978-1-4673-2605-6/12/$31.00 © 2012 IEEE

Design and Performance of Low Power Solar-PV Energy Generating System with Zeta Converter

Abstract—This paper presents the design procedure and performance of a solar-PV (photovoltaic) energy generating system using an isolated zeta converter for meeting an energy demand of rural households. The solar-PV generating system consists of solar panels, a zeta dc-dc converter, a MPPT (maximum power point tracking) controller, energy storage system, VSI (voltage source inverter) and a filter. A feedback PID (Proportional-Integral-Derivative) controller is designed to regulate the output voltage under disturbances at the consumer loads. The system is designed and modelled in Matlab/Simulink and the simulation results are presented to demonstrate its performance in various atmospheric as well as consumer loads condition.

Keywords-Stand-Alone Solar-PV Energy System, MPPT Control, Multi-loop Control, Zeta Converter

I. INTRODUCTION The fossil fuels based energy resources are diminishing and

their adverse affects on the environment are raising the need to look for other sources of energy. Renewable energy sources are achieving high attention as an energy alternative due to factors like environment friendly and inexhaustible in nature. Among many renewable energy sources solar-PV (photovoltaic) is being widely used as small-scale applications and an isolated energy generation [1]. Solar-PV energy system has many advantages over other energy sources as it can convert the solar radiations to electricity without any moving parts in the system and it does not emit any harmful content to the atmosphere. It initially produces the dc power which can further be converted into ac power using a power converter. A low power solar-PV energy system can be set up easily and usually has a low maintenance and long life. The solar-PV system can be used in rural areas where the grid supply is not available. It can be used for many proposes such as water pumping, household appliances, communication towers and for medical facilities. The system cost and conversion efficiency are the factors that influence the utilisation of these systems. The energy generation of the solar-PV system is a function of the solar radiation and the cell temperature. It has certain point on its operating curve which gives maximum power output for a specific radiation and temperature value. Thus a controller is required to operate the PV system on maximum power point and the efficiency and stability characteristics of the output power of the solar-PV system rely upon the controller

performance [2-3]. However, there is a need to explore a MPPT control methods which provides fast response and reduced oscillations to compensate rapidly varying radiation conditions. The power converters for low power solar energy applications are still unexplored and efforts needed in utilization and analysis of low power converters in solar-PV system.

This paper presents a design methodology for a low power solar-PV system along with its controllers. It constitutes a solar panel, an isolated zeta converter, energy storage, dc-ac converter and controllers. The modified P&O (Perturbation and Observation) method is used with varying step size for MPPT (Maximum Power Point Tracking) and a feedback regulator is used with the dc-ac converter. The system is designed and modelled in Matlab/Simulink to demonstrate its performance in various states of input and load variations. In addition, simulation results are presented for the improved power quality at the consumer load end during various dynamic system conditions.

II. SYSTEM TOPOLOGY AND SPECIFICATIONS Fig.1 shows the topology of the solar-PV stand-alone energy

generating system. It consists of a solar-PV panel connected with an isolated zeta converter through a MPPT controller.

Fig.1 System topology of stand-alone Solar-PV energy generating system

The solar-PV panel is taken as rated capacity of 1kW and the output voltage produced by this is regulated through a MPPT controller and is fed to the dc-dc converter. This system is designed to feed average ac consumer loads of 350W for 24 hrs. The zeta converter compensates the variation in the PV panel output voltage and boosts up this voltage to the constant dc voltage of 360V.

Bhim Singh Fellow, IEEE,

Dept. of Electrical Engineering, IIT Delhi, Hauz Khas

New Delhi-110016, India bhimsinghiitd@gmail.com

A. L. Vyas Instrument Design Development Centre,

IIT Delhi, Hauz Khas New Delhi-110016, India

alvyas@iddc.iitd.ac.in

Neha Adhikari Instrument Design Development Centre,

IIT Delhi, Hauz Khas New Delhi-110016, India

nehaadhikari2008@gmail.com

III. CONTROL STRATEGY A MPPT controller is used to extract the maximum power

from the solar-PV system in varying radiations and temperature conditions [4]. The PWM control technique is used in the single phase VSI with a PID controller for load voltage regulation. The control strategy is presented as follows.

A. Control Strategy for MPPT The solar-PV array has nonlinear characteristic and the

power output depends upon environmental conditions such as cell temperature and solar radiation. It is observed that as the operating voltage of the system increases the power output and after a certain point it further increases in voltage which leads to decrease in output power. Thus this point is known as maximum power point. A control mechanism is required to track this point and restricts the system to operate on it. The perturbation and observation method is used for MPPT due to its simplicity in design and improved response. This method measures the power output and determines the increment or decrement [5-6]. If the power is increased from the previous value then it goes for increment else decrement a step. This method has a complication as the obtained maximum power point oscillates around it. The oscillation can be minimized by reducing the step size but again it increases the response time so here a variable step size is considered. Fig.2 shows the flowchart of the variable step P&O algorithm.

Fig.2 Flowchart of the variable step P&O algorithm for MPPT

In this method, the step size is determined from the amount of change in power due to change in the voltage. As the ratio of change in power due to change in the voltage increases, the step size for the duty ratio increases and on the contrary if this ratio decreases then it leads to reduce the step size. This method makes the controller robust against fast variations and

minimizes the oscillations in output of PV array. It also provides fast response. The duty ratio of the isolated zeta converter is continuously regulated through this MPPT controller. Thus MPPT controller generates PWM pulses for the power switch of the isolated zeta converter.

B. Control Strategy for VSI A single phase VSI is adapted in this system for providing a

220V, 50Hz ac output to consumer loads and the function of the feedback controller coupled with the VSI is being described in this section. The aim of the controller is to regulate the output voltage against the input and load disturbances and to maintain the device current within the specified range [7]. It consists of two control blocks, voltage and current regulators. It takes the output voltage and an inductor current as feedback signals for the voltage regulator and the current regulator. The output voltage of the VSI is compared with the reference voltage and error voltage signal is fed to a PID (proportional-integral- derivative) controller, which generates a reference signal for the current controller. The current controller compares this reference signal with the measured inductor current and a P (proportional) controller generates the signal for the PWM generator. For the generation of switching signals, a unipolar PWM method is used. The modulation index of the VSI is changed by the PWM controller according to the various disturbances. The inclusion of the current control block provides fast response and has an advantage of limiting the device current which accomplishes the system to perform under highly nonlinear loads. The gain parameters of the controller blocks need to be adjusted properly to ensure voltage and current regulations in varying dynamics of the system. The Ziegler Nichols step response method [8-9] is used here for the tuning of gain parameters. The Ziegler Nichols have presented mathematical formulas as shown in Eq. (1)-(4) for tuning of gains, based on the step response of the system. It presents the gain values as a function of the two parameters of the process reaction curve. First parameter is the TD, delay time that is the time required by the system to respond and the second one is Tr, response time, the time taken by the system to obtain a stable response. These parameters sre obtained by drafting a tangent on the response curve. For a PID controller the gains are obtained as, K PID 1.2 T T⁄ (1)

TiPID=2Tdtv (2)

TdPID=0.5Tdtv (3)

where, KpPID is the proportional gain for the PID voltage controller. TiPID is the integral time constant for the PID voltage controller. TdPID is the derivative time constant for the PID voltage controller. Tdtv is the delay time of the system response. Trv is the response time of the system response. The value calculated through response curve for KpPID is 1.19, TiPID is 0.97 and TdPID is 1.23.

For tuning of the gain parameter of a P current controller, the same step response method suggested by the Ziegler Nichols is

used. The proportional gain, KpP for the P controller can be calculated as,

KpP= Tri Tdti⁄ (4)

where, the Tri is the response time of the system for the current controller, Tdti is the delay time of the system response. From Eq.(4), the value of KpP is calculated as 0.37.

IV. DESIGN AND MODELING This section presents the design and modelling of the PV

panel, a dc-dc converter, a single phase VSI and an output filter. The solar-PV system is configured for low power applications which can be utilized as to supply the electricity in rural households for lighting and other low power loads. The design methodology and modeling for the system components are presented as follows.

A. Modeling of PV Cell and Panel Selection

The solar-PV panel is modelled by a current source in parallel with diode and a series resistance [10]. The resistance (Rse) in series represents the system resistance. The output voltage of the solar-PV array (Vpv) can be formulated as follows,

Vpv=( AKT q⁄ )ln IG-Ipv+IsIs

-IpvRse (5) where, A is the constant (Ideality factor), K is the Boltzman

constant (1.385 X 10-23 N.m/K), Tc is the cell temperature (in K), q is the charge (1.6X 10-19 C), IG is the light generated current (A), Ipv is the output current of the PV array (A), IS is the diode saturation current (A).

The light generated current (IG) and the diode saturation current (Is) is expressed as follows,

IG= Ics+Ksc Tc-298 G⁄ (6) Is=Isr Tc Tr⁄ 3exp qEG AK⁄ 1 Tr⁄ - 1 TC⁄ (7) where, Ics is the short circuit current of the cell (A), KSC is the

short circuit current temperature coefficient, G is the solar radiations (W/m2), Tr is the reference temperature (K), Isr is the diode saturation current at reference temperature (A) and EG is the band gap of silicon (eV). A solar-PV cell is modelled in Matlab-Simulink using Eq. (5)-(7).

For modelling a 1 kW solar-PV system four panels of 250W are connected together, for which open circuit voltage is 172.84 V, voltage at maximum power point is 142 V, current at maximum power point is 7.04 A and short circuit current is 7.63 A. The simulated results for the model of solar-PV array for different solar radiations are shown in Fig.3.

Fig.3 Characteristics of PV Array for the model for different solar radiations

B. Design of Isolated Zeta Converter

An isolated zeta converter is utilized in this system to regulate the the output voltage of the PV array. It consists of a transformer, two capacitors along with the primary and secondary windings of the transformer and an inductor at the output side [11]. The switching pulses are generated through a PWM generator using MPPT controller. The input voltage for the converter varies as the output of the PV array changes with radiations. The turn ratio for the transformer (n) considering the converter is calculated as [12],

n= Vc 1-DVinD

(8) where, Vc is the output voltage of the converter (360V), Vin

is the input voltage to the converter (Vin=Vpv=80-170V). D is the duty ratio of the converter (0.4-0.9). The turn ratio is calculated as 1:7 using Eq. (8).

The intermediate capacitor for the converter should be high enough to reduce the ripple at the output side. It is designed as [12],

Cim= VcDRfsΔVcim

(9) where, fs is the switching frequency of the converter (50kHz)

and ΔVcim is the value of allowed ripple voltage through the capacitor (0.5V). The value of intermediate capacitor is calculated as 50µF using Eq.(9).

The magnetizing inductance is considered in the converter along with the primary winding of the transformer. The value of magnetizing inductance for the converter should be enough to maintain continuous current in the inductor and to maintain the converter in the CCM (continuos conduction mode) [13-14]. The value of magnetizing inductance (Lm) is calculated as follows,

Lm= VinfsΔILm

(10) where, ΔLi is the value of ripple current allowed through the

inductance (0.1A). The Lm is calculated as 5mH. The output inductance of the converter is designed

considering that it must provide a filtering because of the variation in the input voltage, which may cause high ripple in the output inductor. The value of output inductor (Lo) is designed as follows,

L0= Vc 1-fsΔIL1

(11) where, ΔIL0 is the ripple current allowed through the output

inductor (0.3A), Dmax is maximum duty ratio of the dc-dc converter (0.9), The value of output inductor is calculated as 2.4 mH.

The output capacitance (Co) for the converter is responsible for reducing the ripple in the output voltage and should be high enough to maintain the dc link voltage for the battery and VSI. It is designed as follows,

Co1-D Vc

8Lo2fs

2ΔVco (12)

where, ΔVco is the ripple voltage through the output capacitor of the converter (0.5V). Its value is calculated as 100 µF.

The zeta converter is connected in series with the PV panel through input capacitor (Ci). This minimizes the ripple current through the PV panel and the value of Ci is calculated as,

Ci=DIpv

ΔVcifsw(min) (13)

where, ΔVci is the ripple voltage through the input capacitor of the converter (0.5V), Ipv is the current output of the solar-PV array (2-7A )and fsw is the switching frequency of the converter (50kHz). The value for input capacitor is calculated as 60 µF. The converter is designed using all these values of parameters and is modelled in Simulink.

C. Selection Criteria of Battery Rating

The output power from the solar-PV system is fluctuating in nature as it is a function of environmental conditions. It is required to add a storage system with it to ensure the supply during the low radiation time [15]. The consumer load on this system is considered of 350W and the batteries are selected as to store enough energy for feeding load up to 24 hrs. The total Ah (Amp-hrs) capacity required for the battery can be calculated as follows,

Capacity AH = Load W *Time (hrs)Battery Voltage (V)

(14)

The battery capacity for a 350W load and 24hrs storage with voltage of 360V is calculated as, 21 Ah. After considering the depth of discharge and battery efficiency the batteries for this system are taken as 50 Ah. Thus 17 batteries of 24V, 50Ah are considered in this system.

D. Single Phase VSI and Output Filter Design

The solar-PV panel generates the dc output power. A power converter is required to convert this power for feeding ac consumer loads. Thus a single phase VSI is used in this system to convert the dc power into the sinusoidal ac output voltage. An ac power is produced from the VSI by proper switching signals to its switches [16-17]. These switching signals are generated by a PWM controller. However the produced output ac voltage contains harmonics. A low pass filter is used with the VSI to reduce the harmonic content from its output and provides a 220V, 50Hz supply. The switches of the VSI are selected as per the rating of the load on the VSI. Here the consumer load is considered to be 350W at 220V, 50 Hz. The power factor is considered as 0.8, thus it needs 437.5 VA. Thus the rating for the switches is taken as 600V, 16A to feed this load and makes the system to withstand in nonlinear load conditions.

An LCL filter is used in this system to maintain the power quality at the load end. The value of inductor in the filter should be high enough to filter the harmonics in the output voltage. The filter inductance at the VSI side, Lf1 is calculated as [18],

Lf1= VLf1.(fsi)Δ

(15)

where VLf1 is the voltage across the filter inductor, Di is the duty tatio of the inverter switches, fsi is the switching frequency

of the VSI (20kHz), ΔILf1 is the ripple current through the filter inductance (0.5A). The value of filter inductance is calculated as 2.25 mH using Eq.(15). The value of filter inductance at the consumer load side Lf2 is taken as half of the Lf1 to achieve better filter effect at the VSI side [19-20], thus Lf2 is calculated as 1.2mH. The filter capacitor is calculated using the resonance frequency of the filter. The filter resonance frequency should be at least ten times higher of the cut off frequency and below the half of switching frequency. The switching frequency of the VSI is taken 20 kHz, so the resonance frequency is considered as 2 kHz. Thus, the value of filter capacitance is calculated as 8.1 µF.

V. RESULTS AND DISCUSSION The solar-PV system is designed with a zeta dc-dc converter

and variable step P&O MPPT method and modeled in Matlab/Simulink. Performance of the system is studied under various conditions as follows.

A. System Performance under Variable Loads

Fig.4 shows the performance of the system under a variable load. The solar radiation (G) is considered under steady state condition at 1000 W/m2 and the consumer load is considered as varying from 350 W to 100 W at 0.5s and again increased to 250W at 0.7s. As the load decreases at 0.5s, a decrease in the output current (Io) is observed. The increment in the output current is also seen as the load increases at 0.7s. These results demonstrate that the feedback controller of the VSI is performing satisfactorily because the output voltage of the VSI (Vo) remains constant in spite of load variations.

Fig.4 System performance under linear load variations

The output voltage of solar-PV array (Vpv) and current (Ipv) is observed constant as the solar radiations are constant. The output power of the solar array is obtained as 1kW and the output voltage of the converter is remains same at 360V. Along with the variation in the load there is a variation in the battery charging current. The controller of VSI is performing well as under the load variation the output voltage is observed constant.

B. System Performance under Variation in Solar Radiation

The performance of the system is also studied under varying solar radiations and the simulation results are presented in Fig.5. The solar radiation is considered as 500 W/m2 and at 0.5s to 0.7s it gradually increases to 1000 W/m2. It can be observed that, as the solar radiation increases, the output power of the solar-PV array is increased to 1000 W from 480W. These results conforms the operation of the MPPT controller to the variation in solar radiation. The operating point of the solar-PV system should be changed to extract the maximum power and the same is observed here as a variation in the PV array voltage and current.

Fig.5 System performance under varying solar radiation

C. System Performance under Nonlinear Loads

Fig.6 shows the performance of the system under nonlinear load conditions. A full bridge diode rectifier with the parallel resistive load resistance and a parallel filter capacitor is taken

as a nonlinear load and the system performance is analyzed with the radiation decreased to 500 W/m2 from 800W/m2.

Fig.6 System performance at solar radiation variation under non-linear load

The system is found to be performing satisfactorily under nonlinear load conditions as the voltage is regulated to a constant value.

D. System Performance Analysis with Harmonic Spectra

The power quality issue is also studied under variety of loads and the variation in the input conditions for the solar-PV array. The harmonic spectra for the output voltage and current for the linear load condition is shown in Fig.7. These results show that the THDs (Total Harmonics Distortion) for the output voltage and current are 1.27% and 2.14% respectively.

Fig.7 Harmonic spectra of output voltage and current under linear load

condition

0 200 400 600 800 10000

0.5

1

Frequency (Hz)

Fundamental (50Hz) = 311.4, THD= 1.27%

Mag

(% o

f Fun

dam

enta

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0.7 0.71 0.72 0.73 0.74 0.75-200

0200

Time (s)

Vo(

V)

0 200 400 600 800 10000

1

2

Frequency (Hz)

Fundamental (50Hz) = 1.09 , THD= 2.14%

Mag

(% o

f Fun

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0.7 0.71 0.72 0.73 0.74 0.75-1

0

1

Time (s)

Io(A

)

The harmonic spectra of the output ac voltage and load current for the nonlinear load are shown in Fig.8. The THDs for output voltage and current are 2.62% and 62.76% respectively.

Fig.8 Harmonic spectra of output voltage and current under non-linear load

condition

These results demonstrate that the THD of the output voltage obtained for linear and nonlinear loads are under specified limit of 5%.

VI. CONCLUSION A stand-alone solar-PV system using an isolated zeta

converter has been designed for feeding an average consumer load of 350 W. The system has been modelled in Matlab/Simulink and simulated results have been demonstrated for the variation in solar radiation and the consumer loads. The designed MPPT controller has been found working satisfactorily. The feedback controller for the VSI has also performed satisfactorily under load disturbances. The THD of the output voltage in nonlinear load condition is found within IEEE-519 standard limit of 5%. The results obtained validate the designed system configuration with isolated Zeta converter for low power applications.

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0.4 0.41 0.42 0.43 0.44 0.45-200

0200

Time (s)

Vo(V

)

0 200 400 600 800 10000

1

2

Frequency (Hz)

Fundamental (50Hz) = 311.8 , THD= 2.62%

Mag

(% o

f Fun

dam

enta

l)

0.2 0.21 0.22 0.23 0.24 0.25-202

Time (s)

Io(A

)

0 200 400 600 800 10000

20

40

60

Frequency (Hz)

Fundamental (50Hz) = 3.1 , THD= 62.76%M

ag (%

of F

unda

men

tal)