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A statistical model to determine the capacity of battery–supercapacitor hybrid energy storage system in autonomous microgrid
Electrical Power and Energy Systems 54 (2014) 516–524
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A statistical model to determine the capacity of battery–supercapacitor hybrid energy storage system in autonomous microgrid Hongjie Jia, Yunfei Mu ⇑, Yan Qi Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 31 May 2012 Received in revised form 15 July 2013 Accepted 19 July 2013
Keywords: Autonomous microgrid Battery–supercapacitor hybrid energy storage system (BSHS) Hysteretic loop control strategy (HLC) Capacity statistical model Monte Carlo simulation (MCS)
a b s t r a c t Battery–supercapacitor hybrid energy storage system (BSHS) is a key component for regulating the frequency in autonomous microgrid. The lifetime and capacity are two important aspects for the efficient and economic use of BSHS. In this paper, the above two aspects are investigated in detail. Firstly, a new frequency control strategy based on hysteretic loop is developed for BSHS to extend the battery lifetime by avoiding small charge/discharge cycles. Then a capacity statistical model which is composed of statistical analysis, time-domain simulation and a capacity determination algorithm is proposed. Monte Carlo simulation is implemented to the statistical model to obtain the capacity distributions of BSHS. Finally, a benchmark low voltage microgrid is established as the test system using the commercial software DIgSILENT. Simulation results verify the effectiveness of the hysteretic loop control strategy and the capacity statistical model. The obtained capacity distributions of BSHS are used to determine the optimum capacity according to the needs of operation. The results also show that the hysteretic loop control strategy can reduce the capacity of Battery Energy Storage System (BESS) while increase the capacity of Supercapacitor Storage System (SCSS). Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The distributed generation using renewable energy is the most promising solution to de-carbonize the power industry in the future [1,2]. Microgrid (MG) which is defined as a low voltage (LV) network with a cluster of distributed generators (DGs) and loads connected to it is an effective structure for the integration of DGs [3]. The MG can operate either in grid connected mode or autonomous mode [4]. The DGs with intermittent nature (e.g., wind turbine (WT), photovoltaic (PV) generators, etc.) will cause the imbalance between power supply and demand in MG. As a result, frequency is a critical issue for the stable operation of MG. In the grid connected mode, MG exchanges power with the upstream grid to keep the balance between power supply and demand; while in the autonomous mode, the frequency issue becomes extremely serious. The conventional DGs, such as gas engine and microturbine can partly solve the above problem in MG, but these devices with slow dynamic response speed are hard to satisfy the frequency regulation requirement of MG. To solve this problem, the introduction of energy storage system (ESS) is considered as an effective solution. The ESS with ⇑ Corresponding author. Address: Room 627, Building 26(E), School of Electrical Engineering & Automation, Tianjin University, 92, Weijin Road, Tianjin 300072, People’s Republic of China. E-mail addresses: [email protected] (H. Jia), [email protected] (Y. Mu), qiyan.tju.fl[email protected] (Y. Qi). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.07.025
the characteristic of fast dynamic response can maintain power balance by exchanging instantaneous power with MG [5]. Two hot issues related to ESS in MG are as follows: 1.1. Frequency regulation Several studies have been carried out on ESS for regulating the frequency of autonomous MG [6–8]. The single type based ESS (e.g., battery, supercapacitor, fuel cell, etc.) has difficulty in satisfying the requirements of power and energy density simultaneously. For this reason, the hybrid energy storage system which can make full use of the complementary characteristics of each kind ESS is introduced to solve this problem. In particular, the battery–supercapacitor hybrid energy storage system (BSHS) with the advantages of high power and energy density is widely studied. In [9], a dynamic control strategy of DC/DC converter for the energy management between battery and supercapacitor was introduced. A control strategy for BSHS to improve the energy efficiency was proposed in [10], which also extends the service life of battery. Fuzzy logic control was applied to BSHS with advantage of no need for the precise model of BSHS in [11]. 1.2. ESS capacity determination The capacity is another issue for ESS. Usually, the ESS devices are over-sized to guarantee the operation reliability which will
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cause high investment cost. For this reason, a capacity optimization approach of battery energy storage system (BESS) for frequency regulation in an autonomous power system was presented in [12]. The approach uses sensitivity analysis technique to determine the BESS capacity for the largest economic performance index. In [13], numerical simulations based on historic frequency measurements are used to determine the minimum possible capacity which takes battery state of charge (SOC) limitation into consideration. A SOC-based control strategy is proposed and used in [14] for pursuing the optimum ESS capacity by keeping the battery SOC around 50%. But the above approaches are all deterministic based which may lead to impractical results. Besides, the increasing penetration of controllable loads (e.g., electric vehicles, refrigerator and air conditioners, etc.) in MG can contribute to the frequency response by the demand management without disturbing the users’ normal use [15]. In this case, the needed ESS capacity can be reduced by the coordination between these controllable loads and ESS. Therefore, it is important to determine the ESS capacity in a statistical way. This paper concentrates on both of the above two issues for autonomous MG. Firstly, a hysteretic loop control (HLC) strategy for frequency regulation is proposed, which can avoid small charge/discharge cycles on battery and extend the service life of battery. Secondly, a statistical model using Monte Carlo simulation (MCS) is developed to determine the capacity distributions of BSHS. Compared with the results obtained in [12–14], the capacity distributions are more flexible which can be used by engineers to choose the optimum capacity according to the needs of operation. Rest of the paper is organized as follows: Section 2 describes the principle of HLC strategy for BSHS in autonomous MG. The statistical model to determine the capacity distributions of BSHS is depicted in Section 3. A case study for demonstrating the above two methodologies is given in Section 4. Conclusions are stated in Section 5. 2. Frequency control strategy for autonomous microgrid In autonomous MG, one of the basic requirements is to maintain the frequency within an acceptable range. The WT and PV systems both operate at the maximum power points for efficient operation and their power outputs are intermittent [16]. In this paper, BSHS is used to keep the balance of instantaneous power and regulate the frequency of autonomous MG due to its fast-responding speed. The control scheme of BSHS is shown in Fig. 1, which is composed of three units. The frequency control unit (FCU) calculates the power references of BSHS (Pref,bat and Pref,sc) according to the new HLC strategy proposed in this paper. The automatic control unit (ACU) provides the pulse width modulation signals of BSHS (mbat, and msc) according to the outputs of frequency control unit. Proportional plus integral controller (PI controller) in ACU is used for no-error control of the power outputs of DGs/ESS. The function of pulse generation unit (PGU) is to generate the switching pulse signals which are used for driving converters.
517
In this paper, a HLC is developed for BSHS to regulate the frequency of autonomous microgrid. Compared with the classical hybrid control (CHC) strategy proposed in [10], a hysteretic loop is introduced in HLC to avoid the small charge/discharge cycles on BESS. The principle of HLC strategy is depicted in Fig. 2. The output of droop control loop is the power reference of BSHS Pref. Then Pref is divided into low-frequency components Pref,bat and high-frequency components Pref,sc by a low-pass filter. The low-frequency components are supplied by the BESS with high energy density, while high-frequency components are supplied by supercapacitor storage system (SCSS) with high power density and long service life. The SCSS acts as a ‘‘power buffer’’ to avoid large instantaneous charge/discharge current on BESS and extend the service life of battery. The basic principle of power distribution is having the battery to support system energy and the supercapacitor to meet the power requirement [9]. In order to avoid small charge/discharge cycles on BESS, the power output of BESS is controlled by a hysteretic loop (see Fig. 2). As shown in Fig. 3, four threshold levels placed symmetrically around frate (50 Hz) are used to define a control range and a non-working range in the allowed frequency range [fmin, fmax]. Three trigger signals (frate, fmin þ Df and fmax Df ) are introduced to determine the actions of BESS. If the measured frequency value fmeas reaches the trigger value fmin þ Df or fmax Df , then the BESS switches on and keeps working in the control range until the value of fmeas reaches frate. In this process, BESS exchanges power with MG to support the frequency and the power output of BESS Pref,bat equals to P 0ref;b . If the value of fmeas reaches frate, then the BESS stops working until fmeas reaches other trigger signals. During this period, the BESS is in non-working range to avoid small charge/discharge cycles. Therefore, the BESS switches between control range and non-working range according to the value of frequency. The difference between Pref and the output of hysteretic loop (Pref,b) is the power reference of SCSSPref,sc. Meanwhile, the battery SOC should be kept within a proper range [SOCmin, SOCmax] in the control process to avoid the battery degradation [17]. 3. Capacity statistical model of BSHS In this section, a statistical model using MCS is proposed to determine the capacity distributions of BSHS. The capacity of BSHS should be large enough to satisfy the requirement of frequency regulation. However, it is not economical to install over-sized BSHS. Therefore, the optimum capacity of BSHS in this paper is the minimum capacity which can satisfy the requirement of frequency regulation. The framework of capacity statistical model is depicted in Fig. 4. As Fig. 4 shows, the inputs of statistical model are historical data of wind speed/irradiance/loads and the outputs are the capacity distributions of BSHS. Firstly, statistical analysis is applied to the historical data to generate random powers of WT/PV/loads on a certain confidence level. Secondly, time-domain simulations of MG based on HLC are carried out to obtain the BSHS power. Finally,
Fig. 1. The control scheme of BSHS.
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Meanwhile, the distribution ranges of parameters c and k on a certain confidence level are obtained. Then the wind speed v at each specific time along a day is generated randomly based on the obtained parameters. The corresponding distribution range of wind speed on the predefined confidential level is obtained and shown in Fig. 5b. Finally, the random power output of a WT generatorPWT is obtained by the simplified model as shown in the following equation [19]:
8 mv cin > < P r v rat v cin PWT ðv Þ ¼ P r > : 0
Fig. 2. Principle of hysteretic loop control.
v cin 6 m 6 v rat v rat 6 mv cou m 6 v cin ; m P v cou
where Pr is the rated power; vrat is the rated wind speed; vcin is the cut-in wind speed and vcou is the cut-out wind speed. Following the same statistical method as wind speed, Fig. 6 shows the statistical analysis results of irradiance. The irradiance s at a specific time follows the normal distribution, whose pdf is expressed as follows [20]:
1 ðs lÞ2 pðsÞ ¼ pffiffiffiffiffiffiffiffiffiffi exp 2r2 2pr
! ð3Þ
where l is the expectation and r is the standard deviation. Then the random output range of a PV system is calculated by the implicit equation as shown in the following equation [21]:
Fig. 3. Control range and non-working range of BESS.
U pv þ Ipv Rs 1 Ipv ¼ NP ISC NP I0 exp nNS V T
ð4Þ
where ISC is the short circuit current of a PV module [A];I0 is the diode saturation current [A]; n is the ideal constant of diode; VT is the thermal potential of a module [V];NP is the number of PV modules in parallel; NS is the number of PV modules in series. Also, the random characteristic of loads in the MG is considered by the MCS in this paper. It is assumed that the load at each load bus also follows the normal distribution (depicted in (3)) at each time during time-domain simulation process, with the parameters of lL and rL. 3.2. Capacity determination algorithm Fig. 4. Framework of capacity statistical model.
the data of BSHS power are processed by the capacity determination algorithm and the capacity distributions of BSHS are obtained using MCS. The HLC for time-domain simulation of MG is introduced in Section 2. In this section, the statistical analysis and capacity determination algorithm are introduced.
3.1. Statistical analysis In order to carry out MCS, the precise power distributions of WT and PV systems in the MG should be determined firstly. The distributions of wind speed and irradiance for one day are obtained by statistical analysis based on the historical data. Fig. 5 shows the statistical analysis results of wind speed in a certain area of China from a ten-year’s data. As shown in Fig. 5a, the wind speed v at a specific time follows the Weibull distribution [18], whose probability density function (pdf) is expressed in the following equation:
pðv Þ ¼
k v k1 v k exp c c c
where k is the shape parameter and c is the scale parameter.
ð1Þ
Considering the uncertainties from intermittent DGs and loads, a capacity determination algorithm is proposed to determine the capacity distributions of BSHS. The capacity includes power capacity and energy capacity. Power capacity is the maximum instantaneous output that the ESS can provide which is usually measured in kilowatts (kW). Energy capacity is the amount of electrical energy that the ESS can store which is measured in kilowatt-hours (kW h) [22]. 3.2.1. Capacity of BESS The BESS is used to provide the MG with energy support. It is assumed that the frequency of MG is regulated by a BESS with enough capacity. As shown in Fig. 7, the power above the time-axis means the battery is discharging for regulating the frequency. Conversely, the power curve below the time-axis means the battery is charging to maintain the frequency at a reasonable range. In order to ensure every single charging or discharging process is not limited by the rated power of BESS, the absolute value of the largest power corresponds to the minimum power capacity of BESS. Samples the output power of BESS, The energy capacity of BESS should be considered at the same time. As depicted in Fig. 7, the negative area A means the BESS is storing energy for frequency regulation, and the minimum required energy can be realized by a BESS with capacity jAj in the X1 region. Meanwhile, the areas of B, C, D have the same meanings
H. Jia et al. / Electrical Power and Energy Systems 54 (2014) 516–524
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Fig. 5. The statistical analysis results of wind speed.
Fig. 6. The statistical analysis results of irradiance.
Eb ¼ Eb;min =ðSOCmax SOCmin Þ
ð6Þ
3.2.2. Capacity of SCSS The SCSS is used to compensate the power fluctuations of MG. The SCSS power output for the MG frequency regulation is shown in Fig. 8. The power profile shows that the SCSS experiences frequent charge/discharge cycles and the power fluctuates severely
Fig. 7. BESS power profile for one day.
with A (the positive areas B, D mean the BESS is releasing energy for frequency regulation). The minimum energy capacity of BESS without SOC limitation Eb,min is the maximum energy required for the whole successive simulation period from A to D, which is shown as follows:
Eb;min ¼ MaxfjAj; jA þ Bj; jA þ B þ Cj; jA þ B þ C þ Djg
ð5Þ
As depicted in Section 2, the SOC of battery should be kept within a proper range [SOCmin, SOCmax], which means Eb,min is only part of the energy capacityEb. Therefore, the energy capacity considering SOC limitation is shown as follows:
Fig. 8. SCSS power profile for one day.
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around the time-axis, which follows the power distribution principle depicted in Section 2. The capacity determination of SCSS is similar as the BESS. The minimum power capacity Pc and energy capacity Ec,min can be obtained. Usually, Ec,min is converted into the capacitor value Cc to express the energy capacity of supercapacitor. The relationship between Ec,min and Cc is given in the following equation:
Ec;min ¼
1 C c ðV 2max V 2min Þ 2
ð7Þ
where Vmax and Vmin are the allowed minimum and maximum terminal voltage of supercapacitor, separately. Therefore, the energy capacity of supercapacitor Cc is expressed as follows:
C c ¼ 2 Ec;min =ðV 2max V 2min Þ
ð8Þ
3.3. Flowchart of capacity statistical model The flowchart of capacity statistical model is shown in Fig. 9. As shown in Fig. 9, a set of random parameters [c, k, l, r, lL, rL] generate a set of capacity results [Pb, Eb, Pc, Cc]. Based on statistical analysis, a large number of random scenarios on a certain confidence level are generated using MCS and then a series of BSHS
capacities are obtained. The MCS terminates when ITER reaches the maximum simulation times Nmax and the corresponding capacity distributions of BSHS are determined.
4. Numerical studies This section presents a case study to illustrate the performance of HLC strategy and verify the effectiveness of capacity statistical model. The benchmark LV network [23] built in DIg SILENT software is shown in Fig. 10, which comprises a LV feeder, loads, several microgeneration systems (WT, PVs, fuel cell and microturbine) and BSHS. To simplify the study, fuel cell and microturbine models are replaced by DC voltage sources, and their power outputs are set to be constant. As shown in Fig. 10, a hybrid WT/PV system is connected to bus 15 and a single PV system is connected to bus 17. The WT/PV control parameters are shown in Appendix A and B. The BSHS is connected to bus 13. A typical battery model taking SOC into consideration and a non-linear supercapacitor model are used in this case [24]. The battery and supercapacitor are connected to MG by independent inverters separately for flexible control. The parameters of BSHS model and control systems are shown in Appendix C and D.
Fig. 9. Flowchart of capacity statistical model.
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Fig. 12. Power outputs of DGs and microgrid frequency.
Fig. 10. Benchmark low voltage microgrid.
4.1. The performance of HLC strategy The wind speed and irradiance data of an autumn day in a certain area of China are shown in Fig. 11a and b, separately. The typical load profiles (in mean values lL) are shown in Fig. 11c in which the loads 4, 12, 17 represent the typical residential loads and loads 13, 19 represent the typical commercial loads.
Fig. 11. Simulation environment.
Fig. 12a shows that the outputs of WT and PV systems fluctuate with the variations of wind speed and irradiance. The BSHS is used to compensate the imbalance between the power supply and demand. As Fig. 12b shows, under HLC strategy, the SCSS responds to fast power fluctuations, which causes frequent charge/discharge cycles on the SCSS. Meanwhile, the battery only works at intervals to provide the MG with energy. The frequency under HLC is shown in Fig. 12c, where the allowed frequency range is set to be [49.97 Hz, 50.03 Hz] and the value of Df is set to be 0.02. As depicted in Section 2, when the frequency reaches 50.02 Hz or 49.98 Hz, the BESS is triggered for frequency response with SCSS until the frequency reaches 50.0 Hz. When the value of frequency reaches 50.0 Hz, the battery is out of service and only the SCSS works to regulate the frequency until the frequency reaches 50.02 Hz or 49.98 Hz. It shows that the frequency under HLC is controlled within the predefined range [49.97 Hz, 50.03 Hz] and the battery and supercapacitor make full use of their complementary characteristics. The battery output comparison between HLC and classical hybrid control (CHC) strategy proposed in [10] is shown in
Fig. 13. Battery output comparison under different control strategies.
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Fig. 14. Distribution ranges of wind speed and irradiance.
Fig. 13. Between 4 and 15 h, the power output of BESS under HLC is zero and the SOC of battery is unchanged which means the BESS is out of service, while the power output and SOC under CHC fluctuates continuously, which indicates that the battery experiences small charge/discharge cycles. Compared with CHC, the BESS under HLC only works at intervals for frequency regulation which can avoid small charge/discharge cycles on battery. Based on the analysis above, the HLC strategy not only can regulate the frequency within the predefined control range, but also can avoid the small charge/discharge cycles on the battery.
Fig. 16. Cumulative probability functions of BSHS capacity under different control strategies.
4.2. Capacity distributions of BSHS This section verifies the effectiveness of the capacity statistical model firstly and then analyzes the influence from different control strategies on the capacity of BSHS. 4.2.1. The capacity distributions of BSHS The distribution ranges of wind speed and irradiance on the confidence level of 99% are shown in Fig. 14 and the loads are
generated randomly using normal distribution based on the typical load profiles shown in Fig. 11a. The previous methods to obtain the capacity of ESS are ‘‘worst scenario’’ based and the results are conservative. The statistical model using MCS presented in this paper can solve this problem in a statistical way. The capacity probability distributions of BSHS under HLC and CHC are shown in Figs. 15 and 16. Figs. 15 and 16 show the capacity distributions of BESS and SCSS. According to the cumulative probability functions shown in Fig. 16, the energy capacity and the corresponding power capacity of BSHS can be determined on each specific cumulative probability level. As depicted in Table 1, the results on three typical levels (50%, 75% and 90%) are given. For example, the BESS energy capacity Eb,HLC corresponding to the cumulative probability of 90% under HLC is 641.6552 kW h and that of 75% is 600.2094 kW h. The energy capacity of BESS is saved by 41.4458 kW h when the cumulative probability is 75%. This is meaningful when there are high penetrations of controllable loads which can contribute to the frequency response of MG [14]. With the development of demand side management in microgrid, the capacity statistical model proposed in this paper offers a flexible way for engineers to choose the optimum capacity of BSHS for MG according to the needs of operation.
Table 1 BSHS capacity comparisons at different cumulative probability. The value of cumulative distribution
Fig. 15. Probability distributions of BSHS capacity under different control strategies.
Eb,HLC (kW h) Eb,CHC (kW h) Pb,HLC (kW) Pb,CHC (kW) Cc,HLC (F) Cc,CHC (F) Pc,HLC (kW) Pc,CHC (kW)
50%
75%
90%
546.4927 591.3565 53.5924 53.5913 6.1793 5.8010 58.4052 54.1861
600.2094 640.6201 57.9635 57.8214 6.9663 6.7438 62.1191 58.9540
641.6552 695.0820 62.5392 62.1991 7.9687 7.8683 66.5202 62.5392
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level. As shown in Table 1, at the cumulative probability of 90%, the power capacity of SCSS under HLC is 66.5202 kW and that under CHC is 62.5392 kW. Compared with CHC, the SCSS power capacity under HLC is increased by 6.3% at the cumulative probability of 90%. This is because under HLC, the frequency regulation is dependent on SCSS when the BESS is in non-working range and parts of the SCSS power are larger than those under CHC, which can give full play to the high power density characteristic of SCSS. Meanwhile, the energy capacity of SCSS under HLC is a little larger than that under CHC, which can be seen from Table 2.
Table 2 Parameters of BSHS capacity distributions.
Eb,HLC (kW h) Eb,CHC (kW h) Pb,HLC (kW) Pb,CHC (kW) Cc,HLC (F) Cc,CHC (F) Pc,HLC (kW) Pc,CHC (kW)
Expectation
Standard deviation
550.3697 591.3551 54.3257 54.2800 6.1914 5.8743 58.5658 54.7267
69.3879 76.878 6.2955 6.2512 1.354 1.4206 5.9819 6.2012
4.2.2. Capacity comparisons of BSHS under different control strategies In this part, the impact from different control strategies on the distributions of BSHS capacity is investigated using the statistical model.
5. Conclusions A statistical model using MCS to determine the capacity distributions of BSHS is proposed in this paper for ESS planning in MG. The advantage of this statistical model is that the capacities of BSHS at different cumulative probability levels can be determined. Compared with the deterministic based methods, the statistical model is more flexible for engineers to choose the optimum capacity according to the needs of operation. Additionally, the influence from different control strategies on the capacity distributions of BSHS is studied and compared in this paper. Compared with CHC, the HLC strategy proposed in this paper can reduce the energy capacity of BESS to a certain extent while increase the capacity of SCSS. Although the power capacity of SCSS is increased, it can give full play to the high power density characteristic of SCSS. Besides, the HLC can avoid small charge/discharge cycles on battery, which can extend the service life of battery. With the surging development of MG, the capacity statistical model definitely provides a useful tool for ESS planning and coordinating the ESS capacity with load-demand management, which is also the work to be studied in future.
4.2.2.1. BESS capacity comparison. The parameters of BESS capacity distributions under HLC and CHC are shown in Table 2. The energy capacity expectation of BESS under HLC is smaller than that under CHC by 40.9854 kW h, and the standard deviation of BESS energy capacity under HLC is also smaller than that under CHC by 7.4901 kW h. Fig. 16a shows that the cumulative probability values under HLC are higher than that under CHC at the same capacity level, which means the energy capacity under HLC is smaller than that under CHC at the same cumulative probability level. As shown in Table 1, at the cumulative probability of 90%, the energy capacity of BESS under HLC is 641.6552 kW h and that under CHC is 695.0820 kW h. Compared with CHC, the HLC strategy can save the BESS energy capacity by 7.7% at the cumulative probability of 90% for the HLC strategy can avoid small charge/discharge cycles on BESS. The power capacity distributions of BESS under HLC are similar with that under CHC, which can be seen from Table 1 and Fig. 16d. This is because the HLC only avoids small charge/discharge cycles on battery and the maximum charge/discharge power is almost unchanged.
Acknowledgements This work is supported by Special Fund of the National Basic Research Program of China (‘‘973’’ Program, Grant No. 2009CB219701), National Natural Science Foundation of China (Grant Nos. 51277128, 513111017, 51377117 and 51307115), Tianjin Municipal Science and Technology Development Program of China (Grant No. 09JCZDJC25000) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090032110064).
4.2.2.2. SCSS capacity comparison. Table 2 shows that the power capacity expectation of SCSS under HLC is larger than that under CHC, and Fig. 16d also shows that the power capacity under HLC is larger than that under CHC at the same cumulative probability
Appendix A. Dynamic parameters of WT system (Definition of parameters referring to [18])
WT model
Inverter
Pr (kW)
vrat (m/s)
vcin (m/s)
vcou (m/s)
60
13
3
20
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
0.5
0.08
0.5
0.08
0.2
0.01
0.2
0.01
Appendix B. Dynamic parameters of PV system (Definition of parameters referring to [20])
PV model
Inverter
Voc (V)
ISC,ref (A)
Pmax,ref (W)
Vmp,ref (V)
Imp,ref (A)
k (J/K)
q(c)
J
c
21.7
3.35
53
17.4
3.05
1.38e23
1.6e19
6.5e4
3
A
n
Rs (X)
Eg,ref (c)
T (K)
Tr (K)
NP
NS
m
1.76
1.5
0.3162
1.237q
321.3
298
12
46
36
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
5
0.05
5
0.05
0.4
0.01
0.4
0.01
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Appendix C. Dynamic parameters of BESS system (Definition of parameters referring to [23])
Battery model
Inverter
V0 (V)
K
Q
Rb (X)
A
B
SOC0
NP
NS
226.25
8.9
3
20
18.644
2.3
0.6
2
4
Kd
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
10
0.8
0.1
0.8
0.1
0.2
0.01
0.2
0.01
Appendix D. Dynamic parameters of SCSS system (Definition of parameters referring to [23])
Supercapacitor model
Inverter
V0 (V)
R (X)
C (F)
800
0.01
10
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
0.8
0.05
0.8
0.05
0.2
0.01
0.2
0.01
References [1] Verma YP, Kumar A. Potential impacts of emission concerned policies on power system operation with renewable energy sources. Int J Electr Power Energy Syst 2013;44:521–9. [2] Prenc R, Škrlec D, Komen V. Distributed generation allocation based on average daily load and power production curves. Int J Electr Power Energy Syst 2013;53:612–22. [3] Alvarez E, Campos AM, Arboleya P, Gutiérrez AJ. Microgrid management with a quick response optimization algorithm for active power dispatch. Int J Electr Power Energy Syst 2012;43:465–73. [4] Waleed Al-Saedi, Lachowicz Stefan W, Daryoush Habibi, Octavian Bass. Power quality enhancement in autonomous microgrid operation using particle swarm optimization. Int J Electr Power Energy Syst 2012;42(1):139–49. [5] Tan X, Li Q, Wang H. Advances and trends of energy storage technology in microgrid. Int J Electr Power Energy Syst 2013;44(1):179–91. [6] Ramon Zamora, Srivastava Anurag K. Controls for microgrids with storage: review challenges and research needs. Renew Sustain Energy Rev 2010. [7] Ngamroo I. Application of electrolyzer to alleviate power fluctuation in a standalone microgrid based on an optimal fuzzy PID control. Int J Electr Power Energy Syst 2012;43(1):969–76. [8] Vachirasricirikul S, Ngamroo I. Robust controller design of microturbine and electrolyzer for frequency stabilization in a microgrid system with plug-in hybrid electric vehicles. Int J Electr Power Energy Syst 2012;43:804–11. [9] Camara MB, Gualous H, Gustin F, Alain B, Brayima B. DC/DC converter design for supercapacitor and battery power management in hybrid vehicle applications-polynomial control strategy. IEEE Trans Ind Electron 2010;57(2):587–97. [10] Zhang Y, Jiang Z, Yu X. Control strategies for battery/supercapacitor hybrid energy storage systems. In: Energy 2030 conference; 2008. p. 1–6. [11] Li Q, Chen W, Li Y, Liu S, Huang J. Energy management strategy for fuel cell/ battery/ultracapacitor hybrid vehicle based on fuzzy logic. Int J Electr Power Energy Syst 2012;43:514–25. [12] Sigrist L, Lobato E, Rouco L. Energy storage systems providing primary reserve and peak shaving in small isolated power systems: an economic assessment. Int J Electr Power Energy Syst 2013;53(1):675–83.
[13] Oudalov A, Chartouni D, Ohler C. Optimizing a battery energy storage system for primary frequency control. IEEE Trans Power System 2007;22(3):1259–66. [14] Li X, Hui D, Lai X. Battery energy storage station (BESS)-based smoothing control of photovoltaic (PV) and wind power generation fluctuations. IEEE Trans Sustain Energy 2013;4(2):464–73. [15] Jia H, Mu Y, Qi Y. Frequency response of autonomous microgrid based on family-friendly controllable loads. Sci China Tech Sci 2013;56(3):693–702. [16] Koizumi H, Mizuno T, Kaito T, Noda Y, Goshima N, Kawasaki M, et al. A novel microcontroller for grid-connected photovoltaic systems. IEEE Trans Ind Electron 2006;53(6):1889–97. [17] Mu Y, Wu J, Ekanayake JB, Jenkins N, Jia H. Primary frequency response from electric vehicles in the Great Britain power system. IEEE Trans Smart Grid 2013;4(2):1142–50. [18] Yao DL, Choi SS, Tseng KJ, Lie TT. A statistical approach to the design of a dispatchable wind power-battery energy storage system. IEEE Trans Energy Convers 2009;24(4):916–25. [19] Mu Y, Jia H. An approach to determining the local boundaries of voltage stability region with wind farms in power injection space. Sci China Tech Sci 2010;53(12):3232–40. [20] Handbook on statistical distributions for experimentalists. Christian Walck. Particle Physics Group University of Stockholm. Stockholm, Sweden; 2007. [21] Kim SK, Jeon JH, Cho CH, Kim ES, Ahn JB. Modeling and simulation of a gridconnected PV generation system for electromagnetic transient analysis. Sol Energy 2009;83(5):664–78. [22] David Connolly. An investigation into the energy storage technologies available, for the integration of alternative generation techniques; 2007. [23] Papathanassiou S, Hatziargyriou N, Strunz K. A benchmark low voltage microgrid network. In: Proceedings of CIGRE symposium; 2005. p. 1–8. [24] Liu Xiong, Wang Peng, Loh Poh Chiang, et al. Control of hybrid battery/Ultracapacitor energy storage for stand alone photovoltaic system. Energy Convers Congr Expos 2010:336–41.
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
A statistical model to determine the capacity of battery–supercapacitor hybrid energy storage system in autonomous microgrid Hongjie Jia, Yunfei Mu ⇑, Yan Qi Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin 300072, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 31 May 2012 Received in revised form 15 July 2013 Accepted 19 July 2013
Keywords: Autonomous microgrid Battery–supercapacitor hybrid energy storage system (BSHS) Hysteretic loop control strategy (HLC) Capacity statistical model Monte Carlo simulation (MCS)
a b s t r a c t Battery–supercapacitor hybrid energy storage system (BSHS) is a key component for regulating the frequency in autonomous microgrid. The lifetime and capacity are two important aspects for the efficient and economic use of BSHS. In this paper, the above two aspects are investigated in detail. Firstly, a new frequency control strategy based on hysteretic loop is developed for BSHS to extend the battery lifetime by avoiding small charge/discharge cycles. Then a capacity statistical model which is composed of statistical analysis, time-domain simulation and a capacity determination algorithm is proposed. Monte Carlo simulation is implemented to the statistical model to obtain the capacity distributions of BSHS. Finally, a benchmark low voltage microgrid is established as the test system using the commercial software DIgSILENT. Simulation results verify the effectiveness of the hysteretic loop control strategy and the capacity statistical model. The obtained capacity distributions of BSHS are used to determine the optimum capacity according to the needs of operation. The results also show that the hysteretic loop control strategy can reduce the capacity of Battery Energy Storage System (BESS) while increase the capacity of Supercapacitor Storage System (SCSS). Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction The distributed generation using renewable energy is the most promising solution to de-carbonize the power industry in the future [1,2]. Microgrid (MG) which is defined as a low voltage (LV) network with a cluster of distributed generators (DGs) and loads connected to it is an effective structure for the integration of DGs [3]. The MG can operate either in grid connected mode or autonomous mode [4]. The DGs with intermittent nature (e.g., wind turbine (WT), photovoltaic (PV) generators, etc.) will cause the imbalance between power supply and demand in MG. As a result, frequency is a critical issue for the stable operation of MG. In the grid connected mode, MG exchanges power with the upstream grid to keep the balance between power supply and demand; while in the autonomous mode, the frequency issue becomes extremely serious. The conventional DGs, such as gas engine and microturbine can partly solve the above problem in MG, but these devices with slow dynamic response speed are hard to satisfy the frequency regulation requirement of MG. To solve this problem, the introduction of energy storage system (ESS) is considered as an effective solution. The ESS with ⇑ Corresponding author. Address: Room 627, Building 26(E), School of Electrical Engineering & Automation, Tianjin University, 92, Weijin Road, Tianjin 300072, People’s Republic of China. E-mail addresses: [email protected] (H. Jia), [email protected] (Y. Mu), qiyan.tju.fl[email protected] (Y. Qi). 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.07.025
the characteristic of fast dynamic response can maintain power balance by exchanging instantaneous power with MG [5]. Two hot issues related to ESS in MG are as follows: 1.1. Frequency regulation Several studies have been carried out on ESS for regulating the frequency of autonomous MG [6–8]. The single type based ESS (e.g., battery, supercapacitor, fuel cell, etc.) has difficulty in satisfying the requirements of power and energy density simultaneously. For this reason, the hybrid energy storage system which can make full use of the complementary characteristics of each kind ESS is introduced to solve this problem. In particular, the battery–supercapacitor hybrid energy storage system (BSHS) with the advantages of high power and energy density is widely studied. In [9], a dynamic control strategy of DC/DC converter for the energy management between battery and supercapacitor was introduced. A control strategy for BSHS to improve the energy efficiency was proposed in [10], which also extends the service life of battery. Fuzzy logic control was applied to BSHS with advantage of no need for the precise model of BSHS in [11]. 1.2. ESS capacity determination The capacity is another issue for ESS. Usually, the ESS devices are over-sized to guarantee the operation reliability which will
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cause high investment cost. For this reason, a capacity optimization approach of battery energy storage system (BESS) for frequency regulation in an autonomous power system was presented in [12]. The approach uses sensitivity analysis technique to determine the BESS capacity for the largest economic performance index. In [13], numerical simulations based on historic frequency measurements are used to determine the minimum possible capacity which takes battery state of charge (SOC) limitation into consideration. A SOC-based control strategy is proposed and used in [14] for pursuing the optimum ESS capacity by keeping the battery SOC around 50%. But the above approaches are all deterministic based which may lead to impractical results. Besides, the increasing penetration of controllable loads (e.g., electric vehicles, refrigerator and air conditioners, etc.) in MG can contribute to the frequency response by the demand management without disturbing the users’ normal use [15]. In this case, the needed ESS capacity can be reduced by the coordination between these controllable loads and ESS. Therefore, it is important to determine the ESS capacity in a statistical way. This paper concentrates on both of the above two issues for autonomous MG. Firstly, a hysteretic loop control (HLC) strategy for frequency regulation is proposed, which can avoid small charge/discharge cycles on battery and extend the service life of battery. Secondly, a statistical model using Monte Carlo simulation (MCS) is developed to determine the capacity distributions of BSHS. Compared with the results obtained in [12–14], the capacity distributions are more flexible which can be used by engineers to choose the optimum capacity according to the needs of operation. Rest of the paper is organized as follows: Section 2 describes the principle of HLC strategy for BSHS in autonomous MG. The statistical model to determine the capacity distributions of BSHS is depicted in Section 3. A case study for demonstrating the above two methodologies is given in Section 4. Conclusions are stated in Section 5. 2. Frequency control strategy for autonomous microgrid In autonomous MG, one of the basic requirements is to maintain the frequency within an acceptable range. The WT and PV systems both operate at the maximum power points for efficient operation and their power outputs are intermittent [16]. In this paper, BSHS is used to keep the balance of instantaneous power and regulate the frequency of autonomous MG due to its fast-responding speed. The control scheme of BSHS is shown in Fig. 1, which is composed of three units. The frequency control unit (FCU) calculates the power references of BSHS (Pref,bat and Pref,sc) according to the new HLC strategy proposed in this paper. The automatic control unit (ACU) provides the pulse width modulation signals of BSHS (mbat, and msc) according to the outputs of frequency control unit. Proportional plus integral controller (PI controller) in ACU is used for no-error control of the power outputs of DGs/ESS. The function of pulse generation unit (PGU) is to generate the switching pulse signals which are used for driving converters.
517
In this paper, a HLC is developed for BSHS to regulate the frequency of autonomous microgrid. Compared with the classical hybrid control (CHC) strategy proposed in [10], a hysteretic loop is introduced in HLC to avoid the small charge/discharge cycles on BESS. The principle of HLC strategy is depicted in Fig. 2. The output of droop control loop is the power reference of BSHS Pref. Then Pref is divided into low-frequency components Pref,bat and high-frequency components Pref,sc by a low-pass filter. The low-frequency components are supplied by the BESS with high energy density, while high-frequency components are supplied by supercapacitor storage system (SCSS) with high power density and long service life. The SCSS acts as a ‘‘power buffer’’ to avoid large instantaneous charge/discharge current on BESS and extend the service life of battery. The basic principle of power distribution is having the battery to support system energy and the supercapacitor to meet the power requirement [9]. In order to avoid small charge/discharge cycles on BESS, the power output of BESS is controlled by a hysteretic loop (see Fig. 2). As shown in Fig. 3, four threshold levels placed symmetrically around frate (50 Hz) are used to define a control range and a non-working range in the allowed frequency range [fmin, fmax]. Three trigger signals (frate, fmin þ Df and fmax Df ) are introduced to determine the actions of BESS. If the measured frequency value fmeas reaches the trigger value fmin þ Df or fmax Df , then the BESS switches on and keeps working in the control range until the value of fmeas reaches frate. In this process, BESS exchanges power with MG to support the frequency and the power output of BESS Pref,bat equals to P 0ref;b . If the value of fmeas reaches frate, then the BESS stops working until fmeas reaches other trigger signals. During this period, the BESS is in non-working range to avoid small charge/discharge cycles. Therefore, the BESS switches between control range and non-working range according to the value of frequency. The difference between Pref and the output of hysteretic loop (Pref,b) is the power reference of SCSSPref,sc. Meanwhile, the battery SOC should be kept within a proper range [SOCmin, SOCmax] in the control process to avoid the battery degradation [17]. 3. Capacity statistical model of BSHS In this section, a statistical model using MCS is proposed to determine the capacity distributions of BSHS. The capacity of BSHS should be large enough to satisfy the requirement of frequency regulation. However, it is not economical to install over-sized BSHS. Therefore, the optimum capacity of BSHS in this paper is the minimum capacity which can satisfy the requirement of frequency regulation. The framework of capacity statistical model is depicted in Fig. 4. As Fig. 4 shows, the inputs of statistical model are historical data of wind speed/irradiance/loads and the outputs are the capacity distributions of BSHS. Firstly, statistical analysis is applied to the historical data to generate random powers of WT/PV/loads on a certain confidence level. Secondly, time-domain simulations of MG based on HLC are carried out to obtain the BSHS power. Finally,
Fig. 1. The control scheme of BSHS.
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Meanwhile, the distribution ranges of parameters c and k on a certain confidence level are obtained. Then the wind speed v at each specific time along a day is generated randomly based on the obtained parameters. The corresponding distribution range of wind speed on the predefined confidential level is obtained and shown in Fig. 5b. Finally, the random power output of a WT generatorPWT is obtained by the simplified model as shown in the following equation [19]:
8 mv cin > < P r v rat v cin PWT ðv Þ ¼ P r > : 0
Fig. 2. Principle of hysteretic loop control.
v cin 6 m 6 v rat v rat 6 mv cou m 6 v cin ; m P v cou
where Pr is the rated power; vrat is the rated wind speed; vcin is the cut-in wind speed and vcou is the cut-out wind speed. Following the same statistical method as wind speed, Fig. 6 shows the statistical analysis results of irradiance. The irradiance s at a specific time follows the normal distribution, whose pdf is expressed as follows [20]:
1 ðs lÞ2 pðsÞ ¼ pffiffiffiffiffiffiffiffiffiffi exp 2r2 2pr
! ð3Þ
where l is the expectation and r is the standard deviation. Then the random output range of a PV system is calculated by the implicit equation as shown in the following equation [21]:
Fig. 3. Control range and non-working range of BESS.
U pv þ Ipv Rs 1 Ipv ¼ NP ISC NP I0 exp nNS V T
ð4Þ
where ISC is the short circuit current of a PV module [A];I0 is the diode saturation current [A]; n is the ideal constant of diode; VT is the thermal potential of a module [V];NP is the number of PV modules in parallel; NS is the number of PV modules in series. Also, the random characteristic of loads in the MG is considered by the MCS in this paper. It is assumed that the load at each load bus also follows the normal distribution (depicted in (3)) at each time during time-domain simulation process, with the parameters of lL and rL. 3.2. Capacity determination algorithm Fig. 4. Framework of capacity statistical model.
the data of BSHS power are processed by the capacity determination algorithm and the capacity distributions of BSHS are obtained using MCS. The HLC for time-domain simulation of MG is introduced in Section 2. In this section, the statistical analysis and capacity determination algorithm are introduced.
3.1. Statistical analysis In order to carry out MCS, the precise power distributions of WT and PV systems in the MG should be determined firstly. The distributions of wind speed and irradiance for one day are obtained by statistical analysis based on the historical data. Fig. 5 shows the statistical analysis results of wind speed in a certain area of China from a ten-year’s data. As shown in Fig. 5a, the wind speed v at a specific time follows the Weibull distribution [18], whose probability density function (pdf) is expressed in the following equation:
pðv Þ ¼
k v k1 v k exp c c c
where k is the shape parameter and c is the scale parameter.
ð1Þ
Considering the uncertainties from intermittent DGs and loads, a capacity determination algorithm is proposed to determine the capacity distributions of BSHS. The capacity includes power capacity and energy capacity. Power capacity is the maximum instantaneous output that the ESS can provide which is usually measured in kilowatts (kW). Energy capacity is the amount of electrical energy that the ESS can store which is measured in kilowatt-hours (kW h) [22]. 3.2.1. Capacity of BESS The BESS is used to provide the MG with energy support. It is assumed that the frequency of MG is regulated by a BESS with enough capacity. As shown in Fig. 7, the power above the time-axis means the battery is discharging for regulating the frequency. Conversely, the power curve below the time-axis means the battery is charging to maintain the frequency at a reasonable range. In order to ensure every single charging or discharging process is not limited by the rated power of BESS, the absolute value of the largest power corresponds to the minimum power capacity of BESS. Samples the output power of BESS, The energy capacity of BESS should be considered at the same time. As depicted in Fig. 7, the negative area A means the BESS is storing energy for frequency regulation, and the minimum required energy can be realized by a BESS with capacity jAj in the X1 region. Meanwhile, the areas of B, C, D have the same meanings
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Fig. 5. The statistical analysis results of wind speed.
Fig. 6. The statistical analysis results of irradiance.
Eb ¼ Eb;min =ðSOCmax SOCmin Þ
ð6Þ
3.2.2. Capacity of SCSS The SCSS is used to compensate the power fluctuations of MG. The SCSS power output for the MG frequency regulation is shown in Fig. 8. The power profile shows that the SCSS experiences frequent charge/discharge cycles and the power fluctuates severely
Fig. 7. BESS power profile for one day.
with A (the positive areas B, D mean the BESS is releasing energy for frequency regulation). The minimum energy capacity of BESS without SOC limitation Eb,min is the maximum energy required for the whole successive simulation period from A to D, which is shown as follows:
Eb;min ¼ MaxfjAj; jA þ Bj; jA þ B þ Cj; jA þ B þ C þ Djg
ð5Þ
As depicted in Section 2, the SOC of battery should be kept within a proper range [SOCmin, SOCmax], which means Eb,min is only part of the energy capacityEb. Therefore, the energy capacity considering SOC limitation is shown as follows:
Fig. 8. SCSS power profile for one day.
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around the time-axis, which follows the power distribution principle depicted in Section 2. The capacity determination of SCSS is similar as the BESS. The minimum power capacity Pc and energy capacity Ec,min can be obtained. Usually, Ec,min is converted into the capacitor value Cc to express the energy capacity of supercapacitor. The relationship between Ec,min and Cc is given in the following equation:
Ec;min ¼
1 C c ðV 2max V 2min Þ 2
ð7Þ
where Vmax and Vmin are the allowed minimum and maximum terminal voltage of supercapacitor, separately. Therefore, the energy capacity of supercapacitor Cc is expressed as follows:
C c ¼ 2 Ec;min =ðV 2max V 2min Þ
ð8Þ
3.3. Flowchart of capacity statistical model The flowchart of capacity statistical model is shown in Fig. 9. As shown in Fig. 9, a set of random parameters [c, k, l, r, lL, rL] generate a set of capacity results [Pb, Eb, Pc, Cc]. Based on statistical analysis, a large number of random scenarios on a certain confidence level are generated using MCS and then a series of BSHS
capacities are obtained. The MCS terminates when ITER reaches the maximum simulation times Nmax and the corresponding capacity distributions of BSHS are determined.
4. Numerical studies This section presents a case study to illustrate the performance of HLC strategy and verify the effectiveness of capacity statistical model. The benchmark LV network [23] built in DIg SILENT software is shown in Fig. 10, which comprises a LV feeder, loads, several microgeneration systems (WT, PVs, fuel cell and microturbine) and BSHS. To simplify the study, fuel cell and microturbine models are replaced by DC voltage sources, and their power outputs are set to be constant. As shown in Fig. 10, a hybrid WT/PV system is connected to bus 15 and a single PV system is connected to bus 17. The WT/PV control parameters are shown in Appendix A and B. The BSHS is connected to bus 13. A typical battery model taking SOC into consideration and a non-linear supercapacitor model are used in this case [24]. The battery and supercapacitor are connected to MG by independent inverters separately for flexible control. The parameters of BSHS model and control systems are shown in Appendix C and D.
Fig. 9. Flowchart of capacity statistical model.
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Fig. 12. Power outputs of DGs and microgrid frequency.
Fig. 10. Benchmark low voltage microgrid.
4.1. The performance of HLC strategy The wind speed and irradiance data of an autumn day in a certain area of China are shown in Fig. 11a and b, separately. The typical load profiles (in mean values lL) are shown in Fig. 11c in which the loads 4, 12, 17 represent the typical residential loads and loads 13, 19 represent the typical commercial loads.
Fig. 11. Simulation environment.
Fig. 12a shows that the outputs of WT and PV systems fluctuate with the variations of wind speed and irradiance. The BSHS is used to compensate the imbalance between the power supply and demand. As Fig. 12b shows, under HLC strategy, the SCSS responds to fast power fluctuations, which causes frequent charge/discharge cycles on the SCSS. Meanwhile, the battery only works at intervals to provide the MG with energy. The frequency under HLC is shown in Fig. 12c, where the allowed frequency range is set to be [49.97 Hz, 50.03 Hz] and the value of Df is set to be 0.02. As depicted in Section 2, when the frequency reaches 50.02 Hz or 49.98 Hz, the BESS is triggered for frequency response with SCSS until the frequency reaches 50.0 Hz. When the value of frequency reaches 50.0 Hz, the battery is out of service and only the SCSS works to regulate the frequency until the frequency reaches 50.02 Hz or 49.98 Hz. It shows that the frequency under HLC is controlled within the predefined range [49.97 Hz, 50.03 Hz] and the battery and supercapacitor make full use of their complementary characteristics. The battery output comparison between HLC and classical hybrid control (CHC) strategy proposed in [10] is shown in
Fig. 13. Battery output comparison under different control strategies.
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Fig. 14. Distribution ranges of wind speed and irradiance.
Fig. 13. Between 4 and 15 h, the power output of BESS under HLC is zero and the SOC of battery is unchanged which means the BESS is out of service, while the power output and SOC under CHC fluctuates continuously, which indicates that the battery experiences small charge/discharge cycles. Compared with CHC, the BESS under HLC only works at intervals for frequency regulation which can avoid small charge/discharge cycles on battery. Based on the analysis above, the HLC strategy not only can regulate the frequency within the predefined control range, but also can avoid the small charge/discharge cycles on the battery.
Fig. 16. Cumulative probability functions of BSHS capacity under different control strategies.
4.2. Capacity distributions of BSHS This section verifies the effectiveness of the capacity statistical model firstly and then analyzes the influence from different control strategies on the capacity of BSHS. 4.2.1. The capacity distributions of BSHS The distribution ranges of wind speed and irradiance on the confidence level of 99% are shown in Fig. 14 and the loads are
generated randomly using normal distribution based on the typical load profiles shown in Fig. 11a. The previous methods to obtain the capacity of ESS are ‘‘worst scenario’’ based and the results are conservative. The statistical model using MCS presented in this paper can solve this problem in a statistical way. The capacity probability distributions of BSHS under HLC and CHC are shown in Figs. 15 and 16. Figs. 15 and 16 show the capacity distributions of BESS and SCSS. According to the cumulative probability functions shown in Fig. 16, the energy capacity and the corresponding power capacity of BSHS can be determined on each specific cumulative probability level. As depicted in Table 1, the results on three typical levels (50%, 75% and 90%) are given. For example, the BESS energy capacity Eb,HLC corresponding to the cumulative probability of 90% under HLC is 641.6552 kW h and that of 75% is 600.2094 kW h. The energy capacity of BESS is saved by 41.4458 kW h when the cumulative probability is 75%. This is meaningful when there are high penetrations of controllable loads which can contribute to the frequency response of MG [14]. With the development of demand side management in microgrid, the capacity statistical model proposed in this paper offers a flexible way for engineers to choose the optimum capacity of BSHS for MG according to the needs of operation.
Table 1 BSHS capacity comparisons at different cumulative probability. The value of cumulative distribution
Fig. 15. Probability distributions of BSHS capacity under different control strategies.
Eb,HLC (kW h) Eb,CHC (kW h) Pb,HLC (kW) Pb,CHC (kW) Cc,HLC (F) Cc,CHC (F) Pc,HLC (kW) Pc,CHC (kW)
50%
75%
90%
546.4927 591.3565 53.5924 53.5913 6.1793 5.8010 58.4052 54.1861
600.2094 640.6201 57.9635 57.8214 6.9663 6.7438 62.1191 58.9540
641.6552 695.0820 62.5392 62.1991 7.9687 7.8683 66.5202 62.5392
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level. As shown in Table 1, at the cumulative probability of 90%, the power capacity of SCSS under HLC is 66.5202 kW and that under CHC is 62.5392 kW. Compared with CHC, the SCSS power capacity under HLC is increased by 6.3% at the cumulative probability of 90%. This is because under HLC, the frequency regulation is dependent on SCSS when the BESS is in non-working range and parts of the SCSS power are larger than those under CHC, which can give full play to the high power density characteristic of SCSS. Meanwhile, the energy capacity of SCSS under HLC is a little larger than that under CHC, which can be seen from Table 2.
Table 2 Parameters of BSHS capacity distributions.
Eb,HLC (kW h) Eb,CHC (kW h) Pb,HLC (kW) Pb,CHC (kW) Cc,HLC (F) Cc,CHC (F) Pc,HLC (kW) Pc,CHC (kW)
Expectation
Standard deviation
550.3697 591.3551 54.3257 54.2800 6.1914 5.8743 58.5658 54.7267
69.3879 76.878 6.2955 6.2512 1.354 1.4206 5.9819 6.2012
4.2.2. Capacity comparisons of BSHS under different control strategies In this part, the impact from different control strategies on the distributions of BSHS capacity is investigated using the statistical model.
5. Conclusions A statistical model using MCS to determine the capacity distributions of BSHS is proposed in this paper for ESS planning in MG. The advantage of this statistical model is that the capacities of BSHS at different cumulative probability levels can be determined. Compared with the deterministic based methods, the statistical model is more flexible for engineers to choose the optimum capacity according to the needs of operation. Additionally, the influence from different control strategies on the capacity distributions of BSHS is studied and compared in this paper. Compared with CHC, the HLC strategy proposed in this paper can reduce the energy capacity of BESS to a certain extent while increase the capacity of SCSS. Although the power capacity of SCSS is increased, it can give full play to the high power density characteristic of SCSS. Besides, the HLC can avoid small charge/discharge cycles on battery, which can extend the service life of battery. With the surging development of MG, the capacity statistical model definitely provides a useful tool for ESS planning and coordinating the ESS capacity with load-demand management, which is also the work to be studied in future.
4.2.2.1. BESS capacity comparison. The parameters of BESS capacity distributions under HLC and CHC are shown in Table 2. The energy capacity expectation of BESS under HLC is smaller than that under CHC by 40.9854 kW h, and the standard deviation of BESS energy capacity under HLC is also smaller than that under CHC by 7.4901 kW h. Fig. 16a shows that the cumulative probability values under HLC are higher than that under CHC at the same capacity level, which means the energy capacity under HLC is smaller than that under CHC at the same cumulative probability level. As shown in Table 1, at the cumulative probability of 90%, the energy capacity of BESS under HLC is 641.6552 kW h and that under CHC is 695.0820 kW h. Compared with CHC, the HLC strategy can save the BESS energy capacity by 7.7% at the cumulative probability of 90% for the HLC strategy can avoid small charge/discharge cycles on BESS. The power capacity distributions of BESS under HLC are similar with that under CHC, which can be seen from Table 1 and Fig. 16d. This is because the HLC only avoids small charge/discharge cycles on battery and the maximum charge/discharge power is almost unchanged.
Acknowledgements This work is supported by Special Fund of the National Basic Research Program of China (‘‘973’’ Program, Grant No. 2009CB219701), National Natural Science Foundation of China (Grant Nos. 51277128, 513111017, 51377117 and 51307115), Tianjin Municipal Science and Technology Development Program of China (Grant No. 09JCZDJC25000) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090032110064).
4.2.2.2. SCSS capacity comparison. Table 2 shows that the power capacity expectation of SCSS under HLC is larger than that under CHC, and Fig. 16d also shows that the power capacity under HLC is larger than that under CHC at the same cumulative probability
Appendix A. Dynamic parameters of WT system (Definition of parameters referring to [18])
WT model
Inverter
Pr (kW)
vrat (m/s)
vcin (m/s)
vcou (m/s)
60
13
3
20
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
0.5
0.08
0.5
0.08
0.2
0.01
0.2
0.01
Appendix B. Dynamic parameters of PV system (Definition of parameters referring to [20])
PV model
Inverter
Voc (V)
ISC,ref (A)
Pmax,ref (W)
Vmp,ref (V)
Imp,ref (A)
k (J/K)
q(c)
J
c
21.7
3.35
53
17.4
3.05
1.38e23
1.6e19
6.5e4
3
A
n
Rs (X)
Eg,ref (c)
T (K)
Tr (K)
NP
NS
m
1.76
1.5
0.3162
1.237q
321.3
298
12
46
36
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
5
0.05
5
0.05
0.4
0.01
0.4
0.01
524
H. Jia et al. / Electrical Power and Energy Systems 54 (2014) 516–524
Appendix C. Dynamic parameters of BESS system (Definition of parameters referring to [23])
Battery model
Inverter
V0 (V)
K
Q
Rb (X)
A
B
SOC0
NP
NS
226.25
8.9
3
20
18.644
2.3
0.6
2
4
Kd
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
10
0.8
0.1
0.8
0.1
0.2
0.01
0.2
0.01
Appendix D. Dynamic parameters of SCSS system (Definition of parameters referring to [23])
Supercapacitor model
Inverter
V0 (V)
R (X)
C (F)
800
0.01
10
Tl
Kp
Tp
Kq
Tq
Kiq
Tiq
Kiq
Tiq
0.01
0.8
0.05
0.8
0.05
0.2
0.01
0.2
0.01
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