A multi verse optimization based MPPT controller for drift avoidance in solar system

Abstract

This paper proposes Multi verse optimization (MVO) based MPPT controller to mitigate the possibility of losing tracking direction in solar photovoltaic system under variable irradiance. Generally conventional Perturb & Observe and hill climbing MPPT techniques are used due to effortless implementation. However, these techniques are not capable of handling oscillations in power at MPP and exhibit drift under variable irradiance conditions which leads to power loss. Therefore a hybrid of standard MVO and direct duty cycle control is proposed to minimize the inadequacies occurring in conventional controllers. Three cases i.e. constant irradiance, rapid and step changes in irradiance are considered for the analysis. The supremacy of proposed method is justified by comparing it with traditional P&O, Particle swarm optimization (PSO) based MPPT and Grey wolf optimization (GWO) based MPPT techniques. It is observed from the results that MVO based MPPT controller is capable of avoiding drift and offers fast convergence. Therefore proposed controller outperforms in terms of tracking efficiency, settling time, peak overshoot, and integral absolute error.

Keywords

Solar PV system MPPT optimization technique multi verse optimization

1 Introduction

In recent years, the rapidly decreasing fossil fuels have necessitated the use of renewable energy resources. The renewable energy has various advantages such as pollution free, zero fuel cost and almost negligible maintenance cost. Solar energy is one of the most popular sources of energy and becoming more important day by day. However, poor conversion efficiency of solar PV system requires large number of modules which increases the overall cost of system in comparison to fossil fuel for a particular application. Therefore, a power converter circuit is generally used between PV array and load to achieve maximum power transfer. The task is accomplished by incorporating maximum power point tracking (MPPT) techniques to control switching action of power converters. Under uniform solar irradiance, P-V curve has single maximum power point (MPP), but it exhibits multiple local peaks along with global peak when partial shading condition occurs. The non-uniform irradiance and partial shading lead to a highly complex behaviour of PV array.

Various conventional MPPT methods have been reported in literature for PV systems such as Perturb and Observe (P&O) [1, 2], incremental conductance [3], hill climbing method [4], open circuit voltage [5] and short circuit current [6] etc. P&O and hill climbing MPPT techniques are popular and extensively used because of their simplicity and easy implementation. However, these techniques have some drawbacks like low tracking efficiency, oscillations at steady state and partial shading condition. Tracking of global maximum power point (GMPP) is a difficult task because conventional algorithms get trapped at local maxima. Further these algorithms also lose the tracking direction under changing irradiance which results in reduced efficiency of the system [7].

Various researchers have incorporated soft computing techniques e.g. fuzzy logic control and ANN in conventional MPPT techniques to overcome these issues [8 –11]. H. Patel and V. Agarwal [12] incorporated PI controller in the modified P&O technique to extract maximum power. C. Larbes et al. [13] and A. Messai et al. [14] presented a Genetic algorithm tuned fuzzy logic controller based MPP tracker. Conjunction of optimization technique along with conventional MPPT makes them more effective, accurate and less time consuming. K. Ishaque et al. [15] proposed MPPT algorithm by modifying particle swarm optimization to reduce the steady state oscillations. The authors have utilized duty cycle approach along with PSO to track the global peak. Results are analysed on the basis of tracking speed & oscillations at steady state and compared with hill climbing algorithm to justify the performance of proposed controller. S. Mohanty et al. [16] proposed MPPT technique with direct duty cycle control using GWO under changing irradiance condition. The proposed scheme is compared with Perturb & observe and improved particle swarm optimization to analyze the effectiveness of designed controller. J. Ahmed and Z. Salam [17] designed cuckoo search algorithm based MPPT controller and the efficacy of proposed method is proved in terms of tracking ability and transient response as compared to P&O and PSO based MPPT techniques.

It is revealed from the literature that soft computing controllers provide superior performance over conventional MPPT techniques, but these approaches suffer from system dependency problem and require excessive prior knowledge of system and large memory. Furthermore, fuzzy and ANN based controllers when incorporated independently do not succeed to track global MPP under partial shading conditions [18]. It is also recommended that use of optimization techniques provide an alternative for efficient solar photovoltaic system. However, the techniques suggested in literature are computationally complex and require high convergence time to reach the global MPP due to large search space [19]. Literature also reveals that MVO algorithm is computationally less complex, requires less memory, provides fast convergence and better tracking ability as compared to other evolutionary algorithms [20]. These issues motivated the authors to utilize nature-inspired Multi Verse Optimization (MVO) algorithm in direct duty cycle MPPT control scheme. The incorporation of direct duty cycle control along with MVO algorithm may lead to improvement in system performance due to the advantage of local maxima skipping ability of MVO. The two diode configuration of solar system along with boost converter is considered in this work. The performance of designed controller is evaluated using standard MPPT efficiency test. Various other performance indices such as transient & steady state response and convergence time are also considered for analyzing the controller performance.

The remaining paper is organized as follows: Section II describes the mathematical modelling of solar PV system and power converter. In section III problem formulation and proposed control strategy are described. Simulation results and discussion are given in section IV followed by conclusion in section V.

2 Mathematical modelling of solar PV system

The mathematical modelling of solar PV system is necessary to emulate its behaviour and analyse the performance using various softwares. Solar power generation system consists of mainly three units i.e. solar PV array, power converter circuit and load. Power converter maintains the output power of PV panel at rated output. In this work a standalone solar PV system is considered along with resistive load.

2.1 Solar PV system

A solar cell can be modelled using single diode model, two diode model and three diode model. In the present work two diode model of solar PV cell is considered. The model is more accurate and fast as it gives superior performance when subjected to variable insulation and temperature. It offers improved results under low irradiance level. This is due to the consideration of recombination loss in the depletion region [21, 22]. The two diode model of solar cell is depicted in Fig. 1. If V is the solar PV output voltage then output current equation using two diode model is given as follows: $I = I_{ph} - I_{d_{1}} - I_{d_{2}} - \frac{{VN}_{P} + N_{S} {IR}_{S}}{N_{S} R_{P}}$ (1) where

Output current

Photo generated current

Diode current for diode d₁

Diode current for diode d₂

Number of cells in series

Number of parallel strings

Series resistance

Parallel resistance

I_{d_{i}} = I_{{rs}_{i}} N_{P} [e^{(\frac{V + \frac{N_{S}}{N_{P}} {IR}_{s}}{a_{i} N_{S} V_{T_{i}}})} - 1]

(2)

I_{{rs}_{i}} = (I_{SC} + K_{I} (T - T_{ref})) [e^{(\frac{V_{oc} + K_{V} (T - T_{ref})}{a_{i} N_{S} V_{T_{i}}})} - 1]

(3) where I_{rs
_i} and a₁ are reverse saturation current and diode ideality factor of ith diode respectively. V_{t
_i} represents thermal voltages of ith diode and is equal to kt/q. k, T and q denote Boltzmann constant, electron charge and temperature respectively.

Fig.1

Two diode configuration of solar system.

Photo generated current is given as:

I_{ph} = \frac{G}{G_{STC}} (I_{ph - STC} + K_{I} (T - T_{ref}))

(4) Figure 2 illustrates the PV array in series parallel configuration. Specifications of considered solar PV module, MSX-60 are given in Table 2 [21]. Figure 4 shows the effect of changing environmental conditions i.e. variation in (a) irradiance, (b) temperature and (c) series resistance, on voltage-power and voltage-current curves of solar system.

Fig.2

Solar PV array.

2.2 DC-DC converter model

When source is directly connected to load, the PV module output power is infrequently maximum and optimal power is not obtained all the time. This issue is handled using power converter interfaced between solar system and load. It transfers maximum power from solar panel to load. Three basic DC to DC converter configurations i.e. boost, buck and buck-boost converter are generally used. In this paper, boost converter shown in Fig. 3 is employed. The specifications of considered power converter are given in Table 1. $V_{PV} = (1 - D) V_{o}$ (5) where V_pv and V_o represent the solar panel voltage and converter output voltage respectively. D denotes the duty ratio of power converter.

Fig.3

DC-DC Boost converter.

Table 1

Specifications of boost converter

S.N.	Parameters Description	Symbol	Value
1	Inductor	L	1mH
2	Input capacitor	C ₁	470
3	Output capacitor	C ₂	220
4	Switching frequency	f	50kHz

Table 2

Specifications of solar system MSX-60 module under standard test condition

S.N.	Parameter	Symbol	Value
1	Open circuit voltage	V _oc	21.1 V
2	Short circuit current	I _sc	3.8 A
3	Voltage at MPP	V _mpp	17.1 V
4	Current at MPP	I _mpp	3.5 A
5	V_oc temperature coefficient	K _V	–0.08 V/°C
6	I_SC temperature coefficient	K _I	3e^–3 A/°C
7	Nominal temperature	T _ref	25°C
8	Nominal irradiance	G _STC	1000 W/m²

Fig.4

I-V & P-V curve of solar panel for changing environmental conditions.

3 Control strategy

The present work focuses on the design of a MPPT controller which is capable to mitigate drift problem occurring in solar system under variable solar irradiance so that maximum possible power is obtained. The optimization problem is thus formulated as: $Maximize P (D)$ (6) $Subject to D_{min} \leq D \leq D_{max}$ (7) where P (D) represents the solar output power. D_min and D_max are the lower and upper boundaries of duty cycle respectively.

Fig.5

Flowchart for perturb and observe technique

Literature reveals that P&O is a broadly used conventional MPPT technique for maximum power extraction from solar panel due to various advantages mentioned earlier. In P&O, a perturbation in PV array voltage is given and change in output power is observed. At each step, output power is compared with the previous power to find the direction of perturbation in next step. In case of the positive power difference, perturbation in voltage occurs in the same direction as previous otherwise direction of perturbation is changed so as to track MPP. The technique may be modelled using Equations (8 and 9). Flowchart of P&O method is illustrated in Fig. 5. $\begin{matrix} V (k) = V (k - 1) + φ \\ if P (k) > P (k - 1) \end{matrix}$ (8) $\begin{matrix} V (k) = V (k - 1) - φ \\ if P (k) < P (k - 1) \end{matrix}$ (9) where V and φ denote controlled voltage and perturbation length of controlled voltage respectively. k and k - 1 represent the current and previous instants respectively.

3.1 Multi verse optimization based MPPT controller

Although performance of ANN and fuzzy based MPPT controller is superior to conventional techniques but these controllers seem incapable to find global maximum point on P-V curve when variable irradiance condition occurs. Moreover, these controllers show efficient performance for input in the range of training data but fail to handle other random inputs. Hence performance depends highly on previous knowledge of inputs. The accurate functioning of system requires proper training of input variable. Further ANN and fuzzy based MPPT controllers are more complex as compared to evolutionary algorithm based MPPT techniques. The application of evolutionary algorithms in MPPT has capability to perform better under variable insulation [18].

Fig.6

(a) White hole (b) Black hole (c) Warm hole [20]

Multi verse optimization is a nature-inspired algorithm developed by Seyedali Mirjalili [20] which mimics the behaviour of multi verse theory [23, 24]. It claims the existence of multiple universes in the world. The three main concepts of multi verse theory i.e. white holes, black holes and warm holes as shown in Fig. 6 are utilized for Multi verse optimization algorithm. Objects from different universes interact through white or black holes whereas objects in the same universe interact via warm holes. Interaction of object through white hole and black hole replicate the exploration process in optimization technique whereas exploitation process is accomplished by transformation through warm hole. The main advantage of MVO is its high exploration and ability to skip local maxima. The process of interaction of objects between universes generally depends on the inflation rate. The inflation rate of a universe is proportional to its fitness function. A universe having higher inflation rate is considered as the source universe as it has higher probability of having a white hole. In contrary, the universes with low inflation rate have the maximum probability of containing black hole and thus considered as destination universe.

Integral Absolute Error (IAE) of generated power which is proportional to inflation rate of universe, is considered as fitness function for the current optimization problem. Mathematically it is given as follows: $IAE = \int_{0}^{t} | e (t) | dt$ (10) where, e (t) = p_true (t) - p_out (t). p_true (t) represents the theoretical maximum power and P_out(t) is the output power extracted from PV system using MPPT controller.

Fig.7

Convergence curves of MVO, GWO & PSO based MPPT.

Fig.8

IAE value for different MPPT techniques.

The optimization starts by creating a random solution. Every universe is considered as solution and objects in the universe are analogous to variables. The selection of solution is accomplished on the basis of its inflation rate i.e. fitness value. In this work, duty cycle is analogous to the variable and 20 universes (search agents) are considered for every iteration. Set of universe for each variable is termed as universe population U_population as shown in Equation (11).

Fig.9

Tracking performance of different MPPT control techniques for constant irradiance.

$U_{population} = [\begin{matrix} x_{1}^{1} & x_{1}^{2} & \dots & x_{1}^{v} \\ x_{2}^{1} & x_{2}^{2} & \dots & x_{2}^{v} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ x_{n}^{1} & x_{n}^{2} & \dots & x_{n}^{v} \end{matrix}]$ (11) where n denotes the universe and v represents the number of variables. The selection of best solution is accomplished by Equation (12) which shows the exchanging mechanism of variables between the universes through white/black hole tunnels.

$x_{i}^{j} = {\begin{matrix} x_{k}^{j} & if & r_{1} < NI (U_{i}) \\ x_{i}^{j} & if & r_{1} \geq NI (U_{i}) \end{matrix}$ (12)

where $x_{i}^{j}$ represents the jth variable of ith universe and $x_{k}^{j}$ represent jth variable of kth universe. r₁ represents a random number generated in the range of [0, 1] and NI (U_i) denotes normalized inflation rate of ith universe. The Roulette wheel mechanism is utilized to mathematically model white and black hole tunnels and trade-off parameters between the universes. In this work MVO optimized duty ratio is used to control the switching action of power converter for maximum power point tracking.

Fig.10

Tracking performance under rapid changes in irradiance

4 Result & discussion

The prime objective of the present research is to analyse the optimization of duty cycle using MVO for efficient MPPT operation. Various softwares are available for economic, effective, flexible and off-line simulation of a wide range of systems. In the present work experimentations are performed in MATLAB SIMULINK on Intel, i3 processor with 4GB RAM PC. MATLAB/SIMULINK is a valuable learning platform as it is the most trusted and available software in industries, research centers and academic institutes. It provides flexible platform to users [25] as it can simulate a variety of highly non linear and complex systems, power electronic circuits and distributed generation power system [26] etc. However the model may be simulated on other suitable software platforms also. Rigorous simulation is carried out so as to evaluate the performance of proposed MVO-MPPT technique. The traditional P&O, PSO and GWO based MPPT algorithms are also designed and tested for comparative analysis. The optimized value of perturbation length for P&O based MPPT as reported in [22] i.e. 0.5% of V_oc, is considered for the present work. The performance of designed MPPT controller is analysed by calculating its efficiency. The expression for efficiency η_MPPT is given as follows: $η_{MPPT} = \frac{P_{out} (t)}{P_{True} (t)}$ (13)

The average efficiency is measured as: $η_{MPPT (avg)} = \frac{\int P_{out} (t) dt}{\int P_{True} (t) dt}$ (14)

Fig.11

Tracking performance of designed MPPT controllers for step changes in irradiance.

4.1 Error and convergence analysis

Figure 7 shows the convergence curves for MVO, GWO and PSO based MPPT techniques. It is observed that MVO-MPPT controller converges fast as compared to the other methods. IAE value and power tracking performance of designed MPPT controllers are depicted in Figs. 8 and 9 respectively. The results indicate that MVO-MPPT controller outperforms the other controllers under fixed environmental conditions. The conventional P&O method shows large oscillations at maximum power point. Quantitative performance analysis in terms of settling time, rise time, and peak overshoot are shown in Table 3. It is depicted from results that MVO-MPPT controller provides less IAE & peak overshoot and offers fast convergence as compared to other meta heuristic based MPPT controllers.

Table 3
Quantitative performance analysis of designed MPPT controllers

Performance index MVO-MPPT GWO-MPPT PSO-MPPT P&O-MPPT

Settling time [s] 0.0078 0.0082 0.0082 0.1939

Rise time [s] 0.0016 0.0017 0.0018 0.0028

Peak overshoot [W] 0.3481 0.4986 0.5308 0.6328

Performance index	MVO-MPPT	GWO-MPPT	PSO-MPPT	P&O-MPPT
Settling time [s]	0.0078	0.0082	0.0082	0.1939
Rise time [s]	0.0016	0.0017	0.0018	0.0028
Peak overshoot [W]	0.3481	0.4986	0.5308	0.6328

4.2 Drift avoidance

The performance of solar photovoltaic system under changing environmental conditions is highly complex due to its non-linear characteristics. Drift problem is a major issue which occurs due to incorrect estimation of perturbation direction for increasing irradiance. Almost all traditional MPPT algorithms suffer from drift. Thus an efficient MPPT controller is required to overcome this issue. In this paper extensive simulation study is performed by considering different patterns of irradiance. Figure 10 shows the tracking performance of designed controllers under trapezoidal and triangular patterns. In both the cases P&O algorithm loses tracking direction whereas MVO-MPPT offers negligible drift as compared to the other controllers. Thus the proposed MVO-MPPT controller has the ability to estimate tracking direction correctly even under varying irradiance.

Figure 11 shows power point tracking performance for step changes in irradiance. It is observed from the results that MVO-MPPT controller performs better than PSO & GWO based MPPT controllers. However, P&O algorithm performs less efficiently and takes large convergence time. The performance of designed controllers is also evaluated by standard MPPT efficiency test. The average efficiency of solar PV system is evaluated using equation (14) for different irradiance levels i.e. 400 W/m², 600 W/m², 800 W/m² and 1000 W/m². The average efficiency for the four cases is shown in Table 4. Results reveal that MVO-MPPT controller has the highest average efficiency among designed controllers. Hence it is obvious from the analysis that MVO optimizes the maximum power point tracking controller in a better way and efficiency of the solar PV system under variable irradiance is increased in comparison to the other designed controllers.

Table 4
Efficiency of solar system using different MPPT techniques

Irradiance W/m² Theoretical Efficiency (%)

Maximum Power [W] MVO-MPPT GWO-MPPT PSO-MPPT P&O-MPPT

400 22.8797 97.93 96.89 95.67 86.66

600 35.3757 98.89 98.29 97.78 92.97

800 47.7584 99.28 99.12 98.10 91.00

1000 59.9605 99.40 99.30 98.40 87.96

Irradiance W/m²	Theoretical	Efficiency (%)
400	22.8797	97.93	96.89	95.67	86.66
600	35.3757	98.89	98.29	97.78	92.97
800	47.7584	99.28	99.12	98.10	91.00
1000	59.9605	99.40	99.30	98.40	87.96

5 Conclusion

In this paper MVO based MPPT controller is designed and successfully implemented for efficient power tracking of solar photovoltaic system under changing environmental conditions. The advantages of multi verse optimization are utilized in combination with direct duty cycle control to implement the MPPT controller. The MVO provides fast convergence as compared to other meta heuristic algorithms. The performance of MVO-MPPT controller is analyzed on the basis of drift avoidance capability, IAE, system efficiency and step response characteristics. The adequacy of proposed controller is validated by considering constant irradiance, rapid as well as step change in irradiance. Simulation results reveal that the proposed control scheme offers less drift and IAE in comparison to other techniques. Hence it is concluded that in order to augment the system efficiency and reduce computational overhead MVO algorithm is the best choice for MPPT controller design.

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A multi verse optimization based MPPT controller for drift avoidance in solar system

Abstract

Keywords

1 Introduction

2 Mathematical modelling of solar PV system

2.1 Solar PV system

Table 3 Quantitative performance analysis of designed MPPT controllers Performance index MVO-MPPT GWO-MPPT PSO-MPPT P&O-MPPT Settling time [s] 0.0078 0.0082 0.0082 0.1939 Rise time [s] 0.0016 0.0017 0.0018 0.0028 Peak overshoot [W] 0.3481 0.4986 0.5308 0.6328

References

Table 3
Quantitative performance analysis of designed MPPT controllers

Performance index MVO-MPPT GWO-MPPT PSO-MPPT P&O-MPPT

Settling time [s] 0.0078 0.0082 0.0082 0.1939

Rise time [s] 0.0016 0.0017 0.0018 0.0028

Peak overshoot [W] 0.3481 0.4986 0.5308 0.6328