# Design and Experimental Results of Battery Charging System for Microgrid System

Authors: Byunggyu Yu
Journal: International Journal of Photoenergy
 (2016)

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## Abstract

Nowadays, many countries have paid attention to renewable energy due to fossil fuel crisis and its related environmental pollution. In particular, following the government supply business for renewable energy industry, the private sectors drive the stable power supply by using renewable sources for both microgrid system and standalone application. Battery charging and discharging control system of microgrid system are critical to extend lifetime of standalone photovoltaic system. Corresponding to this demand, this paper presents the development of battery charging and discharging system based on battery modeling, SOC (state of charge) estimation, and its implementation for 5 kW. As a result, the conversion efficiency shows 96.35% with over 95% charging performance.


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## Body

## 1. Introduction

A microgrid system is defined as an autonomous energy grid system to operate in parallel with or independently of the traditional grid [1, 2]. In accordance with the growing industry trend on renewable energy, microgrid systems integrated with renewable energy resources are becoming widespread in the world [3–5]. This type of microgrid system consisted of several renewable energy resources like photovoltaic generation and a battery backup system like lead-acid battery system [6–8]. In particular, battery system is the key component to stabilize the microgrid system as a concrete grid voltage function. Typically, lead-acid battery is mostly used for storage system, but it has relative short lifetime for a stable operation. Thus, the battery charging and discharging system are regarded as one of the most essential systems for the long lifetime operation [9–12]. The battery systems for both microgrid system and standalone PV generation are different from the conventional system for UPS (uninterruptable power supply), because the charging and discharging profiles are depending on the environmental condition like irradiance. Corresponding to this demand, this paper presents the development of battery charging and discharging system based on battery modeling, SOC (state of charge) estimation, and its implementation.This paper consisted of three sections. Firstly, the modelling of battery and battery charger/discharger is presented. Secondly, based on the modeling, the simulation of the target system is conducted with topology design for 5 kW. Lastly, with the proposed control algorithm, the final system output is implemented to verify the proposed algorithm and hardware.


## 2. Battery Modeling

It is required to have appropriate battery modeling to implement a battery charging and discharging system. Typically, this modeling can be classified into three categories. One is an electrochemical modeling, and it is too complicated to apply even though it shows the highest accuracy [13]. The second one is a mathematical modeling and it is acceptable to apply under some limited condition [14]. The third one is based on the electrical modeling by using voltage source, resistor, and capacity and it is practical for battery charging system implementation. In particular, this paper uses the electrical modeling for battery as in Figure 1. In order to model battery electrical characteristic, it is assumed that SOC function is used to improve the modeling accuracy as the following equation:(1)SOC=Ah_init-∫IbatteryoutdtAh_rate,where Ah_rate is the battery rating and Ah_init is the initial battery charging state.Figure 1
Battery electrical modeling.


## 3. System Configuration

Battery system is installed to regulate the DC bus among PV generation, wind turbine, and local loads in Figure2. Specifically, the battery charger is implemented by using 5 kW bidirectional buck-boost converter. As shown in Figure 3, the operating mode between charging mode and discharging mode is determined by monitoring DC bus voltage and current. In other words, when it is the charging mode, the charger is operated as buck converter. While it is the other mode, the charger is operated as the boost converter.Figure 2
Standalone micropower grid configuration.Figure 3
Battery charger system diagram.


### 3.1. Buck Converter for Charging Mode

Buck converter is called a step-down converter, at which the input voltage magnitudev1 is decreased from the output voltage v2 by the on/off control of switch S1 (Figure 4(a)). When the switch S1 is on during DT, where the switching duty ratio is D and the switching period is designated as T, the inductor voltage vL is determined by the following equation. During the short switching period T, both v1 and v2 are assumed as constant values.(2)vL=v1-v2=LdiLdt,diLdt=ΔiLΔt=v1-v2L,ΔiLon=v1-v2LDT.Figure 4
Battery charger operational circuit diagram. (a) Buck converter for charging mode; (b) boost converter for discharging mode.
(a) (b)When the switchS1 is off during (1-D)T, the inductor voltage vL is determined by the following equation.(3)vL=-v2=LdiLdt,diLdt=ΔiLΔt=-v2L,ΔiLoff⁡=-v2L1-DT.Under the steady state condition for the continuous current control, the net inductor current change during one switching cycle is equal to zero as following equation.(4)ΔiLon+ΔiLoff⁡=0,v2=Dv1.Thus, the output voltagev2 is equal to Dv1.Since the average capacitor (C2) current is equal to zero at the steady state, the average inductor current should be equal to the load current. R is representing the load resistance for the 5 kW battery charger converter. Since the nominal battery bank voltage is 240 V, the nominal load resistance can be calculated by the power definition. This is because the load current through R is limited by the controller. Thus, R is used for the converter design. Thus, (5)IL=IR=v2R.The maximum inductor current and the minimum inductor current can be calculated from the inductor average current and the net inductor current change.(6)IL,max=IL+ΔiL2,IL,min=IL-ΔiL2.For the continuous current mode of inductor current, the minimum inductor currentIL,min should be more than zero. Thus, the minimum inductance can be calculated from the fixed switching frequency f.(7)Lmin=1-DR2f.From the designed switching 12 kHz and 5 kW converter power capacity, the minimum inductanceLmin can be calculated by 877 uH.For the capacitance design, the capacitanceC2 can be calculated by the designed voltage ripple ratio.(8)ΔQ=C2Δv2,(9)ΔQ=12T2ΔiL2=TΔiL8.When the current variation is 40% and the ripple voltageΔv2 is designed as 1 V, the designed capacitance C2 can be designed as 87.5 uF.


### 3.2. Boost Converter for Discharging Mode

Boost converter is called a step-up converter, at which the input voltage magnitudev2 is decreased from the output voltage v1 by the on/off control of switch S2 (Figure 4(b)). When the switch S2 is on during DT, where the switching duty ratio is D and the switching period is designated as T, the inductor voltage vL is determined by the following equation.(10)vL=v2=LdiLdt,ΔiLΔt=ΔiLDT=v2L,ΔiLon⁡=v2LDT.When the switchS1 is off during 1-DT, the inductor voltage vL is determined by the following equation.(11)vL=v2-v1=LdiLdt,diLdt=ΔiLΔt=v2-v1L,ΔiLoff⁡=v2-v1L1-DT.Under the steady state condition for the continuous current control, the net inductor current change during one switching cycle is equal to zero as following equation.(12)ΔiLon+ΔiLoff⁡=0,v1=v21-D.Thus, the output voltagev1 is equal to v2/(1-D).Since the average capacitor (C1) current is equal to zero at the steady state, the average inductor current should be equal to the load current. Thus, (13)IL=IR=v1R=v21-D2R.The maximum inductor current and the minimum inductor current can be calculated from the inductor average current and the net inductor current change.(14)IL,max=IL+ΔiL2,IL,min=IL-ΔiL2.For the continuous current mode of inductor current, the minimum inductor currentIL,min should be more than zero. Thus, the minimum inductance L can be calculated from the fixed switching frequency f.(15)Lmin=D1-D2R2f.From the designed switching 12 kHz and 5 kW converter power capacity, the minimum inductanceLmin can be calculated by 884 uH.For the capacitance design, the capacitanceC2 can be calculated by the designed voltage ripple ratio.(16)ΔQ=C1Δv1,ΔQ=v1RDT.When the ripple voltageΔv1 is designed as 1 V, the designed capacitance C1 from (8) can be designed as 400 uF.


## 3.1. Buck Converter for Charging Mode

Buck converter is called a step-down converter, at which the input voltage magnitudev1 is decreased from the output voltage v2 by the on/off control of switch S1 (Figure 4(a)). When the switch S1 is on during DT, where the switching duty ratio is D and the switching period is designated as T, the inductor voltage vL is determined by the following equation. During the short switching period T, both v1 and v2 are assumed as constant values.(2)vL=v1-v2=LdiLdt,diLdt=ΔiLΔt=v1-v2L,ΔiLon=v1-v2LDT.Figure 4
Battery charger operational circuit diagram. (a) Buck converter for charging mode; (b) boost converter for discharging mode.
(a) (b)When the switchS1 is off during (1-D)T, the inductor voltage vL is determined by the following equation.(3)vL=-v2=LdiLdt,diLdt=ΔiLΔt=-v2L,ΔiLoff⁡=-v2L1-DT.Under the steady state condition for the continuous current control, the net inductor current change during one switching cycle is equal to zero as following equation.(4)ΔiLon+ΔiLoff⁡=0,v2=Dv1.Thus, the output voltagev2 is equal to Dv1.Since the average capacitor (C2) current is equal to zero at the steady state, the average inductor current should be equal to the load current. R is representing the load resistance for the 5 kW battery charger converter. Since the nominal battery bank voltage is 240 V, the nominal load resistance can be calculated by the power definition. This is because the load current through R is limited by the controller. Thus, R is used for the converter design. Thus, (5)IL=IR=v2R.The maximum inductor current and the minimum inductor current can be calculated from the inductor average current and the net inductor current change.(6)IL,max=IL+ΔiL2,IL,min=IL-ΔiL2.For the continuous current mode of inductor current, the minimum inductor currentIL,min should be more than zero. Thus, the minimum inductance can be calculated from the fixed switching frequency f.(7)Lmin=1-DR2f.From the designed switching 12 kHz and 5 kW converter power capacity, the minimum inductanceLmin can be calculated by 877 uH.For the capacitance design, the capacitanceC2 can be calculated by the designed voltage ripple ratio.(8)ΔQ=C2Δv2,(9)ΔQ=12T2ΔiL2=TΔiL8.When the current variation is 40% and the ripple voltageΔv2 is designed as 1 V, the designed capacitance C2 can be designed as 87.5 uF.


## 3.2. Boost Converter for Discharging Mode

Boost converter is called a step-up converter, at which the input voltage magnitudev2 is decreased from the output voltage v1 by the on/off control of switch S2 (Figure 4(b)). When the switch S2 is on during DT, where the switching duty ratio is D and the switching period is designated as T, the inductor voltage vL is determined by the following equation.(10)vL=v2=LdiLdt,ΔiLΔt=ΔiLDT=v2L,ΔiLon⁡=v2LDT.When the switchS1 is off during 1-DT, the inductor voltage vL is determined by the following equation.(11)vL=v2-v1=LdiLdt,diLdt=ΔiLΔt=v2-v1L,ΔiLoff⁡=v2-v1L1-DT.Under the steady state condition for the continuous current control, the net inductor current change during one switching cycle is equal to zero as following equation.(12)ΔiLon+ΔiLoff⁡=0,v1=v21-D.Thus, the output voltagev1 is equal to v2/(1-D).Since the average capacitor (C1) current is equal to zero at the steady state, the average inductor current should be equal to the load current. Thus, (13)IL=IR=v1R=v21-D2R.The maximum inductor current and the minimum inductor current can be calculated from the inductor average current and the net inductor current change.(14)IL,max=IL+ΔiL2,IL,min=IL-ΔiL2.For the continuous current mode of inductor current, the minimum inductor currentIL,min should be more than zero. Thus, the minimum inductance L can be calculated from the fixed switching frequency f.(15)Lmin=D1-D2R2f.From the designed switching 12 kHz and 5 kW converter power capacity, the minimum inductanceLmin can be calculated by 884 uH.For the capacitance design, the capacitanceC2 can be calculated by the designed voltage ripple ratio.(16)ΔQ=C1Δv1,ΔQ=v1RDT.When the ripple voltageΔv1 is designed as 1 V, the designed capacitance C1 from (8) can be designed as 400 uF.


## 4. Experimental Results

The proposed battery charging system was implemented by using buck converter as designed in the previous section. The electrical specification is listed in Table1. Figure 5 shows the implemented system front-view.Table 1
Electrical specification.
Item Value Bus voltage (v1) 380 V Nominal battery voltage (v2) 240 V Rated power capacity (P) 5 kW Inductance (L) 880 uH Bus capacitance (C1) 400 uF Battery capacitance (C2) 94 uF Switching frequency (f) 12 kHzFigure 5
System hardware front-view picture.Figure6 shows the experimental waveforms for both CC and CV modes. DC link voltage is implemented by DC power supply and batteries are stacked to generate 240 V. Buck-boost converter is implemented for battery charging operation. The charging current is designed as 3 A, while the maximum charging current is limited as 10 A, and the temperature is controlled to be less than 50°C. When the battery voltage reaches the nominal battery voltage, the charging mode moves from constant current (CC) mode to constant voltage (CV) mode as shown in Figure 6. As a result, SOC as a charging performance index, is estimated over 95% with 96.35 conversion efficiency.Figure 6
Experimental result for battery charging performance. (a) CC mode; (b) CV mode.
(a) (b)


## 5. Conclusion

This paper presents the development of battery charging and discharging system based on battery modeling, SOC estimation, and its implementation. As a result, the conversion efficiency shows 96.35% with over 95% charging performance. Based on the presented design and experimental results for battery charging system, the battery backup system can be expected to be of high efficiency with long lifetime.



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*Source: 7134904-2016-10-27.xml*