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IRPT Based Control of a 50 kW Grid Interfaced Solar Photovoltaic Power Generating System with Power

Quality Improvement

Bhim Singh, Fellow IEEE Electrical Engineering Department

Indian Institute of Technology Delhi New Delhi-110016, India

bhimsingh1956@gmail.com

D. T. Shahani IDD Centre

Indian Institute of Technology Delhi New Delhi-110016, India

dt.shahani@gmail.com

Arun Kumar Verma IDD Centre

Indian Institute of Technology Delhi New Delhi-110016, India

arunverma59@gmial

Abstract— This paper deals with a modified instantaneous reactive power theory (IRPT) based control of a grid interfaced solar photovoltaic (SPV) power generation which also mitigates power quality problems in three-phase four wire (3P4W) distribution system. This is a double stage SPV power generating system which accommodates wide varying input voltage. The proposed grid interfaced SPV generating system consists of a PV array, a DC-DC boost converter, a three leg VSC (Voltage Source Converter), an isolated Y-Δ transformer, a grid and connected linear/nonlinear loads. The DC bus voltage of a three-phase VSC is regulated using a PI (Proportional Integral) voltage controller. The SPV energy is injected in to the DC bus of VSC during sunshine hours. The proposed SPV power generating system provides the zero voltage regulation (ZVR) or power factor correction (PFC) along with harmonics elimination, load balancing and neutral current compensation in 3P4W distribution system. MATLAB/Simulink based simulation results are presented to validate the design and control of SPV power generating system for feeding 3P4W loads with improved power quality.

Keywords— Instantaneous Reactive Power Theory (IRPT), Solar Photo Voltaic (SPV), Neutral Current Elimination, Zero Voltage Regulation (ZVR) and Power Factor Correction (PFC).

I. INTRODUCTION Solar photovoltaic (SPV) energy is most important energy as it is green, pollution free and having no threat to environment. Earlier SPV based electrical power generation has been limited to stand alone SPV power generation, however, now grid interfaced SPV generating systems are becoming popular [1-3]. There are many potential configurations available in the literature like single stage grid interfaced, two stage grid interfaced and multi level grid interfaced for SPV power generating system. The two stage SPV power generating system has not considered the PQ (Power Quality) problems in detail with and without availability of sun [4-6]. The grid interfaced SPV generating systems have used various control algorithms which have focused on PQ problems limited to itself like, low harmonic distortion and high power factor and harmonic compensation and mainly focused on the PQ

improvement on converter side only [7-11]. However, the PQ problems are dominant in the grid because of various nonlinear loads in distributed system. These PQ issues are poor power factor, voltage regulation and reactive power compensation at AC mains. The effective control of SPV generating system has been an important task in these systems which may be effectively used for mitigation of PQ problems of AC distribution system caused by nonlinear and unbalanced loads. Maximum power point tracking (MPPT) from SPV array is also a challenging task and several methods of MPPT are used [12, 13]. In the proposed SPV generating system, the basic advantage of using a Y-∆ transformer is used to eliminate the triplen harmonics and zero sequence currents in the Δ connected windings of the transformer [14]. It results in the reduced ratings of the VSC devices. A VSC also helps in the compensation of reactive power and harmonic reduction of connected load at PCC (point of common coupling). The circulating current in the VSC is reduced as the neutral current is compensated in the secondary windings of the Y-∆ transformer. In this proposed research work, a two stage SPV power generating system is used with the features of reactive power compensation for PFC or zero voltage regulation (ZVR), load balancing, harmonics current elimination and neutral current compensation. There are many control techniques available to control the SPV power generating system, here an IRPT (Instantaneous Reactive Power Theory) [15] based control algorithm is used for these functions of power quality improvements in 3P4W distribution system.

II. SYSTEM CONFIGURATION The proposed SPV generating system is shown in Fig.1. A photovoltaic array is designed to generate 50 kW as a peak power under standard operating conditions and this peak power is tracked from PV array using P&O (“Perturb and Observe Method”) algorithm. A DC-DC boost converter implements MPPT (Maximum Power Point Tracking). The common DC link voltage is regulated using a DC bus voltage PI controller of VSC. A VSC with a Y-∆ transformer provides

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the compensation of the neutral current, reactive power and balancing of consumer loads connected at PCC. The VSC consists of six IGBTs (Insulated Gate Bipolar Junction Transistors), interfacing inductors and DC bus capacitor. The VSC is used for reactive power compensation of 40 kVAR of a 50 kW, 0.8 lagging power factor load in a 3P4W distribution system where a 50kW SPV power is injected at PCC which also reduces the overall losses in the system.

III. DESIGN OF PROPOSED SPV GENERATING SYSTEM

A three-phase 50 kW SPV generating system has a three-leg VSC and a Y-Δ transformer. The selection of components like IGBTs, inductors, DC bus capacitor and the ripple filter is made according to design requirements. The design of the system is given as follows.

Fig.1 Schematic Configuration of the Proposed SPV Power Generating

System

A. Design of Solar Photovoltaic Array The PV panel is designed for a 50 kW peak power capacity. A solar PV module is formed by connecting solar cells in series. Each cell has an open circuit voltage of 0.5 V to 0.6 V [16] and short circuit current (Isc) of 4A. The generalized equation for an active power for SPV array is given as, PmaxM = VmppM * ImppM (1) Maximum power occurs generally at PmaxM = (85% of Voc * 85 % of Isc ) thus ImppM is 3.3A and VmppM is 0.42V of each cell. 720 cells are connected in series to achieve a maximum voltage of 302V as Vmpp of SPV for proposed system. The total calculated maximum power is given as, Pmax = Vmpp * Impp = 50 kW (2) From (2) to achieve a 50kW peak power capacity [16], the required value of maximum current (Impp) is 165.56 A, to achieve this current (165.56/3.3) 50 solar cells are connected in parallel respectively.

B. Selection of DC Capacitor Voltage In order to achieve proper compensation, the minimum DC bus voltage of VSC should be greater than twice the peak of the phase voltage of the system as [17],

(2 2 ) 3dc LLV V= (3)

Where VLL is the AC line output voltage of VSC and its value is 239.6V. The estimated value of the Vdc from Eq. (3) is obtained as 391.87 V and it is selected as 400 V.Selection of DC Capacitor Voltage

C. Design of DC-DC Boost Converter Fig.1 shows a DC-DC boost converter used in this system. The DC-DC boost converter is used to track the MPP and to boost the input of SPV array which used to feed the active power at the DC bus of the VSC. The value of the ripple current for the boost converter is given as,

1(1 )

(2 )dc

b sw

V D DiL f

−Δ = (4)

where D is Duty cycle Δi1 is input current ripple and for this design the value of Δi1 is considered 5% of boost converter inductor current i1 (= P/Vin) =165.56A. Thus the calculated value of Δi1 is 8.25A. fsw is switching frequency and the value of fswb is considered as 10 kHz. Where Vo, Lb and fS are fixed value. The condition of maximum value of the ripple current given as,

1( )0

( )Δ

=d idD

(5)

The value of D corresponding to maximum ripple current is obtained from (5) is 0.5. The value of inductance (Lb) from Eq. (4) is obtained as 1.12 mH and the selected value is 1.25mH.

D. Design and Selection of DC Link Capacitor The value of DC link capacitor is estimated using energy conservation principle. The design of DC link capacitor (Cd) of VSC depends on the instantaneous energy available to the VSC at the time of transients. By using the principle of energy conservation the value of DC capacitor is given as [17],

2 21

1 32

⎡ ⎤− =⎣ ⎦ sd dc dcC V V V Itα (6)

where Vdc is the reference DC voltage and Vdc1 is the minimum voltage level of DC bus, α is the overloading factor, Vp is the phase voltage, I is the phase current, and t is the time by which the DC bus voltage is to be recovered. Considering the minimum voltage level of the DC bus, Vdc1 = 380 V, with nominal Vdc = 400V, V = 138.560 V, I = 120.28 A, t = 250 μs, a = 1.2, the calculated value of Cd is 4522.28 μF and it is selected as 5000 μF.

E. Selection of VSC Source AC Inductor The VSC source inductance (Lf ) is given as[17],

3

( )( )

3

12=

Δdc

fs

mVL

hf i (7)

where ∆i is current ripple, fs is the switching frequency, (Vdc) is DC bus voltage, m is the modulation index and h is the overload factor. Considering, ∆i, = 3%, fs = 10 kHz, m = 0.9, Vdc = 400 V, h = 1.2, the Lf value is calculated to be 2.16 mH. A round-off value of Lf of 2.5 mH is selected in this investigation.

F. Design of Ripple filter A first order filter is tuned at half the switching frequency (fsh = 10kHz) is used to filter the harmonics from the voltage at the PCC. At a frequency of 5 kHz by considering a small impedance of 8 ohms for harmonic voltage, the ripple filter capacitor is designed as Cf = 10 μF. A series resistance (Rf ) of 5 Ω is included in series with the capacitor (Cf). The calculated value of the impedance circuit is 391Ω at fundamental frequency, which is quite large, due to this the ripple filter extracts very small fundamental current.

G. Design of Voltage Source Converter A three phase voltage source converter is shown Fig.1. The VSC consists of six switching devices. The IGBTs with anti parallel diodes are used in VSC for compensating the reactive power, harmonics of consumer loads. A three - phase VSC for compensation of 239.6 V, 50 kW at 0.9 p.f. lagging load and SPV generation is designed here. The value of rms load current is given as,

0

03 3( )= =rms

o

VA PIV PF V

(8)

where VA = (Load Power/PF)

The rms value of load current from Eq. (8) is estimated as 133.6A for a 50 kW load. Since the crest factor (CF) of the current of the nonlinear load is order 2, the peak load current (Ip) is given as,

( )=P rmsI CF I (9) So the value of peak current from Eq. (9) is estimated as 267 A. By considering a safety factor of 1.2, the standard rating of the IGBT device is selected 300 A. For the VSC voltage of 239.6V rms, peak voltage of this three phase VSC is given as,

2 *=peak rmsV V (10) The value of peak voltage from Eq. (10) is estimated as 338.79V. By considering the safety factor of 1.5, the device rating is estimated 508.18V. So the IGBTs of 500V and 300A are selected to form the VSC.

H. Design of a Y-∆ Transformer Based on the compensation current provided by the VSC, the current rating of the transformer winding is decided. The calculated primary winding voltage is, Va=VLL/(√3)=415/√3=239.60V (11) The star-delta transformer provides an isolation, step up of SPV voltage and compensation of the neutral current and at

the same time if there is a variable DC link voltage then it takes care of low DC link voltage too. The grid side is connected in star thus it can eventually step up the voltage in case of low DC link. Total apparent power for a linear load is given as,

2 2 2 (50 * 0.6)50 62.50.8reqS P Q kVA= + = + =

(12)

where P is active power of 50kW of SPV and Q is reactive power of the consumer loads of 50kW connected at PCC respectively. By taking the effect of harmonics and distortion factor it is also selected to consider the case of nonlinear loads. The required transformer design needs three single phase transformers of 25 kVA, 240V/240V, totaling of 75kVA.

IV. CONTROL TECHNIQUE FOR PROPOSED SPV GENERATING SYSTEM

The control technique used here to control the proposed system is based on the IRPT for VSC. There is a separate control for MPPT using a DC-DC boost converter. The control strategy is given in following sections. A. Control of DC-DC Boost Converter for MPPT A DC-DC boost converter is used to achieve MPPT employing a P& O algorithm. Due to variable solar radiation, the varying output voltage of the SPV is fed to the DC–DC boost converter as input voltage. A PV array voltage and power are used as inputs to the controller which decides the duty ratio of the boost converter corresponding to peak power point. The incremental change in D is considered 0.01. This P&O control algorithm tracks the maximum power Ppv, maximum current Ipv, and maximum voltage Vpv. The change in power at tth instant is given as,

1−= −t tdp p p (13) The change in power with respect to voltage is tracked and given as,

1

1

−

−

−=

−t t

t t

p pdpdv v v

(14)

and accordingly the increment and decrement in duty cycle is resulted in the corresponding control signal and it is compared with a saw-tooth waveform of 10 kHz and its output controls the duty cycle of the boost DC-DC converter for MPPT. B. IRPT based Control of VSC

The grid feeds an active power to connected consumer loads at PCC. However, it supplemented by SPV power generation through DC link voltage controller of VSC. The DC link PI voltage controller of VSC takes care an injection of SPV power generation, during the availability of sun. In order to generate reference grid currents, the IRPT control algorithm is employed to control the VSC. In the instantaneous reactive power theory (IRPT), the estimation of instantaneous active and reactive powers of the consumer loads is made after

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converting sensed voltages (VLa, VLb, VLc) and load currents (iLa,iLb,ilc) to α-β reference frame as,

( ) ( )1 11 2 22 3

3 30 2 2

− −

=

−

⎛ ⎞⎡ ⎤⎜ ⎟⎡ ⎤ ⎢ ⎥⎜ ⎟⎢ ⎥ ⎢ ⎥⎜ ⎟⎣ ⎦ ⎢ ⎥⎜ ⎟ ⎣ ⎦⎜ ⎟

⎝ ⎠

La

Lb

Lc

vv

vv

v

α

β

(15)

( ) ( )1 11 2 22 3

3 30 2 2

− −

=

−

⎛ ⎞⎡ ⎤⎜ ⎟⎡ ⎤ ⎢ ⎥⎜ ⎟⎢ ⎥ ⎢ ⎥⎜ ⎟⎣ ⎦ ⎢ ⎥⎜ ⎟ ⎣ ⎦⎜ ⎟

⎝ ⎠

LaL

LbL

Lc

ii

ii

i

α

β

(16)

These voltages and currents in the and β reference are used to estimate instantaneous active and reactive powers of the loads. The active power taken by the loads is given as,

( )= + = +w L L dc acp v i v i P Pα α β β (17)

This active power consists of two components a DC component ( Pdc ) and an oscillating component (Pac) which is due to harmonics component, to be fed by VSC. This instantaneous power Pw is passed through a low pass filter (LPF) to extract its DC component the output from LPF is Pdc which is fundamental active power of the loads used in estimation of reference AC mains currents. Similarly instantaneous reactive power of the loads is estimated as,

= − = +w dc acQ v i v i Q Qα β β α (18) This reactive power of the loads consists of DC (Qdc) component as well as AC component (Qac) after passing through LPF this instantaneous reactive power, it is Qdc.

1) Voltage Regulation and Load Balancing The quadrature or reactive power components of grid currents takes care of the voltage drop in the grid (source) impedance by injecting a small reactive power current in to the grid through VSC. It may be lagging in nature if the loads are of leading power factor. For this purpose, a voltage PI controller is used to regulate PCC voltage. The output PI voltage controller is reactive power component supplied by VSC for voltage control. These quadrature or reactive power components are estimated through following basic equations. For PCC voltage regulation, an error voltage of the amplitude of AC terminal voltage at the point of common coupling (PCC) is regulated by a PI AC voltage regulator. The amplitude of voltage at PCC is given as,

( ) ( )1 21 2 2 2 22 3= + +m La Lb LcV v v v (19)

This amplitude is filtered and the voltage error between the reference voltage and this estimated voltage is fed to PI controller which in turn regulates the PCC voltage. The output of the PI controller is reactive power component and it is estimated as,

( ) ( ) ( ) ( ) ( )1 1− −= + − +pq iql n l n ae n ae n ae nQ Q K v v K v (20)

where ( ) ( )mrae n m nv v v= − and Kpq and Kiq are the

proportional and integral gain of the AC voltage PI controller, Ve(n) and Ve(n-1) are the voltage errors at the nth and (n-1)th sampling instant, Ql(n) and Ql(n-1) are the are the output of the AC PI voltage controller at the nth and (n-1)th sampling instant, The reference reactive power at the grid is given as,

* = −g l dcQ Q Q (21) For estimating active power components of grid currents, the active power of consumer loads and output of DC link voltage controller have to be estimated. The DC link PI voltage controller of VSC takes care an injection of SPV power generation, during the availability of sun. Following are the basic equations for estimating active power components at nth instant is given as,

( ) ( ) ( ) ( )1 1( ) − −= + − +l pd idl n de n de n de np n p K v v K v (22)

where vde(n)=vdcr - vdca(n) an error between sensed and reference DC bus voltage of VSC kpq and kpi are proportional and integral gain of the DC voltage PI controller, Vde(n) and Vde(n-1) are the voltage errors at the nth and (n-1)th sampling instant, Pl(n) and Pl(n-1) are the are the output of the PI DC bus voltage voltage controller at the nth and (n-1)th sampling instant,

The reference active power P*g of the grid is given as,

( )* = −g l dcP P n P (23) The estimated reference active and reactive powers of the grid from Eq. (21) and (23) are utilized to obtain reference grid currents in α,β frame are given as,

**

2 2* *

1 ⎡ ⎤⎡ ⎤ ⎛ ⎞⎛ ⎞= ⎢ ⎥⎜ ⎟⎢ ⎥ ⎜ ⎟⎜ ⎟ −+ ⎢ ⎥⎢ ⎥ ⎝ ⎠⎝ ⎠⎣ ⎦ ⎣ ⎦

gs

s g

Pi v vv vv vi Q

α α β

β αα ββ

(24)

These reference grid currents in α,β reference frame are transformed in to a,b,c reference frame by inverse Clark transform in order to produce reference grid currents as,

( ) ( )( ) ( )

*

*

*

*

*

1 0

12 3 2231 3 2

2

−=

−−

⎛ ⎞⎡ ⎤ ⎜ ⎟ ⎡ ⎤⎢ ⎥ ⎜ ⎟ ⎢ ⎥⎢ ⎥ ⎜ ⎟ ⎢ ⎥⎣ ⎦⎢ ⎥ ⎜ ⎟⎣ ⎦ ⎝ ⎠

sa

s

sb

s

sc

ii

ii

i

α

β

(25)

2) Power Factor Correction and Load Balancing The quadrature or reactive power components of grid currents must be zero for power factor correction (PFC) to unity at PCC. Power factor correction can be achieved by putting the value of reactive power component (Q*

g) zero in Eq. (24). Similarly the reference grid currents are generated by using Eq. (25).

3) PWM Generator These reference grid currents (i*sa, i*sb and i*sc) are compared with the sensed grid currents (isa, isb and isc) in the PI current controller for generating gating signals for VSC of SPV power generating system.

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V. MATLAB BASED MODELING Matlab model is developed of the proposed SPV generating system. The simulation parameters are set as following light intensity of SPV array is 1000W/m2 and this solar intensity is also reduced to zero. Temperature is 250C. The SPV array with DC-DC boost converter is used to track MPP, its control through P&O algorithm is implemented using Matlab/Simulink. The Y-∆ transformer which is utilized to compensate neutral current which is also modeled using Matlab/Simulink. The algorithm used for controlling the VSC is realised in Simulink. The reference grid currents are derived from the sensed load voltages (vLa, vLb, vLc ), load currents (iLa, iLb, iLc), and the DC bus voltage of VSC (Vdc). A current controller based on pulse width modulation is used for comparing reference grid currents (i*sa,i*sb,i*sc), and sensed grid currents (isa,isb,isc) to generate the switching pulses for the IGBTs of the VSC.

VI. RESULTS AND DISCUSSION Simulated results of SPV power generating system is demonstrated in this section. The grid interfaced 50 kW solar PV power generating system using IRPT control algorithm is validated under different linear/nonlinear, balanced and unbalanced consumer loads in a 3P4W distribution system.

The nonlinear load is realized by using three single phase diode rectifier with resistance load with capacitance filter. Performance of the proposed SPV system is simulated and waveforms of the grid voltage voltages (Vs), DC bus voltage (Vdc), AC grid currents, (is), load currents, (IL) the active power from /to grid (P), the reactive power (Q), solar PV current (IPV), solar PV voltage (Vpv), solar PV power (Ppv), VSC current (ic ), and terminal voltage at PCC (Vt) are illustrated in Figs.3-5. The AC mains neutral current (isn), transformer neutral current (Itn) and load neutral current (iln) are also depicted in Fig.3-5 under load variations. Following inferences are observed from these simulation results. A. Performance of SPV Power Generating System at

Unbalanced Linear Load for UPF and Load Balancing Performance of the proposed SPV power generating system under linear unbalanced loads at lagging PF in a three-phase four-wire distribution system is illustrated in Fig.2.Load

unbalancing occurs at 0.3 s. by removing load from two phase and continues up to 0.45s. During load unbalancing, the grid currents are sinusoidal and almost balanced. During sun shine hours the active power is supplied from solar PV array. The grid voltage and grid currents are in phase. The AC grid neutral current (isn), transformer neutral current (Itn) load neutral current (iln) are also depicted under load variations. The solar PV generation is reduced to zero at 0.5s and afterwards

Fig.2 Performance of Proposed SPV System at unbalanced Linear Loads for Unity Power Factor and Load Balancing

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required compensation is provided by the VSC thus the grid neutral current appears to be zero.

B. Performance of SPV Power Generating system at Unbalanced Nonlinear Load for UPF and Load Balancing

Fig.3 Performance of Proposed SPV System at unbalanced Linear Loads for Unity Power Factor and Load Balancing

Fig. 4 Performance of Proposed SPV System at Unbalanced Linear Load for Load Balancing and Voltage Regulation

7

Fig.3 shows performance of SPV system under unbalanced nonlinear loads for unity power factor at AC mains. Here it is seen that the load is drawing non-sinusoidal and unbalanced currents but AC grid currents are balanced and sinusoidal due to compensation provided by the VSC. Unbalancing in the nonlinear loads occurs at 0.25 s and continued till 0.5s. The solar intensity becomes zero and now the load is fed through AC grid. The zero sequence fundamental current of the load neutral current resulted in the unbalanced load currents is circulated in the Y-∆ transformer and hence the grid neutral current is maintained at nearly zero.

C. Performance of SPV Power Generating System at Unbalanced Linear Load for Load Balancing and ZVR

In Fig. 4, it has been observed load currents are compensated and the grid currents are balanced and almost sinusoidal. The unbalancing in loads is realized by removing loads from two phases at 0.3s and further continues up to 0.45s. The grid currents are almost balanced in-spite of zero load current in two of the phases. When there is no sun light, reactive power of the load is supplied by VSC. The AC mains neutral current (isn), transformer neutral current (Itn) and load neutral current in the load (iln) are also shown under varying loads. Due to proper compensation, the grid neutral current is close to zero. The DC

bus voltage of VSC is regulated close to the reference value under unbalancing of the loads.

D. Performance of SPV Power Generating System at Unbalanced Nonlinear Load for Load Balancing and ZVR

Fig. 5 shows the performance of the SPV system for voltage regulation mode at nonlinear loads. PCC voltage is regulated to rated value in spite the change in loads. The zero sequence fundamental current of the load neutral current resulted in the unbalanced load currents is circulated in secondary of the Y-∆ transformer hence the neutral current compensation is achieved. E. Power Quality Improvement This IRPT controlled SPV power generating system improves power quality of the 3P4W distribution system. The grid currents are injected in to /or coming out from grid is in phase of grid voltage maintaining unity power factor. The total harmonics distortion in the load current, AC grid current and load voltage are given in Figs. 6a-c. The FFT analysis of the simulated results shows that The THD of the AC grid current is 1.49 % and PCC voltage THD is 0.24 % [18]. The total harmonics distortion of PCC voltage and AC grid current are well within the limit of IEEE 519 standard under nonlinear

Fig.5 Performances of Proposed SPV System at unbalanced Nonlinear Loads for Load Balancing and Voltage Regulation

8

loads having a load current THD of 77.34%.The terminal voltage at PCC is regulated to its reference value in order to maintain zero voltage regulation with reactive power compensation. The Y-Δ transformer is used along with VSC to provide isolation, neutral current compensation and to step up voltage to the grid.

Fig.6a Wave form and Harmonic Spectrum for PCC voltage

Fig.6b Wave form and Harmonic Spectrum for AC grid current

Fig.6c Wave form and Harmonic spectrum of load current

VII. CONCLUSION The proposed grid interfaced SPV power generating system is capable to inject active power in to the grid and able to compensate for load reactive power and load current harmonics. The performance of the SPV grid interfaced system has been validated for load reactive power compensation for unity power factor operation and zero voltage regulation along with harmonics elimination, load balancing and neutral current elimination. The IRPT control algorithm for grid interfaced SPV power generating has been used first time successfully. Both modes of operation of ZVR and UPF of the proposed system have been achieved and performance of the system has been found satisfactory.

VIII. APPENDICES A. Design Parameters of a 50 kW Solar Photovoltaic System Voltage/temperature coefficient (Kv) = -80e-3 V/K, Current/temperature coefficient (Ki) = .003 A/K, B. Parameters for VSC DC bus voltage of VSC: 400 V, DC bus capacitance of VSC: 5000 μF, AC inductor: 2.5 mH, DC voltage PI controller: Kpd = 1.2, Kid = 0.9, PCC voltage PI controller: Kpq = 0.15, Kiq = 0.11, PWM switching frequency: 10 kHz, Ripple filter: Rf = 5 Ω, Cf = 10 μF. AC line voltage: 415 V, 50 Hz, Line impedance: Rs = 0.002 Ω, Ls = 1.6 mH,

REFERENCES

[1] Zekei Sen, “Solar Energy Fundamentals and Modeling Techniques Atmosphere, Environment, Climate Change and Renewable Energy,” Springer-Verlag London Limited, 2008.

[2] Remus Teodorescu, Marco Liserre and Pedro Rodrıguez, “Grid Converters for photovoltaic and wind power system,” John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, United Kingdom. 2011.

[3] B. Verhoeven and B.V. Kema, “Utility aspects of grid connected photovoltaic power systems,” International Energy Agency Photovoltaic Power Systems, IEA PVPS T5-01, 1998. [Online]. Available: www.iea-pvps.org.

[4] P.G Barbosa, L.G.B. Rolim, E.H. Watanabe and R. Hantitsch, “Control strategy for grid connected DC-AC converter with load power factor correction,” IEE Proc. Genr. Transm.Distrib, Vol.145, no.5, pp. 487-491, Sept.1998.

[5] Jing Li, Fang Zhuo, Xianwei Wang, Lin Wang and Song Ni, “A grid-connected PV system with power quality improvement based on boost + dual-level four-leg inverter, ” in Proc. IEEE 6th International on Power Electronics and Motion Control Conference, 2009. IPEMC '09. vol., no., pp.436-440, 17-20 May 2009.

[6] S. Balathandayuthapani, C. S. Edrington, S. D. Henry and J. Cao, “Analysis and Control of a Photovoltaic System: Application to a High-Penetration Case Study, ” IEEE Systems Journal, vol.6, no.2, June 2012.

[7] R.I. Bojoi, L.R. Limongi, D. Roiu and A. Tenconi, “Enhanced Power Quality Control Strategy for Single-Phase Inverters in Distributed Generation Systems," IEEE Transactions on Power Electronics, vol.26, no.3, pp.798-806, March 2011.

[8] Bo Yang, Wuhua Li, Yi Zhao and Xiangning He, “Design and Analysis of a Grid-Connected Photovoltaic Power System, ” IEEE Transactions on Power Electronics, vol.25, no.4, pp.992-1000, April 2010.

[9] Rong-Jong Wai and Wen-Hung Wang, “Grid-Connected Photovoltaic Generation System," IEEE Transactions on Circuits and Systems I: Regular Papers, vol.55, no.3, pp.953-964, April 2008in Electric Power Systems, IEEE Standard 519, 1992.

[10] Yu-Kang Lo, Ting-Peng Lee, and Kuan-Hung Wu, “Grid-Connected Photovoltaic System With Power Factor Correction,” IEEE Transactions on Industrial Electronics, Vol. 55, no. 5, pp.2224-2227, May, 2008.

[11] R.A. Mastromauro, M. Liserre, T. Kerekes and A. Dell'Aquila, “A Single-Phase Voltage-Controlled Grid-Connected Photovoltaic System With Power Quality Conditioner Functionality, ” IEEE Transactions on Industrial Electronics, vol.56, no.11, pp.4436-4444, Nov. 2009.

[12] N. Femia, G. Petrone, G. Spagnuolo and M. Vitelli, “A Technique for Improving P&O MPPT Performances of Double-Stage Grid-Connected Photovoltaic Systems, ” IEEE Transactions on Industrial Electronics, vol.56, no.11, pp.4473-4482, Nov. 2009.

[13] T. Esram and P.L Chapman, “Compression of photovoltaic array maximum power point tracking technique,” IEEE Trans. on Energy Con., vol.22, no.4, pp. 439-449, June,2007.

[14] B. Singh, P. Jayaprakash, and D.P. Kothari, “Three-phase four-wire dstatcom with H-bridge VSC and star/delta transformer for power quality improvement,” in Proc. of IEEE INDICON 2008, Vol. 2, Dec. 2008, pp.412 - 417.

[15] H. Akagi, E.H. Watanable and M. Aredes, “Instantaneous power theory and application to power conditioning,” Jhon Wiley & sons, New Jersey, USA, 2007.

[16] Y. T. Tan, D. S. Kirschen, and N. Jenkins, “A model of PV generation suitable for stability analysis,” IEEE Trans. Energy Con., vol. 19, no. 4, pp. 748–755, Dec. 2004.

[17] B. N. Singh, P. Rastgoufard, B. Singh, A. Chandra, and K. A. Haddad, “Design, simulation and implementation of three pole/four pole topologies for active filters,” Inst. Electr. Eng. Proc. Electr. Power Appl., Jul. 2004, vol. 151, no. 4, pp. 467–476.

[18] IEEE Std. 519, “IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems”, available on http://ieeexplore.ieee.org.