Research Article | Open Access

# Analysis of a Microgrid under Transient Conditions Using Voltage and Frequency Controller

**Academic Editor:**Pavol Bauer

#### Abstract

This paper presents an investigation of voltage-and-frequency-(VF-) based battery energy storage system (BESS) controller used in micro grid for analyzing the optimum capability of plant. Microgrid is formed by using three hydropower plants feeding three-phase four-wire load. The proposed controller is used for load balancing, harmonic elimination, load leveling, and neutral current compensation. The proposed BESS controller permits the selection of an optimum voltage level of battery and allows independent current control of each phase. The main emphasis is given on maintaining constant voltage and frequency within the micro grid during transient conditions. Micro grid with power plant and its controller is modeled in MATLAB/Simulink using Power System Blockset (PSB) toolboxes.

#### 1. Introduction

Existing and new generating plants cause depletion of fossil fuels, global warming, and pollution. This diverts researchers’ attention towards renewable energy resources. The renewable energy sources such as wind, small-hydro, biomass, geothermal are inexhaustible in nature and easily available in our country. Also remotely located villages, islands, hills, military equipment, and so forth are some of the areas which are mainly isolated from the power system grid and in these areas wind and hydro-energy are available abundantly. Thus for supplying energy in such areas, isolated system, micro-or minigrid system, is an emerging concept and draws the attention of many researchers. Micro-grid is the small scale energy system equipped with distributed energy resources, electronic equipments, loads, ancillary facilities, and so forth. In micro grid system, micro-generators are operated parallel to the loads, usually through some voltage-source-inverter-(VSI-) based or current-source-inverter-based system that can operate in controllable systems. The concept of micro grid was first introduced in 2001 by Lasseter [1]. A number of new technologies and innovative ideas are proposed [2–10] till now. Uno et al. [2] describe the supply and demand stability in micro grid for different connections. Later on the scheme based on power electronics devices with distributed generation (DG) is used to form micro grid [3]. The micro grid thus formed can work in grid connected mode as well as in islanded mode with the help of power electronic converter. A new concept was introduced in which two inverters are used, one in shunt and another in series with individual DG forming micro grid [4]. The former is used for balancing the voltage and the latter is used for balanced the line current. Small-signal stability for conventional power systems is well established, but for inverter-based micro grids there is need to analysis, how the circuit and control features give rise to particular oscillatory modes and which of them have poor damping. Thus the author develops the state-space modeling for such inverters based micro-grid [5]. Moving further micro grid not only deals with power sharing or transient stability problems but also deals with over voltage, under voltage, oscillations, offset voltage, and so on. Hence Wu et al. describe the existing problems and the possible solution in micro grid [6]. When micro grid is working in islanded mode proper synchronization between generators is required, if not so large transient current will flow. A concept of soft connection scheme based on classical zero crossing detector was introduced for synchronization of generators forming micro grid [7]. In spite of synchronization there is another problem of proper load sharing in autonomous micro grid. Thus a new concept was developed by Majumder et al. [8], in which high gain angle droop control scheme is used for proper load sharing in micro grid. A supplementary loop is proposed for each DG to stabilize the system using high angle droop gain. Further a mathematical model that predicts the effect of voltage offset on reactive power sharing between inverters in micro grid was introduced [9]. Active synchronizing control scheme was introduced by author, which is required when micro grid consists of multiple DGs. Further the author concluded that the scheme is useful for islanded and reconnected mode [10].

Past research indicates that a self excited induction generator (SEIG) has emerged as a suitable candidate for isolated system [11–14] because of its many advantages such as its small size and weight, robust construction, reduced unit size and maintenance cost, brushless rotor construction, absence of a separate excitation source, and self protection against severe over loads and short circuits. In order to utilize the full potential of the energy source, several such generators may have to be operated in parallel. There is no problem of synchronization and hunting in SEIG thus here it is used as generator in forming micro grid.

In this paper micro grid is formed using hydro power plants located at some distance far from each power plant. Hydro-electric plants can provide cheap, clean, and reliable electricity for villages. Power generated by these plants is almost constant for 24 h a day. If light load condition arises the extra power will be stored in battery and if load increases then deficit power will be supplied by the battery. Hydroelectric plants convert the kinetic energy of a waterfall into electric energy [15]. In this paper main emphasis is given on the transient condition within the micro grid and optimum utilization of BESS controller during this condition.

*Focus of the Paper*

So many authors work on the power sharing between generators during grid connected mode and islanded mode. In case of grid connected mode, the generators of micro grid are connected to the load as well as to the main grid. The loads are shared by the main grid and generator of micro grid. Hence the generators of micro grid are not fully loaded. Now if a fault occurs in the main grid it gets isolated from the rest of the system (forming micro grid), this mode is known as islanded mode. The generators of micro grid (which are not fully loaded) now shared power within themselves and maintain constant voltage and frequency at load ends.

But this paper deals with islanded mode only and the generators which are forming micro grid are fully loaded during healthy condition. If the fault occurs in any of the generator and it gets isolated then also the load of the faulty generator is shared by the rest of the generators in micro grid and thus maintains voltage and frequency constant at the load ends.

In addition, this paper also describes the concept of micro grid in which SEIGs are connected in parallel forming micro grid with their individual load. The hydroturbines are used as prime mover for SEIGs which are used to deliver power. The system consists of squirrel cage induction generator with capacitor bank. The capacitor bank is used to cater reactive power requirement. A controller is connected in parallel to the load to improve the stability of the system under transients. In spite of the above advantage SEIG is superior compared to other electric generator because there is no need of synchronization between two asynchronous generators.

#### 2. System Description and Working

The schematic diagram of micro grid is shown in Figure 1. The system consists of three small hydro-turbines which are used as prime movers for SEIGs. Single hydro power plant consists of asynchronous generator (SEIG) with the excitation capacitor, consumer load and a voltage source converter with a battery energy storage system (BESS) based voltage and frequency controller. The self-excited induction generator has been found to be an attractive competitor to the synchronous generator due to several advantages as discussed in above section. A major drawback of SEIG’s is their poor voltage regulation under varying load conditions even for fixed prime movers speeds. The star connected 3-phase capacitor bank is used for generator excitation and value of excitation capacitor is selected to generate the rated voltage at no load condition while additional demand of power during full load and faulty condition is met by controller because of having capability of bidirectional flow of active and reactive power.

The reactive power requirement can be compensated by converter based compensators like DSTATCOM and DVR. This paper deals with BESS as a controller. The BESS controller consists of DSTATCOM and a battery connected parallel to DC link of DSTATCOM. Basic principle of active and reactive power sharing starts with the active and reactive power flows between two ac sources through line impedance as shown in Figure 2. The active power and reactive power are given by: If the line is mainly inductive, where the resistance can be neglected, the typical phase angle between two voltages is These equations imply that the active power is proportional to phase angle and reactive power is proportional to voltage differences between the two systems, respectively. For this reason, in BESS controller two PI controllers are there to control active and reactive powers by varying its output frequency (that generates the phase-angle difference as a result) and voltage levels. As a result, the and droop strategies provide a stable active and reactive power sharing between the generators. Thus constant power requirement of SEIGs and load is met by IGBT based current controlled voltage source converter (CC-VSC) along with battery energy storage system (BESS) at its DC link. The output of VSC is connected through the AC filtering inductor at the point of common coupling between every micro source and load.

The basic principle of regulating the frequency by the controller is that it maintains the constant output power at the generator terminal voltage because input power from the turbine is constant so the frequency at the terminal remains constant [11]. In given configuration if no load condition arises the extra power is used to charge the battery and during heavy load condition CC-VSC is able to regulate the reactive power and frequency. If one of the SEIG is shut down due to faulty condition, the terminal voltage and frequency are still regulated.

#### 3. Control Strategy

The proposed system consists of three hydro power plants which are operating parallel forming micro grid. Each plant consists of self excited induction generator, with load and its controller. The control strategy for the other two plants is also the same. Figure 3 shows the control strategy of the proposed voltage and frequency controller which is based on the generation of reference source currents [13–15]. Three-phase reference source currents are having two components, one is in-phase component or active power component (, , ) while the other one is in-quadrature component or reactive components (, ).

In-phase component of reference source current is estimated by taking the difference of amplitude of rated generated current () and output of frequency PI controller () [13].

The amplitude of rated current of the generator is calculated as where is the rated generated power () and is rms voltage of the asynchronous generator.

The frequency error is given as where is reference frequency (50 Hz in present system) and is the frequency of the voltage of an asynchronous generator. The instantaneous value of is estimated using phase locked loop (PLL).

At the th sampling instant, the output of PI frequency controller () is as: where and are the proportional and integral gains of frequency PI controller.

From (1) and (2) at the th sampling instant, the amplitude of active component of current is The instantaneous values of in-phase components of reference source currents are estimated as Multiplication of with in-phase unit amplitude templates () yields the in-phase component of reference source currents. These templates are three-phase sinusoidal functions which are derived by dividing the ac voltages , and by their amplitude . The instantaneous line voltages at the IAGs terminals (, , and ) are considered close to sinusoidal and their amplitude is computed as The unity amplitude templates having instantaneous value in phase with instantaneous voltage (, , and ), which are derived as [3, 8, 9]: To generate the quadrature component of reference source current, another set of sinusoidal quadrature unity amplitude templates (, , ) is obtained from in-phase unit vectors (, and ). The multiplication of these components with output of PI terminal voltage controller () gives the quadrature or reactive component of reference source currents.

The ac voltage error at the th sampling instant is where is the amplitude of reference ac terminal voltage and is the amplitude of the sensed three-phase ac voltage at the IAG terminals at th instant.

The output of the PI controller () for maintaining constant ac terminal voltage at the th sampling instant is expressed as where and are the proportional and integral gain constants of the proportional integral (PI) controller. and are the voltage errors in th and ()th instant. The output of PI controller () is considered the amplitude of quadrature component of the reference source current at ()th instant.

The instantaneous quadrature components of the reference source currents are estimated as where , and are another set of unit vectors having a phase shift of 90° leading with respect to the corresponding unit vectors , , and which are estimated as The total reference source currents are the sum of in-phase and quadrature components of the reference source current as: The reference source currents (, , and ) are compared with the sensed source currents (, , and ). The current errors are computed as These error signals are then given to ON/OFF switching patterns of the gate drive (IGBT) signals to generated pulse from the hysteresis current controller.

##### 3.1. Design of BESS Controller

Battery Energy Storage System (BESS) consist of lead-acid batteries, power conversion unit, and control system. The latter two are already discussed in the above section. The batteries are mainly used by power generating utilities, power distribution utilities, and power consumers. Main economic benefits of using BESS by power distributor and consumers is its ability to shave peak demands of loads by mean of discharging stored battery energy.

Lead-acid batteries are electrochemical devices that can be charge and discharge many times. Each cell of this battery consists of two electrodes. The positive electrode is of lead oxide (PbO_{2}) and negative electrode is of sponge lead (Pb) [16]. When these electrodes are immersed in sulfuric acid electrolyte, a nominal open-circuit potential of 2V/cell is created. When circuit between two electrodes is closed, battery discharges its stored energy.

Thevenin equivalent circuit of the battery-based model [17, 18] is shown in Figure 4.

The terminal voltage of the equivalent battery is obtained as where is the line rms voltage ( V).

At no load, voltage across the terminals of SEIG is rated voltage of 415 V. The battery voltage must be more than the peak of line voltage for satisfactory operation of Hysteresis controller. A slightly higher round-off value of 750 V is considered.

Since the battery is an energy storage unit, its energy is represented in kWh when a battery is used to model the battery unit, the equivalent capacitance can be determined from: In the given Thevenins equivalent model is the equivalent resistance (external + internal) of a parallel/series combination of the battery, which is usually a small value. The parallel circuit of and is used to describe the energy and voltage during charging or discharging. in parallel with represents self discharging of the battery, since the self discharging current of a battery is small, the value of resistance is large. From these equations, different parameters of a battery (, ) are selected and given in the appendix. Here it is considered that the battery is having energy storage of 6 kW for 4 h peaking capacity, and its variation in voltage of 740–760 V.

The greatest potential for BES is in multifunction applications. These include(i)Peak shaving of customer load.(ii)Load leveling—also benefits the electric utility.(iii)Energy/power for uninterruptable loads.(iv)Generation reserve requirement.(v)Automatic generation control (area control error (ACE) requirement).(vi)Deferment of new transmission construction.(vii)Reduction of magnetic field effects.

#### 4. MATlAB Simulink Model

Figure 5 shows the MATLAB/Simulink based model of micro grid in which micro sources connected in parallel operate along its controller, respectively. Each micro source has its own load and is connected to the other micro source through short transmission line. Line resistance and reactance is also considered. The model consists of three hydro power plants each having induction generator with its prime movers, each of 7.5 kW, 415 V, 50 Hz, 4-pole and each having star connected capacitor bank to provide reactive power at no load condition. The additional requirement of power during transient condition is provided by voltage frequency based BESS controller. The sub models of DSTATCOM controllers are shown in Figures 6 and 7 which are formed by all equations which are describe in Section 3. The proposed system is modeled using simulink and PSB toolboxes in MATLAB version of 7.8, in discrete mode at 5e-6 sec step size with ode 23tb (stiff/TR-BDF-2) solver along with the saturation characteristics of the machine as determined by synchronous speed test. Available universal bridge is used to model the VSC. Thevenin’s equivalent battery energy storage system is modeled as in [13, 14, 16, 18] using passive components and a dc battery. The resistive/inductive balanced/unbalanced load is considered as linear load.

#### 5. Results and Discussion

The performance of the proposed controller in micro grid is demonstrated with balanced/unbalanced linear, nonlinear and dynamic loads. Simulation waveforms for the entire three micro sources are presented in Figures 8–11. The subscript 1, 2, 3 are used for plant 1, plant 2, and plant 3. All the waveforms are represented using these subscripts for all type of loads. The waveforms consist of generator voltage (), generator current (), load current (), controller current (), load neutral current (), load neutral current controller (), neutral current (), terminal voltage (), frequency (), and battery current () with respect to time (sec.), presented in the figures. Generator “3” is disconnected at 2.7 sec and reconnected at 2.9 sec. The voltage and current of the disconnected generator remain same after connection to the micro grid. In this paper the following four cases are discussed.

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##### 5.1. Performance of Microgrid with BESS Feeding Balanced/Unbalanced Resistive Load

The performance of BESS based VF controller for micro grid with balanced/unbalanced resistive load is shown in Figures 8(a) and 8(b). Before the application of consumer load, the battery consumes all the generated active power. Star connected three single phase load each of 2.5 KW is applied at 2.2 sec. At 2.3 sec one phase is open and later on at 2.4 sec another phase is open hence load becomes unbalanced. Results include charging and discharging of battery and maintaining load balancing. Later on one by one phases are reconnected to the system. Hence the balanced, unbalanced, and no load condition voltage and frequency of the system remain constant.

##### 5.2. Performance of Microgrid with BESS Controller after Removing One Micro-Source

The performance of BESS based VF controller is shown in Figures 8(a) and 8(b). At 2.6 sec balanced resistive loads is applied to the system and at 2.7 sec fault is occur between hydro plant “3” and its load “3” so it get disconnected from the rest of the micro source. The plant remains disconnected from “2.7 to 2.9 sec” and again it is connected to the system at “2.9 sec.” During the disconnected interval 2.7 sec to 2.9 sec there is discharging of battery “1” and “2” as they have to share the extra load of micro source “3.” As is seen in waveform of Figure 8, terminal voltage and frequency of the system remain constant even after removal of one micro source.

##### 5.3. Performance of Microgrid with BESS Feeding Balanced/Unbalanced Reactive Load and Removal of One Micro-Source

Similarly, the performance of BESS based VF controller for micro grid with balanced/unbalanced reactive load is shown in Figures 9(a) and 9(b). Star connected three single phase load of each 2.5 KW and 1.87 KVAR is applied at 2.2 sec. At 2.3 sec one phase is open and later on at 2.4 sec another phase is open hence load becomes unbalanced and results in charging and discharging of battery, which shows load balancing of BESS fed VF controller. Again at 2.6 sec balanced load is applied to the system. Now at 2.7 sec a 3-phase fault occurs between load and hydroplant “3” so this plant is out of order and unable to support its load from 2.7 sec to 2.9 sec. It is seen from the waveform even if one plant is off the BESS based VF controller works and supplies the power during faulty condition. In this way, BESS keeps the overall generated power constant at the generator terminal which in turn regulates the system frequency.

##### 5.4. Performance of Microgrid with BESS Feeding Balanced/Unbalanced Nonlinear Load and Removal off One Micro Source

Similarly, the performance of BESS based VF controller for micro grid with balanced/unbalanced non-linear load is shown in Figures 10(a) and 10(b). Star connected three single phase diode rectifier based non-linear load is applied at 2.2 sec. At 2.3 sec one phase is open and later on at 2.4 sec another phase is open hence load becomes unbalanced and results in charging and discharging of battery, which shows load balancing of BESS fed VF controller. Again at 2.6 sec balanced load is applied to the system. Now at 2.7 sec a 3-phase fault occurs between load and hydroplant “3” so this plant is out of order and unable to support its load from 2.7 sec to 2.9 sec. As is seen from the waveform even if one plant is off the BESS based VF controller works and supplies the power during faulty condition. In this way, BESS keeps the overall generated power constant at the generator terminal which in turn regulates the system frequency.

##### 5.5. Performance of Microgrid with BESS Feeding Balance Dynamic Load and Removal of One Micro-Source

The performance of BESS controller for micro grid with balanced dynamic load is shown in Figures 11(a) and 11(b). At 2.2 sec direct on line starting of induction motor of 2 kW, 50 Hz asynchronous motor is applied and sudden changes are observed in load current, due to high starting current. A minor discharge of battery is observed to regulate the frequency but after 4-5 cycles when sudden starting current is controlled, voltage and current at the generator terminal remain constant. At 2.4 sec load torque is 75 Nm and at 2.4 it is increased to 157 Nm; if it is applied on the motor shaft then the motor load current is increased but the controller performance is desirable. Now at 2.7 sec a 3-phase fault occurs between load and hydro plant “3” so this plant is out of order and unable to support its load from 2.7 sec to 2.9 sec. As is seen from the waveform even if one plant is off the BESS based VF controller works and supplies the power to load during faulty condition. In this way, BESS keeps the overall generated power constant at the generator terminal which in turn regulates the system frequency.

#### 6. Conclusion

A detailed analysis of a micro grid with three micro sources under different load conditions is dealt with in this paper. The proposed BESS controller based voltage and frequency with each micro source regulates the terminal voltage and frequency of the source and hence stabilizes the micro grid. The mathematical model for BESS controller is analyzed for transient and dynamic condition. The controller provides desirable feature of synchronous condenser operating in capacitive and inductive modes. The capability of BESS based VF controller is demonstrated for load balancing, load leveling, and harmonic eliminations in linear, nonlinear, and dynamic loads. The BESS controller also works satisfactorily during removal of one micro source but as the whole system is connected in parallel other controller shares the load of that removed power generating plant and hence maintains the voltage and frequency of the whole system constant. Though due to battery energy storage system the size and the cost of the controller is increased but reliability of system with its VF control, outweighs this added cost. The implementation of this technology reinforces the use of such system where the grid connection has not reached yet and also in remote areas where renewable sources are available in abundance.

#### Appendix

(I)Machine parameters: 7.5 kW, 415 V, 50 Hz, Y-connected, 4-pole, Ω, Ω, Ω, kg-m^{2}.(II)Controller parameters: , , , .(I)Battery parameters: mH, Ω and

*μ*f, K, Ω, F.(IV)Consumer Loads(a)Resistive load = 2.5 kW single phase loads.(b)Reactive load = 2.5 kW, 1.875 KVAR 0.8 PF lagging single phase loads.(c)Nonlinear load = 2.5 kW with 100

*μ*F capacitor and 8 mH inductor at DC end of single phase diode rectifier.(d)Dynamic load = induction motor 2 kW, 50 Hz, 4 pole, 415 V.

#### References

- B. Lasseter, “Microgrids (distributed power generation),” in
*Proceedings of IEEE Power Engineering Society Winter Meeting*, vol. 1, pp. 146–149, Columbus, Ohio, USA, February 2001. View at: Publisher Site | Google Scholar - Y. Uno, G. Fujita, R. Yokoyama, M. Matubara, T. Toyoshima, and T. Tsukui, “Evaluation of micro-grid supply and demand stability for different interconnections,” in
*Proceedings of the IEEE International Power and Energy Conference (PECon '06)*, pp. 612–617, November 2006. View at: Publisher Site | Google Scholar - F. Katiraei, M. R. Iravani, and P. W. Lehn, “Micro-grid autonomous operation during and subsequent to islanding process,”
*IEEE Transactions on Power Delivery*, vol. 20, no. 1, pp. 248–257, 2005. View at: Publisher Site | Google Scholar - Y. Wei Li, D. M. Vilathgamuwa, and P. Chiang Loh, “A grid-interfacing power quality compensator for three-phase three-wire microgrid applications,”
*IEEE Transactions on Power Electronics*, vol. 21, no. 4, pp. 1021–1031, 2006. View at: Publisher Site | Google Scholar - N. Pogaku, M. Prodanović, and T. C. Green, “Modeling, analysis and testing of autonomous operation of an inverter-based microgrid,”
*IEEE Transactions on Power Electronics*, vol. 22, no. 2, pp. 613–625, 2007. View at: Publisher Site | Google Scholar - C. X. Wu, F. S. Wen, and Y. L. Lou, “The existed problems and possible solutions of micro-grid based on distributed generation,” in
*Proceedings of the 3rd International Conference on Deregulation and Restructuring and Power Technologies (DRPT '08)*, pp. 2763–2768, April 2008. View at: Publisher Site | Google Scholar - B. Adhikary, B. Ghimire, and P. Karki, “Interconnection of two micro hydro units forming a mini-grid system using soft connection,” in
*Proceedings of IEEE Region 10 Conference (TENCON '09)*, November 2009. View at: Publisher Site | Google Scholar - R. Majumder, B. Chaudhuri, A. Ghosh, R. Majumder, G. Ledwich, and F. Zare, “Improvement of stability and load sharing in an autonomous microgrid using supplementary droop control loop,”
*IEEE Transactions on Power Systems*, vol. 25, no. 2, pp. 796–808, 2010. View at: Publisher Site | Google Scholar - S. V. Iyer, M. N. Belur, and M. C. Chandorkar, “Analysis and mitigation of voltage offsets in multi-inverter microgrids,”
*IEEE Transactions on Energy Conversion*, vol. 26, no. 1, pp. 354–363, 2011. View at: Publisher Site | Google Scholar - C. Cho, J.-H. Jeon, J-Y. Kim, S. Kwon, K. Park, and S. Kim, “Active synchronizing control of a microgrid,”
*IEEE Transactions on Power Electronics*, vol. 26, no. 12, pp. 3707–3719, 2011. View at: Publisher Site | Google Scholar - C. V. Nayar, J. Perahia, F. Thomas, S. J. Phillips, T. Pryor, and W. L. James, “Investigation of capacitor-excited induction generators and permanent magnet alternators for small scale wind power generation,”
*Renewable Energy*, vol. 1, no. 3-4, pp. 381–388, 1991. View at: Google Scholar - A. Chandra, B. Singh, B. N. Singh, and K. A. Haddad, “An improved control algorithm of shunt active filter for voltage regulation, harmonic elimination, power-factor correction, and balancing of nonlinear loads,”
*IEEE Transactions on Power Electronics*, vol. 15, no. 3, pp. 495–507, 2000. View at: Publisher Site | Google Scholar - B. Singh, G. Kasal, A. Chandra, and K. Haddad, “Battery based voltage and frequency controller for parallel operated isolated asynchronous generators,” in
*Proceedings of IEEE International Symposium on Industrial Electronics (ISIE '07)*, pp. 883–888, June 2007. View at: Publisher Site | Google Scholar - B. Singh and G. K. Kasal, “Voltage and frequency controller for a three-phase four-wire autonomous wind energy conversion system,”
*IEEE Transactions on Energy Conversion*, vol. 23, no. 2, pp. 509–518, 2008. View at: Publisher Site | Google Scholar - P. K. Goel, B. Singh, S. S. Murthy, and N. Kishore, “Isolated wind-hydro hybrid system using cage generators and battery storage,”
*IEEE Transactions on Industrial Electronics*, vol. 58, no. 4, pp. 1141–1153, 2011. View at: Publisher Site | Google Scholar - M. D. Aderson and D. S. Carr, “Battery energy storage technology,”
*Proceedings of the IEEE*, vol. 18, no. 3, pp. 475–479, 1993. View at: Publisher Site | Google Scholar - M. Ceraolo, “New dynamical models of lead-acid batteries,”
*IEEE Transactions on Power Systems*, vol. 15, no. 4, pp. 1184–1190, 2000. View at: Publisher Site | Google Scholar - N. Jantharamin and L. Zhang, “A new dynamic model for lead-acid batteries,” in
*Proceedings of the 4th IET International Conference on Power Electronics, Machines and Drives (PEMD '08)*, pp. 86–90, April 2008. View at: Publisher Site | Google Scholar

#### Copyright

Copyright © 2012 Monika Jain et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.