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A New Controller to Enhance PV System Performance 

Based on Neural Network 
Roshdy Abdelrassoul, SM, IEEE, Yosra Ali and Mohamed Saad Zaghloul 

Arab Academy for Science, Technology and Maritime Transport (AASTMT), Alexandria, Egypt
 

roshdy@ieee.org, yosra_alii@hotmail.com, 

dr_mszaghloul@yahoo.com
 

Abstract - In recent years, a radical increase of 

photovoltaic (PV) power generators installation has 

taken place because of the increased efficiency of 

solar cells, the growth of manufacturing technology of 

solar panels, in addition to the  government support 

policy. This paper shows the operation and modeling 

of photovoltaic systems, particularly designing neural 

controller to control the system. Neural controller is 

optimized using particle swarm optimization (PSO), 

which leads to getting the best performance of the 

designed PV system. By using neural network, the 

maximum overshoot and rise time obtained become 

0.00001% and 0.1798 seconds, respectively. Also, 

this paper strikes  a comparison between some kinds 

of controller for the PV system. 

 

Keywords - Particle Swarm Optimization, neural 

network and photovoltaic. 

 

I. INTRODUCTION 

 

The study of renewable energy sources has been an 

inclusive concern to the world, and has drawn the 

attention of many institutions, like the European 

Commission and others. Renewable energy is a clean 

energy system that has no effect during or after 

generation on the environment and this has grabbed 

the attention of researchers to make continuous 

improvement in solar energy. Renewable energy is 

numerous, abundant, sustainable, and can be utilized 

from different origins such as wind, solar, tidal, hydro, 

geothermal and biomass. 

 

Solar energy could be one of the important sources 

as substitution energy for the hereafter. There are two 

kinds of technology that has anticipated solar energy, 

solar thermal and solar PV. A PV cell (solar cell) 

transforms sunlight into electrical energy by the 

photovoltaic effect. 

 

The solar PV system exhibits various advantages, 

such as, it needs little maintenance and produces no 

environmental pollution. PV module presents the 

fundamental power conversion unit of a PV generator 

system. 

 

II. LITERATURE REVIEW  

 

Many papers have presented different simulations of 

PV system. In [1], a procedure for the simulation of 

photovoltaic modules with MATLAB/Simulink is 

presented. One-diode equivalent circuit is employed 

in order to investigate I-V and P-V characteristics of 

solar module. The final model takes irradiation, 

operating temperature in Celsius and module voltage 

as input and gives the output current Ipv and output 

voltage Vpv. Also, in [2], a one-diode equivalent 

circuit-based versatile simulation model in the form of 

the masked block PV module is proposed. By using 

the model, it is allowed to estimate the behavior of PV 

module with respect to changes in irradiance 

intensity, ambient temperature and parameters of the 

PV module. In another study [3], a fractional-order 

PID (FOPID) controller [4-6] is designed to control a 

DC-DC boost converter in a PV-system. In order to 

obtain the best system performance, parameters of 

the proposed controller are tuned by using Particle 

Swarm Optimization (PSO) algorithm. In another 

paper [7], the effect of uniform and non-uniform 

irradiance on a series of connected solar PV array is 

presented in detail under MATLAB-Simulink 

environment. The proposed simulation model helps 

the researchers to investigate the characteristics of a 

PV array under different irradiance and temperature 

conditions [7]. 

 

This paper is framed around three major parts. First, 

an overview of mathematical model of the PV system 

is summed up. Second, a neural controller is 

designed to enhance the performance of the system. 

Finally, in order to obtain the best system 

performance, neural network of the proposed 

controller is optimized using the PSO. The system 

response is tested under various solar irradiation and 

constant temperature. Percentage overshoot (Mp) 

and rise time (Tr) are measured and compared with 

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other papers. The comparison shows that the system 

with the neural controller performs better than other 

systems with different kinds of controller. 

 

III. MATHEMATICAL MODEL OF THE PV SYSTEM 

 

1. Mathematical Model of PV Panel 

The first part of the system is the solar cell. Solar 

cells are in fact large area semiconductor diodes. 

Due to the photovoltaic effect, energy of light (energy 

of photons) is converted into electrical current. The 

equivalent circuit for the simplest solar cell consists of 

a diode and a current source connected in parallel, as 

shown in Figure 1 [8]. The source current is directly 

proportional to the solar radiation and diode 

represents the PN junction of a solar cell. 
 

 
 

Fig.1. One diode model of PV cell 

 

Equation of the load current is: 

 

𝐼 = [(𝐼𝑝ℎ ×𝑁𝑝) − 𝐼𝑑 − 𝐼𝑠ℎ ]                                   (1) 

 

Where: 
 
(Iph) is photocurrent (A); 
(Id) is diode current; 
(Ish) is the current loss because of the shunt 
resistance; and (Np) the parallel connected PV cell 
number that effects the module current. 
 
The thermal voltage equation is: 
 

𝑉𝑡 =
𝑘𝑇

𝑞
                                                                      (2) 

 

Where: 

 

(k) is boltzmann constant, 1.38×10-23 J/K ; 

(T) is solar cell temperature (K ); and 

(q) is charge of electron, 1.6×10-19 C. 

The researchers represent the reverse saturation 

current equation for the proposed PV system using 

simulink on matlab as shwon in Figure. 2: 

 

 

 
 

Fig.2. Reverse saturation current

 

𝐼𝑠 = [(
1

𝑇
−

1

𝑇𝑟𝑒𝑓
) × ((𝑞2×𝐸𝑔 )/(𝑘×𝑛)) 𝑒

𝑢 [
𝐼𝑟𝑠

(𝑇 𝑇𝑟𝑒𝑓⁄
)

3]]             (3) 

 

Where: 

 

(T)  the temperature of the PV panel; 

(Tref)  the refrence temperature of the PV panel; 

 

 

The researchers represent the reverse saturation 

current at top equation for the proposed PV system 

using simulink on matlab as described in Figure. 3: 

 

 

 

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Fig. 3. Reverse saturation current at the top equation 

 

𝐼𝑟𝑠 =  [(𝑉𝑜𝑐 ∗ 𝑞)/(𝐾 ∗ 𝑐 ∗ 𝑇 ∗ 𝑛)] [
𝐼𝑠𝑐

(𝑒 𝑢 − 1)
⁄ ]           (4) 

  

where: 

 

(Voc) open circuit voltag; and 

(Isc)  short circuit current. 

Shunt current equation: 
 

𝐼𝑠ℎ =  (𝑉 + 𝐼 𝑅)/𝑅𝑝                                                   (5) 

 

Where: 

(Ish) shunt current; 

(Rs) the series resistance of the PV panel; and 

(Rp) the parallel resistance of the PV panel. 

 

Diode current equation for the proposed PV system is 

described in Figure.4 as the researchers present it 

using Simulink on MATLAB: 
 

 
 

Fig. 4. Diode current 

 

𝐼𝑑 =  [[(
𝑉

𝑁𝑠
⁄ ) +  (

𝐼 ∗ 𝑅𝑠
𝑁𝑠

⁄ )] /[𝑛 ∗ 𝑉𝑡 ∗ 𝑐]] [(𝑒
𝑢 − 1) ∗ 𝐼𝑠 ∗ 𝑁𝑝 ]      (6) 

 

Where: 

 

(Id) diode current; 

(Ns) the series connected PV cell number that effects 

module voltage; and 

(Vt) thermal voltage; 

phase current equation: 

 

𝐼𝑝ℎ =  [((𝑇 − 𝑇𝑟𝑒𝑓 ) ∗ 𝐾) +  𝐼𝑠𝑐 ] ∗ 𝐼𝑟𝑟                           (7) 

 

Where:  

(Irr) irradiation. 

 

2. Converter Model 

 

The second part of the system is the converter. A 

boost DC-DC converter is used as a power electronic 

interface between the load and PV panels in the P-V 

system. The converter is a powerful electronic device 

used to produce a higher regulated output voltage 

from a lower unregulated input voltage [3]. The circuit 

of the converter consists of an inductor L, a power 

switch S, a diode, D, a filter capacitor C and a load 

resistor R, as shown in Figure 5 [3]. 

 

 
 

Fig. 5. Boost converter circuit 

 

The working principle of the converter is cleared as 

follows: When the switch is in the ON mode, the diode 

is reverse biased (OFF). In this mode, the inductor is 

directly connected to the input voltage source and 

stores energy. Meanwhile, the load is powered by the 

capacitor. When the switch is OFF mode, the diode is 

forward biased (ON). In this mode, both the stored 

energy of the inductor and the input voltage source 

supply power to the load. The capacitor and the 

inductor values of the converter are calculated 

respectively by using the formulas [8]:  
 

𝐶𝑚𝑖𝑛 =  
𝐷𝐼𝑜𝑢𝑡(max)

𝑓𝑠∆𝑉𝑜𝑢𝑡
                                                       (8) 

 

𝐿𝑚𝑖𝑛 =  
(𝑉𝑜𝑢𝑡−𝑉𝑖𝑛)𝑉𝑖𝑛

∆𝐼𝐿𝑓𝑠𝑉𝑜𝑢𝑡
                                                  (9) 

 

Where:  

 

(Cmin) and (Lmin) are the minimum capacitor and 

inductor values;  

(Vin ) and(Vout) are the input and output voltage of the 

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converter;  

(fs) is the switching frequency;  

(∆Vout) is the output voltage ripple;  

(∆IL ) is the inductor current ripple; and 

(D) is the duty cycle, which is the ratio between the 

pulse duration and period of a rectangular waveform. 

 

3. Neural Network Controller 

 

The third part in the system is the controller. There are 

numerous controllers that can be used to control 

dynamic systems like the PV systems.  In this paper, 

neural network controller is used because neural 

networks are mostly used for fuzzy, difficult problems 

that do not yield to traditional algorithmic approaches. 

Many algorithms can be used to optimize the 

controller, such as Genetic algorithms (GA) [9], 

Differential Evolution (DE) algorithm [10] and PSO 

algorithm [11]. In this paper, Particle Swarm 

Optimization (PSO) will be used because it does not 

have genetic operators like crossover and mutation, 

since particles update themselves with the internal 

velocity. They also have memory, which is important 

to the algorithm, as will be explained later in the 

algorithm. Many papers used Proportional Integral 

Derivative controller (PID) instead of neural network. 

Neural network is more complex than PID controller 

but neural network gives a better response than the 

PID controller and some other kinds of controllers. In 

this paper, the neural network controller supported the 

designed model of the PV system. 

 

A neural network is a method of computation modeled 

after the brain [12]. They contain a series of 

mathematical equations that are used to emulate 

biological processes such as learning and memory. 

What makes the artificial neural network unique from 

many other computer algorithms is its primitive ability 

to learn. Through a process of training and being told 

what the correct output is when given a set of inputs,  

the artificial neural network eventually learns the 

correct behavior, and can reproduce correct outputs 

on its own when given a set of inputs. 

 

A neural network can predict an outcome based on 

the values of some predictor variables. Networks are 

programmed to adjust their internal weights based on 

the mathematical relationships identified between the 

inputs and outputs in a data set. 

 

 

 
 

Fig. 6. Diagram of an artificial neural network 

 

Table 1 is a brief glossary showing some common 

terms in the field of neural networks and their 

equivalent in statistics. Neural Networks are known to 

be universal function approximates. Various 

architectures are available to approximate any 

nonlinear function. Different architectures allow for 

generation of functions of different complexity and 

power. Those different architectures are: 
 

• Feedforward networks 

• Feedback networks 

• Lateral networks 

 
Table 1. Common Terms in Neural Networks and their Equivalent in 

Statistics 

 

 

 

 

 

Neural networks Statistics 

Input 
Independent (predictor) 

variable 

Output 
Dependent (outcome) 

variable,  predicted value 

Connection weights Regression coefficients 

Bias weight Intercept parameter 

Error Residuals 

Learning, training Parameter estimation 

Training case, pattern Observation 

Cross-entropy 
Maximum likelihood 

estimation 

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In a neural network, the weights connecting two nodes 

are usually represented as  where i and j are 

subscripts for the two nodes being connected. 

Estimating the optimal values of these connection 

weights is the major purpose behind training a neural 

network model. The network training algorithm is used 

to gradually adjust the weight and in the network to 

minimize the difference between the predicted output 

of the network op and the known value of the outcome 

variable tp.  This difference is known as the error of a 

neural network and is similar to the concept of 

minimizing the residuals in statistical regression. The 

total error (E) of a neural network is usually 

determined over the whole data set and may be 

calculated as shown in equation (10): 

 

                                             (10) 
 

Where E is the total error of the network op and   is the 

desired or known Neural Networks versus Logistic 

Regression. 

 

IV. PARTICLE SWARM OPTAMIZATION (PSO) 

 

The Particle swarm optimization (PSO) method, 

suggested by Kennedy and Eberhart [13], is a 

computational search algorithm used to optimize a 

problem iteratively [14]. The algorithm is based on 

imitating the behaviors of a bird flock (particles) with 

the help of the mathematical velocity and position 

formulas of the particles. Each particle in the 

population has a memory to keep its previous best 

position called Pbest (candidate solutions, local 

minima) and fitness value. Also, the particle with 

minimum fitness value is called Gbest (global 

minima). The flowchart of the algorithm is given in 

Figure 7. Mathematical representations of the velocity 

and position of the particles are given below, 

respectively. Where i is the number of the particle, d is 

the dimension, c1 and c2 are the acceleration constant 

of the velocity, w is the inertia weight, and r1 and r2 are 

the uniformly random numbers. Optimum values for 

these parameters are needed to reach robust transfer 

function for PV system. PSO is used widely in many 

applications due to its many advantages including its 

simplicity and easy implementation. PSO has no 

crossover and mutation process; however, the search 

can be done by the speed of the particle. Only the 

optimum particle can transmit information to the other 

particles, and the speed of searching is very fast. 

Thereby, the researchers used PSO as an 

optimization tool to find the optimum values for those 

parameters. The basic PSO algorithm consists of 

three steps generating positions of particles and 

velocities, velocity update, and position update. Each 

particle represents a possible solution to the problem 

that changes its position from one iteration to another 

based on velocity updates. First, the positions, xid, 

and velocities, vid, of the initial swarm of particles are 

randomly generated. The PSO consists of many 

particles which form a swarm, design space. At each 

step, each particle updates its velocity and distance 

according to Equation (8) and Equation (9), 

respectively. 
 

 
 

Fig. 7. A general flowchart of PSO 

 
(11) 

                                                (12) 
 

The algorithm is ended when the stopping criteria are 

met.       
 

V. SIMULATION RESULTS 
 

According to the case study which is getting the best 

performance of a PV system by reducing rise time and 

the percentage overshoot, a neural controller is used 

as shown in Figure 8. Figures 9 and 10 represent the 

I-V and P-V characteristics of the system, respectively, 

with a solar irradiation input of 800W/m2. Table 2 

shows the system parameters. 

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Fig. 8. Simulink/MATLAB architecture for the PV system with neural controller  

 

 
 

Fig. 9. Current – Voltage (I-V) characteristics of PV System 

 

 
 

Fig. 10 Power– Voltage (P-V) characteristics of PV System 

 

 

 

 

 

 

Table 2. Parameters of PV System 
 

 Parameters of Boost Converter 

20kHz Sampling frequency (Ts) 

5kHz Switching frequency (fs) 

24V Output voltage (VO) 

5% 
Max. output voltage ripple 

(∆VC) 

5% Max. input current ripple (∆I) 

6.8mF Input capacitor (Cin) 

11.5mF Output capacitor (Cout) 

1.25mH Inductor (L) 

12.5-25-50Ohm Load (R) 

 PV panel parameters 

1 Nsc 

5 Npc 

17V Vr 

3A Ir 

3.10-3mA/oC 
 

-73.10-3mW/oC Β 

3.5 Isc 

1000W/m2 Gr 

25oC Tcr 

 

 

 

 

 

 

 

 

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There are a lot of types and training algorithms for 

neural network. In the proposed case, the researchers 

do not know which one will fit the best performance 

Therefore, they used the PSO to obtain the best 

neural type, training algorithm, number of hidden 

layers, and number of perceptions per layer. In this 

case, four parameters have to be determined. These 

parameters are shown in Table 3. 

 
Table 3. Input Parameters of PSO 

 

Parameters Description Constrains 

𝑘1 Neural type From 1 to 4 

𝑘2 Training algorithm From 1 to 12 

k3 Number of layers From 1 to 10 

𝑘4 Number of perception From 1 to 10 

 

In equation 12, the d represents the dimension 

number while the Pid represents the best previous 

position and the global best position is stored in Pg. 

To ensure good coverage of the design space, the 

velocity update formula includes some random 

parameters, represented by the uniformly distributed 

variables, Rand. The three terms of the velocity 

update equations represent current motion, particle 

own memory, and swarm influence. Accordingly, the 

original PSO algorithm used the value of 2 for both 

constants C1 and C2. In the proposed problem, the 

objective function is minimizing the overshoot, rise 

time for the PV system. Also, the researchers used a 

swarm size of 49 in their proposed algorithm. In each 

iteration of PSO, the best parameters  is stored as the 

global minimum. The parameters that should be 

optimized are summarized in Table 3. Once the PSO 

chooses the optimum parameter k1, k2, k3, and k4, 

those parameters are set as the final parameters for 

setup the neural network to operate as a controller 

instead of PID. Hence, the number of dimensions, d, 

in Equation 12 is equal to 12. All the possible types 

and algorithms for k1 and k2 are mentioned in Table 

4.  

 

 

 

 

 

 

 

 

 

According to PSO, the optimum parameters are 2, 1, 

1 and 10 for k1, k2, k3 and k4, respectively. This 

result reflects that the best type which fits the best 

performance for PV system is feed forward neural 

network with Levenberg-Marquardt training method, 

train lm. The upcoming Figure 11 will illustrate the 

overshoot 0.00001% and that rise time equals 0.170 

seconds. 

 

 
 

Fig. 11. Structure of the proposed neural network  
 

 
 

Fig. 12. The value of MSE  

 

 
 

Fig. 13. Step response of process with neural controller unig 

Simulink 

 

 

 

 

 

 

 

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Table 4. All Possible Values and Types for k1 and k2 

 
 

VI. COMPARISON WITH PREVIOUS WORK 
 

Figure 14 [15] shows the output voltage versus the 

time and the maximum overshot almost is zero. The 

simulation results clearly show that the PID controller 

gives a much better control of PV system rather than 

the FOPID controller. When PID tuned by a genetic 

algorithm is used as a control for the PV system, the 

rise time was 0.175 second and percentage overshoot 

was almost zero. In comparison to [3], this work 

reduced the overshoot with 0.7% and the rising time 

by 0.545 seconds.  

 

Also, the neural network has better impact on the PV 

system rather than PID and FOPID [3] controllers. For 

Neural Network controller, the overshot was 0.00001, 

meanwhile the rise time was 0.170 seconds and Table 

4 shows a comparison between all the controller types 

for PV system. In table 4, the first parameter is the 

maximum overshoot and the second  parameter is the 

rise time. Figure 15 shows the result of the three 

different types of the controller that used to enhance 

the performance of our PV system. The line by the red 

circles represents the result of PID controller tuned by 

GA algorithm, the line by the blue crosses represents 

the results of the neural PSO controller and the line by 

the black dashes represents the results of a previous 

work [3]. Figure 16 shows the same result as Figure 

15 but with zoomed x-axis and y-axis. 

 
 

Fig. 14. Output voltage versus time 
 

 
 

Fig. 15. Output voltage versus time. 

 

 
 

Fig. 16. Output voltage versus time with zoomed x-axis and y-axis 

 

Table 5. Comparison between this Work and Previous Work [3,14] 

 

Parameters 
PID with 

genetic algoritm 
[3] 

Neural 
network 

controller 

Mp 0.1 0.8 0.00001 

Tr 0.175 0.72 0.170 

P 1.7130 19.22 - 

I 3.8 8.32 - 

D 0.001 0.056 - 

 

 

 

Parameters Value Type 

k1 

1 Cascade forward net 

2 Feed forward net 

3 Pattern net 

4 Fit net 

k2 

1 trainlm 

2 trainbr 

3 trainbfg 

4 trainrp 

5 trainscg 

6 traincgb 

7 traincgf 

8 traincgp 

9 trainoss 

10 traingdx 

11 traingdm 

12 traingd 

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VII. CONCLUSION AND FUTURE WORK 

 

PV system is one of vital renewable energies in the 

present world. Therefore, researchers made a lot of 

research on PV panels to enhance its performance. 

This paper introduces a mathematical model for PV 

system with neural controller. The neural controller is 

used to enhance the output of PV system. The PSO is 

used to optimize the neural controller, which led to 

minimum overshoot and minimum rise time. The 

overshoot is reduced to be 0.00001% and the rise 

time is set to 0.170 seconds. The results show that 

neural controller has a better response compared with 

some other kind of controllers.  

 

For future work, different kinds of controller can be 

used to control the PV system and different algorithms 

can be replaced instead of PSO to optimize the neural 

network controller. The following points may be 

considered: 

 

• Using different algorithms to tune the Neural 

Network (NN) controller. 

 

• Using other kinds of controllers to control the PV 

system and comparing it with the other types 

used. 

 

• Using a combination of back propagation and 

neural network hybrid PSO-BP. 

 

• To reach a real time system, the different types of 

controllers can be implemented on Field 

Programmable Gate Array (FPGA). 
 

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