This paper discusses realtime peak shaving algorithms for a largescale battery energy storage system (BESS). Although several transmission and distribution functions could be implemented for diverse purposes in BESS applications, this paper focuses on a realtime peak shaving algorithm for an energy time shift, considering wind power generation. In a high wind penetration environment, the effective load levels obtained by subtracting the wind generation from the load time series at each longterm cycle time unit are needed for efficient peak shaving. However, errors can exist in the forecast load and wind generation levels, and the realtime peak shaving operation might require a method for wind generation that includes comparatively large forecasting errors. To effectively deal with the errors of wind generation forecasting, this paper proposes a realtime peak shaving algorithm for threshold valuebased peak shaving that considers fuzzy wind power generation.
1. Introduction
Recently, we have been being experiencing a severe climate change because of increased CO
_{2}
emission rates resulting from the increased energy demand for industrial development. Several organizations around the world are looking for various ways to solve this problem. One solution might be the application of energy storage systems, which can play an important role in actively coping with the problem resulting from the variability of renewable energy resources, by storing energy that can later be consuming as needed. This paper focuses on the application of a battery energy storage system (BESS).
A BESS has several functions
[1

4]
that can be implemented to support a transmission and distribution grid. Among these, suppressing the peak load demand and equalizing the load levels with a largescale BESS is a longterm cycle application. This function is referred to as an energy time shift. In the daily load curve for a system, there is a difference between the peak and minimum load levels. Another longterm cycle function of system marginal price (SMP)based shaving can be implemented by a wholesale purchasing agency to maximize the benefit from charging and discharging schedules.
Power management systems (PMSs) for a largescale BESS were proposed in
[5]
. A PMS is used to obtain data for monitoring the system condition and selecting the active and reactive power settings for a local or dispersed power conditioning system (PCS) for the BESS. The ultimate goal of a PMS is maintaining the interoperability of the BESS with the operation strategies for an external electrical system implemented for reliability. The facilities for the demonstration research with a 4 MW and 8 MWh BESS at ‘Jochun’ was tested in the longterm and shortterm cycle operation modes.
This paper proposes a realtime peak shaving algorithm that considers wind power generation. As in
[6]
, the algorithm using a particular level of wind penetration employs the effective load curves, which are obtained by subtracting the wind generation from the load time series at each longterm cycle time unit. However, it should be noted that there are errors in the forecast load and wind generation values, and the realtime peak shaving operation might require a wind generation method with comparatively large forecasting errors. To effectively cope with the wind generation forecasting errors, this paper employs fuzzy wind power generation curves in a realtime algorithm for threshold value peak shaving. This paper includes illustrative examples to show the effectiveness of this realtime algorithm for peak shaving.
2. Peak Shaving Algorithm
The applicable schemes for using largescale batteries in power systems can essentially be divided into longterm and shortterm cycle modes. Peak shaving for an energy time shift can be considered to be the main function of battery energy storage in a longterm cycle operation. As in
[5]
, several other longterm cycle operation functions could be described, considering system security. However, based on the purpose, the total state of charge (SOC) of the participating BESS modules with a PCS must be in an adequate range to be ready just in case, and the active and reactive power ordered by the PCS of the BESS can be used for system margin enhancement, loss minimization, etc. Shortterm cycle operation with a BESS includes the mitigation of the fluctuating characteristic of renewable energy and frequency regulation with automatic generation control (AGC) or governor free (GF) actions.
In the literature, there are several approaches to peak shaving with energy storage devices. In
[7]
, offline and online peak shaving algorithms were described for a local load with renewable energy sources. The offline algorithm can provide scheduling with the assumption that the real load curve is known in advance; the online algorithm might then include the uncertainty of the load curve. In
[8]
, fundamental algorithms for peak shaving were proposed. In
[9]
, a fuzzy load model for uncertain load curves was adopted in the scheduling formulation for peak shaving. In
[9]
, a model predictive control method was employed to reduce the peak electricity demand in building climate control based on spot price forecasting. This paper describes a peak shaving method that determines a charging/discharging schedule to minimize the peak shaving threshold value, P
_{shave}
, considering the load data.
 2.1 Charging/Discharging Model for BESS
To determine the charging and discharging schedule for the longterm cycle operation of the BESS, a BESS model is needed that explains the behavior for the given charging and discharging actions by the PCS in the system. The most important aspect of this model is the SOC characteristic, which depends on the active power injection and consumption.
Through the observation of the equivalent circuit from the viewpoint of the change in SOC during operation, the following difference equation can be obtained:
where the following notations can be made:

EB(k): state of charge atk,

PB(k): power output at the point ofk,

ΔT: longterm time unit (30 min),

α: coefficient of loss by converter loss,

β: coefficient of loss by battery current loss,

γ: coefficient of selfdischarging.
In the model of Eq. (1), the loss terms totally depend on the active power output, which is the control input at each time period. As seen, two “±” signs are used for the loss coefficients in Eq. (1). If P
_{B}
(k) is positive, “+” is used; otherwise “” is taken. It should be noted that a positive P
_{B}
(k) represents the discharging state. The difference Eq. (1) is adequate for the scheduling problem of peak and SMP shaving, because it explains the longterm cycle charging and discharging behaviors in terms of the change in the SOC of the BESS.
 2.2 Peak Shaving Formulation
This subsection describes the fundamental peak shaving formulation. This algorithm is used to determine the charging and discharging schedule using the load data.
where
P_{shave}
is the threshold value for peak shaving, and
P_{fill}
is that for load filling. This algorithm has the purpose of minimizing
P_{shave}
during discharging periods and maximizing
P_{fill}
during charging periods. In Eq. (2)
P_{L}
(
k
) denotes the load level at time
k
. In Eq. (2),
M
and
N
stand for the starting and ending times for the scheduling;
P_{L}
(
k
) represent the scaleddown load level at time period
k
;
P
_{Bmin}
and
P
_{Bmax}
are the minimum and maximum designed power outputs, respectively;
E
_{Bmin}
and
E
_{Bmax}
are the minimum and maximum limits of the SOC, respectively, and corresponding constraints are needed to prevent overcharging and discharging; and
E_{Bo}
is the initial SOC right before the starting period of the scheduled discharge.
3. Wind Power Generation Forecasting Based on Fuzzy Modeling
In probability theory, a normal or Gaussian distribution is a very commonly occurring continuous probability distribution. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for realvalued random variables whose distributions are unknown.
Different probability distribution functions may be selected for different kinds of uncertain values
[10]
. The normal distribution function is used in this paper. The general formula of the probability density function for a normal distribution with uncertain variable x is given below:
where
x
is the uncertain variable for the probability function;
μ
is the mean value of the uncertain value, also called the location parameter; and
σ
is the standard deviation of the uncertain value, also called the scale parameter. The shape of the plot of the normal probability density function is shown in
Figure 1
. In this paper, the normal distribution is converted into trapezoidal fuzzy curves with four discrete points. The normal distribution curve is constructed based on wind power generation data with a sampling time of 30 min.
Normal distribution curve.
Power load data, especially for residential loads, are variable and uncertain. For example, the variability of the electricity consumption of a single residential customer generally depends on whether family members are home and on the time of use of a few highpower appliances with relatively short usage durations during the day, and is subject to very high uncertainty. Probabilistic analysis and fuzzy theory can be used to analyze the uncertainty of the load
[11]
.
A method for describing a membership function involves the application of data on the average value m and maximum error e of the input quantity. In practical applications, this method may be used to describe the values of wind power generation. In this case, the fuzzy parameters can be defined as follows
[12]
:
where e is the maximum error.
A trapezoidal fuzzy curve can be drawn using Eq. (4) and is shown in
Figure 2
. This paper calculates the fuzzy percentage using this curve. Four fuzzy forecasting wind power generation curves are made using these percentages. The formula for calculating the percentage is as follows:
Trapezoidal fuzzy model derived from given normal distribution function.
Wind power generation data are forecast using these four fuzzy forecasting wind power generation curves for realtime peak shaving. If the real wind power generation at an arbitrary point is smaller than the value of
fuzzy
(1), the realtime peak shaving algorithm chooses the
fuzzy
(1) wind power generation curve after this arbitrary point. Similarly, if the real wind power generation at an arbitrary point is greater than the value of
fuzzy
(4), the realtime peak shaving algorithm chooses the
fuzzy
(4) wind power generation curve after this arbitrary point. However, if the real wind power generation is in the region of
fuzzy
(1)(4), the method used to forecast the wind power generation changes. For example, if the real wind power generation is located in the region of
fuzzy
(1)(4), the algorithm calculates the percentage of real values from the nearest point, which becomes the starting point of the forecast wind power generation.
In the realtime operation, the applied level of wind generation is based on the fuzzy wind model at the following time period, which depends on the wind generation level at the previous longterm time unit. When the error between the real and forecast wind generation values is less than
fuzzy
(1) at the previous time unit, the wind generation is set to the lowest wind generation corresponding to the value with the error of
fuzzy
(1). When the error is between
fuzzy
(1) and
fuzzy
(2) or between
fuzzy
(3) and
fuzzy
(4), the wind generation level with the same fuzzy membership value is chosen. When the error is between
fuzzy
(2) and
fuzzy
(3), the wind generation level with the same distance from
fuzzy
(2) is employed. When the error is greater than
fuzzy
(4), the wind generation is set to the largest level in the fuzzy wind model. This forecasting is performed for the following longterm time periods.
4. Simulation and Results
This section describes the process of creating the trapezoidal fuzzy curve and gives corresponding examples of the application of the peak shaving algorithm. The wind power generation was classified on an hourly basis to generate the trapezoidal fuzzy curve and each fuzzy percentage. Thereafter, a normal distribution was made using the wind power generation data with respect to time.
Figure 3
shows a trapezoidal fuzzy curve that was drawn using this method. The fuzzy model might have different values over the entire period. This paper uses a 48 × 4 matrix that includes the endpoints of the trapezoidal models at all the periods using historical power generation data with 30min intervals.
Table 1
lists the percentages of the endpoints of the fuzzy model at each time period in reference to the expectation, as determined in this paper.
Normal distribution and trapezoidal fuzzy curves for wind power generation.
Percentages of endpoints of fuzzy model for wind power generation
Percentages of endpoints of fuzzy model for wind power generation
The same fuzzy model could also be applied to load curves, as in
[7]
. However, in
[7]
, the method used for the fuzzy model construction was not mentioned. This paper adds wind power generation data to the grid and performs realtime peak shaving under the assumption that the real load data are obtained. This paper illustrates the applicability of a fuzzy curve for wind power generation data.
Figures 4
and
5
show the real load curve and real wind power generation curve, respectively. Figure 6 shows four fuzzy curves based on the forecast wind power generation curve. In
Figures 4
–
6
, the xaxis denotes the longterm time unit (30 min) intervals over the course of a day.
Example of real load curve.
Example of wind power generation curves.
Trapezoidal fuzzy model based on expected wind power generation curve.
Figure 7
shows the peak shaving results using real load and real wind power generation data.
Figure 8
illustrates the peak shaving results using real load and forecast wind power generation data.
Figure 9
shows the peak shaving results using real load and wind power generation data after the application of the fuzzy model. In
Figures 7
–
9
, the
x
axis denotes the realtime unit (2 min). This paper reports a realtime peak shaving simulation that divides the longterm time unit into 10 sections because the fuzzy wind power generation changes as a result of the real wind power generation data at each point. In other words,
Figures 7
–
9
show the combined peak shaving results at the corresponding realtime units.
Peak shaving results using real wind power generation curve.
Peak shaving results using forecast wind power generation curve.
Peak shaving results using fuzzy model of wind power generation.
In a realtime simulation performed using the developed realtime mode emulator, one day is divided into five portions, and each portion starts from an longterm time unit: 1, 11, 21, 31, or 41. This is because different errors are expected between the real and forecast values of the wind power generation data at each portion. In other words, the error rate might be different depending on the time of day.
Table 2
lists the error at each longterm section, 1–10, 11–20, 21–30, 31–40, and 41–48, compared to the results when using the real wind power generation data. In the process of peak shaving, the effective load was adopted, which is the load subtracted by the wind power generation. As listed in the table, the error rates at each section are smaller when using the fuzzy model of wind power generation. The same characteristic is seen in the overall error rate.
Error rate of peak shaving results
5. Conclusions
This paper presented longterm cycle control strategies for a largescale BESS. The main focus of this paper was illustrating the applicability of a fuzzy model for the forecast wind power generation as an input for realtime peak shaving. This operation mode could be used to perform an energy time shift, and minimize the threshold value obtained from the difference between the upper and lower loads. This paper included an illustrative example showing the performance of the algorithm with real load and wind power generation data using real, forecast, and fuzzy modelbased curves with the developed realtime operation simulator.
Conflict of Interest No potential conflict of interest relevant to this article was reported.
BIO
Subin Son received B.S. in Electrical and Information Engineering from Seoul National University of Science & Technology in 2013. He is a graduate student at Seoul National University of Science & Technology. His research areas of interest are T&D application of battery energy storage systems, and power system operation.
Phone: +8229709873
Email: subregas@seoultech.ac.kr
Hwachang Song received B.S., M.S. and Ph.D. in Electrical Engineering from Korea University in 1997, 1999 and 2003, respectively. He was a postdoctoral visiting scholar at Iowa State University from 2003 to 2004. He was working as a faculty member in the School of Electronic and Information Engineering, Kunsan National University, from 2005 to 2008. Currently, he is an associate professor in the Department of Electrical and Information Engineering, Seoul National University of Science ＆ Technology. His research areas of interest are nonlinear optimization, power system stability and control, battery energy storage systems, and system modeling.
Phone: +8229706402
Email: hcsong@seoultech.ac.kr
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