Novel optimization technique to charge E-rickshaw battery using single sensor based MPPT of SPV module

Abstract

The battery era has started to compensate the demand of the energy while the charging issues still exist. Thus, demand of reliable and optimized charging is required to charge cell/battery. In this paper novel optimized technique is proposed, based on gravitational search algorithm (GSA) to charge e-rickshaw battery using single sensor based maximum power point tracking (MPPT) of solar photovoltaic (SPV) module. There are various metaheauristic and heuristic techniques are available like Cauchy and Gaussian sine cosine optimization (CGSCO) intelligent technique, evolutionary algorithms, stochastic algorithms, Swarm optimization technique, ant colony technique, neural algorithms, fuzzy logic algorithms to optimize the charging current of cell/battery. These techniques take more iteration to give the optimal solution. Moreover, GSA is the high level intelligent technique which is used in multi area to optimize the various parameters in engineering fields. It is very ease to find the optimal solution in search space. This approach is novel in the field of e-rickshaw battery charging. Therefore, the mathematical algorithm based on GSA has been developed to optimize the current of charging cell/battery. The performance of GSA optimization technique is verified and compared with the metaheauristic based CGSCO optimization technique. It is observed that GSA is easy to design and reduce the cost of charger.

Keywords

Gravitational search algorithm gravitational constant boost converter insolation agent

1 Introduction

The energy demand increases with technology advancement in exponential form. This energy is produced from various sources (conventional and non conventional). The need of green energy is demand of present era as energy production from various sources increases the CO₂ level of atmosphere. The Ozone layer also affected which causes whole world atmosphere polluted dearly. The polluted environment affected all living things on the earth. Recently, it has observed air pollution level in capital of India and surrounding area, which causes massive air borne diseases and health related problems. Thus, eco-friendly energy production is required to bridge the gap of the demand. The production of solar and wind energy is good option in present era. The energy tapped from Sun radiation is the best option as it is noise less and pollution free. It is one of the fields of energy production which is not fully utilized in last few decades. The energy production by solar photo voltaic is pollution free and noise less [1]. As solar energy production depends on the solar radiation. Thus, sun radiation is required to generate electricity while in Indiareception of sun radiation is 4 to 5 hours on an average in one day. Analysis and behavior of SPV has been presented in MATLAB using five parameters [2]. MPPT technique is utilized to receive maximum insolation from Sun. This maximum production of energy is utilized by individual capacity and for grid connected system whereas absence of sun radiation, need of storage electricity to execute the demand. The solar energy needs cell/ battery to store the electricity. It minimizes conventional form of energy production. The cell/battery needs reliable and optimized charger to minimize the charging time, designing cost, and compact size. A novel P&O MPPT is applied to track unexpected change in insolation [3, 4]. The maximum power from solar panel can be regulated by Takagi-Sugeno fuzzy-logic approach [5]. In DC-DC converter, fuzzy based MPPT controller with learning automata algorithm [6] is employed to optimize the duty cycle. Many new techniques like incremental conductance MPPT, fast-converging MPPT, particle swarm optimization is adapted to mitigate fast changing environment of SPV [7 –9]. Power quality issues have been discussed by many authors while working with solar bounded energy. Power quality of unbalanced and nonlinear load is improved by applying power angle control [10]. Current and voltage harmonics is eliminated [11] and voltage sag and voltage swell also mitigated by Unified Power Quality Conditioner [12]. An E-rickshaw battery is exposed to extreme stresses due to continuous charging and discharging. The fuzzy logic based controller are employed to ease high stresses in cell/battery charging [13, 14]. A modified clonal selection algorithm is used to reduce the operating cost of micro grids, sufficient storage battery device [15]. There are many optimized techniques (hill climbing optimization, cuckoo search optimization, gray wolf optimization, particle swarm optimization, CGSCO etc.) used for reliable charging [16, 17]. However, the scope of improvement for charging cell/battery compels the authors to develop new technique to optimize charging of DC based electric-rickshaw (e-rickshaw). Moreover, many intelligent approaches are suggested by researchers to mitigate battery charging problems. Hence, high level intelligent strategies like evolutionary algorithms, stochastic algorithms, and physics related algorithms, neural algorithms, fuzzy logic algorithms and etc. are used to explore and exploit the search space to find best possible solutions [18].

In this paper novel optimized technique is used, based on gravitational search algorithm (GSA) to charge e- rickshaw battery using single sensor based MPPT of solar photovoltaic (SPV) module [19]. The GSA optimization technique is based on Newtonian gravitational force & first law of motion. This technique is developed by Rasedi et al. [20]. In this technique, the force of attraction between objects and first law of motion is formulated to optimize the charging current. According to this technique, every particle (agent) in the search space attracts other agents. The movements of agents in the search depend upon their masses. Every mass in the search space could be a solution. Lighter masses moves faster as compared to heavier masses. This concept is used to develop optimal technique.

Moreover, GSA is the high level intelligent technique which is used in multi area to optimize the various parameters in engineering fields. It is very ease to find the optimal result in search space. This approach is novel in the field of e-rickshaw battery charging. Therefore, the mathematical algorithm based on GSA has been developed to optimize the current of charging cell/battery. The performance of GSA optimization technique is verified and compared with the metaheauristic based CGSCO optimization technique. It is observed that GSA is easy to design and reduce the cost of charger.

In the next section, mathematical modeling of SPV is discussed. In section 3, solar mounted SPV scheme is presented. Proposed technique is discussed in section 4. In section 5, Result and discussion has been presented. The last section concludes the proposed work.

2 Modeling of solar PV system

Equivalent circuit model of solar photo voltaic cell is represented by one or two diode model. Authors have decided to analyze mathematical modeling by using one diode model. Analysis of one diode model of SPV is simple and easy in calculation as it has only one exponential term as shown in Fig. 1 (a) and equation (1). One diode model of SPV cell consists of one current source, a parallel diode, equivalent series resistance and parallel resistance. Solar cells are connected in series, parallel or combination of series and parallel, depending on requirement. Series connection is provided to increase the output voltage and parallel connection is provided to increase the output current. The circuit diagram of series and parallel combination scheme with bypass diode parallel with each PV module and blocking diode in series with PV module is shown in Fig. 1(b).

Fig.1

(a) Equivalent circuit diagram of one diode model SPV module. (b) Series and parallel combination of SPV module.

Mathematical analysis of SPV is carried out by taking one diode configuration as shown in Fig. 1 (b). The output current (I_PV) of one diode model is calculated as: $IP V = I_{P h} - I_{D} - I_{P} .$ $I P V = I_{P h} - I_{D 0} (e^{H} - 1) - \frac{V_{P V} + I_{P V} R_{S}}{R P}$ (1)

where, $H = \frac{q \times (V_{P V} + I_{P V} R_{S})}{N_{CS} K T_{C} a_{if}}$ , I_Ph is the SPV photo current. I_D0 is SPV cell diode leakege current. V_PV is the load voltage of solar module. R_S (0.345Ω) is equivalent series resistance and R_P (10000Ω) is the leakage resistance, N_S is the total series cells, q [1.60210 - 19C] electron charge, K [1.38×10-23J/K] ‘Boltzmann’ constant, T_C is the working temperature of the SPV cell, a_if is the ideality factor of the diode (1 ≤ a_if ≤ 1.5).

The output current of SPV cell and reverse saturation current of diode are expressed as: $IP h = (\frac{R_{P} - R_{S}}{R_{P}} I_{S C} + α_{i} (T_{C} - T_{ref})) \frac{S}{S_{r e f}}$ (2) $I_{D 0} = \frac{I_{SC} + α_{i} (T_{C} - T_{ref})}{e^{\frac{V_{OC} + β_{V} (T_{C} - T_{ref})}{N_{CS} K T_{C} a_{if}} \times q} - 1}$ (3)

where, V_OC and I_SC are open circuit voltage across solar cell output and short circuit current respectively, α_i is the coefficient of current (0.0017A/K) and β_v is the coefficient of voltage (–0.123V/K), T_ref is the temperature at standard test condition (STC).

3 Proposed configuration

The proposed solar mounted charging scheme of e-rickshaw is shown in Fig. 2. It consists of solar mounted e-rickshaw, boost converter, GSA based MPPT controller and batteries. For smooth functioning of e-rickshaw, vehicle parameters, operation parameters and life cycle parameters has to be addressed. The technical specifications of e-rickshaw are given by Table 1.

Fig.2

Solar mounted charging scheme of e-rickshaw.

Table 1

Technical Parameters

Technical Parameters	Mean Values
Motor Capacity	850 W (Mode Value – 650 W)
Battery Voltage (System Value)	48V
Single Battery Capacity (Peak)	85 Ah
Maximum Load Capacity	380 kilograms (5 people)
Vehicle Weight (Approximate Figure- Large Variations)	215 kilograms (With Batteries)
Maximum Speed	33 Kmph
Charging Time	8.2 hours (8 hours and 12 Minutes)
Distance Covered (1 Charge)	63 Kilometers
Battery Recycling Time Period	7.5 Months

The output of solar mounted e-rickshaw is fed to the battery through MOSFET based boost converter. Its switching frequency is controlled by GSA based MPPT controller by using feedback charging current. Strings of four lead acid batteries in series are used for charging.

4 Novel optimization technique based on GSA

A novel GSA optimization technique is developed by authors to optimize the charging current. GSA is based on gravitational force and first law of motion. It is proposed by agents and performance. The agents are related to particles and performance is related to its mass. According to the gravitational force every particles attract other particles in the universe. Due to this gravitational force all the smaller particles moves towards heavier masses. The mass which moves slowly assures the exploitation step of the algorithm.

There are four terms to represent an agent (particle) in GSA, as agent location, inertial mass, active and passive gravitational mass. Every location of the agent could be a solution of the proposed problem. The fitness function determines gravitational and inertial masses. Since, lighter mass attracts towards heavier mass. Therefore, it represents best promising solution in the investigating space. For applying GSA optimization, the gravitational force is taken as inversely proportional to distance(R) between masses instead of R ² as it gives better result.

The position of i ^th agent at any time in the search area is given by,

$χ_{i} = (x_{i}^{1} . . . ., x_{i}^{d} . . . ., x_{i}^{n}) for i = 1, 2 \dots \dots . N$ (4)

where N is the number of agents, $x_{i}^{d}$ represents the location of i ^th agent in the d ^th dimension.

At a particular time ‘τ ’, the force of attraction between mass ‘i’ and mass‘j’is given as: $F_{ij}^{d} = G (τ) \frac{M_{pasi} (τ) \times M_{actj} (τ)}{R_{ij} (τ) + ε} (x_{j}^{d} (τ) - x_{i}^{d} (τ))$ (5)

where, M_actj is active mass of agent j, M_pasi is passive mass of agent i, ε(<1) is a constant, and R_ij (τ) is the Euclidian distance between masses i and j. The Euclidian distance is given by: $R_{ij} (τ) = {∥ χ_{i} (τ), χ_{j} (τ) ∥}_{2}$ (6)

The total force exerted from other masses on agent i in a dimension d is given by: $F_{i}^{d} (τ) = \sum_{j = 1, j \neq i}^{N} {rand}_{j} F_{ij}^{d} (τ)$ (7)

where, rand _j is a arbitrary number in the interval [0, 1].

Hence, acceleration $α_{i}^{d} (τ)$ of the i^th agent at time τ, and in direction d^th, is given by first law of motion; $α_{i}^{d} (τ) = \frac{F_{i}^{d} (τ)}{M_{inri} (τ)}$ (8)

The next velocity and position is calculated as follows: $u_{i}^{d} (τ + 1) = {rand}_{i} \times u_{i}^{d} (τ) + α_{i}^{d} (τ) .$ (9) $x_{i}^{d} (τ + 1) = x_{i}^{d} (τ) + u_{i}^{d} (τ + 1)$ (10)

The GC is initialized at as follows:

G (τ) = G (G₀, τ)

Assuming all the masses are equal, therefore, we write following equations: $M_{acti} = M_{pasi} = M_{inri} = M_{i}, i = 1, 2 \dots \dots N$ (11) $m_{i} (τ) = \frac{{fit}_{i} (τ) - Z (τ)}{B (τ) - Z (τ)}$ (12) $M_{i} (τ) = \frac{m_{i} (τ)}{\sum_{j = 1}^{N} m_{j} (τ)}$ (13)

where fit _i(τ) is the value of fitness of the agent at the time τ, and for minimization of best(B) and worst(Z) agents at the time τ is defined as given by, $B (τ) = min_{j \in {1, . . . ., N}} {fit}_{j} (τ)$ (14) $Z (τ) = max_{j \in {1, . . . ., N}} {fit}_{j} (τ)$ (15)

the best and worst agents at the time τ is defined for maximization as follows: $B (τ) = max_{j \in {1, . . . ., N}} {fit}_{j} (τ)$ (16) $Z (τ) = min_{j \in {1, . . . ., N}} {fit}_{j} (τ)$ (17)

By utilizing the utility of exploration and exploitation to find the global MPPT, the agents with bigger mass chosen. There may be trapping problem with reduction of agents with time lapse. GSA algorithm has capability to explore local maxima at beginning. With lapse of time, exploration diminishes and exploitation starts. The GSA performance is improved by trade off between exploration and exploitation of the best agents. The best agents are defined by K_best and it is function of time. Stating value of K_best is taken as K₀ and it decreases with time. The GSA algorithm starts with all agents and with lapse of time K_best decreases linearly. And best agent is the optimal solution. Thus, equation (12) modified as follows, $F_{i}^{d} (τ) = \sum_{j \in K_{best}, j \neq i} {randjF}_{ij}^{d} (τ)$ (18)

The various stages of the proposed GSA algorithm are as follows:

Identify the search space.

Initial Values taken at random.

Evaluate the fitness agents.

Update the values of Gravitational constant, G(τ), M_i(τ), B(τ) and Z(τ),

for i = 1,2,…,… N.

Compute all force in various directions.

Compute the Velocity and acceleration.

Update the agent’s position.

If end criteria is not achieved repeat steps (iii) to (vii).

Stop.

The following parameters are used to simulate high level agent based intelligent GSA algorithm are, G = 89, N = 40, number of iterations = 10, mass update constant = 0.97 and force update constant = 0.6413.

The proposed GSA algorithm flow chart is shown in Fig. 3.

Fig.3

Proposed GSA flow chart.

5 Results and discussion

The performance estimation of the suggested current (single) sensor based system is carried out using GSA optimization technique. For better results the proposed technique is tested at the extremely variable environmental circumstances. The interval of variation of operating temperature and solar insolation is taken as 10 s. The solar insolation and temperature variations are shown in Figs. 4 and 5 respectively. Figures 4 and 5 consist of three patterns (pattern-1, 2 and 3) and pattern of SPV curves is shown in Fig. 6. The proposed charging scheme is simulated in MATLAB. For simulation, a solar panel of V_OC = 320 V, I_sc= 6A, P_MPP = 1.57 kW at STC, and the battery Specifications: 48 V, 3.84 kWh (4 cells of 12 V, 80 Ah) are considered.

Fig.4

Insolation pattern variation.

Fig.5

Temperature pattern variation.

Fig.6

Pattern of SPV curves.

The simulation results are shown as follows: (i) Fig. 7, duty cycle waveform, (ii) Fig. 8, power waveform and (iii) Fig. 9, charging current waveform of SPV. In the Fig. 10, the results have been shown in bar chart from. It is clear from results in the bar chart, the performance of GSA is superior in each sample as compared with CGSCO technique. The average tracking time of GSA is only 1.78 s, whereas, in CGSCO is 1.89 s. The average tracking efficiency of CGSCO is 98.29% while in GSA is 98.91%. The tracking time and % tracking efficiency improvements w.r.t. CGSCO technique is very significant; also the performance of GSA is much better.

Fig.7

MOSFET duty cycle (a) GSA and (b) CGSCO.

Fig.8

SPV power (a) GSA and (b) CGSCO.

Fig.9

Charging current (a) GSA and (b) CGSCO.

Fig.10

GSA performance: (a) charging current, (b) number of iterations, (c) tracking efficiency, (d) tracking time.

6 Conclusions

A novel optimized technique to charge e-rickshaw battery using single (current) sensor based mppt of SPV module has been proposed. Here, single sensor is used to optimize the charging power of cell/battery. The optimal charging of cell/battery is achieved by choosing correct duty cycle of MOSFET based boost converter. The best possible value of duty cycle is achieved by a new high level optimization technique (GSA). The GSA optimization technique is extremely robust, consistent and, easy to implement. Also, performance of single sensor based GSA has been compared with metaheauristic CGSCO algorithm. The simulated results are shown in bar chart in terms of number of iterations, tracking time and tracking efficiency. Performance of SPV charging scheme by GSA technique is tremendously quick and extremely efficient. In addition, on financial level, the GMPP tracking is reliable, economical, hassle free maintenance, and computational load is also incredibly less. Thus, GSA based optimized technique simple, efficient andeconomical.

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