Comparison study of lead-acid and lithium-ion batteries for solar photovoltaic applications

Received Feb 1, 2021 Revised Mar 5, 2021 Accepted Mar 13, 2021 The battery energy storage systems are very essential for maintaining constant power supply when using solar photovoltaic systems for power generation. The viability and ability of battery energy storage systems are assessed based on battery usage in Solar Photovoltaic utility grid-connected systems. The power supply quality and reliability are improved by utilizing battery energy storage technologies in conjunction with solar photovoltaic systems. This paper presents a comparative analysis of Lead-Acid Storage battery and Lithium-ion battery banks connected to a utility grid. The battery mathematical model simulation study gives their performance characteristics of these batteries under grid-connected loads. Cost-benefit analysis of battery usage for determining the best battery suitable for solar photovoltaic system applications is also presented in this paper.


INTRODUCTION
The battery energy storage system used in standalone photovoltaic systems has greatly increased in recent years [1]. Battery energy storage systems are used to augment the power supply or act as a backup power supply when the primary source fails. The power delivered by the storage system should be of the same quality and sustain the load for a predetermined duration of time. Typical Battery energy storage systems consist of a battery bank and a control circuit to manage the power delivery to the load [2]. The power management may involve feedback loops to maintain constant current or voltage and also monitor and throttle the battery temperature [3].
The core part of the battery management system is the type of battery used. The characteristics of the battery will determine the type of controls needed to operate the storage system [4]. In this paper, we consider using two types of batteries namely lead-acid and lithium-ıon batteries. In most of the literature available experiments have been done to analyze the discharge characteristics of batteries [5]- [15]. In this paper, the charging characteristics of the batteries are also taken into account along with the cost-benefit analysis. The paper is organized in the following manner. The description of the utility grid-connected PV Array is discussed in Section 2. The battery's description is given briefly in Section 3. The proposed equivalent circuit model for battery types with mathematical equations are discussed in Section 4. The simulation scenarios and results are discussed in Section 5. The cost comparison of batteries are given in Section 6. The conclusion made finally given in Section 7.

DETAILED DESCRIPTION OF 100 KW UTILITY GRID CONNECTED PV ARRAY
Power delivered by 100-kW PV array is channeled through a DC-DC boost converter which is connected to a three-phase three-level Voltage Source Converter (VSC). A three-phase three-level VSC feeds into a coupling transformer used to deliver power to a 25kV grid. The algorithm employed in maximum power point tracking (MPPT) is 'ıncremental conductance + ıntegral regulator' [16]. The components contained in the detailed model [17], [18] are: a. PV Array: Maximum power delivered by PV array is 100 kW at 1000 W/m 2 solar irradiance. b. DC-DC boost converter: At maximum power, PV output voltage is 273 V DC which is increased to 500 V DC by DC-DC boost converter of 5-kHz. The optimization of the switching duty cycle is done by an MPPT controller by using the 'Incremental Conductance + Integral Regulator' algorithm. The duty cycle is automatically varied by the MPPT system to provide the voltage required to take out maximum power. c. Three-level Three-phase VSC: The output voltage of the boost converter is converted from 500 V DC to 260 V AC by 1980-Hz Three-level Three-phase VSC and thus power factor of unity is maintained. The external control loop and internal control loops are the two control loops employed in the VSC control system [19] . Voltage regulation of DC link for +/-250 V is made with external loop control and Id and Iq grid currents regulation are made with internal loop control. The output DC voltage of the external controller is given by reference current Id. The power factor of unity is maintained by setting reference current Iq to zero. PWM Generator uses three modulating signals Uabc_ref generated from current controller output voltages Vd and Vq. The voltage controllers, current controllers, and unit of PLL Synchronization use sample time of 100 microseconds generated by the control system. Waveforms of PWM get a suitable resolution by setting a quick sample time of 1 microsecond for Boost and VSC converters Pulse generators. Capacitor bank: VSC harmonics are filtered by setting capacitor bank value to 10-kvar. Three-phase coupling transformer: Three-phase coupling transfer of rating 100-kVA 260V/25kV is used for stepping up the VSC output voltage of 260 V AC to 25 kV AC. Utility grid: The utility grid consists of a 25-kV distribution feeder+120 kV equivalent transmission system. 330 Sun Power modules (SPR-305E-WHT-D) are used in the 100-kW PV array. 5 modules are connected in series making a string, such 66 strings are connected in parallel. The solar cell equivalent circuit is shown in Figure 1. Solar cell characteristics are given by (1) [18].  Figure 1. Solar cell equivalent circuit with Rs and Rf [18] The dc-bus link voltage is stepped up by a dc-dc boost converter which is connected to PV Array. Boost converter suitable switching regulates the voltage of PV for maximum average PV array power output. PV Array operational voltage at a given irradiation condition varies with the PV power flow. By using the DC link in between, the Inverter and boost converter is connected. One module specifications given by the manufacturer are: a. The number of series-connected PV cells is 96 per module.
b. The open-circuit voltage of the cell is Voc= 64.2 V c. Short-circuit current of the cell is Isc = 5.96 A d. The voltage at maximum power is Vmp =54.7 V e. Current at maximum power is Imp= 5.58 A f.
Power per module = 54.7 x 5.58 = 305.2 W Which gives a total output power of PV Array = number of strings in parallel × number of modules per string × power per module = 66×5×305.2 W= 100.7 kW approximately. The solar irradiance (W/m 2 ) and temperature (deg. C) are the two inputs given to the block of PV Array. The block of the signal builder is used to set the input values for PV Array solar irradiance and temperature.

CHARACTERISTICS OF BATTERY
One or more electrochemical cells that are connected externally to deliver power to electrical devices form a rechargeable battery. In Electrochemical cells, energy is stored in a chemical form which gives energy in an electrical form on connecting load to it. A battery which is the rechargeable battery has the following: a. The current is entered into a polarized electrical device by the acceptance of electrons at the positive electrode (cathode). The reduction process is involved here. b. The current leaves the polarized electrical device by the generation of electrons at the negative electrode (anode). The oxidation process is involved here. c. The electron's electrical conduction between anode and cathode is done by the substance called electrolyte. The energy in chemical form is converted into electrical form during the battery discharge process. The electrolyte is generally split into movable ions due to the oxidation and reduction of the negative and positive electrode. The external circuit connected to the battery receives energy from those electrons. The energy in electrical form is converted into chemical form during the charging process of the battery. The external power source supplies energy to the cell.
The battery generates current by the electrons transfer occurs between the electrodes. The potential difference between the anode and cathode gives the battery an open circuit voltage , when an external load is not connected to the battery. The open-circuit voltage is generally a function of SOC i.e. (SOC). The state of charge (SOC) and capacity (Q) of the battery also affects the performance of the battery.

Li-ion battery
The active components involved in a lithium-ion battery are a negative electrode (cathode) having oxide of the lithiated metal and copper current collector, a positive electrode (anode) having layer structure graphitic carbon and aluminum current collector, electrolyte solution LIPF 6 -EC-DMC (lithium hexafluoro phosphate-ethylene carbonate-dimethyl carbonate) which is an electronic insulator and good ionic conductor. Polyethylene Separator is used to prevent contact between the electrodes. The operation of Lithium-Ion battery and its charging and discharging chemical reactions can be found in [20].

Lead-acid storage battery
The active components involved in lead-acid storage battery are negative electrode made of spongy lead (Pb), positive electrode made of lead dioxide (PbO 2 ), electrolyte solution of sulphuric acid (H 2 SO 4 ) and Separator which is used to prevent ionic flow between electrodes and increasing of internal resistance in a cell. Operation of Lead-Acid Storage battery and its charging and discharging chemical reactions can be found in [21], [22].

BATTERY MODEL
A generic battery model from MATLAB SimPower systems library [23]- [49] with appropriate parameters is used for analyzing battery charging and discharging characteristics performance.
The battery open circuit voltage is a function of the state of charge (SOC) [50]. The maximum battery energy extracted is represented by Q in (3) [51].
Battery SOC is given in (4).

Lithium-Ion battery
The discharge controlled voltage is given in [52]. It solves the problem caused due to the algebraic loop during the system simulation in Matlab/Simulink. The resistance of polarization during discharge for all kinds of battery is similarly given in [53]. During the charging process, the voltage of the battery is increased due to the absorption of too much energy on the system. The resistance of polarization during charge is given in,

Lead-acid storage battery
Exponential voltage includes a hysteresis phenomenon between battery charge-discharge given by (8)-(10), [54], [55]. i(t) sign is given by u(t). During the discharge process, u(t)=0 and during the charging process u(t)=1. So, the discharge controlled voltage is given in, The lead-acid storage battery voltage decreases slowly due to the full charging of the battery based on the magnitude of the current. The end of charge is not the same for this battery like other batteries. Overcharging the battery decreases the battery voltage slowly [19]. The resistance of polarization given in :

Equivalent model summary
Discharge and Charge equations for Lithium-Ion battery and Lead-Acid Storage battery are shown in Table. 1.

SIMULATION SCENARIOS AND RESULTS
Two battery types Lead-Acid Storage Battery and Lithium-Ion Battery having a rating of 582.5 V at 100 % SOC and 100 Ah Capacity are used. Two simulation scenarios have been carried out to understand the discharging and charging performance of the batteries. The proposed system block diagram for simulation as shown in Figure 2. Scenario 1: Boost Converter and VSC Converter will not get any pulses from t = 0 sec to t = 0.05 sec. DC link capacitors are charged by boosting the PV voltage above 500 V. Voltage across DC link capacitors is used to drive the voltage source inverter which acts as a three-phase rectifier. Boost and VSC circuits get activated at t=0.05 sec. The voltage of Vdc=500V at the DC link is maintained. The duty cycle applied to boost converter is 0.5.
Initially, at t=0.05 sec, only PV Array alone is catering to the power demand of the utility grid. When Solar irradiance falls from 1000 W/m 2 to 250 W/m 2 at t=1sec as shown in Figure 3, the PV Array is unable to support the power demand alone, now power from the battery energy storage bank is drawn to compensate for the shortage of the power delivered by the PV Array.
At t= 1.2 sec, the Steady-state is reached. Output power of PV Array at t=0.05 sec+ is Pmean = 96 kW. MPPT is enabled at t=0.4 sec. The MPPT regulator starts regulating PV voltage by varying the duty cycle to extract maximum power. From t=1 sec to t=12 sec batteries start delivering power to the utility grid. The discharging performance comparison of two batteries such as Lithium-ion and Lead-Acid Storage battery is carried out. The input values are given to the PV Array by the signal builder block. The PV Array Irradiance Ir, Temperature, Mean Power (Pmean) and Mean Voltage (Vmean); Duty Cycle of Boost Converter is shown in Figure 3.    The battery performances characteristics are shown in graphs for exact values at points of interest are given in Tables 2, 3, 4, and 5. Throughout the discharging time as observed in our simulation study [ref Figure 9], Lithium-Ion battery has delivered the higher power to the utility grid. Further, when we continue to discharge the battery banks, on reaching 20% SOC, the Lead-Acid Storage Battery Bank fails to deliver any power as the battery bank's current falls to zero [ref Figure 5]. The Lithium-Ion battery bank continues to deliver substantial power to the utility grid. This shows that Lithium-Ion batteries are capable of deep discharge i.e. Lithium-ion batteries have a higher depth of discharge and higher specific energy when compared to Lead-Acid Storage batteries. Even though the SOCs of Lithium-Ion and Lead-Acid batteries do not differ much while charging [ref Figure 11]. Batteries Comparison at different percentages of SOCs The batteries comparison at a different percentage of SOCs is shown in the Figure 6, utility grid voltage va and ia the utility grid voltage is maintained at 20 kV for batteries at different SOCs and Grid Current is approximately 3.5 A is shown in Figure 8.  It is also noticed from behavior that Lithium-Ion Battery bank having the same rated capacity delivered higher power [ref   Initially at t=0sec, PV Array alone is catering to utility grid power demand. When Solar irradiance increases from 1000 W/m2 to 1600 W/m2 at t=1sec as shown in Figure 10, the excess power generated by the PV array is used to charge the battery bank. The input values are given to the PV Array by the signal builder block. The battery banks are charged while maintaining constant power output to the utility grid. The voltage controller circuit comprises of boost converter connected to input terminals of the battery bank. PWM controller is used for generating gating signals for IGBT Switch. By varying the duty cycle of the IGBT Switch, the charging voltage is controlled. Charging performance comparison of two battery types Lithium-ion and Lead-Acid Storage battery is carried out.
At close to 80% SOC, Lead-Acid Storage Battery terminal voltage increases rapidly. Because of this maintaining the same rate of charge as earlier will require more power in case of the constant charging voltage, the lead-acid storage battery will take more time to charge as the charging current decreases as can be inferred from Figure 12.

COST COMPARISON OF LEAD-ACID AND LITHIUM-ION BATTERIES
When comparing the cost of different types of batteries, it is important to consider various parameters and their effects on costs. Each of these parameters for different batteries has different values and because of this, it is difficult to conclude by comparing these values directly. For example, the price of a Lithium-Ion battery is very high when compared to a lead-acid storage battery but the maintenance cost of the Lithium-Ion battery is very low. This may translate into a lower overall cost of Lithium-Ion battery in the long run.
One way to address the above issue is to come up with a heuristic metric by taking the required battery parameters into account. As use case is storage battery for PV grids, it is to come up with a heuristic while taking the following parameters into account. These are Battery Cost in USD, Maintenance cost, Depth of Discharge, Cycle Life, Battery Life, and Battery Efficiency. Note: Gravimetric energy density is not considered because it is not an important factor for static battery applications. Based on the relation between various parameters, we have arrived at metric given by expression Based on the above heuristic, Lead-Acid Battery is 2.79 times costlier than Lithium-Ion Battery. The values used for the computation of said heuristic metric are shown in Table 5

CONCLUSION
The following conclusions can be derived from the results obtained from section 5 and 6. A comparative analysis of two types of batteries is presented in this paper. Results show that Lithium-Ion battery has better discharging voltage, discharging current than Lead-Acid Storage battery at various percentages of state of charge. It is also observed that while maintaining constant load voltage, Lithium-Ion battery delivers more power to utility grid. Lead-Acid battery consumes more power when charged to 100% state of charge. Lead-Acid Storage Battery is 2.79 times costlier than Lithium-Ion Battery. So, for a solar photovoltaic system with high power demand, a Lithium-Ion battery is more suitable both performance-wise and cost-wise.