station control strategy, and $F_{df\max }^{sig}$ and $F_{df\min }^{BSCO}$ are the most values of Equations (44) and (45), respectively.

4. Centralized Peaking Control Strategy for Communication Systems

Given the considerable diversity in the operational modes of base stations in the region, the virtual battery is employed to address the objective functions of each scenario independently, adopting the alternating direction multiplier method through the virtual battery energy management center. In order to satisfy the coordinated operation of each scenario, the virtual battery employs the alternating direction multiplier method to solve the objective function of each scenario separately through the virtual battery energy management center. Thereafter, the multiplier is iterated according to the constraints of the overall level in the region, with the objective of minimizing the total cost of the operation of each scenario and optimizing the performance of the peak shifting in the region. Furthermore, this approach ensures the normal operation of the base stations.

4.1. Virtual Battery Peaking Trading Process

The battery pack in the energy storage section has the capacity to absorb energy as a load, thereby increasing the power consumption of the grid during the trough period. It can also release energy to reduce the overall power consumption of the base station, thus balancing the high load of the grid during the peak period. The total dispatch capacity of the battery pack in the energy storage section is considerable and enables a rapid response. Its specific peak shifting strategy is as follows: a real-time update of the minimum reserve capacity of the base station, and on the basis of the minimum reserve capacity of the battery pack, flattening the load curve and lower the operation cost.

As a provisional scheduling component, the temperature control aspect of the virtual battery can not only alter the dimensions of the air conditioning load by regulating the length of the temperature-adjustable interval, but also stagger the temperature adjustment in order to avoid the peak and trough periods of the load curve coinciding with the peak and trough periods of the daily power consumption of the base station. Consequently, the design of the peaking strategy for the temperature control aspect of the virtual battery of the base station is as follows: In the peak period of the power grid, the upper limit of the temperature interval is increased in order to enhance the adjustable potential of the temperature control part. Conversely, in the peak period of the grid, the lower limit of the temperature interval is decreased in order to lower the room temperature as much as possible and store the temperature in advance. In order to reduce the indoor temperature during the grid trough period, it is possible to reduce the lower limit value of the temperature interval as much as possible. This can be completed in advance of the temperature storage process, as shown in Figure 6, which illustrates the virtual battery scheduling process.

4.2. Coordinated Control Model of Virtual Battery under Multiple Scenes in the Region

The virtual battery control strategy for base stations in the study area consists of virtual battery clusters in multiple scenarios, and there is a power and information exchange between different typical scenarios in the area, so the optimization strategy in an area is mainly based on the virtual battery cluster power scheduling plan formulated based on different adjustable potentials in multiple scenarios to achieve the operator’s minimum total operating cost and the efficient use of distributed energy storage. Figure 7 shows the virtual battery cluster control diagram.

4.3. Real-Time Scheduling Model for Virtual Battery Charging and Discharging

4.3.1. Objective Function of Real-Time Scheduling Model

The objective of large-scale virtual battery dispatching is to guide operators to participate in the orderly regulation of the grid through tariffs. This requires that the tariffs satisfy the requirements of operators to reduce operating costs while also complying with the conditions of the grid company to flatten the load curve. Therefore, the optimal economy and the smoothest load curve are taken as the objective functions.

(1)

Economic Optimization

$$\min F^{pri}=\sqrt{{\displaystyle \frac{1}{T}}{{\displaystyle \sum _{t=1}^T\left(P_t^{load}+{\displaystyle \sum _{m=1}^M{P}_{m,t}^{ba}}-{\displaystyle \sum _{m=1}^M\left({\mu }_{m,t}^{re}{P}_{m,t}^{es}+P_{m,t}^{adj}\right)}\right)}}^2}$$

(49)

(2)

Optimized Peak Performance

By regulating the charging and discharging behavior of the virtual battery of the base station in such a way that the base station avoids the peak period of power consumption and staggered power preparation, it is able to optimize the regional demand for electricity. The peaking performance of the base station is reflected by the load variance, with a smaller load variance resulting in a smoother curve and an optimal peaking performance. Therefore, the peak peaking performance of the optimal objective function is:

$$\min F^{per}=C{H}^{pe}+C{H}^{se}+C{H}^{toc}+C{H}^{uic}-I{N}^{ps}$$

(50)

where $C{H}^{pe}$ is the cost of purchasing electricity from the grid company by the base station operator; $C{H}^{se}$ is the maintenance cost of the energy storage part of the virtual battery, which is related to the number and depth of discharges; $C{H}^{toc}$ is the cost of penalizing the indoor temperature excursion of the base station; $C{H}^{uic}$ is the cost of incentivizing the users to reduce the demand for communication; and $I{N}^{ps}$ is the peaking benefit of the energy storage part of the virtual battery of the base station.

$$C{H}^{pe}={\displaystyle \sum _{t=1}^T{C}_t^{BS}{\displaystyle \sum _{m=1}^M(P_{m,t}^{BS}+0.5}}{P}_{m,t}^{es}(1-{\mu }_{m,t}^{re})+P_{m,t}^a)$$

(51)

The cost of power purchased by the operator from the grid company encompasses the expenditure incurred by three principal categories of power-consuming equipment: communication systems, energy storage systems, and temperature control systems.

$$C{H}^{se}=C^{es}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{m=1}^M\left|P_{m,t}^{es}{\mu }_{m,t}^{re}\right|}}$$

(52)

where $C^{es}$ represents the maintenance cost of the battery, which is dependent upon the depth and frequency of its charging and discharging.

$$C{H}^{toc}=C^{pun}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{m=1}^M(T_{m,t}-}}{T}^{\lim })$$

(53)

where $C^{pun}$ represents the penalty cost associated with a deviation in temperature from the optimal temperature, which in turn affects the equipment of the base station and incurs a penalty cost.

$$C{H}^{uic}={\displaystyle \sum _{t=1}^{T}C{H}_t^{exc}}{I}_t$$

(54)

where $I_t$ is the number of users in the region at moment t. The incentive user cost is calculated by applying the incentive coefficients at different moments.

In order to encourage user adaptation, base station operators adjust the network costs for users, thereby creating an incentive for users to reduce the cost of their communication needs.

$$I{N}^{ps}={\displaystyle \sum _{t=1}^T{C}_t^{sell}}{\displaystyle \sum _{m=1}^M{P}_{m,t}^{es}(1-{\mu }_{m,t}^{re})}$$

(55)

where $C_t^{sell}$ is the virtual battery electricity sales tariff and the virtual battery of the base station receives the electricity sales revenue by supplying the reserve excess electricity to the grid.

4.3.2. Constraints of Real-Time Scheduling Model

(1)

Battery Charge State Constraints

$$SO{C}_{m,t}^{\min }\le SO{C}_{m,t}\le SO{C}_{m,t}^{\max }$$

(56)

where $SO{C}_{m,t}^{\min }$ and $SO{C}_{m,t}^{\max }$ are the upper and lower limits of the charging state of the energy storage part of the virtual battery of the base station m at time t, respectively, and the upper and lower limits are determined by the spatio-temporal characteristics of the base station. $SOV{C}_{m,t}^{\min }$ and $SOV{C}_{m,t}^{\max }$ are the upper and lower limits of the charging state of the temperature-controlled part of the virtual battery of base station m at moment t, respectively: $SOV{C}_{m,t}^{\min }=0$, $SOV{C}_{m,t}^{\max }=1$.

(2)

Charge and Discharge Power Constraints

$$\left\{\begin{array}{c}{P}_{m,t}^{char}\le P^{char\max }\\ P_{m,t}^{diss}\le P^{diss\max }\end{array}\right.$$

(57)

$$P^{a\min }\le P_{m,t}^a\le P^{a\max }$$

(58)

where $P^{char\max }$ and $P^{diss\max }$ are the maximum charging power and maximum discharging power, respectively; and $P^{a\max }$ and $P^{a\min }$ are the maximum power and minimum power for air conditioning operation, respectively. The charging and discharging power constraints are only for the virtual batteries participating in the scheduling.

(3)

Virtual Battery State Constraints

$${\mu }_{m,t}^{re}\le {\mu }_{m,t}^{po}$$

(59)

The operational state of the virtual battery must align with the optional operational scheduling scheme, which is calculated based on the previous moment. It must not contradict the optional method.

4.3.3. Model Solving of Real-Time Scheduling Model

The virtual battery peaking problem is a multi-objective optimization solution. The article employs the alternating direction multiplier method to resolve the multi-scenario virtual battery optimization peaking strategy of the base station. The ADMM method represents a significant approach for resolving convex optimization problems with separability. The ADMM method combines the high decomposability of the dyadic ascent method and the strong convergence of the multiplier method, offering a solution that is both fast and effective. The basic approach is to decompose the problem that is solved by alternating iterations, converging the original objective problem with its dyadic variables. The standard form of the ADMM is as follows:

$$\left\{\begin{array}{c}\min F^{pri}(x)+F^{per}(z)\\ s.t.Ax-Bz=c\end{array}\right.$$

(60)

where $F^{pri}(x)$ and $F^{per}(z)$ are two convex functions, respectively, where $x,z,c$ is a function variable.

The solution can be obtained by using the generalized Lagrangian relaxation method:

$$L_{\rho }(x,z,\lambda )=F^{pri}(x)+F^{per}(z)+{\lambda }^{\mathrm{T}}(Ax-Bz-c)+\rho /2{‖Ax-Bz-c‖}_2^2$$

(61)

where $L_{\rho }(x,z,\lambda )$ is the augmented Lagrangian function; $\lambda$ is the dyadic variable; and $\rho$ is the penalty parameter vector. The iterative update by the ADMM method can be obtained as follows:

$$\left\{\begin{array}{c}{x}^{k+1}=\underset{x}{\arg \min }{L}_{\rho }(x,z^k,{\lambda }^k)\\ z^{k+1}=\underset{z}{\arg \min }{L}_{\rho }(x^{k+1},z,{\lambda }^k)\\ {\lambda }^{k+1}={\lambda }^k+\rho (A{x}^{k+1}-B{z}^{k+1}-c)\end{array}\right.$$

(62)

where $k$ is the number of iterations the ADMM method solves for the two objective functions of economic cost and peaking performance by iterating the two objective functions, the $k+1$ iteration of performance is obtained by the $k$ iteration of cost, and similarly, the $k+1$ iteration of cost is obtained by the $k$ iteration of performance.

$$\left\{\begin{array}{c}\kappa =‖x^{k+1}-z^{k+1}‖\\ {\kappa }_x=‖x^{k+1}-x^k‖\\ {\kappa }_z=‖z^{k+1}-z^k‖\end{array}\right.$$

(63)

where $\kappa$, ${\kappa }_x$, and ${\kappa }_z$ are the number of iterations of the equation residuals of Equation (63), respectively, and when the equation residuals reach the set convergence accuracy, the optimal solution can be obtained by convergence through the ADMM method. The upper control center collects the latest values of each variable to update the Lagrange multipliers, and then returns the updated values of the multipliers to each subproblem for the next iteration.

By changing the two terms in Equation (61), we can obtain:

$$\begin{array}{l}({\lambda }^k{)}^{\mathrm{T}}(Ax-B{z}^k-c)+\rho /2\Vert Ax-B{z}^k-c{\Vert }^2=\rho /2\Vert Ax-B{z}^k-c+({\lambda }^k/\rho ){\Vert }^2\\ -{‖{\lambda }^k‖}^2/2\rho \end{array}$$

(64)

The last term of this equation is treated as a constant term in the k + 1th iteration, so it can be ignored. Further rewriting of Equation (62) is as follows:

$$\left\{\begin{array}{c}{x}^{k+1}=\underset{x}{\arg \min }(F^{pri}(x)+\rho /2\Vert Ax-B{z}^k-c+{\mu }^k{\Vert }^2)\\ z^{k+1}=\underset{z}{\arg \min }(F^{per}(z)+\rho /2\Vert A{x}^{k+1}-Bz-c+{\mu }^k{\Vert }^2)\\ {\mu }^{k+1}={\mu }^k+(A{x}^{k+1}-B{z}^{k+1}-c)\end{array}\right.$$

(65)

In the equation, ${\mu }^k={\lambda }^k/\rho$ further converts the computing mode to a parallel computing mode by selecting the average value calculated in the previous iteration for the next iteration. Therefore,

$${\delta }_x^k={\delta }_z^k=(x^k+z^k)/2$$

(66)

By substituting Equation (66) into Equation (65) and further simplifying it, we can obtain:

$$\left\{\begin{array}{c}{x}^{k+1}=\underset{x}{\arg \min }(F^{pri}(x)+\rho /2\Vert Ax-B{\delta }_x^k-c+{\mu }^k{\Vert }^2)\\ {\mu }^{k+1}={\mu }^k+(A{x}^{k+1}-B{\delta }_x^{k+1}-c)\\ z^{k+1}=\underset{z}{\arg \min }(F^{per}(z)+\rho /2\Vert Bz-A{\delta }_x^k-c+{\mu }^k{\Vert }^2\\ {\mu }^{k+1}={\mu }^k+(B{z}^{k+1}-A{\delta }_x^{k+1}-c)\end{array}\right.$$

(67)

When the criterion Equation (68) is fully converged, it is considered that the algorithm converges:

$$\left\{\begin{array}{c}{\kappa }^{k+1}=‖x^{k+1}-z^{k+1}‖\le \xi \\ {\kappa }_x^{k+1}=‖x^{k+1}-x^k‖\le \xi \\ {\kappa }_z^{k+1}=‖z^{k+1}-z^k‖\le \xi \end{array}\right.$$

(68)

where $\xi$ is the convergence threshold of the algorithm. In the subsequent calculation and processing, $\xi =0.001$.

The optimization scheduling process of base station batteries in the region based on the ADMM algorithm proposed in this article is shown in Figure 8.

The overall scheduling process is described as follows:

(1)

The power company, in conjunction with the base station operator, analyzes the past data of base station users and optimizes the initial scheduling plan for base stations in different types of areas.

(2)

Each regional base station shares its minimum backup power demand and rechargeable capacity information through the battery energy management system. The battery energy management system calculates and solves the optimal scheduling plan for each region.

(3)

Each base station forms a battery energy management system for the entire area through different types of battery energy management systems, ensuring that user signals are not affected and meeting the scheduling needs of the power company as much as possible.

5. Simulation Analysis

5.1. Virtual Battery Cluster Scheduling Potential Mining

Calculation Example 1 utilizes the base station business volume of four distinct living areas, each containing 1000 5G base stations, as the original data. It is assumed that all base stations have uniform specifications. Figure 9 illustrates the typical daily load curve and its change in the base station business volume under different scenarios, while

Table 1. Data related to time-of-use tariffs.

Point	The Twelve Two-Hour Divisions of the Day	Electricity Price (yuan/kWh)
Trough (as opposed peaks)	0:00–8:00	0.320
Heights	8:00–12:00	1.102
Level ground	12:00–14:00	0.661
Heights	14:00–18:00	1.102
Level Ground	18:00–21:00	0.661
Trough (as opposed peaks)	21:00–24:00	0.320

presents the time-sharing tariff.

5.1.1. Tapping the Potential of the Virtual Battery Energy Storage Segment

A single base station energy storage system is configured with a set of 48 V/400 A-h energy storage batteries. The initial charge state of the batteries is assumed to obey a normal distribution, assuming that the base station has a uniform specification and its parameters are shown in

Table 2. Parameters of the energy storage system.

Parameters	Numerical Value
Base station full load power	5 kW
Rated capacity of energy storage	38.4 kWh
Energy storage charging (discharging) efficiency	0.95
Energy storage to avoid overcharging SOC cap	0.9
Energy storage to avoid overdischarging SOC Lower limit	0.1
Battery cycle times	10,000
Maximum battery charging power	5 kW
Maximum battery discharge power	5 kW

.

The system is complex due to the dense distribution of communication base stations, which makes it challenging to schedule a single base station. To address this complexity, we generated the minimum power reserve of the four categories of base stations, as shown in Figure 10. This figure presents the data on the energy storage of 1000 base stations and the load rate of different regions of the base stations. The objective was to reduce the complexity of the analysis of the virtual battery. Finally, the probabilistic distance fast reduction method is employed to complete the reduction of scenarios and simplify and categorize the data, thereby reducing the number of 1000 base stations to 10 categories, as shown in Figure 11. The minimum reserve power demand curves of the four categories of areas are then obtained through virtual battery management system aggregation, as shown in Figure 12.

5.1.2. Virtual Battery Temperature Control Section Potential Exploitation

The number of air conditioners is one per base station. The temperature change data for a 24 h period in a specific location are selected as the ambient temperature for all scenes in the region, as illustrated in Figure 13. The parameter settings for the temperature control system are presented in

Table 3. Parameters of temperature control system.

Parameters	Numerical Value
Equivalent thermal resistance	2 °C/kW
Equivalent heat capacity	7 kJ/°C
Upper temperature limit	30 °C
Lower limit of temperature	20 °C
Setting temperature ideal value	25 °C
Air conditioning system factor	0.02 kW/Hz
Air conditioning constant factor	0.3 kW
Coefficient of heat generation	0.5 kW
Conversion efficiency	0.9

.

The adjustable temperature intervals of the four types of zones are obtained by virtual battery management system aggregation after applying the probabilistic distance fast reduction method to the upper and lower temperature limit reductions of 1000 base stations, as shown in Figure 14.

5.1.3. Virtual Battery Scheduling Potential Preliminary Analysis

The periods of time where the potential for virtual battery scheduling is greater than the average value are derived from the example data. These periods correspond to those with the strongest scheduling potential for the four types of scenarios, as shown in

Table 4. Scheduling potential peak hours.

Different Scenarios	Energy Storage Battery Dispatch Higher Potential Time Period	Temperature-Controlled Air-Conditioning Scheduling Higher Potential Time Period
Office area	01:00–07:00 21:00–24:00	09:00–10:00 13:00–17:00 22:00–24:00
Downtown	01:00–07:00 18:00–24:00	10:00–11:00 13:00–24:00
School district	01:00–16:00	01:00–02:00 09:00–19:00 22:00–24:00
Accommodation	01:00–09:00 21:00–24:00	10:00–18:00 22:00–24:00

.

The analysis of Table 4 reveals that the time period overlap range of scheduling potential strong zones in the three types of scenarios in the energy storage battery part, with the exception of the school zone, is considerable, with a concentration in the night and morning time periods. In contrast, the time period of scheduling potential stronger zones in the school zone is the longest. The stronger time periods for heat storage in temperature-controlled air conditioning are relatively decentralized and mirror the energy storage part in that the school zone has the longest time period for strong zones of dispatch potential in all the scenarios. Furthermore, the strong zones of dispatch potential of the two parts have the longest overlap, which is the most suitable for participating in grid auxiliary services.

5.2. Multi-Scenario Hibernation Control Considering Virtual Battery Potential Exploitation

Example 2 sets the area of each scenario area as 2000 m × 2000 m, 30 base stations are evenly distributed, and the coverage of all base stations is 0.104 km². The overall power consumption of BBU $P_{m,t}^{BBU}=290 \mathrm{W}$, the static power of AAU $P^{AAUBS}=640 \mathrm{W}$, the dormant power of base station $P_{m,t}^{SL}=500 \mathrm{W}$, and the power required for the switching state of the base station $P^{CHA}=20 \mathrm{W}$. The user thermal noise and other signal interference coefficients $N_0={10}^{-9} \mathrm{W}$, channel fading coefficients $A_{PL}=37.6$ and $B_{PL}=128.1$, loss fixing parameters $K_{CG}^{BS}=-35 \mathrm{dB}$, loss fixing indices $\delta =2.5$, specified user base station spacing $d_{CG}^{BS}=1 \mathrm{m}$, fixed noise power $P_{no}^{BA}={10}^{-9} \mathrm{W}$, the total number of resources at the base station $Y=30$, channel bandwidth $B=20 \mathrm{MHz}$, the maximum number of users that can be serviced ${\Omega }^{\max }=30$, and the maximum transmission power of the base station $P_m^{BS\max }=5 \mathrm{kW}$. The upper limit of the transmission traffic of the base station $L^{\max }={10}^4\mathrm{Mbps}$ and the minimum user adaptation $fi{t}_{\min }={10}^{-3}$. The user’s traffic demand at moment t is a segmented random value, which is taken at different times of the day in the corresponding interval and does not change with the scenario in which the user is located.

$$L_i\in \left\{\begin{array}{c}[70,80]Mbps,01:00\le t<04:00\\ [50,70]Mbps,04:00\le t<08:00\\ [80,100]Mbps,08:00\le t<24:00\end{array}\right.$$

(69)

Setting the customer network fee incentive factor based on the peak peaking potential data $C{H}_t^{exc}$ is shown in Figure 15.

In order to determine the optimal control strategy for the dormant network, the connection scenario of the office area is analyzed. This is achieved by considering the network fee incentive coefficients and by selecting the 13:00 moment with the highest number of people connected to the base station and the 06:00 moment with the lowest number of people, which is illustrated in Figure 16. Based on this, the comparison of the number of base station operations obtained after sleep control for the four regions is shown in Figure 17, the blue circle in the figure represents the user, and the red circle represents the base station

The application of decentralized dormancy control to base stations in different regions enables the comparison of their economic costs before and after control, as demonstrated in

Table 5. Economic cost analysis before and after control.

Cost Changes before and after Dormancy Control	Office Area	Downtown	School District	Residential Areas
Total cost before control/USD	1299.46	1184.75	1161.6	1189.96
Post-control power purchase cost/USD	1019.94	807.08	681.10	788.02
Post-control maintenance cost/USD	61.56	83.88	78.66	79.56
Post-control user incentive cost/USD	86.62	74.28	97.37	66.26

.

A comparison of Table 5 reveals that following the implementation of the dormant control strategy, the school zone exhibited the lowest total cost and the greatest reduction, whereas the office zone demonstrated the opposite pattern, with the highest total cost and the smallest reduction. The overall comparison of each zone through the dormant strategy indicates a reduction of 10.11% to 26.21%.

5.3. Multi-Scenario Virtual Battery Peak Situation

In Example 3, four scenarios are set up in the region, with a total of 40,000 base stations or 80,000 base stations distributed uniformly in two scales to access the virtual battery management system and participate in the scheduling. The internal parameters of the base stations are the same as those described in Section 4.2.

Figure 18 presents a comparison diagram of the daily load curves of base stations engaged in scheduling operations under different scales. The results indicate that after participating in scheduling, base stations exhibit a notable peak shaving effect during the 09:00–13:00 period and a pronounced valley filling effect during the 01:00–05:00 period. However, in the later period, due to the accelerated overall rise of the load curve, the peak shifting effect is less pronounced than in the early period. Furthermore, the effect of peak shifting is significantly enhanced with an increase in the scale of scheduling participation. The hybrid control strategy for base stations enables the effective utilization of the differing power reserve and temperature regulation resulting from the varying communication loads of base stations. This allows for the full utilization of the virtual battery, the reduction of daily load fluctuations, and the improvement of the stability of the power grid.

Table 6. Economic cost analysis before and after scheduling.

Changes in Economic Costs	40,000 Units in the Region Participating	80,000 Units in the Region Participating
Reduced cost of purchased electricity for operators after dispatch/USD	2,249,818.71	5,170,825.05
Increased maintenance costs for battery storage after dispatch/USD	329,108.88	666,116.79
Temperature bias after control cost of moving penalties/USD	17,612.41	29,060.48
Post-control user incentive cost/USD	89,894.81	180,059.04
Partial peaking of energy storage earnings subsidy/USD	340,950.02	677,119.50

presents a comparative analysis of the economic cost following the participation of base stations in scheduling at different sizes. As the number of base station sizes participating in grid-assisted services increases, the greater the scheduling capacity of the energy storage, and the greater the number of incentivized users, the more effective the reduction of the total operating cost will be.

6. Conclusions

The objective of this paper is to present a hybrid control strategy for communication base stations that considers both the communication load and time-sharing tariffs. The communication system introduces a decentralized BTS dormancy mechanism at the moment of a low network load with the objective of reducing the overall energy consumption of the network. The user adaptation index serves as the foundation for the dormancy mechanism, which is designed to maximize the transmission signal quality and optimize the operator’s economic performance. The decentralized control mechanism enables flexible adjustments to the communication system’s operational state, based on the user connections and incentives associated with the electricity tariff. This approach effectively reduces the BTS energy consumption while maintaining communication quality and minimizing energy consumption. This approach allows for the minimization of energy consumption at the base station without any impairment to the communication quality of the users. The temperature control system and the energy storage system adopt a virtual battery management system to centrally control the idle energy storage. The objective function of each scenario is solved separately by using the alternating direction multiplier method. The multipliers are updated and iterated by comprehensively considering the constraints at the overall level in the region. This ensures that the total cost of the operation of each scenario is minimized, while at the same time optimizing the peak shifting performance in the region. To validate the efficacy of the proposed algorithm, a series of simulation cases have been devised. The outcomes demonstrate that the proposed hybrid control method exhibits the following advantages:

(1) The virtual battery model of the base station is capable of establishing the user’s network fee incentive data based on the historical user data, with the objective of optimizing the communication storage scheduling potential.

(2) The dormancy mechanism of a decentralized communication system establishes incentives for users in different regions to adapt in order to prevent base stations from participating in scheduling to the fullest extent due to the disparities in spatial and temporal characteristics. The results of the calculation show that the overall cost reduction of each region through the sleep strategy is 10.11–26.21%.

(3) The centralized virtual battery management system is applicable to the peak control of base stations in different sizes of regions. This system can ensure the reduction of the total cost of operators and the peak-to-valley difference of the power grid. The calculation results show that optimizing the scheduling of base station energy storage based on the sleep strategy in each region can increase revenue subsidies by 13.62–15.83% of the cost reduction, and the overall load consumption of the entire region is reduced by 3.81–7.60%.

This paper considers the peak control of base station energy storage under multi-region conditions, with the 5G communication base station serving as the research object. Future work will extend the analysis to consider the uncertainty of different types of renewable energy sources’ output. This will enable the energy consumption of the base station to be used as a powerful means of consuming renewable energy sources and reducing the impact on the grid when renewable energy sources are connected to the grid.