Improved Model of Base Station Power System for the Optimal Capacity Planning of Photovoltaic and Energy Storage System

Abstract

The widespread installation of 5G base stations has caused a notable surge in energy consumption, and a situation that conflicts with the aim of attaining carbon neutrality. Numerous studies have affirmed that the incorporation of distributed photovoltaic (PV) and energy storage systems (ESS) is an effective measure to reduce energy consumption from the utility grid. The optimization of PV and ESS setup according to local conditions has a direct impact on the economic and ecological benefits of the base station power system. An improved base station power system model is proposed in this paper, which takes into consideration the behavior of converters. And through this, a multi-faceted assessment criterion that considers both economic and ecological factors is established. Then, the PV and ESS capacity optimization for base stations under multiple scenarios is realized. The case study indicates that the optimization process of PV and ESS is significantly influenced by the behavior of the converter.

1. Introduction

The advantages of “high bandwidth, high capacity, high reliability, and low latency” of the fifth-generation mobile communication technology (5G) have made it a popular choice globally [1,2]. However, the widespread deployment of 5G base stations has led to increased energy consumption. Individual 5G base stations require 3–4 times more power than fourth-generation mobile communication technology (4G) base stations, and their deployment density is 4–5 times that of 4G base stations [3,4]. The above phenomenon not only means a huge increase in the power demand of communication base stations, but also leads to a marked increase in carbon emissions.

Currently, the methods for reducing base station energy demand and overall carbon emissions can be divided into two categories: optimization of base station operating modes [5,6,7,8,9] and distributed photovoltaic access [10,11,12]. The method for optimizing base station operating modes does not require any changes to the system’s original power supply structure. The purpose of energy conservation is achieved by adjusting the operating status of base stations [5,6] and even shutting down some base stations according to actual user needs [7,8,9]. Furthermore, references [13,14] propose the integration of partial backup energy storage in base stations into grid dispatch, resulting in increased economic benefits of base stations and improved stability of the distribution network. However, on one hand, optimization of base station operating modes have limited ability to reduce energy demands. On the other hand, it imposes higher requirements on the controllability and perceptibility of power distribution networks and base stations.

Distributed PV generation offers flexible access and low-cost advantages. Integrating distributed PV with base stations can not only reduce the energy demand of the base station on the power grid and decrease carbon emissions, but also effectively reduce the fluctuation of PV through inherent load and energy storage of the energy storage system. As a result, optimizing the configuration of distributed PV and ESS has received increased attention in recent years [10,11,12]. Essentially, this problem is consistent with the optimization problem of distributed energy access in micro grids [15,16,17,18].

In [10,11,15,16] more accurate PV and ESS models are used, which take into account the aging of PV modules and batteries. In [12], An optimization objective named excess energy generation (EEG) is developed to reduce the surplus renewable energy, which cannot be sold to utility grid in off-grid base stations. Moreover, the planning methods are compared and improved in [15,16,17]. Dynamic programming (DP) and mixed integer linear programming (MILP) are compared [15]. And a chance constrained stochastic optimization method [16] and a reformed electric system cascade analysis (RESCA) method [17] is proposed. The impact of constraints on optimization is studied in [17,18]. In [17], different combinations of final excess energy, energy generation ratio, cost of energy, net present cost (NPC), and renewable energy fraction are used as optimization constraints. In [18], the differences in results under different grid constraints were analyzed. However, the behavior of power electronic converters is overlooked in the aforementioned literatures. Among these works, the losses of the converter are considered only in [12,17], but the efficiency of the converter is described by a fixed value in these papers which differs greatly from the actual situation. Power electronic converters play a crucial role in base station power supply systems, as shown in Figure 1. The efficiency of power converters varies greatly with changes in their operating conditions. Ignoring this variability will have a significant impact on the optimization results of system configuration.

An improved base station power system model is established in this paper. The model not only contains the cost and carbon emissions of the converters, PV, and ESS, but also contains the relationship between the converter efficiency and its operating conditions. On this basis, a comprehensive optimization is carried out considering the life cycle cost(LCC), carbon emissions, initial investment cost, and return on investment of the base station power supply system. Moreover, the established model is compared with a model without the real-time efficiency of the converters. The results show that there are significant differences in the system configuration optimization results under the different models mentioned above. Section 2 describes the model for the base station power supply system. Section 3 introduces the optimization method for the base station PV and ESS. In Section 4, three different base station power supply schemes are analyzed under two different climate conditions. Finally, Section 5 concludes the paper.

2. Model of Base Station Power System

The key equipment in 5G base stations are the baseband unit (BBU) and active antenna unit (AAU), both of which are direct current loads. The power of AAU contributes to roughly 80% of the overall communication system power and is highly dependent on the communication volume [19].

Figure 1a,b present two typical schematic diagrams of PV modules connecting to the power system of base stations via alternating current (AC) and direct current (DC) buses, respectively. In order to calculate the economic and ecological results, it is necessary to pre-determine the topology type of each converter in different power supply structures. Among them, the interleaved parallel Boost PFC is selected as the power factor correction (PFC) rectifier, the full-bridge pulse width modulation (PWM) inverter is selected as the inverter, the Boost converter is selected as the PV converter, the bidirectional Buck/Boost converter is selected as the battery management system (BMS) converter, and the LLC resonant converter is selected as the 400 V to 48 V converter.

2.1. Converter Model

In power converters, losses are mainly generated in switch devices, magnetic devices (inductors, transformers), capacitors, control circuits and printed circuit board (PCB) lines. Most of these losses will vary with changes in operating conditions of the converter. In the power supply system of base stations, converters can be categorized into two groups based on their operating conditions. The first group consists of converters whose input-output voltage remains almost constant, which includes PV inverters, PV DC/DC converters, PFCs, and 400 V to 48 V converters. In these converters, the duty cycle and switching frequency nearly keep constant, with the device voltage stress remaining unchanged, while only the current stress varies. The second group consists of converters that experience a wider range of input-output voltage changes, such as the converters connecting energy storage batteries. In these converters, the duty cycle, device voltage stress, and device current stress all undergo variations.

In the first group of converters, according to the relationship between loss and real-time power of the converter, the loss can be divided into three categories [20,21,22]: (1) constant, such as control circuit and magnetic loss; (2) first-order term, such as switch loss and diode conduction loss; (3) second-order term, such as copper loss of magnetic device, switch conduction loss, capacitor loss and PCB line loss.

The relationship between the converter efficiency $\eta$, the converter operating power P and the converter power loss $P_{\mathrm{loss}}$ is shown in the following equation:

$$\eta =1-\frac{P_{\mathrm{loss}}}{P},$$

(1)

where the loss of the converter $P_{\mathrm{loss}}$ is a quadratic polynomial of P:

$$P_{\mathrm{loss}}=\widehat{a}+\widehat{b}P+\widehat{c}{P}^2,$$

(2)

Therefore, the efficiency can be expressed by simplification as:

$$\eta =1-\frac{\widehat{a}}{P}-\widehat{b}-\widehat{c}P,$$

(3)

In order to make the formula more concise, by making $a=-\widehat{a}$, $b=1-\widehat{b}$, and $c=-\widehat{c}$, Equation (4) can be obtained.

$$\eta =\frac{a}{P}+b+cP,$$

(4)

where $\widehat{a}$, $\widehat{b}$, $\widehat{c}$, $a$, $b$, $c$ are fitting coefficients, which need to be calculated based on the converter parameters.

$$\left\{\begin{array}{l}{\eta }_{100}=\frac{a}{100\%}+b+c\cdot 100\%\\ {\eta }_{50}=\frac{a}{50\%}+b+c\cdot 50\%\\ {\eta }_{10}=\frac{a}{10\%}+b+c\cdot 10\%\end{array}\right.,$$

(5)

In fact, the values of $a$, $b$, and $c$ can be obtained by using the efficiencies at any three different loads. But three typical operating conditions of the converter are usually used for calculation. ${\eta }_{100}$, ${\eta }_{50}$, and ${\eta }_{10}$ represent the efficiency of the converter at 100%, 50%, and 10% load, respectively. By substituting them into Equation (4), the system (5) can be obtained. System (6) is the solution to system (5).

$$\left\{\begin{array}{l}a=(4{\eta }_{100}-9{\eta }_{50}+5{\eta }_{10})/36\\ b=(48{\eta }_{100}-99{\eta }_{50}+15{\eta }_{10})/-36\\ c=(8{\eta }_{100}-9{\eta }_{50}+{\eta }_{10})/3.6\end{array}\right.,$$

(6)

Due to variations in battery voltage, the second group of converters cannot maintain a constant duty cycle and device voltage stress. Taking the converter connecting the 48 V DC bus and the energy storage battery as an example, the voltage change range of the bus is relatively small and can be considered constant, but the battery voltage variation is about 30%, resulting in a duty cycle change of about 20%. Therefore, the switching loss of the MOSFETs, the iron core loss of the inductors, and the loss of the capacitors have changed. Its form is as (7):

$$P_{\mathrm{loss}}=\widehat{d}+\widehat{e}{(1-\frac{48}{V_{\mathrm{bat}}})}^{2.14}+\widehat{f}{V}_{\mathrm{bat}}{I}_{\mathrm{in}}+\widehat{g}{I}_{\mathrm{in}}{}^2+\widehat{h}\frac{I_{\mathrm{in}}{}^2}{V_{\mathrm{bat}}}+\widehat{i}\frac{I_{\mathrm{in}}{}^2}{V_{\mathrm{bat}}{}^2},$$

(7)

where $I_{\mathrm{in}}$ is the input current and $V_{\mathrm{bat}}$ is the battery voltage. The term with coefficient $\widehat{d}$ represents the control circuit losses, the term with coefficient $\widehat{e}$ represents the iron losses of the inductor, the term with coefficient $\widehat{f}$ represents the MOSFET switching losses, the term with coefficient $\widehat{g}$ represents the MOSFET conduction losses and the copper losses of the inductor, and the terms with coefficients $\widehat{h}$ and $\widehat{i}$ represent the output capacitor losses. Since the input voltage remains unchanged, the input current and power are proportional. Substituting the above equation into Equation (1) yields the following result:

$$\eta =\frac{d+e{\left(1-\frac{48}{V_{\mathrm{bat}}}\right)}^{2.14}}{P}+f{V}_{\mathrm{bat}}+(g+\frac{h}{V_{\mathrm{bat}}}+\frac{i}{V_{\mathrm{bat}}{}^2})P,$$

(8)

where d to i are all coefficients whose values are determined by circuit parameters and need to be fitted based on the efficiency under different voltages and loads.

2.2. Battery and PV Model

The voltage of the energy storage battery is primarily determined by its state of charge (SOC), internal resistance, and current [23]. Among them, SOC affects the open circuit voltage of the battery, and internal resistance and current affect the voltage drop during battery charging and discharging. Ignoring the influence of temperature and the state of health (SOH) of the battery, the internal resistance is regarded as a constant value, and the relationship between the open circuit voltage of the energy storage battery and SOC is fitted by a polynomial.

The power output of PV modules is mainly influenced by three factors, namely the intensity of solar radiation, the temperature of the modules, and the photoelectric conversion rate of the PV modules [24]. The expression for this relationship is as follows:

$$P_{\mathrm{pv}}={\eta }_{\mathrm{pv}}{P}_{\mathrm{pvn}}\left(\frac{I_{\mathrm{c}}}{I_{\mathrm{stc}}}\right)\left(1-{\gamma }_{\mathrm{T}}\left(T_{\mathrm{c}}-T_{\mathrm{stc}}\right)\right),$$

(9)

where $P_{\mathrm{pv}}$ is the output power of photovoltaic modules, ${\eta }_{\mathrm{pv}}$ represents the efficiency of PV modules, under good maintenance, the attenuation in the first year is generally large, and the attenuation afterwards is relatively uniform, $P_{\mathrm{pvn}}$ represents the rated power of PV modules, $I_{\mathrm{c}}$ and $I_{\mathrm{stc}}$ respectively represent the current solar irradiance and standard irradiance, ${\gamma }_{\mathrm{T}}$ is the temperature coefficient, $T_{\mathrm{c}}$ and $T_{\mathrm{stc}}$ respectively represent the current PV component temperature and the PV component temperature under standard conditions.

2.3. Economic Model

In terms of economy, the LCC, return on investment and initial investment are used as standards. The calculation of LCC is shown in the following [14]:

$$C_{\mathrm{L}\mathrm{C}}=C_{\mathrm{I}}+C_{\mathrm{O}}+C_{\mathrm{D}},$$

(10)

where $C_{\mathrm{L}\mathrm{C}}$ is the life cycle cost, $C_{\mathrm{I}}$ is the initial investment cost, $C_{\mathrm{O}}$ is the operating cost, and $C_{\mathrm{D}}$ is the disposal cost.

The initial investment cost is the equipment purchase and installation cost in the construction process of the base station power supply system. In order to calculate the net present value cost over the full life cycle, the influence of the discount rate must be considered. The formula is shown in the following [18]:

$$C_{\mathrm{I}}=(C_{\mathrm{I}}^{\mathrm{trans}}+C_{\mathrm{I}}^{\mathrm{pv}}+C_{\mathrm{I}}^{\mathrm{bat}}+C_{\mathrm{I}}^{\mathrm{fixed}})\times \frac{\gamma {(1+\gamma )}^{\mathrm{L}\mathrm{C}}}{{(1+\gamma )}^{\mathrm{L}\mathrm{C}}-1}\times \mathrm{L}\mathrm{C},$$

(11)

where $\gamma$ is the discount rate, LC is the system life cycle, $C_{\mathrm{I}}^{\mathrm{trans}}$, $C_{\mathrm{I}}^{\mathrm{pv}}$, $C_{\mathrm{I}}^{\mathrm{bat}}$, and $C_{\mathrm{I}}^{\mathrm{fixed}}$ respectively represent the converter, PV module, energy storage battery and equipment installation costs. The calculation formula is shown in (12).

$$\left\{\begin{array}{l}{C}_{\mathrm{I}}^{\mathrm{pv}}={\delta }_{\mathrm{PV}}\cdot P_{\mathrm{pvn}}\\ C_{\mathrm{I}}^{\mathrm{trans}}={\displaystyle \sum _{i=1}^n({\delta }_{\mathrm{trans}\_\mathrm{i}}\cdot N_{\mathrm{trans}\_\mathrm{i}})}\\ C_{\mathrm{I}}^{\mathrm{bat}}={\delta }_{\mathrm{bat}}\cdot C_{\mathrm{bat}}\end{array}\right.,$$

(12)

where ${\delta }_{\mathrm{PV}}$ is the unit price of PV modules, $P_{\mathrm{pvn}}$ is the rated power of PV modules; ${\delta }_{\mathrm{trans}\_\mathrm{i}}$ is the unit price of the converter, and $N_{\mathrm{trans}\_\mathrm{i}}$ is the number of this type of converter used; ${\delta }_{\mathrm{bat}}$ is the unit capacity price of energy storage batteries, and $C_{\mathrm{bat}}$ is the installed capacity of energy storage batteries.

The operating cost is composed of the energy cost and maintenance cost. The calculation formula is as (13) [17]:

$$C_{\mathrm{O}}=C_{\mathrm{M}}+C_{\mathrm{E}},$$

(13)

where $C_{\mathrm{M}}$ is the maintenance cost, and $C_{\mathrm{E}}$ is the cost of electricity purchasing from the power grid. The maintenance cost mainly comes from routine maintenance of base station power system and replacement of energy storage batteries that have reached their cycle life. Energy cost is the cost of purchasing electricity from the power grid. The specific expression is (14):

$$\left\{\begin{array}{l}{C}_{\mathrm{E}}={\displaystyle \sum _{i=1}^n\beta \cdot P_{{\mathrm{G}}_{\mathrm{i}}}\cdot t_{\mathrm{i}}}\\ C_{\mathrm{M}}={\displaystyle \sum _{t=1}^{LC}\frac{a_{\mathrm{t}}{C}_{\mathrm{I}}+{\delta }_{\mathrm{bat}}\cdot C_{{\mathrm{bat}}_{\mathrm{t}}}}{{(1+\gamma )}^t}}\end{array}\right.,$$

(14)

where $\beta$ is the unit price of electricity, $P_{{\mathrm{G}}_{\mathrm{i}}}$ is the power purchased from the power grid during this period, $t_{\mathrm{i}}$ is the length of this period, $a_{\mathrm{t}}$ is the maintenance coefficient of year t, and $C_{{\mathrm{bat}}_{\mathrm{t}}}$ is the energy storage battery capacity that needs to be replaced in year t.

The disposal cost is calculated as the multiplication of the recycling prices of the converters, PV modules and energy storage batteries by their respective quantities.

$$C_{\mathrm{D}}={\beta }_{\mathrm{PV}}\cdot P_{\mathrm{pvn}}+{\beta }_{\mathrm{bat}}\cdot C_{\mathrm{bat}}+{\beta }_{\mathrm{t}}\cdot P_{\mathrm{t}},$$

(15)

where ${\beta }_{\mathrm{PV}}$, ${\beta }_{\mathrm{bat}}$ and ${\beta }_{\mathrm{t}}$ respectively represent the disposal price of PV modules, energy storage batteries and converters. $P_{\mathrm{PV}}$, $C_{\mathrm{bat}}$, and $P_{\mathrm{t}}$ respectively represent the installed capacity of PV modules, energy storage batteries and converters.

2.4. Ecological Model

In terms of ecological, the reduction of carbon emissions during the lifecycle of the base station power supply system is used as a standard. The base station power supply system generates carbon emissions through two main sources: installation carbon emissions and operating carbon emissions. Installation carbon emissions are generated during the stages of manufacturing, transportation, abandonment, and disposal of the equipment. And operating carbon emissions stem from the usage of electricity supplied by the grid.

$$Ce=C{e}_{\mathrm{i}}+C{e}_{\mathrm{o}},$$

(16)

where $C{e}_{\mathrm{i}}$ is installation carbon emissions, $C{e}_{\mathrm{o}}$ is operating carbon emissions, and the specific calculation formula is as (17) and (18):

$$C{e}_{\mathrm{i}}={\lambda }_{\mathrm{PV}}\cdot P_{\mathrm{pvn}}+{\lambda }_{\mathrm{bat}}\cdot C_{\mathrm{bat}}+{\lambda }_{\mathrm{t}}\cdot P_{\mathrm{t}},$$

(17)

$$C{e}_{\mathrm{o}}={\lambda }_{\mathrm{grid}}\cdot W_{\mathrm{grid}}$$

(18)

where ${\lambda }_{\mathrm{PV}}$, ${\lambda }_{\mathrm{bat}}$, ${\lambda }_{\mathrm{t}}$, and ${\lambda }_{\mathrm{grid}}$ respectively represent the carbon emission coefficients of PV modules, energy storage batteries, converters and Chinese grid. And $W_{\mathrm{grid}}$ represents the amount of electricity that the base station receives from the power grid during its life cycle. It should be noted that the $C_{\mathrm{bat}}$ is the energy storage battery capacity that needs to be replaced throughout the entire life cycle.

3. Capacity Configuration Optimization

3.1. Objective Function

In the evaluation of the base station power system, the units of economic and ecological results are different. For easy comparison, they will be normalized as (19):

$$\left\{\begin{array}{l}{F}_1=1-{\lambda }_1\frac{C_{\mathrm{L}\mathrm{C}}}{C_{\mathrm{L}\mathrm{C}0}}\\ F_2=1-{\lambda }_2\frac{C_{\mathrm{I}}}{C_{\mathrm{I}0}}\\ F_3={\lambda }_3\frac{C_{\mathrm{L}\mathrm{C}0}-C_{\mathrm{L}\mathrm{C}0}}{C_{\mathrm{I}}-C_{\mathrm{I}0}}\\ F_4=1-{\lambda }_4\frac{Ce}{C{e}_0}\end{array}\right.,$$

(19)

where $F_1$, $F_2$, $F_3$, and $F_4$ represent the dimensionless values of the LCC, initial investment cost, investment return rate, and carbon emissions reduction, respectively. $C_{\mathrm{L}\mathrm{C}0}$ and $C{e}_0$ are the LCC and carbon emissions of the base station without PV and ESS. ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$, and ${\lambda }_4$ are used to adjust the starting scores of the base station without PV and ESS. In this paper, the LCC, return on investment, and carbon reduction score of base stations without PV and ESS are set to 0.6, and the initial investment cost score is set to 1.0.

Therefore, the expression for the objective function can be written in the following form:

$$\max f={\alpha }_1{F}_1+{\alpha }_2{F}_2+{\alpha }_3{F}_3+{\alpha }_4{F}_4,$$

(20)

where ${\alpha }_1$, ${\alpha }_2$, ${\alpha }_3$, and ${\alpha }_4$ are the weighting coefficients for the LCC, initial investment cost, return on investment, and carbon reduction, respectively. These coefficients can be adjusted to change the focus of the evaluation model. In this paper, the weights of ecology and economy are equal, and the weights of the three sub items of economy are also equal. The carbon reduction weighting coefficient is set to 1/2, while the remaining coefficients are set to 1/6.

3.2. Constraint Condition

To ensure the normal operation of the base station, the power of PV, ESS, grid electricity, and the base station should meet the following requirements:

$$P_{5\mathrm{G}}={\eta }_1{P}_{\mathrm{pv}}+{\eta }_2{P}_{\mathrm{bat}}+{\eta }_3{P}_{\mathrm{pfc}},$$

(21)

where ${\eta }_1$, ${\eta }_2$, and ${\eta }_3$ are the transmission efficiencies of the PV, ESS, and grid-side converters. $P_{5\mathrm{G}}$, $P_{\mathrm{pv}}$ and $P_{\mathrm{bat}}$ is the real-time power of the base station equipment, PV module and battery. $P_{\mathrm{pfc}}$ is the real-time power of the PFC converter and also the power obtained from the power grid.

To avoid battery overcharging and over-discharging, and to extend battery life, the battery capacity should meet the following requirements [18]:

$$\left\{\begin{array}{l}SO{C}_{\min }\le SOC\le SO{C}_{\max }\\ SOC=SOC\pm \frac{P_{\mathrm{bat}} \times t \times {\eta }_{\mathrm{bat}}}{C_{\mathrm{bat}}}\end{array}\right.,$$

(22)

where t is the charging or discharging time, ${\eta }_{\mathrm{bat}}$ is the battery charging efficiency and $C_{\mathrm{bat}}$ is the capacity of the battery.

3.3. Power Output Strategy

The optimization results of PV capacity and ESS capacity are heavily influenced by the power output strategy. The specific power scheduling process is as follows: Firstly, the output of PV is compared to the base station load, followed by a comparison of the SOC of the battery at that time. If the PV power exceeds the base station load, priority is given to charging the energy storage battery. However, if the energy storage battery cannot fully absorb the excess generated power, the output of the PV generation will be decreased. When the generated PV power is less than the base station load, priority is given to discharging the energy storage battery. In cases where the energy storage battery cannot meet the power demand, additional electricity will be purchased from the grid to make up for the shortfall.

3.4. Solution Algorithm

The optimization problem is solved using the traversal algorithm, with the search range covering the area where $C_{\mathrm{L}\mathrm{C}}$ is less than $C_{\mathrm{L}\mathrm{C}0}$. However, this range cannot be determined beforehand, so dynamic adjustment is required during the solving process. Based on the changing characteristics of LCC, the solution method shown in Figure 2 is obtained. Firstly, calculate the LCC without PV and ESS as the condition of loop end. Then, increase the battery capacity in steps from 0 until $C_{\mathrm{L}\mathrm{C}}>C_{\mathrm{L}\mathrm{C}0}$, and record the maximum battery capacity $C_{\mathrm{bat}-\max }$. Then, increase the installed PV power and repeat the above steps, but adjust the end condition to $C_{\mathrm{L}\mathrm{C}}>C_{\mathrm{L}\mathrm{C}0}$ and $C_{\mathrm{bat}}>C_{\mathrm{bat}-\max }$. Finally, when the installed PV capacity reaches a value where $C_{\mathrm{L}\mathrm{C}}$ is greater than $C_{\mathrm{L}\mathrm{C}0}$ regardless of the battery capacity, the loop is terminated and the optimal configuration in the record is output. The scanning path is shown in the lower left corner of Figure 2. The area enclosed by the red line is the calculated range. The green shaded area is the range where $C_{\mathrm{L}\mathrm{C}}$ is less than $C_{\mathrm{L}\mathrm{C}0}$, which is the range where the optimal solution may exist. The black arrow represents the direction of scanning.

4. Case Study

Using climate data from Guangxi and Xinjiang, China, and real load data collected from a certain base station, an analysis was conducted with the relevant parameters shown in

Table 1. Case parameters.

Parameters	Value
electricity price (USD)	0.094
battery price (USD/kWh)	126.57
PV module price (USD/kW)	309.39
battery carbon emission coefficients (kg/kWh)	91.21
PV module carbon emission coefficients (kg/kW)	2522.7
grid carbon emission coefficients (kg/kWh)	0.81129
maximum power point voltage of PV module (V)	38
first-year power degradation of PV module	2%
Annual power degradation of PV modules	0.55%

. Optimization of PV and ESS was carried out for three schemes:

Scheme 1: The classic scheme in which the base stations are only powered by grid electricity.

Scheme 2: The PV modules are connected in series to obtain higher voltage and are connected to the AC bus of the base station through an inverter with MPPT function. ESS is connected to the 48 V DC bus through bidirectional DC/DC converter.

Scheme 3: The PV modules are connected to the 48 V DC bus through a Boost converter with MPPT function, and ESS is also connected to the 48 V DC bus through the bidirectional DC/DC converter.

Except Scheme 1, the PV and ESS access capacity need to be optimized for the other two schemes. Considering the service life of PV modules, the optimization period is set to 15 years. To ensure power supply after a power outage, the ESS needs to have a minimum capacity of 6 kWh, and this part of ESS does not participate in output scheduling to ensure sufficient power. The optimization results and specific analysis are shown in Table 1.

4.1. Economic Results

Taking Scheme 1 and Scheme 2 under Xinjiang climate conditions as an example, Figure 3 illustrates the impact of different power converter models on the estimation of LCC. Figure 3a presents the result obtained by using the dynamic power converter model proposed in this paper. Figure 3b–d represent the results obtained by assuming the power converter efficiency at 100%, 95% and 90%, respectively, wherein the flat section indicates the LCC using the Scheme 1, while the curved sections reflect the LCC using the Scheme 2.

Table 2. Optimal LCC Under Different Converter Model.

Scheme	Converter Model	Lifecycle Cost (USD)	PV (kW)	ESS (kWh)
Scheme 1	Dynamic	77,900	-	-
Scheme 1	η = 100	74,410	-	-
Scheme 1	η = 95	77,580	-	-
Scheme 1	η = 90	81,110	-	-
Scheme 2	Dynamic	61,210	20	23
Scheme 2	η = 100	55,650	23	59
Scheme 2	η = 95	59,120	22.5	42
Scheme 2	η = 90	62,630	21.5	22

displays the minimum LCC and the optimal PV and ESS configuration for different converter models.

In the absence of PV and ESS, the use of the dynamic efficiency converter model and the 95% fixed efficiency model for LCC calculations yields quite approximate results. However, when calculating the LCC of Scheme 2, which includes PV and ESS, the results obtained through the dynamic efficiency converter model are closer to those obtained using the 90% fixed efficiency model. This indicates that the efficiency of the converters may even be lower than the 90%, primarily due to the fact that the converters frequently operate under unfavorable conditions when PV and ESS incorporated. This indicates that the fixed efficiency converter model cannot adapt to various different operating conditions. Therefore, the dynamic efficiency converter model was used to calculate the LCC of base station power supply systems under two different climatic conditions. The results are shown in

Table 3. Optimal LCC Under Different Climate.

Scheme	Climate	Lifecycle Cost (USD)	PV (kW)	ESS (kWh)
Scheme 1	Guangxi	77,900	-	-
Scheme 2	Guangxi	64,910	24	23
Scheme 3	Guangxi	60,150	32.5	78
Scheme 1	Xinjiang	77,900	-	-
Scheme 2	Xinjiang	61,210	20	23
Scheme 3	Xinjiang	55,860	28.5	79

.

Xinjiang has a more abundant solar resource, as well as more significant variations in the length of day and night. Therefore, considering the LCC, the required PV installation capacity is lower, while the proportion of ESS installation is higher. Furthermore, increasing ESS and PV can generate higher income in Xinjiang than in Guangxi province.

In addition to the LCC, initial investment and return on investment are also issues that operators must consider. The increase in investment from adding PV and ESS capacity is linear, while the decrease in LCC is clearly nonlinear. Taking Scheme 2 under Guangxi climate conditions as an example, its return on investment is shown in Figure 4. Profit can only be obtained when the return on investment exceeds 1. When the installed PV capacity is less than the base station’s daily load, the return on investment of PVs remains relatively stable, but it gradually decreases as the installed PV capacity increases. The return on investment of adding ESS is consistently lower than that of PVs, but its trend is different. When the installed PV capacity is low, the return on investment of ESS is very low or even negative, whereas it is slightly higher when the installed PV capacity is high.

4.2. Ecological Results

The overall ecological results are shown in Figure 5. And the maximum carbon reduction under different schemes is shown in

Table 4. Maximum Carbon Reduction under Different Climate.

Scheme	Climate	Lifecycle Cost (USD)	PV (kW)	ESS (kWh)
Scheme 2	Guangxi	160.8	47.5	88
Scheme 3	Guangxi	179.6	43	71
Scheme 2	Xinjiang	205.8	44.5	83
Scheme 3	Xinjiang	221.4	39.5	71

. While the carbon reduction trend of Scheme 2 and Scheme 3 is essentially similar, the latter has a greater overall carbon reduction effect. This is because of the higher overall efficiency of Scheme 3, which enables it to achieve higher carbon reduction with fewer installations of PV and ESS. Disregarding converter losses, the optimal results for Guangxi’s climate conditions are 42 kW of installed capacity for PV and 105 kWh of ESS. In Xinjiang’s climate conditions, the optimal results are 40 kW of installed capacity for PV and 71 kWh of ESS. There is a significant difference between these results and the results that consider the converter efficiency.

4.3. Comprehensive Optimization Results

The four graphs on the left-hand side of Figure 6 compares the optimization results under different optimization objectives. The gray line represents the scheme without PV and ESS, which is currently the most widely used scheme. Its greatest advantage is that the initial investment is very low, but its economic and ecological performance is the worst among all schemes. The purple line represents the optimization result that pursues the highest return on investment. Although the return on investment is high, the actual installed capacity of PVs and ESS is very small, which has little actual effect on the LCC and carbon emission reduction. The results of pursuing the lowest LCC and the lowest carbon emissions are similar. LCC and carbon emissions are closely related to energy consumption within the lifecycle so there is a strong coupling relationship between them. The challenge with these schemes is that the initial investment is relatively high, which will create significant pressure on cash flow, and the overall return on investment is not ideal. The results of comprehensive optimization consider these problems and obtain the lowest possible carbon emissions and LCC while controlling the initial investment and maintaining a high return on investment.

The specific data are as follows: the Scheme 1, which serves as a benchmark and has a comprehensive score of 0.667 under any circumstances. Under the climate conditions in Guangxi, the Scheme 2 the highest comprehensive score of 0.782 when the ESS capacity is 7 kWh and the PV access capacity is 14.5 kWh. At this point, the LCC score reaches 96.9% of the optimum cost optimization result, the carbon emission reduction score reaches 86.5% of the maximum carbon emission reduction optimization result, and the return on investment score reaches 93.6% of the maximum investment return optimization result. The Scheme 3 had the highest comprehensive score of 0.805 when the ESS capacity is 24 kWh and the PV access capacity is 20.5 kW. At this point, the LCC score reaches 97.1% of the optimum cost optimization result, the carbon emission reduction score reaches 90.6% of the maximum carbon emission reduction optimization result, and the return on investment score reaches 83.9% of the maximum investment return optimization result.

Under the climate conditions in Xinjiang, the Scheme 2 had the highest comprehensive score of 0.824 when the ESS capacity is 18 kWh and the PV access capacity is 19.5 kWh. At this point, the LCC score reaches 99.8% of the optimum cost optimization result, the carbon emission reduction score reaches 89.2% of the maximum carbon emission reduction optimization result, and the return on investment score reaches 82.2% of the maximum investment return optimization result. The Scheme 3 had the highest comprehensive score of 0.847 when the ESS capacity is 15 kWh and the PV access capacity is 17 kW. At this point, the LCC score reaches 94.6% of the optimum cost optimization result, the carbon emission reduction score reaches 87.3% of the maximum carbon emission reduction optimization result, and the return on investment score reaches 84.9% of the maximum investment return optimization result.

The two graphs on the right-hand side of Figure 6 show a comparison between the optimum DC access scheme and optimum AC access scheme, under climate conditions in Xinjiang and Guangxi. It can be observed that the DC access scheme has advantages over the AC access scheme in comprehensive score, and both AC and DC access schemes are significantly better than the scheme without PV and ESS.

5. Conclusions

The influence of converter behavior in base station power supply systems is considered from economic and ecological perspectives in this paper, and an optimal capacity planning of PV and ESS is established. Comparative analyses were conducted for three different PV access schemes and two different climate conditions. The main conclusions are as follows:

• The loss of power converters significantly affects the optimization of base station PV and ESS. Calculating with a fixed efficiency cannot accurately reflect the actual situation.
• The proposed evaluation method achieves a balance in LCC, initial investment, return on investment, and carbon emissions.
• From the perspective of LCC and carbon emissions, base stations with lower annual irradiance levels can install more PV. However, when considering the return on investment, the opposite is true.