battery energy storage system

Measurement 49 (2014) 15–25

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Heuristic optimization of state-of-charge feedback controller parameters for output power dispatch of hybrid photovoltaic/battery energy storage system Muhamad Zalani Daud ⇑, Azah Mohamed, Ahmad Asrul Ibrahim, M.A. Hannan Department of Electrical, Electronic, and Systems Engineering, University Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

a r t i c l e

i n f o

Article history: Received 31 July 2013 Received in revised form 11 October 2013 Accepted 18 November 2013 Available online 1 December 2013 Keywords: Photovoltaic Renewable energy dispatch Battery energy storage Optimal control

a b s t r a c t Output power fluctuation of photovoltaic (PV) sources is a problem of practical significance to utilities. To mitigate its impacts, particularly on a weak electricity network, a battery energy storage (BES) system can be used to smooth out and dispatch the output to the utility grid on an hourly basis. This paper presents an optimal control strategy of BES state-ofcharge feedback (SOC-FB) control scheme used for output power dispatch of PV farm. The SOC-FB control parameters are optimized by using heuristic optimization techniques such as genetic algorithm (GA), gravitational search algorithm (GSA), and particle swarm optimization (PSO) in Matlab. In addition, an improved BES model is developed in PSCAD/EMTDC software package, in which GA is used to evaluate the optimal parameters. The studied multi-objective optimization problem also considers the evaluation of the optimal size of the BES. The performance of the proposed optimal SOC-FB control scheme is validated by comparing the results obtained from Matlab and PSCAD/EMTDC and with results from previous works. Finally, the best set of parameters are used to further validate the proposed method by using data obtained from the actual output of a grid-connected PV system. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Presently, the allocated quota for PV-based renewable energy (RE) generation in Malaysia is more than half (57%) of the total RE generation quota, which provides additional opportunities for large-scale integration of grid-connected PV systems. Several contributing factors to PV investment include attractive feed-in tariff rates and government incentives and subsidies. Consequently, by 2020, Malaysia’s RE penetration is expected to grow steadily, with a new target of 2080 MW [1]. However, increased PV penetration adversely affects power networks. One current major issue is output power fluctuation ⇑ Corresponding author. Tel.: +60 3 89216590. E-mail addresses: [email protected] (M.Z. Daud), [email protected] (A. Mohamed), [email protected] (A.A. Ibrahim), [email protected] (M.A. Hannan). 0263-2241/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.11.032

[2–7]. Large power ramps, both positive and negative, can negatively affect the performance of an electric network, typically when the PV system is implemented in weak, remote, or island power networks [5–7]. Fluctuation causes difficulties for distributed generation (DG) operators to predict their output, which affects generation scheduling processes [2]. A large-scale residential PV demonstration project in Japan [4] suggests that the total fluctuated power injected to the utility grid has to be mitigated typically around noon. Many works related to mitigation strategies have been published in the literature [2,4–6,8]. A dump load with a controller is traditionally used to dissipate unwanted access power and minimize its impact on nearby critical loads as well as excessive stress received by the utility grid [9]. Generation curtailment is another method, in which the maximum power point (MPP) tracking controller is used to operate the DG below the MPP or temporarily

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island the generation during severe power fluctuation [2]. Recently, the use of battery energy storage (BES) to smooth out output power fluctuation of RE sources has been a promising solution [5,6]. However, adopting a large-scale BES for such purpose is challenging because BES is expensive. Therefore, control strategies are to be developed for BES to ensure efficient power smoothing performance as well as to minimize BES installation and operational costs. In [5,6], several control strategies for BES have been developed to smooth PV and wind outputs and dispatch the total power injected to the utility grid on an hourly basis. However, typical one-week data were used for PV/BES and wind/BES system controllers, which are unreliable if both performance and adequate BES sizing are to be evaluated [10]. Furthermore, the control scheme for SOC demonstrated poor dispatching performance, given that the parameters for the SOC controller were obtained based on conventional hand-tuning method [5]. Although [11] evaluated the BES capacity for dispatch strategy based on an analysis of statistical long-term input data, this study only focused on wind sources. Recently, GA-based optimization of SOC-FB controller was developed for optimal power dispatching of PV sources [10]. However, the controller parameters were evaluated by using only GA and therefore evaluating performances by using other new and more reliable heuristic optimization algorithms is desirable. In other applications, several studies have centered on parametric optimization of hybrid system PID controllers by using GA and PSO [12,13]. In [14], the controller parameters were assessed by using the simplex algorithm for BES buck-boost converter to regulate the DC bus voltage for RE sources. This paper presents an enhanced control scheme for hybrid PV/BES system to dispatch the output to the utility grid on an hourly basis while providing optimal regulation of SOC. A multi-objective optimization problem is considered and heuristic optimization techniques such as GA, PSO, and the recently introduced gravitational search algorithm (GSA) [15] are used to evaluate the SOC-FB parameters for optimal power set point tracking and determined an adequate size of BES. An improved BES model is also developed in the PSCAD/ EMTDC software in addition to using the existing BES model in Matlab. Finally, a comparison is made on the performance of GA, PSO and GSA in obtaining optimal SOC-FB control parameters, and the results obtained from actual PV output data are presented. Section 2presents the concept of the strategy for hourly output power dispatch of the hybrid PV/BES system, in which SOC-FB control method is described. Section 3describes the dynamic modeling of BES system, including the improved battery model and simulation set-up for the optimization of SOC-FB control parameters. Section 4discusses the simulation results. Section 5concludes this paper.

2. Review of power dispatch strategy that uses PV/BES system RE dispatch may be considered as an economic dispatch that allows adjustment of the output power from the generation units as the load changes [16]. Fig. 1 shows

the system configuration and operating concept of the hybrid PV/BES hourly dispatch strategy. As shown in Fig. 1(a), the BES is connected to the point of common connection (PCC) together with the grid-connected PV system through a voltage-sourced converter (VSC). The PV system maximum power point tracker extracts the maximum convertible power from the PV array and injects its available power to the utility grid at unity power factor by using conventional active and reactive power control of VSC1. The fluctuated power injected to the PCC is regulated by the BES charge/discharge power (PBES) so that the net (PTOTAL) power is delivered according to the reference PSET value, as shown in Fig. 1(b). PSET is the hourly set-point curve commanded to the BES controller for charging/discharging operations. It is considered as the hourly forecasted PPV output that comes from the forecasting model [17–19]. To minimize the impact of fast power ramps, both positive and negative, the PSET data are initially passed to the ramp rate limiter where the data is modified as follows:

RDRL 6 PSET ðtÞ  PSET ðt  1Þ 6 RURL;

ð1Þ

where RDRL and RURL are ramp-down and ramp-up rate limits, respectively. The difference between PSET and PPV then becomes the reference BES power (PBES,ref) to be injected or absorbed during regulation service. Importantly, the forecast error for PSET should be assumed at a minimum of 10% mean absolute error (MAE) as suggested in previous works [5,6]. The use of minimum 10% MAE value is considered adequate because as has been described in [19], using diagonal recurrent wavelet neural network would give forecast accuracy up to approximately 90%. Furthermore, the uncertainty model developed in [18] for the case of Kuala Lumpur, Malaysia using the generalized regression neural network model gives hourly solar radiation forecast accuracy at only 6% error. Considering that PSET tracking requires continuous charging/discharging of BES power, the operation is subjected to BES operational constraints, such as SOC operable limits and depth of discharge, voltage exponential limits, and current limit through the VSC2. Therefore, for safety and economical purposes, the SOC of the BES should be controlled during charge/discharge operation to control all the BES operational constraints at the desired range. Fig. 2 shows the SOC-FB control scheme at the outer control loop of VSC2 with the corresponding current generation blocks. Based on Fig. 2, the BES d-axis current component is derived from PBES,ref, which is the output of the SOC-FB controller. The SOC-FB controller regulates the SOC at an appropriate level while ensuring that operational constraints, such as charge/discharge current and BES terminal voltage, do not exceed their specified range. The current reference Id,ref is later fed to the inner current control loop of VSC2, where current is regulated according to the conventional current-mode control scheme of VSC [10,20]. Given that BES charge/discharge through VSC2 only involves active power component (d-axis), reactive power control is not shown in Fig. 2. Further details on the role of reactive power control of the considered BES VSC can be found in [10].

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17

Fig. 1. Simplified control diagram for the hybrid PV/BES system for output power dispatch.

Fig. 2. Block diagram of the SOC-FB controller with the corresponding active current reference generator for the VSC2.

Based on Fig. 2, the remaining energy level (REL) is the feedback signal in p.u., which is defined as follows:

REL ¼ C BES 

Z

P BES dt;

ð2Þ

where CBES is the BES capacity. The SOC is controlled when REL variation is regulated at the desired range. REL variation depends on the control parameters, namely, the SOC time constant, TSOC, and the SOC margin rate denoted by Msoc. The a  TSOC-fold waveform is applied to the PSET signal so that the BES output can be adjusted to the discharging direction when REL is at its high level and vice versa when REL is at its low level. a is the coefficient, which is defined as follows [3]:

a ¼ C BES ð1  2MSOC Þ=ðT SOC  PPV;rated Þ;

ð3Þ

where PPV,rated is the rated capacity of the PV farm. The offset signal specifies the percentage of BES energy in p.u. to be used for regulation. The output from the SOCFB controller provides the BES reference power in which the current reference component of the d-axis can be derived as follows:

Idref ¼ 2PBES;ref =3V sd ;

ð4Þ

where Vsd is the d-axis component of BES terminal voltage at the PCC.

3. Modeling of system components and simulation setup PV modeling is well described in the literature and can be found in [20,21]. In the present study, the average PPV data for input to the SOC-FB controller were obtained from the simulation model in [21] and based on the historical input data of Malaysia for 1 year [18]. Using the PPV data, the SOC-FB controller is evaluated such that the active current injection from the BES model is used to calculate PBES. PTOTAL, which is the sum of PPV and PBES, is then calculated. For the BES model, a dynamic model based on the formulation developed in [22] is available in Matlab. The model is represented by the discharge curves of the most commonly used chemical storage devices, such as lead– acid, lithium–ion, nickel cadmium, and nickel metal hydride. The user can create a user-defined model according to the available data from the manufacturer discharge curves from the datasheet. However, our simulation requires a BES model to simulate the charging/discharging behavior of a long-running simulation over hours of operation in the daytime. As such, in addition to the existing model in Matlab, an improved BES model is also developed for comparison purposes. The improved model takes into account of additional non-linear effects so as to obtain a more accurate design of the optimal controller and adequate BES size for power dispatch.

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Ebat ¼ 0:5fðE0 þ 11:5Þ þ ½0:01375ðSOCÞ  Kðð1

3.1. Review of BES dynamic model in Matlab In this work, Matlab simulation considers a dynamic model of a valve-regulated lead–acid (VRLA) battery cell, that is, Yuasa NP4-12 (12 V 4 A h) [23], which is suitable for cyclic operation. The choice of using secondary rechargeable battery type is due to many factors. The modular characteristics of chemical batteries make them flexible in size in which they can be stacked to form larger unit up to multi-megawatt of total output. Furthermore, cost assessment in [24] showed that the VRLA type battery is most suitable for RE applications requiring average charge/discharge time of less than 1 h. High power storage devices such as electric double layer capacitor (EDLC) and flywheel energy storage (FES) are economically not feasible for the present study because in this work, the required energy discharge time for the BES is approximately 25 min on average [10]. Although hybrid storage devices, such as BES/ EDLC or BES/FES are feasible solutions [8], however such devices have drawbacks such as additional cost and control complexity which would add more difficulty in practical installation [25]. For VRLA battery modeling, the terminal voltage Vbat of an individual 12 V cell and the SOC of the model can be calculated as functions of battery current Ibat by using the following equation:

V bat ¼ Ebat  Rint Ibat ;

ð5Þ

 Z   Ibat dt =Q bat ; SOC ¼ 100 1 

ð6Þ

where Rint is the battery internal resistance, Qbat is the cell capacity, and Ebat is the battery electromotive force defined as a function of SOC as follows:

Ebat ¼ E0  K½ð1  SOCÞ=SOCQ bat þ Aexp½Bð1  SOCÞQ bat ; ð7Þ where E0 is the battery open-circuit voltage, K is the polarization voltage, A is the exponential voltage, and B is the exponential capacity. The model parameters represented in Eq. (7) may be approximated by using the manufacturer’s data following the procedures in [22]. 3.2. Development of the improved BES model in PSCAD/ EMTDC The custom BES model in PSCAD/EMTDC was developed because a standard dynamic BES model currently does not exist. In addition to the BES model discussed in Section 3.1 [22], an improved model that accounts for non-linear effects, such as terminal voltage variation, self-discharge, and battery internal impedance, was developed [10,26]. The investigation of the manufacturer’s test data showed that the open circuit voltage and the remaining capacity have an approximately linear relationship, which is given by the following equation [23]:

Ebat ¼ 0:01375ðSOCÞ þ 11:5:

ð8Þ

Rearranging Eqs. (7) and (8), the terminal voltage behavior can be described as follows:

 SOCÞ=SOCÞQ bat  þ A exp½Bð1  SOCÞQ bat g:

ð9Þ

The effects of self-discharge can be considered by using a variable resistance Rsd that is parallel with a controlled voltage source Ebat. This resistance is given by the following equation:

Rsd ¼ 0:039ðSOCÞ2 þ 4:27ðSOCÞ  19:23:

ð10Þ

The Rsd curve parameter in Eq. (10) is obtained from the manufacturer’s data sheet by investigating the remaining battery capacity against storage time. The battery impedance value suggested by the manufacturer needs to be modified to work well with the battery model under study. As suggested in [22], Rint can be established by using the relationship among the nominal voltage (Vnom), nominal capacity (Qnom), and efficiency (g), as follows:

Rint ¼ V nom ½ð1  gÞ=0:2Q nom :

ð11Þ

From the cell model, a BES can be constructed by the series ns and parallel np combinations of an individual cell, in which power is assumed to be uniformly distributed among cells, as follows:

PBES ¼ V bes  Ibes ¼ ns V bat  np Ibat ;

ð12Þ

where ns determines the total output terminal voltage, and np characterizes the capacity or total size of a battery bank in kilowatt hours. Fig. 3 shows the BES model implemented in the PSCAD/ EMTDC software package. Based on the figure, Idbes is assumed as the total current command at the VSC2 terminal when considering a long-running simulation over hours of operation, as in the case of the SOC time constant of (6) at 3600 s (1 h). In other words, by neglecting the small time constant of VSC2 switching, Idbes is obtained by dividing the BES reference power (PBES,ref) in MW by the terminal voltage (Vbes). Changes in Idbes also change the Ibes magnitudes and thus characterize the SOC and Vbes of the model. Neglecting VSC switching is acceptable because in reality, its time constant is relatively small compared to the charge/discharge time of BES in the order of minutes [5,10]. In addition, VSC2 converter loss has to be considered by applying a gain block of 0.97 to the BES output power signal (PBES) to account for 3% loss, as suggested in [5]. 3.3. Simulation set-up and optimization of control parameters Unlike the SOC-FB controller in [3], which was developed for the case of power smoothing, an hourly power dispatch strategy requires the evaluation of the parameters according to the BES size [5,6,10]. Daud et al. [10] discussed that an optimal parameter tuning strategy that uses heuristic optimization approaches is a promising solution for obtaining the best set of parameters while evaluating an adequate size of BES. Considering all the operational constraints required for the continuous operation of BES, an optimal SOC-FB control parameter tuning strategy is developed. The objective of BES power injection/absorption is to compensate for deviation between PSET and PPV

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Fig. 3. Improved BES model in PSCAD/EMTDC with the corresponding charge/discharge current command at its terminal.

so that PTOTAL output follows the PSET curve. In other words, the power tracking of the PV/BES system is performed to follow the PSET curve so that smoothed power is delivered to the utility grid. Here, we can define the control problem as objective function minimization, that is, the optimal tracking of PSET through the BES SOC-FB controller. According to this problem, an objective function is defined as a quadratic cost function, as follows:

OFðxÞ ¼ min

Z

T

 ðPSET ðtÞ  PTOTAL ðtÞÞ2 dt ;

ð13Þ

0

where the vector x represent the SOC-FB control parameters (TSOC and MSOC) and the BES capacity (CBES in A h). The control parameters provide optimal PSET tracking, whereas BES capacity outputs the optimal BES size. Evaluating the performance index of Eq. (13), the constraints specified for the SOC-FB controller is as follows:

SOCmin 6 SOC 6 SOCmax ;

ð14Þ

Ibes;min 6 Ibes 6 Ibes;max ;

ð15Þ

V bes;min 6 V bes 6 V bes;max ;

ð16Þ

where SOCmin and SOCmax are the minimum and maximum SOC operating ranges, respectively. In this study, we define the SOC operable range at a maximum of 70% of the total capacity of BES, that is, SOCmin P 0.3 p.u. and SOCmax 6 1 p.u. The current variables Ibes,min and Ibes,max are the minimum and maximum peak current discharge/ charges, respectively, which accounts for the VSC2 converter rating with IGBT valves. The maximum charge/ discharge current should not exceed ±1  CBES amperes, in which it is limited by the current limiter block, as shown in Figs. 2 and 3, respectively. For example, every generation with CBES = 500 A h will block the current at a maximum of ±0.5 kA. For the voltage constraints, Vbes,min and Vbes,max are the minimum and maximum operational boundaries for the BES terminal voltage, respectively. In this case, the terminal voltage is assumed to be 0.6 kV and should not exceed the minimum cutoff voltage of 0.465 kV [10,23] for charge/discharge current magnitudes at ±1  CBES. Exceeding the minimum voltage will force the BES to operate at the exponential voltage region; in practice, such condition may cause the premature failure or breakdown of the BES [23]. To solve the optimization problem, three heuristic optimization approaches that use GA, GSA, and PSO were

developed in Matlab. The optimization of SOC-FB control parameters and BES size is based on the standard BES model, as discussed in Section 3.1. For comparison purposes, the improved BES model in PSCAD/EMTDC is also evaluated. The generalized simulation set-up for the aforementioned approaches is depicted in Fig. 4. Based on the figure, the simulation model of the SOC-FB control scheme with BES is linked to the optimization algorithm in which the objective function is evaluated. In every generation, the error between PSET and PTOTAL is minimized, in which the parameters of TSOC, MSOC, and CBES are updated by GA, GSA, and PSO, respectively. The newly updated parameters determine the current charging/discharging magnitude (Idbes) at the maximum ±1  CBES rate that will later calculate SOC and Vbes. These BES operational constraints are controlled accordingly to follow the limitations discussed in Section 3.3. Fig. 5 depicts the flowcharts of the parametric optimization processes by using GA, GSA, and PSO. The figure shows that the algorithms first randomly set the initial population that comprises the coordinates of the control parameters (i.e., TSOC, MSOC and CBES). From this population, the fitness value (performance) of each individual in the population is calculated by using the fitness function given in Eq. (13) and is recorded in the workspace. Every generation evaluates the objective function that minimizes the fitness values according to GA, GSA, and PSO specific operators, as denoted in Fig. 5(a), (b) and (c), respectively. The exploration and exploitation processes are terminated when the stopping criterion is met; thus, the best set of parameters is determined. The convergence characteristic of the fitness values of each algorithm depends on their input parameters, which are typically the upper and lower boundaries of the TSOC, MSOC, and CBES. Therefore, to ensure a timely solution from the optimization, a preliminary simulation study was initially conducted to evaluate the desired range of these parameters.

4. Results and discussion In the following subsections, the SOC-FB input data (i.e., PPV and PSET) are first obtained. The validation of the proposed improved BES model is presented, and then followed by the comparison of the results with previous works, including the PSCAD/EMTDC simulation results. Finally,

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Fig. 4. Generalized simulation block diagram for the evaluation of the GA-, GSA-, and PSO-based optimal control parameters for the BES SOC-FB control scheme.

Fig. 5. Flowcharts of the parametric optimization processes for (a) GA, (b) GSA, and (c) PSO.

the validation of the proposed optimal controller with the actual PPV data is discussed. 4.1. Input data for SOC-FB controller The input data for the evaluation of the SOC-FB controller (i.e., PPV and PSET) were obtained from the Malaysian historical radiation and temperature data [18]. The radiation and temperature data were analyzed by using statistics to represent the average one-day input data of a PV system. Pre-processing of the input data was carried out using Matlab. The characteristics for radiation (Gdata) and temperature (Tdata) input data are shown in Table 1 [10]. Table 1 shows that intermittent clouds are mostly formed in the afternoon, typically between 11:00 A.M. and 3:00 P.M. The radiation deviates to a zero mean value at a maximum of ±190 W/m2 in the afternoon and has a

relatively high temperature fluctuation of nearly ±2.4 °C in the late afternoon. Rapid changes in solar radiation magnitudes highly influence the PV system output. Through the simulation of these input characteristics by using the PV model in [21], the PPV data injected to the utility grid were obtained, as shown in Fig. 6. The measurement of PPV data was sampled at 1 min, with PSET curve also calculated. PSET takes the hourly average of PPV values with 10% added MAE noise data to represent the forecast accuracy of the PV output-forecasting model. The rate limiter of ±0.03 MW/min (up and down ramp rates) was also applied to PSET to minimize the output power ramps of the PV farm. 4.2. Validation of the BES model The developed BES model used in the simulation is a 300 kW h (0.6 kV, 500 A h) system that has discharge

21

M.Z. Daud et al. / Measurement 49 (2014) 15–25 Table 1 Average standard deviations of radiation and temperature data for Kuala Lumpur, Malaysia (GPS coordinates: N2 55.804 E 101 46.780). Time (h)

Average standard deviation of radiation, Gdata (W/m2)

Average standard deviation of temperature, Tdata (°C)

8–11 11–15 15–17

±130 ±190 ±150

±1.4 ±1.9 ±2.4

Fig. 6. Average one-year PPV output data for a 1.2 MW PV system with the corresponding PSET value.

characteristics, as shown in Fig. 7. The discharge characteristics represent the different behaviors of voltage curves depending on the discharge current ratings. In this study, the discharge curves of current at 1.5  CBES, 1  CBES, and 0.5  CBES rates of the developed PSCAD/EMTDC model were compared with those of the model in Matlab. Further details on the validation of the 12 V cell characteristics with the manufacturer test data are given in [10]. As shown in Fig. 7, the model accurately represents the standard Matlab model [22] for VRLA battery. As in the case of 0.5  CBES rate, the maximum deviation of the voltage curves was less than 3%. The figure also shows the lowest recommended voltage under load, which is the point at which further discharge is prohibited to ensure safe operation of BES. At a maximum of 1  CBES rate operation, this voltage limit value is equivalent to 0.465 kV. The voltage curve is highly exponential in this region, which would demand exponential current magnitude if constant power is applied to the BES terminal. Additional operations within

Fig. 7. Validation of the discharge characteristics of the developed PSCAD/EMTDC BES model with the standard model in Matlab (⁄C = CBES) [20].

this voltage region may decrease the efficiency of BES [23]. Thus, a preliminary simulation should be conducted to determine the parameter ranges and the minimum BES size required to avoid this voltage operational limit.

4.3. Comparison of results From the preliminary simulation, the maximum and minimum ranges of the control parameters were obtained. These ranges were selected based on the desired operational constraints discussed in Section 3.3. With the use of these input parameters and the SOC-FB input data discussed in Section 4.1, the parametric optimization was performed in Matlab and PSCAD/EMTDC to search for the optimal set of parameters for PSET tracking and the size of BES. In Matlab, GA, GSA, and PSO algorithms were used. Meanwhile, in PSCAD/EMTDC, GA-based optimum run tool was used together with the improved BES model set-up depicted in Fig. 4. Fig. 8 shows the comparison of the convergence criteria for each of the optimization algorithms on minimizing the objective function. As presented in the figure, the Matlab simulations of GA and GSA show comparable performances and are better than PSO. GSA is a newly developed algorithm that renders the fastest convergence speed and the best fitness value, which proves its reliability in providing acceptable solutions for parametric optimization problems. In PSCAD/EMTDC, the convergence criteria for GA are poor compared with Matlab simulations because PSCAD/EMTDC was carried out by using a standard optimization tool, in which the performance solely depends on parameter values included by the user as well as on the designed objective function [27]. In other words, the user is not provided with flexibility in fine-tuning existing codes depending on the user needs. However, with an appropri-

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Fig. 8. Convergence characteristics for GA, GSA, and PSO in Matlab, and GA in PSCAD/EMTDC.

ate design of the objective function for the controller, the obtained optimal parameters provide acceptable results on PSET tracking, as discussed in [10]. Having obtained the best set of parameters, the simulation results for PSET tracking performances, that is, the efficiencies of the proposed optimal controllers, are compared, as shown in Table 2. The table reveals that the efficiency is calculated based on the percentage of unacceptable deviations of the proposed method in comparison with the unacceptable deviations without the use of BES. Assuming that ±0.1 MW is acceptable, dP histogram (in %), which measures this performance, may be represented as follows:

dP ¼

X ðPSET  PTOTAL Þ P 0:1 MW:

ð17Þ

Without BES, dP that exceeds ±0.1 MW is approximately 29.9% with the assumption that all generated power (PPV) are injected to the grid at 3% converter loss. Table 2 shows that the GA-, GSA-, and PSO-based optimal parameter tuning strategies provide highly efficient PSET tracking performances (nearly 90%). Consequently, the PSCAD/EMTDC simulation also greatly improved performance, reaching

up to 87% efficiency, which is significantly higher compared with the conventional SOC-FB (37.6%) [5] and rulebased (75%) control methods [6]. However, the use of the improved BES model in the PSCAD/EMTDC simulation indicates that the BES should be scaled approximately 7% more to use the same set of parameters for the SOC-FB controller. In general, the optimization approaches in Matlab and PSCAD/EMTDC provide the optimal BES size, in which the initially estimated size is reduced by 0.8% (GA), 1.2% (GSA), 2.6% (PSO), and 7% (GA in PSCAD/EMTDC). Based on the parameters in Table 2, Fig. 9 shows an example of the detailed comparison of dP histograms for the cases without BES, conventional SOC-FB, SOC-FB GA (PSCAD/ EMTDC), and SOC-FB GSA (Matlab) controller. Based on Fig. 9(a), without BES, high deviations of nearly ±0.4 MW occur occasionally. With BES used to dispatch the PV power, the conventional SOC-FB method [5] fairly minimizes the large deviations to PSET to less than 0.3 MW, as shown in Fig. 9(b). The dP that exceeds ±0.1 MW for this case is approximately 18.67%. Meanwhile, Fig. 9(c) and (d) shows that the proposed optimal SOC-FB controller based on GA and GSA, which were simulated in PSCAD/EMTDC and

Table 2 Comparison of results of the optimal SOC control performances for PSET tracking. Parameter (unit)

Proposed optimal SOC controller Initial value/range (preliminary simulation)

SOC time constant (h) 0.10 6 TSOC 6 0.75 SOC margin rate (p.u.) 0.38 6 MSOC 6 0.75 BES capacity (A h) 450 6 CBES 6 500 (+15% for PSCAD model) OF(x) 22.89 Elapsed time (s) – PV capacity (MW) – Forecast accuracy of 10 PSET (MAE in %) Terminal voltage (kV) 600 ± 20%

Conventional Rule-based Remarks SOC-FB [5] [6]

GA

GSA

PSO

GA (PSCAD)

0.738 0.551 496 (297.6 kW h) 16.58 4739 1.2 10

0.748 0.575 494 (296.4 kW h) 16.55 4958 1.2 10

0.743 0.576 487 (292.2 kW h) 17.07 4958 1.2 10

0.728 0.746 535 (321 kW h) 17.85 – 1.2 10

0.200 0.700 500 (300 kW h) – – 1.2 10

– – 500 (300 kW h) – – 1.4 10

TSOC MSOC np  4

Max 0.675, Min 0.518 69 ±0.494 89.81

Max 0.674, Min 0.515 70 ±0.487 89.80

Max 0.633, Min 0.518 70 ±0.531 87.9

Max 0.698, Min 0.531 64 ±0.500 37.6

0.6 ± 10%

Vbes

70 ±0.500 75

SOC Ibes dP P ±0.1 MWa

Max 0.676, Min 0.520 State of charge (%) Max 70% of total capacity 67 Current (kA) Max ±1  CBES ±0.496 Overall efficiency (%) – 89.67

ISE in Eq. (13) Toc PPV,rated PSET

a Performance calculated based on the dP histogram of deviations that exceed ±0.1 MW [10]. Efficiency [g = (dP without BES (%)  dP with BES)  100/dP without BES (%)].

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Fig. 9. Comparison in terms of the dP histograms of the proposed method with those of the conventional methods and without the use of BES.

Fig. 10. Hourly dispatching performance of the PV/BES system with the BES profiles by using optimal GSA-based SOC-FB control scheme.

Matlab, respectively, shows very marginal deviations of only 3.6% and 3.05%, respectively. These small deviations reflect

the high efficiency of the proposed optimal control strategies, as highlighted in Table 2.

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Fig. 10 shows the PTOTAL injected to the utility grid with the corresponding BES voltage, SOC, and current profiles. The simulation results were based on the optimal set of parameters obtained by using GSA. In general, PSET can be perfectly tracked by the BES SOC-FB control scheme while meeting all the BES operational constraints to inject the total output power of the PV/BES system on an hourly basis. From Fig. 10(a), the total power injected to the utility grid causes spikes to occur typically between 11:00 A.M. and 3:00 P.M. These spikes occur because of the blocking of the BES current through the saturation limiter at ±1  CBES rate. If the effects of these spikes are acceptable, the BES or converter size does not need rescaling. However, if such spikes are to be mitigated, the BES and power converter size should be rescaled to at least 50% of the proposed original size [10]. Fig. 10 also shows that during regulation, the BES operational constraints are satisfied accordingly. For example, the minimum voltage does not exceed the lowest boundary of 0.465 kV (Fig. 10(b)), and SOC does not exceed its minimum level of 30% (Fig. 10(c)). Fig. 10(d) shows that the maximum and minimum BES charge/discharge currents are prevented from exceeding ±0.494 kA for the assumption of ±1  CBES charge/discharge rate converter ratings. 4.4. Simulation of the GSA SOC-FB controller by using actual PPV data In addition to the simulated results for the calculated average one-day PPV data, the proposed optimal GSA-based SOC-FB controller was also used to study the regulation service provided for an actual PPV output data. Fig. 11 shows the measured PPV data sampled at 5 min, and measured over 5 days from December 30, 2012 to January 3, 2013. The data were obtained from the rooftop PV system

installed at the Universiti Kebangsaan Malaysia [28]. During measurement, most days were clear with intermittent clouds, which were observed typically around noon. As shown in Fig. 11(a), over the five-day running simulation, the fluctuated PPV data can be dispatched on an hourly basis by using 296.4 kW h BES. The SOC was regulated at a maximum of 59% of the total BES capacity, as presented in Fig. 11(b). A zoomed view of the day two simulation (Fig. 11(c)) shows that the impacts of fluctuation and undesired high power ramps were minimized to a certain degree, thereby reducing unnecessary stress to the utility grid. Minimizing these impacts is necessary when a large-scale PV system is installed on a relatively weak electricity grid. 5. Conclusion Undesired effects that result from high output fluctuations of a PV farm connected to the utility grid are reduced by introducing an optimal SOC-FB control scheme for the BES. By using such an optimal control scheme, the net power output of the PV/BES system can be smoothed out and dispatched to the utility grid on an hourly basis. The control parameters and the optimal size of the BES are evaluated by using GA-, GSA-, and PSO-based optimization techniques in Matlab. In addition, GA-based optimization that uses the improved BES model in PSCAD/EMTDC is also considered. In general, the simulation results show high efficiencies of up to 90% for the GA-, GSA-, and PSO-based SOC-FB controllers and approximately 88% for the GAbased SOC-FB controller evaluated in PSCAD/EMTDC. The GSA-based optimization provides high convergence speed with the best fitness values compared with the other techniques. The validation of the GSA-based SOC-FB controller with the actual PPV data indicates an acceptable

Fig. 11. Application of GSA-based optimal SOC-FB controller to the measured PPV data.

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performance, and all the BES operational constraints are regulated at the desired level. The optimal sizes of BES are also evaluated in which the initial estimated size is reduced by 0.8% (GA), 1.2% (GSA), 2.6% (PSO), and 7% (GA in PSCAD/EMTDC). In general, this study facilitates PV output power smoothing efforts by using BES, especially in Malaysia. Acknowledgements

[11]

[12]

[13]

[14]

This work is supported by Universiti Kebangsaan Malaysia under the research Grant ERGS/1/2012/TK02/ UKM01/3. Scholarships provided by Universiti Malaysia Terengganu is also gratefully acknowledged.

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