Hybrid Model-Based BESS Sizing and Control for Wind Energy Ramp Rate Control

Abstract

This paper presents a hybrid model constituting dynamic smoothing technique and particle swarm optimization techniques to optimally size and control battery energy storage systems for wind energy ramp rate control and power system frequency performance enhancement. In today’s modern power system, a high-proportion renewable energy grid is inevitable. This high-proportion renewable energy grid is a power system with abundant integration of renewable energy resources under the presence of energy storage tools. Energy storage tools are integrated into such power systems to balance the fluctuation and intermittence of renewable energy sources. One of the requirements in a high-proportion renewable energy grid is the fractional power balance between generation and load. One of the requirements set by power system regulators is the generation variation between two time points. A power producer is mandated to satisfy the ramp rate requirement set by the grid owner. This paper proposes dynamic smoothing techniques for initial size determination and particle swarm optimization based on optimal sizing and control of battery energy storage systems for ramp rate control and frequency regulation performance of a power system integrated with a large percentage of wind energy systems. Wind energy data taken from Zhangjiakou wind farm in China are used. The results indicate that the battery energy storage system improves the ramp rate characteristics of the wind farm. In addition, the virtual inertia capability of the battery energy storage system enabled the transient and steady-state frequency response of the test power system to improve significantly.

1. Introduction

In the current modern power system, a high-proportion renewable energy grid (HPREG) is inevitable. This HPREG is a power system with abundant integration of renewable energy resources under the presence of energy storage tools (ESTs). However, power generation from wind energy resources is variable, unpredictable and extremely fluctuating. This variable nature of wind energy generation affects the dynamics of the power system manifested in the form of power balance and frequency variation problems. In order to limit the adverse effect of this fluctuating wind energy system, many countries put a limit on the ramp rate level to the generation of energy from wind resources. Note that any power producer participating in the energy market, specifically a power producer from solar and wind energy sources, must satisfy the ramp rate rule described by the grid code of the system owner. If any of the power producers violate this ramp rate rule, a penalty is applied, or the power producer must curtail the extra generation from the wind or solar generation system. The following table,

Table 1. Ramp rate limit of different national grid codes.

Country	Installed Capacity Class	Ramp Rate Rule
Puerto Rico	-	10%/min
Germany	-	10%/min
Denmark	-	5%/min
Mexico	-	30 MW/min
Ireland	-	30 MW/min
Hawaii	-	2 MW/min
China	Installed capacity < 30 MW	3 MW/min and 10 MW/10 min
	Installed capacity < 200 MW	10%/min and 33.3%/10 min
	Installed capacity > 200 MW	15 MW/min and 50 MW/10 min

, shows some of the ramp rate limits imposed by some of the national grid codes in selected countries [1,2,3,4,5].

It can be seen from the table that the ramp rate limits have different meanings or interpretations depending on the national grid codes. For example, some countries express their ramp rate limits as percentage values of wind and solar installed capacity, while others represent their ramp rate limits as simple megawatt restrictions. Additionally, the ramp rate limit timing is also essential. For example, China used this technique to put the ramp rate limit in the national grid code. As a result, the limits are presented as per minute and as per ten-minute values. Therefore, it is the mandate of the power producer to respect and act according to the limits imposed in each national grid code.

In this paper, hybrid optimization-based optimal size determination and application of battery energy storage system (BESS) for ramp rate (RR) improvement of a wind farm is proposed. As presented in the next subtopics, the same technology was proposed, sized and tried for RR control by other researchers. However, most related research, as presented in the literature part, start their analysis of ramp rate improvement and control with an insufficient yet predetermined and preset value of wind energy generation profile. These sorts of data definitely impact the decision in the storage sizing procedure. Therefore, on the one hand, the use of these preset data will result in a smaller storage capacity that might not satisfy the RR demand for most of the points; or on the other hand, the use of preset data might result in a larger storage size that can satisfy RRs but would be too expensive. Moreover, the inclusion of the various cost components providing significance to the cost-effectiveness of power generation companies, such as energy curtailment cost, wind energy RR violation cost and levelized installation cost of storage units, should also be part of these studies. Therefore, in this study, we proposed hybrid optimization models consisting of dynamic smoothing technique (DST) initiated k-means clustering and particle swarm optimization (PSO) based computation algorithms to determine the capacity of the BESS for RR improvement and control of a wind power system. Initially, DST was applied to categorize the historical wind energy generation data for required RR improvement. Secondly, the k-means clustering technique was used to generate representative datasets. Finally, the PSO technique was applied to optimally determine the BESS size for RR control and improvement of the wind farm.

The remaining part of this paper is organized as follows: Section 2 presents the literature review of the latest research and methods used in RR control of a wind energy system. Section 3, on the other hand, presents the methodology followed in the paper consisting of the proposed smoothing methodology, the operation dynamics and the optimal capacity determination of the BESS. Similarly, Section 4 presents the case study data and simulation results and discussion and validation results. Finally, the conclusion, novelty and future work suggestions are presented in Section 5 of the paper.

2. Literature Review

The techniques for calculating the ramp rate of wind energy generation, as presented in some technical literature [6], are presented as follows: (i) the difference between the production level of two endpoints of a 1 min interval, (ii) the difference between the minimum and maximum generation values of a considered interval and (iii) the difference between production level of two points at each second interval, as shown in Figure 1 below.

Similar to the RR calculation methods, there are various techniques by which power producers practice to balance and control the RR in wind energy generation. For example, one of the techniques that use the energy generating operators are supposed to fulfill the national grid code ramp rate limits is by applying fast-acting storage units for RR compensation and control. Using the storage units not only helped the RR control but also had other functions in the power system, such as energy arbitrage, avoiding curtailment of renewable energy generation, frequency regulation, voltage support, and transmission and distribution network outage mitigation [7,8,9]. In standalone systems, such as those working with diesel generator systems and solar energy generation, ESTs have an inevitable advantage towards leveling the solar generation by saving it during high generation time and supplying it during low generation time [10]. In a similar configuration, BESS is applicable to supply a significant portion of loads during long-hour PV autonomy. In [11], a microgrid configuration and a worst-case scenario simulation-based sizing of BESS to supply 75% of the loads (designated as essential loads) of a university campus for 3 h is presented. In the paper, the BESS was designed to present a power quality advantage of stabilizing PV fluctuation to the microgrid of the Ball State University Campus.

Accordingly, much research has been conducted on the application of ESTs for RR improvement and control. In [3], multiple EST options for RR improvement are proposed to take advantage of the wider operating time scales of these multiple ESTs. The application of hybrid ESTs for RR control of a PV system is also proposed in [4]. In such arrangements, the authors followed a scheduling strategy such that the faster-operating storage system would operate to its capacity limit first, and only then the slowest-operating storage system would operate later. In the capacity determination procedure, the energy capacity of the faster and slower operating units is selected from a range of capacities with discrete time steps. The authors in [12,13] proposed a modified version of the maximum power point (MPP) algorithm such that the PV plant will not operate at the point of MPP during fluctuation so as to limit the RR. ESTs such as zinc bromide flow batteries and ultra-capacitors connected directly to the wind turbines by power electronic converters are proposed to control the RR in the wind farm of an installed capacity of 48.3 MW [14]. The researchers in [15] proposed a GA-based optimization technique to determine the capacity of the energy storage unit to reduce the wind energy variability so as to minimize the overall grid power variability as the objective function. The authors in [1] proposed the worst-fluctuation technique to determine the capacity of the storage unit to eliminate the RR problem. In others, researchers proposed conventional techniques consisting of moving average smoothing techniques, both simple moving average and exponential moving average, to smooth out the wind/PV power signals [16]. Even though these techniques can reduce the RR to some degree, they introduce the memory effect problem, which allows the storage unit to work at unnecessary points in time. The drawback of this technique is that the smoothed signal may have a point at which the resulted data are more fluctuating than the original data and requires an unwanted operation for the storage unit. The unwanted fluctuation resulted from the memory effect of the moving average smoothing techniques. The picture below, Figure 2, shows a pictorial representation of the disadvantages of SMA technique, as presented by [17] for a realistic PV output from Oahu Island, Hawaii, on the 18th of March 2010, and its 20 min moving average value [18]. As depicted in the picture, there are points at which the original signal was initially stable in its power generation. In contrast, the moving averaged signal had fluctuations that could force the ESTs to operate unnecessarily. Broken red-circled markers in Figure 2 are used to show these points.

In addition, these techniques have the disadvantage of over-smoothing RRs, which eventually increases the size of the storage units and ultimately results in expensive storage units [19]. Other techniques, comprising of filters, both first-order low pass filter (1-LPF) and second-order low pass filter (2-LPF), power electronic converters, generation curtailment, dumping loads and gas turbines are some of the mechanisms and devices also used in the RR control [14,15,19,20]. Likewise, the Gaussian-based smoothing technique is used in smoothing wind energy fluctuation. The Gaussian function, also known as the Gaussian filter-based smoothing technique, has been extensively applied in computer vision and image processing [16,21].

The basic principle of these techniques is to smooth the high fluctuations in the wind-generated power, which arise due to fluctuations in wind speed. These smoothing methods generate a battery power reference that opposes the wind power variations, as shown in Figure 3. The result is an injected smooth grid power within the acceptable RR limits.

In [22,23], a comparative analysis and in-depth review of numerous PV power generation fluctuation smoothing methods and RR control strategies are presented. According to these research outputs, among all the techniques to counterbalance renewable energy variability, RR control based on ESTs is indicated as the best choice. This advantage of ESTs, particularly BESS, is supported by the wide range of capabilities they had, ranging from a few kilowatts to larger values of hundreds of kilowatts [9].

Energy storage capacity determination for RR improvement of a PV system using rest recover and dynamic rest as controlling strategies is proposed by [24]. The effect of time uncertainties and false forecasted signals for the increased operating cost of diesel generators and a comparative study of BESS for RR improvement of the PV plant is proposed in [20]. Similar studies for determining the capacity of ESTs for RR improvement of a PV power plant are studied by [25,26]. The effect of PV panel arrangement for the system RR under predetermined storage capacity is studied in [27] to investigate the parallel as well as the cascaded PV panel arrangement effect on the entire ramping characteristics of the PV plant. The worst fluctuation model of a PV plant is proposed in [2] for RR improvement under the presence of storage systems. However, the drawback of these models is that the result is highly costly while providing the maximum storage capacity needed to limit RRs. In [28], the authors tried to investigate the effect of large size of PV installations in countering the RR in one section of the array by the remaining parts of the array. A technical report in [29] presented the study of wind energy fluctuation behavior for the Electric Reliability Council of Texas. In this technical report, the influence of the relative direction of change in generation and load to the power system is presented.

3. Methodology

In this part of the paper, the previously proposed smoothing technique, the DST technique, is explained, derived and presented. Similarly, the operation dynamics of the BESS and its optimal capacity determination will be discussed in detail.

3.1. The Dynamic Smoothing Technique

Contrary to some of the previous smoothing techniques, in this smoothing technique, the smoothing constant is continuously changing, dynamically changing constant and, hence, the name dynamic smoothing technique. Additionally, unlike the moving average smoothing techniques, in DST, the smoothing of the wind signal starts as soon as the second point signal is known, whereas, in some of the former methods, either n or n + 1 number of data points need to be recorded for the smoothed signal to be available. Therefore, in the DST algorithm, there is no delay in the operation of the EST for smoothing the wind energy signal, resulting in a good EST operating strategy.

In the DST algorithm, during the high production time, the energy produced from the wind energy system will either be injected into the power grid or directed to the battery or, during low production time, the previously battery-charged energy together with the latest wind energy production will be directed to the grid. In both instances, the capacity determination of the storage unit should be so that the overall injected power to the power system is well smoothed. The determination of the dynamic smoothing constant, the smoothed signal, and the EST reference signal is presented as follows.

In DST smoothing algorithm, the smoothed signal at time $t$ is a function of the unsmoothed signal $P_t$, the previously smoothed signal ${\widehat{P}}_{t-1}$ and the continuously changing smoothing constant $a_t$, as in Equation (1)

$${\widehat{P}}_t=f(P_t,{\widehat{P}}_{t-1},a_t)$$

(1)

After incorporating a multiplying factor, also called the dynamically changing smoothing constant, between the original (unsmoothed) power and the previous time smoothed power signals, the formulation of the smoothed power at time $t$ is presented as in Equation (2)

$${\widehat{P}}_t=a_t\times P_t+(1-a_t)\times {\widehat{P}}_{t-1}$$

(2)

The determination of the value of the multiplying factor could follow after determining the RRs for the original signal and the smoothed signal. In this study, the RR for the original signal $R_t$ at any instant of time $t$ is defined as the time rate of change in two adjacent power measurements as in Equation (3)

$$R_t\le \frac{P_t-P_{t-1}}{\Delta t}$$

(3)

where $\Delta t$ is the time resolution between the two consecutive measurements. In this paper, the value of $\Delta t$ is 60 s. Likewise, the RR for the smoothed signal, ${\widehat{R}}_t$ is defined as the time rate of change in the unsmoothed signal and the previously smoothed signal, as in Equation (4)

$${\widehat{R}}_t\le \frac{P_t-{\widehat{P}}_{t-1}}{\Delta t}$$

(4)

DST dictates both the RR definitions given in Equations (3) and (4) must be satisfied. Suppose one of the two RR formulations violates the RR limit. In that case, a limit is assigned to that particular instance, and the storage system operates in charging or discharging modes based on the direction of RR. Therefore, the overall RR rule $R_r$ is defined as in Equation (5)

$$R_r=\{\begin{array}{l}{\widehat{R}}_t,\hspace{1em}if R_t\le \left|R_{\lim }\right|\&\&{\widehat{R}}_t\le \left|R_{\lim }\right|\\ R_{\lim },\hspace{1em}otherwise\end{array}$$

(5)

After obtaining the newly defined RR, the smoothed power signal is rewritten, as in Equation (6)

$${\widehat{P}}_t={\widehat{P}}_{t-1}+R$$

(6)

By equating Equations (2) and (6), the value of the dynamic smoothing variable ${\alpha }_t$ is solved, as in Equation (7)

$${\alpha }_t=\left|\frac{R}{P_t-{\widehat{P}}_{t-1}}\right|$$

(7)

Once the dynamic smoothing variable is determined, a switching signal is generated to switch the storage unit ON or OFF. The expression for the switching function is given as in Equation (8):

$$S_t=\{\begin{array}{l}0 , for {\alpha }_t=1\\ 1 , for {\alpha }_t<1\end{array}$$

(8)

After determining the switching signal, the smoothed power signal is represented, as in Equation (9). The expression in Equation (9) is called the DST function because it is based on a dynamically changing smoothing constant.

$${\widehat{P}}_t\left(t\right)=a_t\times P_t+\left(1-a_t\right)\times {\widehat{P}}_{t-1}\times S_t$$

(9)

Once the smoothed wind energy signal is determined, the BESS reference signal is generated as in Equation (10).

$$P_t{}^S={\widehat{P}}_t-P_t$$

(10)

where $P_t^S$ is the power injected into or withdrawn from the storage unit.

When assuming a positive reference to the battery power, power absorbed by the battery will be considered positive, and the battery-supplied power will be considered negative. The DST algorithm demands the maximum possible EST to resolve the RR problem. Figure 4 shows a sample DST-based battery power signal with the original wind data signal and the smoothed signal. According to this figure, the battery power required for worst-case scenario analysis was found to be 21.78 MW, as could be seen from the plot in orange color.

3.2. Operation Dynamics of the BESS

In this section, the possible operating dynamics of the storage unit will be discussed in reference to the wind energy production dynamics from one time slot to the other time slot. The BESS operation dynamics are determined according to the wind energy operation dynamics and also based on the storage unit status at different points in time and its power and energy capacity. For example, if the wind energy violates the upper RR limit, the storage unit might absorb some or all of the wind energy generation. However, based on the actual operating status of the storage unit, the absorbed wind energy amount could be variable. Similarly, the wind energy might blow such that it will violate the ramp down limit, or it may be within the ramp up and ramp down limits. Likewise, in these two cases, the BESS may absorb some energy, generate what it has stored or do nothing since the operation dynamics are also dictated by the BESS’s previous status and overall capacity. In situations where the BESS is not acting, the energy curtailment and penalty for violating the RR rule will be applied.

Suppose the wind energy P_w(t + 1) at time t + 1 is such that it is beyond the ramp up limit specified in the grid code as in Equation (11)

$$N_t+R_u\le P_w\left(t+1\right)$$

(11)

where N_t is the nominal power injected into the grid at time t and R_u is the ramp up limit specified in the grid code.

In this case, according to the storage operation $E_{t+1}$ at time $t+1$, there are three possible operating cases for the BESS, which are presented as in Equations (12a)–(12c) (the three equations are dependent on one another) and shown in Figure 5 below with circled numerals.

$$N_t+R_u\le P_w\left(t+1\right)+E\left(t+1\right)$$

(12a)

$$N_t-R_d\le P_w\left(t+1\right)+E\left(t+1\right)<N_t+R_u$$

(12b)

$$P_w\left(t+1\right)+E\left(t+1\right)<N_t-R_d$$

(12c)

Mathematically, the operation dynamics of the BESS involving its energy and power components are given as in Equations (13)–(16)

$$E(t)=E\left(t-1\right)+U_c{P}_c\left(t\right)\Delta t{\eta }_c-\frac{U_d{P}_d\left(t\right)\Delta t}{{\eta }_d}$$

(13)

$$U_c+U_d\le 1$$

(14)

$$\begin{array}{l}0\le P_c\left(t\right)\le P_c^R\left(t\right)\\ 0\le P_d\left(t\right)\le P_d^R\left(t\right)\end{array}$$

(15)

$$0\le E\left(t\right)\le E^R$$

(16)

E(t) is the energy level available at time t, P_c(t) is the charging power at time t and P_d(t) is the discharging power at time t. With a proper sign, P_c(t) and P_d(t) could be defined by a single variable P_b(t), battery power. U_c and U_d are state variables for charging and discharging assuming the value of {0, 1}; η_c and η_d are charging and discharging efficiency of the storage device; P_c^R, P_d^R and E^R are rated charging power, discharging power and energy storage capacity, respectively; ∆t is the time resolution between two measurement intervals. The formula in Equation (14) dictates that the storage unit could not charge and discharge at the same time.

3.3. Optimal BESS Capacity Determination

In the first stage of optimization involving the DST algorithm, the amount of BESS power and energy capacity required is broad and needs adjustment. Two scenarios could be used for this: one is the worst-case scenario. In such cases, the energy storage capacity will take the maximum value. The problem with this procedure is that the resulting storage size is too expensive. The second scenario is to apply the best case with minimal storage capacity. Again, the problem with this procedure is that the objective of smoothing the wind energy signal will not be satisfied. Therefore, the optimal storage sizing must find the appropriate size of energy storage so that the power producer is at the best economic point during the operation and the investment period.

Therefore, optimal capacity determination of the storage unit in the second stage is based on cost-benefit analysis through the PSO algorithm; PSO formulation can be found in [30]. The objective function is such as to minimize the overall daily cost constituting the cost of violating the RR limit, energy curtailment cost and energy storage units investment cost as presented in Equation (17).

$$\min C_{\mathrm{tot}}={\displaystyle \sum _{t=1}^T{C}_t{}^s+C_t{}^{\mathrm{curt}}+C_t{}^{\mathrm{pen}}}$$

(17)

where $C_{\mathrm{tot}}$ is the total cost representing the objective function, $C^s$ is the EST installation (investment) unit cost, $C^{\mathrm{curt}}$ is wind energy curtailment cost of curtailing a unit amount of power, $C^{\mathrm{pen}}$ is the RR violation penalty unit cost, $t$ is the time index and $T$ is the entire duration of the optimization horizon. The above individual cost components of the objective function depending on the power rating and corresponding unit price, as in Equation (18).

$$\begin{array}{l}{C}_t{}^s=u_s\times \left|P_t{}^s\right|\\ C_t{}^{\mathrm{curt}}=u_{\mathrm{curt}}\times P_t{}^{\mathrm{curt}}\\ C_t{}^{\mathrm{pen}}=u_{\mathrm{pen}}\times P_t{}^{\mathrm{pen}}\end{array}$$

(18)

where $u_s$ is the unit cost of the storage unit, $u_{\mathrm{curt}}$ is the unit cost of wind energy curtailment and $u_{\mathrm{pen}}$ is the unit cost of RR violation. Likewise, $P^s$ is the power capacity of the storage unit, $P^{\mathrm{curt}}$ is the amount of the curtailed wind power and $P^{\mathrm{pen}}$ is the magnitude of RR violation power. The power balance function, the RR function and penalty values are defined in Equations (19)–(21), respectively.

$$P_t{}^g=P_t{}^w-P_t{}^s-P_t{}^{\mathrm{curt}}$$

(19)

where $P_t{}^g$ is the power injected to the grid at time $t$, it represents the power balance for the wind energy to the grid, $P_t{}^w$ is the wind energy generation at time $t$, $P_t{}^s$ is the storage (battery) power generated or absorbed by the battery at time $t$ and $P_t{}^w$ is the wind energy curtailed at time $t$.

$$R_t=\frac{P_t{}^g-P_{t-1}{}^g}{\Delta t}$$

(20)

$$P_t{}^{\mathrm{pen}}=0.5\times \left(\mathrm{sign}\left(\left|R_t\right|-R_{\lim }\right)+1\right)\times \left(\left|R_t\right|-R_{\lim }\right)$$

(21)

where $R_{\lim }$ is the RR limit as defined in the grid code.

4. Case Study Results and Analysis

4.1. Case Study Data

This case study performs the proposed DST method for determining the capacity of the BESS for RR control using one-year wind energy data of the Zhangjiakou wind farm in China. This wind farm has 60 wind turbines installed, each with a rated power capacity of 1.5 MW. For this particular study, per-minute recorded data of the wind farm in 2018 were used. In concordance with the state grid code requirement of the Chinese government, the Zhangjiakou wind farm RR limit is 9 MW/min. The remaining numerical data used in the analysis are presented in

Table 2. Numerical data used in the case study.

Category	Variable	Unit	Value
Storage unit levelized cost	Power	USD/MW/min	0.3670
	Energy	USD/MW/min	0.1634
Penalty unit price	Wind curtailment	USD/MW/min	0.1670
	RR violation	USD/MW/min	2.6700
PSO algorithm	Population size	-	1000
	Number of iterations	-	500
	Inertia constant	-	0.9
	Correction factor	-	2

below.

For the proposed work, using the hybrid models of DST-based k-means clustering and PSO-based optimization, the recorded wind energy data are organized as follows: The recorded wind energy data are separated into a one-hour wind energy generation pattern. Then the first stage with the previously defined DST process is carried out to obtain the storage requirement for the individual patterns. Then, each individual pattern holds a single point based on its energy and power requirement. Later, k-means clustering is used to cluster generated entities (patterns) according to the previously derived storage sizes to generate overall representative datasets. In the drawing depicted in Figure 6, the colored asterisk “*” symbols represent the original data points. Similarly, colored circular symbols represent the cluster centroid or the representative data points. The number of optimal cluster sizes is derived from the cluster evaluation function in the software using the “gap” data type for possible cluster numbers ranging from one to forty.

As a result, the DST algorithm is simulated for three particular cases of 20, 25 and 30 clusters. Similarly, the PSO algorithm is simulated for these cases to examine the consistency in the output results and the time it took to compute the results.

The second stage in the BESS capacity determination procedure takes these previously generated representative data, the first stage estimate of storage requirement, and the number of data points embodied by each cluster centroid into account and applies the proposed PSO algorithm. Finally, a record of the result of the PSO algorithm for the individual clusters is taken. For instance, power and energy requirements for the representative cluster points (centroids), overall optimal cost and the number of data points in the cluster are examples of the records from the PSO stage. The final capacity determination for the storage unit follows the expectation equation of a random variable, as in Equation (22).

$$E(X)={\displaystyle \sum _{i}xP(X)}$$

(22)

In the formula, the function represents summation over the centroid points described by the variable $i$, $X$ is the random variable, $x$ is the value of the random variable, $P(X)$ is the probability of the variable $X$ and $E(X)$ is the expected value of the random variable.

4.2. Simulation Results

The simulation results for a cluster of 25 data points are presented as follows in tabular and numerical forms. The result in

Table 3. Record of the simulation result in the case of 25 clusters.

No	Power Capacity	Energy Capacity	Cost	Data Points
1	10.90627	267.7925	8916.519	277
2	11.42239	383.3716	10,788.81	357
3	12.62967	260.7362	9625.084	290
4	18.70516	850.1071	20,835.26	245
5	20.15262	482.263	16,316.5	3358
6	20.87063	681.3739	19,488.48	195
7	24.72118	761.3163	22,445.6	299
8	25.73222	600.1821	20,618.08	180
9	27.93991	760.2882	23,955.87	299
10	29.06907	810.7764	25,190.56	307
11	29.42959	897.015	26,624.41	97
12	30.57693	888.8437	27,054.81	263
13	30.82938	946.9819	27,983.32	292
14	30.89837	989.5323	28,645.53	245
15	31.28085	964.6869	28,548.13	112
16	31.30627	1216.576	32,057.94	72
17	32.09536	1142.462	31,440.14	392
18	33.47312	1082.696	31,233.11	22
19	36.3741	1017.434	31,671.79	215
20	37.61502	966.6972	31,580.28	75
21	37.99988	1249.548	35,839.16	203
22	38.51523	779.0981	29,276.73	6
23	39.11977	1151.223	34,919.54	304
24	41.49581	1162.364	36,365.76	115
25	41.96295	1133.895	36,002.57	36

shows the individual cluster points, their corresponding BESS power and energy capacity, cost and the number of data points presented in the cluster. From the data, the overall results for the individual entities are then determined based on the expectation equation presented in Equation (22). Accordingly, the result for the power, energy and cost components for the BESS are 24.1877 MW, 683.1663 kWh and 21,106.40 USD/day, respectively.

4.2.1. Optimal vs. Instantaneous BESS Power

Figure 7 shows the optimally determined BESS power capacity vs. the instantaneous power requirement for the individual minute-by-minute points. In the figure, the dotted lines represent the battery capacity determined optimally through the proposed algorithm, and the solid lines represent the minute-by-minute power requirements. From the figure, it can be determined that nearly 99% of the data point’s power requirement is satisfied for the RR requirement. Whereas, for the remaining 1% of data points, energy curtailment and penalty for violating the RR limit will be applied.

4.2.2. Validation Results

In order to confirm how the BESS is performing for RR improvement, validation is performed for two random wind energy generation patterns. The validation results are used to see how the already determined BESS capacity is able to improve the RR for selected profiles of wind energy data. That is, upon applying the same optimal procedure, the performance of the BESS in smoothing the wind energy at a random point in the wind energy dataset is analyzed. The result of this performance-checking procedure for the first wind energy signal is presented in Figure 8.

As can be seen from the plot, the original signal plotted in blue color is well smoothed and is plotted with brown color in the same figure. The performance of the BESS for this validation procedure is such that the original RR violation for the particular pattern of wind data being 6.740 MWh is significantly reduced to a value of 0.5891 MWh. For this particular validation test, the RR is improved to 91.26% of its original value. This is a very significant improvement in the wind energy RR. In the process, the battery performance measured with a change in the state of charge was so small that it could not affect the operation of the BESS for the next cycle.

Similarly, the same procedure is applied for a second random wind energy pattern, as shown in Figure 9. The result for this particular case is such that the original RR violation was changed from a value of 2.4950 MWh to a very small value of 0.2194 MWh. Likewise, the RR is improved to a significant percentage of 91.21% from the original RR value.

4.2.3. Frequency Improvement Performance of BESS

The advantage of the BESS to improve the steady state and transient responses of the power system based on its virtual inertia (VI) advantage is assessed. In the process, the model of a multi-machine power system [31], represented in the simulation model and the before and after RR improvement of the wind data, is presented in the command line used in the software. By integrating both models in the command line, the two models are run for the result of the transient and steady-state frequency of the multi-machine power system. The results for both before and after the incorporation of BESS in the model is recorded and presented as follows.

The transient response of the multi-machine power system integrated into the wind power system is shown in Figure 10 below. From the figure, the transient response frequency deviation as a result of the wind energy fluctuation in the RR time frame is seen to be 0.8 Hz. However, after the use of the proposed BESS for RR improvement, the wind energy fluctuation is stabilized. The smoothed wind energy fed to the grid gives the power system a better transient frequency response than the uncompensated wind energy system. The result of the BESS in improving the transient frequency response is shown in Figure 11. From the figure, the transient frequency response is improved from a deviation of 0.8 Hz to a deviation of 0.4 Hz. This is a good improvement that makes the frequency stay in the permissible frequency range.

Similarly, the joint effect of the BESS and the load frequency control capability of the multi-machine power system is checked for the steady-state frequency response of the system. The result shows that the steady-state frequency response of the overall system is found to be within the frequency permissible range. For example, the maximum frequency is 50.04 Hz, while the minimum frequency is 49.97 Hz. The result of this test is presented in Figure 12 below.

5. Conclusions

This paper presented the proposed hybrid optimization models constituting DST and PSO techniques to optimally size a BESS for two tasks of RR improvement and frequency regulation for an HPREG. The DST is used to characterize the long-recorded wind energy generation data and determine a sample BESS capacity for the individual data point. K-means clustering is used for three particular cluster sizes such that the whole data points are grouped to the number of cluster points. Later, representative datasets were generated. Finally, the PSO algorithm is used to determine the overall BESS capacity for the whole dataset assisted by the expectation equation. The resulting BESS capacity for RR improvement of the wind farm was verified for selected data points from the whole dataset. A RR track record for the selected data points was measured before and after the use of the optimal BESS. Similarly, the BESS VI significance was tested for their frequency regulation function. A multi-machine power system integrated into these BESS was simulated so that its frequency response in both the transient and steady-state time frames was recorded before and after the use of the BESS. Therefore, the conclusions from this work can be summarized as follows:

• The work proved the significance of BESS for their advantage of RR improvement and control of an HPREG-based power system as well as their significance for frequency regulation (performance improvement) of a power system.
• Similarly, the work showed a novel way of a hybrid optimization model of applying a huge dataset for planning and component sizing during data uncertainty.
• The optimal result of the BESS showed a significant improvement in the RR level of the wind energy data injected into the grid. In the two verification stages, a ramp rate violation improvement of 91.21% and 91.26% of the orginal value is achieved, respectively. The RR capacity of the BESS from the optimal result satisfies the RR requirement of 99% of the data points, a very significant figure.
• Similarly, the VI advantage of the BESS enabled the frequency performance of the test power system is improved. The transient frequency response is improved to a value of ±0.4 Hz after the integration of the BESS into the test power system. The steady-state frequency response of the test power system was improved to a maximum value of 50.04 Hz, while its minimum frequency was 49.97 Hz. Both of these extreme frequency ranges are within the healthy operation range of a power system.

The novelty of this work is the consideration of large datasets for the optimal capacity determination of the BESS for RR control and improvement of a wind farm, as well as for frequency regulation significance via its VI capability. Similarly, the paper includes energy curtailment cost to the objective function. This has the advantage of reducing the size of the BESS and, obviously, the overall cost of improving the RR.

As a future work, we recommend the optimal operation of the BESS be combined with demand-side management of some parts of the load. Loads on demand-side management could go ON and OFF based on the demand-side control strategy. This might help reduce the amount of abandoned wind energy and/or the capacity of the BESS.