On BESS Capacity Optimization of Hybrid Coal-Fired Generator and BESS Power Station for Secondary Frequency Regulation

Integrating battery energy storage systems (BESS) into a coal-fired generator can enhance power systems’ secondary frequency regulation capability. To this end, this paper proposes a policy to coordinate the BESS and the coal-fired generator to meet the automatic generation control (AGC) requirements and subsequently investigates the optimal BESS capacity to maximize the net profit gained from the frequency regulation. Firstly, probability characteristics of AGC instruction duration period, interval period, regulation rate, and regulation direction are investigated according to the real AGC datalog. The AGC regulation direction would change randomly. Directly switching the BESS between charging and discharging to match the requirement would significantly deplete the lifetime of the battery. Therefore, this paper divides the BESS into two groups, which will be controlled stay in charging and discharging states to respectively respond to the AGC requirement of “up” and “down”. To obtain a cost-effective BESS investment, this paper develops a new sizing method, which optimizes the BESS capacity by simulating the operation of the hybrid coal-fired generator and BESS power station (HCGBPS) over an example day. Finally, the case studies justified the developed sizing method could make satisfying BESS investment decisions to ensure a maximum net profit in operation.

SECTION I. Introduction

Renewable energy, such as solar and wind power, has dominated the alternative options to replace fossil fuels in power systems around the world over the last decades [1], [2]. By the end of 2022, the installed capacity of wind and photovoltaic power in China has reached 365 GW and 392 GW, respectively, ranking first in the world. Apart from clean energy, renewable generation also brings new characteristics compared to traditional power generators: 1) the output of renewable generation is stochastic and uncertain, and 2) the majority of renewable generation is connected to power systems through power electronic interfaces [3]. These characteristics challenge the frequency regulation of power systems, thus threatening frequency security [4], [5].

In power systems, frequency regulation has three levels, e.g., primary, secondary, and tertiary regulation [6]. This paper mainly focuses on secondary frequency regulation. In the secondary frequency regulation, some generators would adjust their output power to match the requirements of controlling both system frequency and the exchange power of tie-line [7], [8]. Load frequency control is another technical measure to regulate the frequency regulation of power systems [9].

At present, coal-fired generators account for the majority of secondary frequency regulation use in China. In operation, the frequency-regulating generators are coordinated by responding to automatic generation control (AGC) instructions issued by system operators. Considering the random and uncertain output from renewable generation, AGC instructions would become more volatile. Under such a situation, the relatively low ramp rate and long response time of the coal-fired generators increase the difficulties of regulation. Also, frequent action of frequency-regulating generators can accelerate mechanical wear, thus depleting the lifetime and increasing maintenance costs for frequency-regulating generators [10], [11], [12].

Recently, the development of electrochemical energy storage technology and corresponding integration technology creates a potential opportunity for relieving the pressure of frequency regulation in power systems resulting from the large-scale integration of renewable energy [13], [14], [15]. On the technical side of providing secondary frequency response, battery energy storage systems (BESS) perform outweigh other solutions in terms of 1) fast and accurate switching between charging and discharging states; and 2) having great instantaneous throughput [16], [17], [18], [19]. In 2011, the National Wind-Solar-Energy Storage-Transmission Pilot Project was completed and put into operation in Zhangjiakou, Hebei Province, China. In the operation, the extremely fast and accurate response ability of BESS verifies BESS is an alternative solution to improve the performance of secondary frequency response for coal-fired generators [20], [21]. Further, with 2 MW BESS deployed in Shijingshan Thermal Power Plant, Beijing, generators performed better in responding to the AGC instructions, thus improving the performance of secondary frequency regulation [22].

BESS can participate in secondary frequency regulation of power systems by two means. The first is acting as an independent subject to relieve secondary frequency regulation pressures of coal-fired generators [23], [24], [25], [26], and the second is operating cooperatively with the coal-fired generators to enhance performances on secondary frequency regulation [27], [28]. At present, a lot of literature focused on how to operate the BESS as an independent subject to respond to the AGC instructions, however, relatively little literature investigated how to coordinate the BESS and the coal-fired generator to respond to the AGC instructions more effectively.

Reference [23] developed a control strategy to enhance the capability of BESS for quickly responding to AGC instructions according to area control error (ACE) signal distribution. Reference [24] developed a method to evaluate the effectiveness of frequency regulation service provided by the BESS in a single-area system. The technical study justifies that BESS is more effective than coal-fired generators in providing frequency regulation service. Reference [25] developed a control strategy of the BESS to improve the short-term dynamic AGC regulation performance. In this reference, the regulation response quality is valuated with the help of power response tolerance margins. Accurately following the AGC instructions leads to more frequent switching between charging and discharging states, which may shorten battery life. In this context, [26] established an online operation policy in response to the instructions considering battery health. References [27] and [28] integrated a battery/flywheel hybrid energy storage system (HESS) into coal-fired generators to help in responding to AGC instructions. Reference [27] developed a stochastic predictive model to optimize charging/discharging power distribution between the battery and the flywheel, which outperformed conventional approaches and provided AGC performance improvement for coal-fired generators. Reference [28] developed a bi-layer optimization to optimize the HESS size considering both the technical and economical performances of the HESS in responding to secondary frequency regulation.

Large-scale integration of volatile renewable energy will cause significant stochastic fluctuation of frequency in power systems [29], [30]. In this situation, the AGC instructions issued by system operators tend to be significantly random. Taking the uncertain nature of the AGC instruction into consideration is necessary when controlling the BESS as an AGC participant [31]. However, many research works, such as those reported in [23], [24], [25], [26], [27], and [28] developed effective operational strategies of the energy storage systems, but did not fully consider the stochastic nature of the AGC instructions. Reference [32] utilized a linear regression model and an autoregressive-moving-average (ARMA) model to predict the hourly AGC energy. Reference [33] employed the Markov process to model the random AGC instruction propagation with an hourly resolution. Reference [34] developed a data-driven method to model the evolving AGC energy hour by hour. The models presented in [32], [33], and [34] aim to describe the hourly energy exchange required by the AGC instructions but are all discrete random process models. Reference [35] developed a continuous random process model based on stochastic differential equations (SDEs), which can jointly consider the probability distribution and the temporal correlations of the AGC instructions.

On this basis, this paper integrates the BESS with coal-fired generators, intending to create a hybrid coal-fired generator and BESS power station (HCGBPS). Coordinated control of the BESS and the coal-fired generator is a very important work, because it can improve the response-ability of the HCGBPS to secondary frequency regulation with the lowest cost. To achieve this goal, this paper investigates the probability characteristics of the AGC instructions from aspects of the duration period (DP), the interval period (IP), the regulation rate (RR) and the regulation direction (RD) based on the field data firstly. Secondly, to mitigate lifecycle depletion for chemical batteries [36], [37], the BESS is divided into two groups of equal capacity. These two groups will respond up and down AGC instructions, respectively, to reduce the frequency of switching between the charging and discharging states of the BESS. Then, this paper optimizes the BESS capacity by taking the sequential Monte Carlo simulation (SMCS) method to simulate the operation of the HCGBPS over an example day. Finally, the case studies justified that the developed method could make an optimal BESS investment decision, i.e., achieving a maximal net profit in participating in secondary frequency regulation resulting from deploying the BESS in coal-fired generators.

The original contributions are presented as follows:

1. Based on the field data, this paper develops four probability models, which are different from those presented in [32], [33], [34], and [35]. These four probability models describe the probability characteristics of the AGC instructions respectively from aspects of the DP, the IP, the RR, and the RD, which establishes an important foundation to design the operating policy of the HCGBPS.

2. This paper develops a topology of the HCGBPS. The BESS is divided into two groups for reducing the frequency of switching between charging and discharging states of the BESS, thus mitigating the lifecycle depletion of the BESS.

3. This paper develops a policy to coordinate the BESS and the coal-fired generator to meet the AGC requirements more effectively, and subsequently presents a new sizing method of the BESS to cost-effectively provide high-quality secondary frequency response for coal-fired generators.

The rest of this paper is organized as follows. Section II presents the probability analysis for the AGC instructions. Section III describes the AGC response strategy in real-time. Section IV sizes the BESS in the HCGBPS to achieve both cost-effective BESS investment and high-quality frequency response. Section V presents the case studies. Section VI gives the conclusion.

SECTION II. Probability Characteristics Analysis for AGC Instructions

To ensure the frequency quality of power systems under the scenario of high renewable penetration, this section investigates the probability characteristics of the AGC instructions from aspects of the DP, the IP, the RR, and the RD. The analyses are executed based on the AGC instructions received by a coal-fired generator in southeast China throughout the December in 2019. The DP, the IP, the RR, and the RD of the collected AGC instructions are discrete. For discrete data, a logarithmic likelihood value is usually utilized to describe the fitting effect of different distributions. The larger the logarithmic likelihood value, the better the fitting effect of the distribution.

A. Probability Characteristics of AGC Instruction Duration Period

The data present that the DP within the AGC instruction is stochastic. The time is between 5 seconds and 100 seconds. By applying the distribution fitting toolbox in MATLAB, Rayleigh distribution can appropriately fit the stochastic characteristics of the DP because corresponding logarithmic likelihood value is larger than that of other distributions, as shown in Fig. 1.

FIGURE 1.

Probability characteristics of the DP within AGC instruction.

The probability density function (PDF) given in Fig. 1 can be expressed as

$$\begin{equation*} {f(T_{\textrm {c}})=\frac {T_{\textrm {c}}}{b^{2}}e^{-\frac {T_{\textrm {c}} ^{2}}{2b^{2}}}} {T_{\textrm {c}} \gt 0} \tag {1}\end{equation*}$$ where, $T_{\mathrm {c}}$ is the AGC instruction DP, and b is a Rayleigh distribution parameter.

B. Probability Characteristics of AGC Instruction Interval Period

The IP is the time between two AGC instruction calls. The data present that the IP of the AGC instruction is between 0 seconds and 60 seconds. For coal-fired generators, the IP could be 0, because the system operators might issue two or more AGC instructions continuously.

By applying the distribution fitting toolbox in MATLAB, the Versatile distribution [38] can appropriately fit the stochastic characteristics of the non-zero IP of AGC instructions because corresponding logarithmic likelihood value is larger than that of other distributions, as illustrated in Fig. 2.

FIGURE 2.

Probability characteristics of AGC instruction non-zero IP.

In this case, the probability characteristics of non-zero and zero IP are fitted separately. A piecewise function is used to formulate the PDF of the IP.

$$\begin{align*} f(T_{\textrm {j}})=\begin{cases} \displaystyle q & {T_{\textrm {j}} =0} \\ \displaystyle {\frac {\alpha \beta \exp \left [{{-\alpha \left ({{T_{\textrm {j}} -\gamma }}\right)}}\right ]}{\left \{{{1+\exp \left [{{-\alpha \left ({{T_{\textrm {j}} -\gamma }}\right)}}\right ]}}\right \}^{\beta +1}}} & {T_{\textrm {j}} \gt 0} \end{cases} \tag {2}\end{align*}$$ where, $T_{\mathrm {j}}$ is the AGC instruction IP; q is a probability that the AGC instruction IP equals to 0 seconds; $\alpha$ , $\beta$ , and $\gamma$ are all Versatile distribution parameters.

C. Probability Characteristics of AGC Instruction Regulation Rate

The RR represents the required speed that the regulating generator should follow to adjust its output power. This value is obtained by dividing the AGC regulation quantity by the DP. The AGC regulation quantity equals the absolute value of deviation between the pre-regulating output power and the target output power of the received AGC instruction. The data present the majority of the RR received by coal-fired generators is between 0 MW/s and 1 MW/s. By applying the distribution fitting toolbox in MATLAB, the logarithmic normal distribution can appropriately fit the stochastic characteristics of the IP because the corresponding logarithmic likelihood value is larger than that of other distributions, as illustrated in Fig. 3.

FIGURE 3.

Probability characteristics of the AGC instruction RR.

The PDF given in Fig. 3 can be expressed as

$$\begin{equation*} f(v)=\frac {1}{v\sqrt {2\pi } \sigma }\exp \left [{{-\frac {1}{2\sigma ^{2}}(\ln v-\mu)^{2}}}\right ] v\gt 0 \tag {3}\end{equation*}$$ where, v is the AGC instruction RR, $\mu$ and $\sigma$ are logarithmic distribution parameters.

D. Probability Characteristics of AGC Instruction Regulation Direction

In secondary frequency regulation, if an AGC instruction gives an order of increasing output power for regulating generators, this is called an up AGC instruction, otherwise, it is called a down AGC instruction. The data present that the coal-fired generator has received a total of 12451 AGC instructions throughout December 2019, of which 6224 are up instructions and 6227 are down instructions, accounting for 49.99% and 50.01%, respectively. It can be seen from the statistics that the AGC instruction RD follows a 0–1 distribution. And the probability of up and down instruction is roughly equal. The PDF of the AGC instruction RD is given by:

$$\begin{equation*} P(x_{\textrm {AGC}} =d)=p^{d}\left ({{1-p}}\right)^{1-d},d=0,1 \tag {4}\end{equation*}$$ where, $x_{\mathrm {AGC}}$ is a stochastic variable representing the AGC instruction RD, with two values of “0” and “1”, where “1” indicates up AGC instruction, while “0” indicates down AGC instruction. p is the probability of up AGC instruction, $p=1$ /2.

SECTION III. Topology and Secondary Frequency Regulation Strategy of the Hybrid Coal-Fired Generator and BESS Power Station

In secondary frequency regulation, it is difficult for the coal-fired generator to fully track the AGC instructions because of the inherent long response time and slow ramp rate. This section presents the design and operation strategy for coordinating the BESS and coal-fired generator, to provide high-quality secondary frequency response.

A. Topology of the Hybrid Coal-Fired Generator and BESS Power Station

Theoretically, if the HCGBPS receives an up AGC instruction, the BESS will inject power into power systems, and vice versa. Section II presents that AGC instruction RD is stochastic. An up or down AGC instruction could be issued at the same probability. In this situation, the BESS will frequently switch between charging and discharging states to participate in secondary frequency regulation, thus degrading the battery cycle life rapidly [36], [37]. To address this problem, the BESS is divided into two groups with equal capacity, as illustrated in Fig. 4. The two groups are respectively named BESS I and BESS II.

FIGURE 4.

Topology of the hybrid coal-fired generator and BESS power station.

In Fig. 4, $P_{\mathrm {g,t}}$ is the output power of a coal-fired generator at time t. $P_{\textrm {b},t}^{\textrm {I}}$ and $P_{\textrm {b},t}^{\textrm {II}}$ are the charging/discharging power of BESS I and BESS II at time t, respectively, where positive values represent that the BESS is discharging, and vice versa; $P_{\textrm {d},t}$ is a sum of charging/discharging power of BESS I and BESS II at time t; $P_{\textrm {d},t}$ is the output power of the HCGBPS at time t, as given by:

$$\begin{equation*} P_{\textrm {d},t} =P_{\textrm {g},t} +P_{\textrm {b},t} =P_{\textrm {g},t} +P_{\textrm {b},t}^{\textrm {I}} +P_{\textrm {b},t}^{\textrm {II}} \tag {5}\end{equation*}$$ In operation, these two groups of batteries illustrated in Fig. 4 are always in different states. So, they can respond to the up and down AGC instructions, respectively, thus avoiding frequent charging/discharging state switching and significantly reduce the cycle life loss of the BESS. To prevent over-charge or over-discharge of batteries, the working state of any group of batteries should be switched immediately when it reaches the maximum or minimal SOC. To ensure the two groups of the BESS are always in different states, the other group of the BESS should be switched synchronously, as shown in Fig. 5.

FIGURE 5.

The timing sequence of the charging/discharging state of the BESS.

Fig. 5 illustrates the timing sequence of the charging/discharging state of the BESS, in which $t_{0}$ is a moment that the working states of the two groups switch. At $t_{0}$ , BESS I is fully discharged and subsequently switched to the charging state. Although BESS II does not reach the maximum SOC, it also synchronously switches to the discharging state to ensure that the two groups of BESS stay in different states.

B. Cooperative Operation Strategy of the Coal-Fired-Generators and BESS

The response of the coal-fired generator is illustrated in Fig. 6 when receiving a up AGC instruction. In contrast, the response of the coal-fired generator is illustrated in Fig. 7 when receiving a down AGC instruction.

FIGURE 6.

The response of the coal-fired generator to up AGC instruction.

FIGURE 7.

The response of the coal-fired generator to down AGC instruction.

In Fig. 6 and Fig. 7, i is an index of the AGC instruction; $T_{\mathrm {s,}i}$ and $T_{\mathrm {e,}i}$ are the starting time and ending time of $i^{\mathrm {th}}$ AGC instruction, respectively; $P_{\textrm {g},i}^{0}$ is the output power of the coal-fired generators when $i^{\mathrm {th}}$ AGC instruction is issued; $P_{\mathrm {AGC,}i}$ is a desired output power of $i^{\mathrm {th}}$ AGC instruction. When $i^{\mathrm {th}}$ AGC instruction is an up order, $P_{\mathrm {AGC,}i}$ is larger than $P_{\textrm {g},i}^{0}$ , as illustrated in Fig. 6. In this situation, the coal-fired generator increases the output power with a maximum ramp-up rate $v_{\mathrm {up}}$ immediately as a response. Otherwise, $P_{\mathrm {AGC,}i}$ is less than $P_{\textrm {g},i}^{0}$ , and the coal-fired generator reduces output power with a maximum ramp-down rate $v_{\mathrm {down}}$ immediately in response to the down AGC instruction.

The response of the coal-fired generator can be divided into the following three cases:

Case I: the coal-fired generator can match the target output power of $i^{\mathrm {th}}$ AGC instruction within the duration period. Thus, the output power of the coal-fired generator before receiving the next AGC instruction (that is, ($i+1$ )^th AGC instruction) is given by:

$$\begin{align*} P_{\textrm {g},t} & =\begin{cases} \displaystyle {P_{\textrm {g},i}^{0} +v_{\textrm {up}} (t-T_{\textrm {s},i})} & {T_{\textrm {s},i} \le t\lt T_{1.i}} \\ \displaystyle {P_{\textrm {AGC},i}} & {T_{1.i} \le t\le T_{\textrm {s},i+1}} \end{cases} \tag {6}\\ P_{\textrm {g},t} & =\begin{cases} \displaystyle {P_{\textrm {g},i}^{0} -v_{\textrm {down}} (t-T_{\textrm {s},i})} & {T_{\textrm {s},i} \le t\lt T_{1.i}} \\ \displaystyle {P_{\textrm {AGC},i}} & {T_{1.i} \le t\le T_{\textrm {s},i+1}} \end{cases} \tag {7}\end{align*}$$ where, $T_{\mathrm {s,}i+1}$ is a starting time of ($i+1$ )^th AGC instruction; $T_{\mathrm {1,}i}$ is a time when the coal-fired generator tracks the target output power of $i^{\mathrm {th}}$ AGC instruction within the duration period of $i^{\mathrm {th}}$ AGC instruction. If $i^{\mathrm {th}}$ AGC instruction is an up order, the the coal-fired generator will adjust output power as (6), otherwise, it will adjust output power as (7).

Case II: The coal-fired generator cannot match the target output power of $i^{\mathrm {th}}$ AGC instruction within the duration period, but can achieve that before receiving the next AGC instruction. The output power of the coal-fired generator before the next AGC instruction is given by:

$$\begin{align*} P_{\textrm {g},t} & =\begin{cases} \displaystyle {P_{\textrm {g},i}^{0} +v_{\textrm {up}} (t-T_{\textrm {s},i})} & {T_{\textrm {s},i} \le t\lt T_{2.i}} \\ \displaystyle {P_{\textrm {AGC},i}} & {T_{2.i} \le t\le T_{\textrm {s},i+1}} \end{cases} \tag {8}\\ P_{\textrm {g},t} & =\begin{cases} \displaystyle {P_{\textrm {g},i}^{0} -v_{\textrm {down}} (t-T_{\textrm {s},i}),} & {T_{\textrm {s},i} \le t\lt T_{2.i}} \\ \displaystyle {P_{\textrm {AGC},i},} & {T_{2.i} \le t\le T_{\textrm {s},i+1}} \end{cases} \tag {9}\end{align*}$$ where, $T_{\mathrm {2,}i}$ is a time when the coal-fired generator tracks the target output power of $i^{\mathrm {th}}$ AGC instruction before the next AGC instruction is issued. If $i^{\mathrm {th}}$ AGC instruction is an up order, the the coal-fired generator will adjust output power as (8), otherwise, it will adjust output power as (9).

Case III: The coal-fired generator cannot match the target output power of $i^{\mathrm {th}}$ AGC instruction until receiving the next AGC instruction. Thus, the output power of the coal-fired generator before the next AGC instruction is given by:

$$\begin{align*} P_{\textrm {g},t} & = {P_{\textrm {g},i}^{0} +v_{\textrm {up}} (t-T_{\textrm {s},i})} {T_{\textrm {s},i} \le t\le T_{\textrm {s},i+1}} \tag {10}\\ P_{\textrm {g},t} & = {P_{\textrm {g},i}^{0} -v_{\textrm {down}} (t-T_{\textrm {s},i})} {T_{\textrm {s},i} \le t\le T_{\textrm {s},i+1}} \tag {11}\end{align*}$$

If $i^{\mathrm {th}}$ AGC instruction is an up order, the the coal-fired generator will adjust output power as (10), otherwise, it will adjust output power as (11).

Fig. 6 and Fig. 7 present that the coal-fired generator cannot match the target output power of $i^{\mathrm {th}}$ AGC instruction immediately under all three cases. Utilizing the BESS could support the coal-fired generator in promoting immediate response-ability for secondary frequency regulation service.

The strategy illustrated in Fig. 5 can ensure that the two groups of BESS always stay in different states. For the convenience of description, BESS I and BESS II are supposed to be discharging and charging state respectively. If $i^{\mathrm {th}}$ AGC instruction is an up order, BESS I discharges to enhance response performances of the HCGBPS to secondary frequency regulation. The discharging power of BESS I before the next AGC instruction is given by:

$$\begin{align*} P_{\textrm {b},t}^{\textrm {I}} =\min \left [{{\begin{array}{cccccccccccccccccccc} {P_{\textrm {d}\max,t}^{\textrm {I}},} & {P_{\textrm {AGC},i} -P_{\textrm {g},t}} \\ \end{array}}}\right ] \tag {12}\end{align*}$$ where, $P_{\textrm {dmax,}t}^{\textrm {I}}$ is the maximum discharge power that BESS I can provide at time t, as given by $$\begin{equation*} P_{\textrm {dmax,}t}^{\textrm {I}} =\min \left [{{\frac {P_{\textrm {dis}} E_{\textrm {c}}}{2},\frac {3600\left ({{S_{\textrm {I},t} -S_{\min }}}\right)E_{\textrm {c}} \eta _{\textrm {d}}}{2\Delta T}}}\right ] \tag {13}\end{equation*}$$ where, $P_{\mathrm {dis}}$ is a rated discharge power of the BESS per unit capacity; $E_{\mathrm {c}}$ is the capacity of the BESS. As illustrated in Fig. 4, BESS is divided into two groups, therefore, the capacities of BESS I and BESS II are all $0.5~E_{\mathrm {c}}$ ; $\eta _{\mathrm {d}}$ is the discharge efficiency of the BESS; $\Delta T$ is the length of the time slot; $S_{\min }$ is the minimum permitted state of charge (SOC) of the BESS; $S_{\mathrm {I,}t}$ is the SOC of BESS I at time t, which can be calculated as: $$\begin{equation*} S_{\textrm {I},t} =S_{\textrm {I},t-1} -\frac {P_{\textrm {b},t-1}^{\textrm {I}} \Delta T}{3600\times 0.5E_{\textrm {c}} \eta _{\textrm {d}} } \tag {14}\end{equation*}$$ where, $P_{\textrm {b},t-1}^{\textrm {I}}$ and ${\mathrm {S}}_{\mathrm {I,}t-1}$ are the discharge power and SOC of BESS I at previous time (that is time t-1), respectively.

If $i^{\mathrm {th}}$ AGC instruction is an down order, BESS II is utilized to enhance response performances of the HCGBPS to secondary frequency regulation by absorbing energy from the grid. The charging power of BESS II before the next AGC instruction is given by:

$$\begin{align*} P_{\textrm {b},t}^{\textrm {II}} =-\min \left [{{\begin{array}{cccccccccccccccccccc} {P_{\textrm {cmax,}t}^{\textrm {II}},} & {P_{\textrm {g},t} -P_{\textrm {AGC},i}} \\ \end{array}}}\right ] \tag {15}\end{align*}$$ where, $P_{\textrm {cmax,}t}^{\textrm {II}}$ , is the maximum charging power that BESS II can provide at time t, as given by: $$\begin{equation*} P_{\textrm {cmax,}t}^{\textrm {II}} =\min \left [{{\frac {P_{\textrm {ch}} E_{\textrm {c}}}{2},\frac {3600\left ({{S_{\max } -S_{\textrm {II},t}}}\right)E_{\textrm {c}}}{2\eta _{\textrm {c}} \Delta T}}}\right ] \tag {16}\end{equation*}$$ where, $P_{\mathrm {ch}}$ is a rated charging power of the BESS per unit capacity; $\eta _{\mathrm {c}}$ is the charging efficiency; $S_{\max }$ is the maximum allowable SOC of the BESS; $S_{\mathrm {II,}t}$ is the SOC of BESS II at time t, as given by: $$\begin{equation*} S_{\textrm {II},t} =S_{\textrm {II},t-1} -\frac {\eta _{\textrm {c}} P_{\textrm {b},t-1}^{\textrm {II}} \Delta T}{3600\times 0.5E_{\textrm {c}} } \tag {17}\end{equation*}$$ where, $P_{\textrm {b},t-1}^{\textrm {II}}$ and ${\mathrm {S}}_{\mathrm {II,}t-1}$ are the charging power and SOC of BESS II at previous time (that is time t-1), respectively.

SECTION IV. BESS Capacity Optimization for the HCGBPS

For the HCGBPS, the response performances for AGC instructions and corresponding benefits from this service are positively correlated to the capacity of the BESS. However, a greater capacity of the BESS indicates higher investment costs. To make the HCGBPS a cost-effective solution, appropriate sizing of the BESS capacity is vital.

As described previously, issuing time and characteristics of the AGC instructions received by the HCGBPS are both random, accordingly, responding behaviors are all random. Therefore, the SMCS method is utilized here to simulate the operation of the HCGBPS during an example day because it can consider these random factors. On top of the simulation, this paper derives the optimal BESS capacity to guarantee a maximal net profit of the HCGBPS from utilizing the BESS to join in the frequency regulation ancillary service [39], [40].

A. BESS Capacity Optimization

The objective of optimizing the BESS capacity is to maximize the net profit of the HCGBPS gained from utilizing the BESS to join in the frequency regulation ancillary service throughout an example day.

$$\begin{equation*} \max V_{\textrm {profit}} =V_{\textrm {benefit}} -V_{\textrm {cost}} \tag {18}\end{equation*}$$ where $V_{\mathrm {profit}}$ is the gained net profit from utilizing the BESS to join in the frequency regulation ancillary service; $V_{\mathrm {cost}}$ is the cost of the BESS by participating in secondary frequency regulation; $V_{\mathrm {benefit}}$ is an increase in income of the HCGBPS gained from utilizing the BESS to join in the frequency regulation ancillary service, as given by: $$\begin{equation*} V_{\textrm {benefit}} =\rho _{1} \left ({{{M}'_{\textrm {UEFAGC}} -M_{\textrm {UEFAGC}}}}\right)+\rho _{2} M_{\textrm {TCDE}} \tag {19}\end{equation*}$$ where, $\rho _{1}$ is a penalty price for unmatched energy in following the AGC instructions (UEFAGC); $M\prime _{\mathrm {UEFAGC}}$ and $M_{\mathrm {UEFAGC}}$ are the total deviation energy between real output power and the set output power of AGC instruction of the HCGBPS during the example day before and after the BESS is utilized, respectively. To encourage BESS participation in secondary frequency regulation, the energy charged/discharged for secondary frequency regulation is financially compensated in implementation rules for auxiliary service management issued by China Southern Power Grid Company Limited. $\rho _{2}$ is a compensation price; $M_{\mathrm {TCDE}}$ is total charging/discharging energy (TCDE) of the BESS throughout the example day. To improve the frequency stability of power systems, from the perspective of system operators, the HCGBPS should match the set output power of the AGC instructions within the duration period. Thus, a constraint responding to the probability of success AGC response (PSAGC) for the HCGBPS during the example day is considered, as given by: $$\begin{equation*} M_{\textrm {PSAGC}} \ge \beta \tag {20}\end{equation*}$$ where, $M_{\mathrm {PSAGC}}$ is the PSAGC of the HCGBPS during the example day, and $\beta$ is an expected level of the PSAGC.

In the BESS capacity optimization described above, $V_{\mathrm {benefit}}$ , ${V} _{\mathrm {cost}}$ and $M_{\mathrm {PSAGC}}$ are all related to the capacity of the BESS deployed in the coal-fired generator. The optimization tends to maximize $V_{\mathrm {profit}}$ by selecting optimal BESS capacity subject to the constraint illustrated as (20).

B. Operation Simulation of the Hcbps

Given that the AGC orders are stochastic, SMCS technology is utilized to simulate the operation of the HCGBPS throughout an example day. The simulation outputs $M_{\mathrm {UEFAGC}}$ , $M_{\mathrm {TCDE}}$ , $M_{\mathrm {PSAGC,}}$ and $V_{\mathrm {cost}}$ are vital inputs for sizing the BESS. The simulation process is shown as follows:

• Step 0:

  Given a maximum number of simulations $h_{\max }$ , the simulation turn index h is set to 1; $M_{\mathrm {UEFAGC}}$ , $M_{\mathrm {TCDE}}$ , $M_{\mathrm {PSAGC}}$ and $V_{\mathrm {cost}}$ are set to 0.

• Step 1:

  The AGC instruction index i is set to 1. The initial states of BESS I and BESS II are set to the discharging state and the charging state, respectively. The SOC of BESS I and BESS II are set to 0.5, i.e., $S_{\mathrm {I,}t}=0.5$ , $S_{\mathrm {II,}t}=0.5$ .

• Step 2:

  Based on stochastic characteristics of the AGC instructions investigated in Section II, this step will generate the RR, the DP, the IP, and the RD values of the $i^{\mathrm {th}}$ AGC instruction randomly. How to generate a random number that respectively obey the distribution illustrated as (1), (2), (3), and (4) is easy, which will not be included here.

• Step 3:

  If the $i^{\mathrm {th}}$ AGC instruction is an up order, BESS in the discharging state will discharge power to the grid for responding to the AGC instruction. At this time, the output power of the coal-fired generator is calculated by (6), (8), or (10), and the discharging power of the BESS is calculated by (12). If the $i^{\mathrm {th}}$ AGC instruction is a down order, BESS in the charging state will take power from the grid for responding to the AGC instruction. The output power of the coal-fired generator is derived by (7), (9), or (11), and the charging power of the BESS is derived by (15).

• Step 4:

  This step will update the SOC of BESS I and BESS II within the duration period of $i^{\mathrm {th}}$ AGC instruction by (14) or (17). If any group of the BESS reaches its maximal or minimal SOC within the duration period of $i^{\mathrm {th}}$ AGC instruction. The working states of BESS I and BESS II exchange synchronously according to the strategy illustrated in Fig. 5.

• Step 5:

  In this step, if the $i^{\mathrm {th}}$ AGC instruction is the last AGC order within the example day, the method will move to Step 6. Otherwise, the method will return to then perform step 2 with $i=i+1$ .

• Step 6:

  This step will calculate $M_{\mathrm {UEFAGC}}$ , $M_{\mathrm {TCDE}}$ , $M_{\mathrm {PSAGC}}$ , and $V_{\mathrm {cost}}$ for the $h^{\mathrm {th}}$ simulation, named as $M_{\mathrm {UEFAGC,}h}$ , $M_{\mathrm {TCDE,}h}$ , $M_{\mathrm {PSAGC,}h}$ , and $V_{\mathrm {cost,}h}$ .

  $$\begin{align*} M_{\textrm {UEFAGC,}h} & =\sum \limits _{i=1}^{N_{h}} {\int _{T_{\textrm {s,}i} }^{T_{\textrm {e,}i}} {\left |{{P_{\textrm {d,}t} -P_{\textrm {AGC},i}}}\right |\textrm {d}t}} \tag {21}\\ M_{\textrm {TCDE,}h} & =\sum \limits _{i=1}^{N_{h}} {\int _{T_{\textrm {s,}i} }^{T_{\textrm {e,}i}} {\left |{{P_{\textrm {b},t}}}\right |\textrm {d}t}} \tag {22}\\ M_{\textrm {PSAGC,}h} & = {P_{\textrm {r}} \{(P_{\textrm {d,}T_{\textrm {e,}i}} -P_{\textrm {AGC},i})=0\},} {i=1,2,\cdots,N_{h}} \tag {23}\\ V_{\textrm {cost,}h} & =\frac {V_{\textrm {invest}} E_{\textrm {c}} }{2}\sum \limits _{k=1}^{m_{h}} {\left [{{\frac {1}{M_{\textrm {life}} \left ({{D_{{\mathrm { I}},k}}}\right)}+\frac {1}{M_{\textrm {life}} \left ({{D_{{\mathrm { I}}{\mathrm { I}},k}}}\right)}}}\right ]} \tag {24}\end{align*}$$ where, $N_{h}$ is the quantity of the AGC instructions received by the HCGBPS throughout the example day; $P_{\mathrm {r}}$ {$\cdot$ } indicates the occurrence probability of the event in the {$\cdot$ }; $P_{\mathrm {d,}T\mathrm {e,}i}$ is the output power of the HCGBPS at closing time $T_{\mathrm {e,}i}$ of the $i^{\mathrm {th}}$ AGC instruction; $V_{\mathrm {invest}}$ is the investment cost of the BESS per unit capacity; $m_{h}$ is several charging-discharging cycles of BESS I and BESS II throughout the example day for the $h^{\mathrm {th}}$ simulation; $D_{\mathrm {I,}k}$ and $D_{\mathrm {II,}k}$ are depth of discharging concerning the $k^{\mathrm {th}}$ charging-discharging cycles of BESS I and BESS II, respectively; $M_{\mathrm {life}}(D_{\mathrm {I},k})$ and $M_{\mathrm {life}}(D_{\mathrm {II},k})$ are the battery lifecycle under depth discharging of $D_{\mathrm {I,}k}$ and $D_{\mathrm {II,}k}$ , respectively, as given by [41]: $$\begin{align*} M_{\textrm {life}} (D_{{\mathrm I},k})& =\sum \limits _{l=0}^{4} {a_{l} D_{{\mathrm I},k}^{l}} \tag {25}\\ M_{\textrm {life}} (D_{{\mathrm I}{\mathrm I},k})=& \sum \limits _{l=0}^{4} {a_{l} D_{{\mathrm I}{\mathrm I},k}^{l}} \tag {26}\end{align*}$$ where $a_{l}$ are fitting coefficients determined by the BESS technical characteristics.

• Step 7:

  This step will update $M_{\mathrm {UEFAGC}}$ , $M_{\mathrm {TCDE}}$ , $M_{\mathrm {PSAGC}}$ , and $V_{\mathrm {cost}}$ by (27), (28), (29), and (30).

  $$\begin{align*} M_{\textrm {UEFAGC}}& =M_{\textrm {UEFAGC}} +\frac {M_{\textrm {UEFAGC},h} }{h_{\max } } \tag {27}\\ M_{\textrm {TCDE}}& =M_{\textrm {TCDE}} +\frac {M_{\textrm {TCDE},h}}{h_{\max } } \tag {28}\\ M_{\textrm {PSAGC}} & =M_{\textrm {PSAGC}} +\frac {M_{\textrm {PSAGC},h}}{h_{\max } } \tag {29}\\ V_{\textrm {cost}} & =V_{\textrm {cost}} +\frac {V_{\textrm {cost,}h}}{h_{\max } } \tag {30}\end{align*}$$

  For the BESS deployed in the coal-fired generator, the battery loss cost is much higher than the maintenance cost of the BESS, therefor maintenance cost of the BESS is not yet considered in calculating $V_{\mathrm {cost}}$ as (30).

• Step 8:

  If the set maximum number of simulations turns $h_{\max }$ is reached, the simulation will complete and output the simulation results. Otherwise, the simulation will return to Step 1 with $h=h+1$ .

To present the comparison study, this paper also simulates the operations of the coal-fired generators without deploying the BESS throughout the example day to calculate $M\prime _{\mathrm {UEFAGC}}$ . The simulation step follows Step 0 to Step 8 without BESS actions.

C. Solutions of the BESS Capacity Optimization

The BESS capacity optimization developed in this paper is a one-dimensional optimization problem. The optimal BESS capacity can be obtained by calculating $V_{\mathrm {profit}}$ and $M_{\mathrm {UEFAGC}}$ of the HCGBPS participating in secondary frequency regulation under different BESS capacities with a predetermined step size.

The paper notes that achieving an optimal capacity for the BESS requires simulating the operation of the HCGBPS throughout the full life cycle of the BESS. However, obtaining sufficient data and running simulations for an extended period can be challenging. Thus, this study conducts BESS capacity optimization using simulation results for a single day as an example.

SECTION V. Case Study

A. Case Study Data

The case study is executed based on a coal-fired generator in southeast China. The selected coal-fired generator has a rated capacity of 480 MW, and its maximum up and down ramp rates are 15 MW/min each. The case HCGBPS is constructed by connecting two groups of the BESS units, as illustrated in Fig. 4. The technical parameters of the BESS per unit capacity (1 MW$\cdot$ h) are provided by a BESS manufacturer located in Nantong, China, which are presented in Tab. 1. For the BESS, SOC thresholds illustrated in Tab. 1 have significant impacts on energy throughput during full battery life cycle. In this paper, $S_{\max }$ and $S_{\min }$ are respectively set to be 90% and 10% to maximize the energy throughput during full battery life cycle. The parameters $a_{0}$ , $a_{1}$ , $a_{2}$ , $a_{3}$ , and $a_{4}$ in (25) and (26) are respectively 20230, -67467, 86484, -37736, and 376.

TABLE 1 Technical Parameters of the BESS (1MW$\cdot$ h)

The penalty price for the UEFAGC (i.e., $\rho _{1}$ ) is set at 1000 /MW$\cdot$ h, while the compensation price for secondary frequency regulation (i.e., $\rho _{2}$ ) is 500 /MW$\cdot$ h. In BESS capacity optimization, the desired PSAGC during the example day is set to be 80%, that is, $\beta$ is 80%.

The stochastic characteristics of the DP, non-zero IP, and the RR of the AGC instructions received by the coal-fired generator are respectively described by Rayleigh distribution, Versatile distribution, and Logarithmic normal distribution. The parameters of these three distributions are determined according to the real AGC instructions received by a coal-fired generator in southeast China throughout the December in 2019, which are presented in Tab. 2. The probability that the system operators issue two or more AGC instructions continuously is 10%, that is the probability of taking zero for IP of the AGC instructions is 0.1.

TABLE 2 Parameters of the Distributions Utilized to Describe Probability Characteristics of the AGC Instructions

B. Simulation Results

To justify the technical feasibility of utilizing the BESS to join in the frequency regulation ancillary service, the total BESS capacity is assumed to be 40 MW$\cdot$ h. In this situation, the operation of the case HCGBPS during the example day is simulated using SMCS technology with 10,000 simulations to ensure accuracy. The day-ahead generation schedule for the case coal-fired generator is used as a basis for the simulation, as shown in Fig. 8.

FIGURE 8.

The day-ahead generation schedule of the case coal-fired generator during the example day.

In a randomly selected simulation from the SMCS, Fig. 9 shows the AGC instructions issued by the system operators, Fig. 10 shows the output power of the coal-fired generator, Fig. 11 shows the charging/discharging power of the BESS, and Fig. 12 shows the output power of the case HCGBPS during the first 5 minutes of the example day.

FIGURE 9.

The AGC instructions issued by the system operators during the first 5 minutes of the example day.

FIGURE 10.

The output power of the coal-fired generator during the first 5 minutes of the example day.

FIGURE 11.

The charging/discharging power of the BESS during the first 5 minutes of the example day.

FIGURE 12.

The output power of the HCGBPS during the first 5 minutes of the example day.

In Fig. 9 and Fig. 10, the shaded areas represent the DP of the AGC instructions. Fig. 9 presents that the system operators issued 5 AGC instructions during the first 5 minutes, respectively at 0 s, 49 s, 156 s, 196 s, and 255 s, including three up AGC instructions and two down AGC instructions. These five AGC instructions closed respectively at 24 s, 124 s, 165 s, 221 s, and 262 s. Fig. 10 presents that the coal-fired generator achieved the desired output power of 5 AGC instructions respectively at 40 s, 89 s, 187 s, 216 s, and 283 s. For the second and fourth AGC instructions, the coal-fired generator can achieve their desired output power during the DP of AGC instructions. For another 3 AGC instructions, the coal-fired generator cannot achieve their desired output power during the DP of AGC instructions, but can achieve that before the next AGC instruction is issued. In addition, UEFAGC always exists even if the coal-fired generator can achieve the desired output power during the DP of AGC instructions because ramp rate of the coal-fired generator is limited.

To address the problem described above, the BESS is controlled to join in the frequency regulation as the strategy developed in Section II-B, thus achieving an impeccable response to the AGC instructions, which can be shown in Fig. 11 and Fig. 12. In Fig. 11, BESS I discharges to match three up AGC instructions (the second, third and fourth AGC instructions). BESS II takes power from the grid to respond to two down AGC instructions (the first and fifth AGC instructions). In general, the two groups of the BESS are typically controlled in different charging/discharging states, assisting the coal-fired generator in responding to the AGC instructions under different RD conditions.

Fig. 13 presents the SOC variation for the BESS throughout the example day. It can be found form Fig. 13 that there are two charging/discharging state transitions for the BESS throughout the example day, respectively occurring at 4:58:10 and 15:02:17. At first, BESS I is controlled to discharge for enhancing the performance of the HCGBPS on responding the up AGC instructions. At this stage, the SOC of BESS I declines continuously and reaches its full discharge capacity at 4:58:10. According to the strategy illustrated in Fig. 5, BESS I is immediately switched to the charging state to prevent over-discharge. Correspondingly, BESS II is switched from the charging state to the discharging state to ensure that the two groups of the BESS remain in different states, even though it does not reach the full charging state. The second charging/discharging state transition occurs at 15:02:17 when BESS II reaches its full discharge capacity. Thus, the charging/discharging state switching strategy illustrated in Fig. 5 can not only strictly ensure the two groups of the BESS are always in different charging/discharging states, but also avoid frequent switches between charging and discharging, mitigating the lifecycle depletion of the BESS significantly.

FIGURE 13.

The SOC of the BESS during the example day.

Tab. 3 presents comparisons of the performance in responding to AGC instructions and the resulting BESS loss cost (BLC) between a sole coal-fired generator and the HCGBPS.

TABLE 3 The Performances on Tracking the AGC Instructions of the Case Coal-Fired Generator and HCGBPS, Together With BLC of the HCGBPS

As shown in Tab. 3, the PSAGC and the UEFAGC during the example day are 40.0% and 70 MW$\cdot$ h, respectively, if only the coal-fired generator provides frequency response. There is above 60% probability that the coal-fired generator cannot reach the set output power within the DP of the AGC instructions. The UEFAGC illustrated in Tab. 3 is a mean value calculated based on simulation results, which can be found from (27). The maximum value of the UEFAGC that appears in the simulation is as high as 88.62 MW$\cdot$ h.

For comparisons, the frequency response performance is significantly enhanced when utilizing the BESS to join in the frequency regulation as the strategy developed in Section II-B. In this situation, the PSAGC of the HCGBPS increases from 40.0% to 98.5% throughout the example day, with an increase of 121.3%. Correspondingly, the UEFAGC of the HCGBPS decreases from 70 MW$\cdot$ h to 1.6 MW$\cdot$ h throughout the example day, with a drop of 97.71%. In addition, the maximum value of the UEFAGC that appears in the simulation is only 2.67 MW$\cdot$ h. Under this circumstance, the two charging/discharging state transitions incur $82\times 10 ^{3}$ BLC.

C. BESS Capacity Optimization

To obtain the optimal size of the BESS, different BESS capacities are considered in the operation simulation for the HCGBPS throughout the example day. The simulation derives the net profit of the HCGBPS gained from utilizing the BESS to join in the frequency regulation (i.e., $V_{\mathrm {profit}}$ ) together with the PSAGC. In the case study, the optimization step size of the BESS capacities is set to be 2 MW$\cdot$ h. In this condition, the values of $V_{\mathrm {profit}}$ , $V_{\mathrm {benefit}}$ , $V_{\mathrm {cost,}}$ and $M_{\mathrm {PSAGC}}$ with different BESS configuration capacities are shown in Fig. 14.

FIGURE 14.

The values of $V_{\mathbf {profit}}$ , $V_{\mathbf {benefit}}$ , $V_{\mathbf {cost,}}$ and $M_{\mathbf {PSAGC}}$ with different BESS configuration capacities.

Fig. 14 presents that a larger BESS capacity brings higher benefits of the HCGBPS gained from utilizing the BESS to join in the frequency regulation ancillary service. When the capacity increase is a fixed value, a higher increasing rate of the $V_{\mathrm {benefit}}$ incurs with a small BESS size. When the BESS capacity increases to a certain extent, the increase of the $V_{\mathrm {benefit}}$ tends to be flat. However, $V_{\mathrm {cost}}$ always presents an approximately linear increase with the increase of the BESS size. Thus, $V_{\mathrm {profit}}$ increases in the beginning but starts to drop after the BESS capacity is 24 MWh. The corresponding net profit is 35,117, which is the the maximum net profit, as illustrated in Fig. 14. Further, the PSAGC increases monotonically with the increase of the BESS capacity. It can be found from Fig. 14 that the PSAGC exceeds 80%, once BESS capacity is larger than 20 MW$\cdot$ h, which satisfies the constraints set in (20). According to the BESS capacity optimization developed in Section IV. A, the optimal configuration capacity of the BESS is selected to be 24 MW$\cdot$ h, because not only the $V_{\mathrm {profit}}$ is is at maximum, but also the constraints set in (20) is satisfied when BESS capacity is 24 MWh.

D. Influence of Penalty Price for UEFAGC on the Optimal Configuration Capacity of the BESS

To investigate the impact of the $\rho _{1}$ on $V_{\mathrm {profit}}$ and the optimal capacity of the BESS, Fig. 15 shows a comparison study where $\rho _{1}$ is 600 /MW$\cdot$ h, 1,000 /MW$\cdot$ h, and 1,400 /MW$\cdot$ h, respectively.

FIGURE 15.

The $V_{\mathbf {profit}}$ of the case HCGBPS in different penalty prices for UEFAGC.

Fig. 15 presents that when the $\rho _{1}$ decreases from 1,000 /MW$\cdot$ h to 600 /MW$\cdot$ h, the $V_{\mathrm {profit}}$ decreases significantly. The maximum $V_{\mathrm {profit}}$ shift to the left of the case when $\rho _{\mathrm {1}}$ is 600 /MW$\cdot$ h. The maximum net profit is 14,479 and the BESS capacity is 18 MW$\cdot$ h. However, the PSAGC of 18 MW$\cdot$ h BESS is lower than 80%, which fails to meet the constraint given by (20). According to the BESS capacity optimization developed in Section IV. A, the optimal capacity of the BESS is 20 MW$\cdot$ h when $\rho _{1}$ is 600 /MW$\cdot$ h, which is the closest capacity with over 80% PSAGC. The corresponding $V_{\mathrm {profit}}$ of the HCGBPS is 14,228. In contrast, when the $\rho _{1}$ increases from 1,000 /MW$\cdot$ h to 1400 /MW$\cdot$ h, the $V_{\mathrm {profit}}$ increases significantly. The maximum $V_{\mathrm {profit}}$ moves to the right of the case when $\rho _{1}$ is 1,400 /MW$\cdot$ h. The maximum net profit is 58,450 and the BESS capacity is 28 MW$\cdot$ h. In this situation, the PSAGC has exceeded 80%, which satisfies the constraint given by (20). Thus, the optimal BESS capacity is 28 MW$\cdot$ h, according to the BESS capacity optimization developed in Section IV. A. It can be seen from the analyses described above that the adjustment of the $\rho _{1}$ will affect the $V_{\mathrm {profit}}$ of the HCGBPS, consequently affecting the optimal configuration capacity of the BESS.

E. Influence of Compensation Price for the Energy Charged/Discharged for Secondary Frequency Regulation on the Optimal Configuration Capacity of the BESS

To investigate the impact of the $\rho _{2}$ on the $V_{\mathrm {profit}}$ and the optimal capacity of the BESS, Fig. 15 shows a comparison study where $\rho _{2}$ is 300 /MW$\cdot$ h, 500 /MW$\cdot$ h, and 700 /MW$\cdot$ h, respectively.

Fig. 16 presents that when $\rho _{2}$ reduces from 500 /MW$\cdot$ h to 300 /MW$\cdot$ h, the $V_{\mathrm {profit}}$ decreases significantly. The maximum $V_{\mathrm {profit}}$ shift to the left of the case when $\rho _{1}$ is 300 /MW$\cdot$ h. The maximum net profit is 24,303 and the BESS capacity is 22 MW$\cdot$ h. Further, when the $\rho _{2}$ increases from 500 /MW$\cdot$ h to 700 /MW$\cdot$ h, the $V_{\mathrm {profit}}$ increases significantly. The maximum $V_{\mathrm {profit}}$ moves to the right of the case when $\rho _{1}$ is 700 /MW$\cdot$ h. The maximum net profit is 46,617 and the BESS capacity is 26 MW$\cdot$ h. For the above cases, PSAGC exceeds 80% and meets the set constraints given in (20). According to the BESS capacity optimization developed in Section IV. A, the optimal capacity of BESS is 22 MWh and 26 MWh, respectively, when $\rho _{2}$ is 300 /MW$\cdot$ h and 700 /MW$\cdot$ h. The analyses described above show that the adjustment of the $\rho _{2}$ will also affect the $V_{\mathrm {profit}}$ of the HCGBPS, consequently affecting the optimal configuration capacity of the BESS.

FIGURE 16.

The $V_{\mathbf {profit}}$ of the case HCGBPS in different compensation prices for the energy charged/discharged for secondary frequency regulation.

SECTION VI. Conclusion

This paper develops a new sizing method of BESS on top of the concept of combined BESS and coal-fired generators to provide high-quality secondary frequency response. The case studies justified that:

1. The HCGBPS has better performance on responding to the AGC instructions than that of the coal-fired generator, and a larger BESS capacity always brings better performance on responding to the AGC instructions, but results in a higher cost.

2. The charging/discharging state switching strategy designed for the BESS can avoid frequent switches between charging and discharging, thus mitigating the lifecycle depletion of the BESS significantly.

3. Both the penalty price for the UEFAGC and the compensation price for secondary frequency regulation have significantly impacts on gained net profit from utilizing the BESS to join in the frequency regulation ancillary service.

4. The developed sizing method could make a satisfying BESS investment decision to ensure a maximum net profit in operation while satisfying the constraint on the PSAGC.

Further, this paper discovered, the investment of BESS is not always profitable. If the BESS capacity exceeds some threshold, determined by the penalty price for UEFAGC and compensation price, the net profit will reduce. This reduction could lead to extreme investment loss if the capacity is too large.

In future work, we will utilize the method developed in this paper to a real HCGBPS to investigate the correlations between simulation results and the actual data, thus providing a basis for improving the method. In addition, we will investigate feedback mechanisms for handling asymmetric SOC and unexpected conditions to improve robustness of the strategy developed in this paper.

ACKNOWLEDGMENT

The authors would like to thank for the support from the National Natural Science Foundation of China and Jiangsu Higher Education Institutions of China.