Grid-Connected Photovoltaic Models for Three-Phase Load Flow Analysis

Syafii, Student Member IEEE Electrical Power Engineering Dept,

Univrsiti Teknologi Malaysia /Electrical Engineering Dept,

Andalas University, Padang, Indonesia Email: syafii@ft.unand.ac.id

Khalid Mohamed Nor, Senior Member IEEE

Electrical Power Engineering Dept, Universiti Teknologi Malaysia

Johor Bahru, Malaysia Email: khalidmn@fke.utm.my

Mamdouh Abdel-Akher,

Member IEEE Electrical Engineering Dept,

South Valley University, Aswan, Egypt

Email: mabdelakher@ieee.com

Abstract— The paper presents grid connected Photovoltaic (PV) models for three-phase distribution load flow analysis. The models comprises of single-diode PV model with and without the effect of the series and parallel resistances, I-V nonlinear question, I–V database and single-phase PV modeled as single-phase real power injection. The three-phase load flow program with Photovoltaic models has been tested using IEEE 13 node feeder. The solution of the base case is compared with the radial distribution analysis package (RDAP) before used to analyze distribution networks. The analysis is carried out with various photovoltaic mathematical models. The simulation results show that the grid-connected three-phase photovoltaic system in distribution network can improve the voltage profile as well as reduce the total system losses. However, single-phase PV DG model does not always guarantee voltage improvements.

Keywords-Three-Phase Load Flow; Photovoltaic Models; Distributed Gneration

I. INTRODUCTION Distributed generations using renewable energy sources,

such as wind, solar photovoltaic and hydro power have received considerable attention in recent years. Grid-connected solar photovoltaic (PV) continued to be the fastest growing power generation technology, with production has been increasing by an average of more than 20 percent each year since 2002 [1]. At the end of 2009, the cumulative global PV installations surpassed 21,000 MW [2]. Therefore, there is a need to improve specific DG model to cover grid-connected photovoltaic energy sources.

Photovoltaic (PV) system directly converts sunlight into the most valuable form of energy known as electricity. The electric power produce at the terminals of a PV device may directly feed small loads such as lighting systems and DC motors. Photovoltaic system requires electronic converters to control output voltage and current as well as the power flow in grid-connected systems application. The impact of grid-connected PV system can be analyzed using three-phase load-flow program. The power system model in the program needs an extension with PV models.

The objective of this paper is to improve Photovoltaic model and study the effect when they are connected in distribution networks. The study includes both voltage profile and system losses. The paper is organized such that Section 2 presents the PV model, section 3 presents the three-phase load flow method, Section 4 shows the system under study, Section 5 gives comprehensive results and the effect of grid-connected PV on both the voltage profile as well as system losses, and finally the conclusions are drawn in Section 6.

II. PHOTOVOLTAIC MODEL Another source of distributed generator is the photovoltaic

systems, which are commonly known as solar panels. Solar panels are made up of discrete PV cells connected together to be PV modules and PV arrays that convert light radiation into electricity. The PV cells produce direct-current (DC) electricity, which must then be inverted for use in an AC system. The systems can be used as single phase source or three phase source and thus can have the unbalancing impact on the grid connected system.

The solar radiation varies according to the orbital variations. The total solar radiation output from the sun in all frequencies at a distance R from the sun centre [3] is equal to:

S = 4πR2 Q(R) (1) If the radiation flux per unit area at a distance R represented by Q(R) and the earth approximately 150x106 km away from the sun. Hence, the total solar output is about 3.8 x 1026 W. Since, the surface area of the earth is 4πr2; the amount of solar radiation per unit area on a spherical planet becomes as 340 W/m2 [3]. Therefore the solar energy has a large potential for future renewable energy sources.

Photovoltaic equivalent circuit consists of a current source driven by sunlight in parallel with a real diode and resistance (Rp) series with resistances (RS) shown in Fig. 1. The output power and voltage varies according to sun radiation.

2010 IEEE International Conference on Power and Energy (PECon2010), Nov 29 - Dec 1, 2010, Kuala Lumpur, Malaysia

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Figure 1. Equivalent circuit for photovoltaic cell

The ideal equivalent circuit of PV cell consists of a current source in parallel with a diode. Ideally the voltage-current (VI) equation of PV cell [1,4] is given by:

)1(,0, −−= akTqV

cellcellpv eIII (2)

Where IPV,cell is the current generated by the incident light (directly proportional to the sun irradiation), I0,cell is the reverse saturation of the diode, q is the electron charge (1.60217646 x 1019 C), k is the Boltzmann constant (1.3806503 x 10-23 J/K), T is temperature of the p-n junction and a is the diode ideality constant.

Figure 2 Characteristic I-V curve of Photovoltaic

Fig. 2 shows the V-I curve and Ppv-V curve originated from

(2). General photovoltaic model using voltage and current of equivalent PV module to calculate the output power [5] as state below:

P=V.I= 1 . ∆ . 1 . ∆ (3)

Where and are short circuit current and open circuit

voltage at reference temperature; α and β are temperature coefficient;

More specific formulation provided in [1] :

)()(

SP

IRVkTq

SC RIVR

eIII S +−⎥⎦

⎤⎢⎣

⎡−−=

+ 110 (4)

The voltage across individual cell can be found from :

V= Vd – I RS (5) When photovoltaic are wired in series the Vmodule calculated by:

Vmodule = n (Vd – I RS) (6)

where n : number of cells

The power output of the PV system can be found by multiply I and V.

The Monte Carlo techniques for photovoltaic generators model in Probabilistic distribution load flow report in [6]. The power output of the PV system (P ) is given by :

. . . . . . (7)

Where : AC is the array surface area [m2]; η is the

efficiency of the PV system in realistic reporting conditions (RRC) [7]; T and T’ are parameters that depend on inclination β, declination δ, reflectance of the ground ρ, latitude , hour angle ω, sunset hour angle ω , day of the year [8].

Some of the previous PV models used for individual or stand alone PV generation analysis. For grid-connected PV models analyzed using single phase load flow formulation for balanced distribution network studies only. The extend grid-connected PV models in the latest unbalanced load flow [9,10] make possible to analyze their impact in unbalanced distribution networks. Brief explanation of these models is given in the next section.

III. THREE PHASE LOAD FLOW ANALYSIS Three-phase load flow is required when solving unbalanced

distribution system. There are many causes of unbalanced condition in a distribution networks. Regarding reference frame, three-phase load flow algorithms can be categorized into two groups. The first group solves using phase component approach and the second used sequence component approach. However the sequence component has some advantages such as the size of the problem is effectively reduced in comparison to phase components approach [9] and easy to handle unbalanced power system components [11].

This project research will develop grid-connected PV models by improve existing three-phase power flow object components software already developed in [9]. The object oriented programming methodology has an ability for updating or adding new algorithm without affecting other components inside the software [12] such as an extension for fault analysis algorithm presented in [13].

A. Sequence Three-Phase Load Flow Problems The sequence three-phase load flow requires power system

models in terms of their sequence components. The three-phase power system models represented by sequence admittance matrices of three sequence network. The sequence admittance matrices comprise of positive-, negative- and zero- sequence decoupled bus admittance matrices. Then, these sequence admittance matrices used to solve the three sequence network in the iteration scheme. The process is repeated until certain preset permissible tolerance reached

The state variable of three-phase voltage updated using the result of three decomposed sub-problem in the iterative

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scheme. The positive-sequence network has been solved using the standard Newton-Raphson method and whereas the negative- and zero-sequence are represented and solved using two nodal voltage equations. The specified values of sequence networks for three decomposed sub-problem calculated by combining the current injection due to loads, distributed load, capacitor bank and system unbalanced. The available of new component need to model in theirs sequence component. This sequence component model reused by existing three-phase load flow component and its power system models [9].

B. Photovoltaic DG Mathematical Model In sequence three phase power flow program, every power

system component need to convert to sequence components using A matrix (8). The A matrix is defined as the symmetrical components transformation matrix:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

2

2

11

111

aaaaA (8)

where a =1.0 ∠120°

The result is sequence model of the component that can be included in three phase power flow algorithm as new class library. By used sequence component model, balanced grid-connected photovoltaic can be modeled in unbalanced system.

The sequence component model allows using the balanced three-phase load flow specifications for generators. Normally at a terminal generator bus, both the positive sequence voltage and the total power leaving the terminal of the actual three-phase bus are specified. The positive sequence voltage magnitude at the terminal bus is the same as the positive sequence network of the generator, and hence, the positive sequence voltage magnitude of the positive sequence network of the generator is specified. The total power specified at the terminal bus is mainly due to the positive sequence network of the generator since there is no induced EMF in both the negative- and zero-sequence networks. Consequently, the specified power of the positive sequence network of is known.

In this paper, the sequence components three-phase power flow algorithm and power system model in [9] are used for developing grid-connected PV model. The new class library to model PV DG have been add in object oriented power system model [9,10] using C++ programming.

TABLE 1. PHOTOVOLTAIC DG MODEL

Photovoltaic Model

Mathematical Model c

Model 1 Single-diode PV model including/without Rs and Rp

I Calculate from :

)(,, 10 −−= akTqV

cellcellpv eIII watts or

)()(

SP

IRVkTq

PV RIVR

eIIIS

+−⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

+ 110

P obtain from V*I for given V V is specified

Model 2 Single-diode PV/ Maximum power output model

Ipv Calculate from : 1 1 ln

a= 1+ln(Iph/I0); b= a/(a+1); P obtain from Vpv*Ipv

Model 3 Single-phase PV

PV model as real Power injection P = Pl-Ppv.

Model 4 I–V curve database

P obtain from VI Curve for given V V is specified

Model 5 (PQ bus)

Ipv and I0 calculate from: ∆∆ / 1

, ∆

)()(

SP

IRVkTq

PV RIVR

eIIIS

+−⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

+ 110

P obtain from Vpv*Ipv

For grid-connected PV DG, the specified voltage and power can be calculated using mathematical model as shown in Table 1. By knowing of injected power, the PV DG can modeled as complex power injection bus or PQ model with Q limit.

IV. DESCRIPTION OF THE TEST SYSTEM The modified IEEE 13 node test feeder Fig. 3 used for PV

DG test cases. The cases presented PV DG model as PQ node. A PV DG with five different model shows as in Table 1 connected at new node 672 via step down transformer with connected to node 671 of original node and original node 634.

This IEEE 13 node [14] used to validate the improved algorithm for analyzing grid-connected different PV models.

The solution of the IEEE 13 node is compared with the

Figure. 3 IEEE 13 node test feeder with PV connected

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solution calculated using the radial distribution analysis program (RDAP) .

V. RESULTS First test is carried out to validate the improved generator

model in three-phase distribution load flow with RDAP software [15]. The loads are the same as the original data except that the distributed load is removed. This is for the sake of comparison between proposed method and the RDAP as the distributed load is modeled differently in the two methods. In this test, the IEEE 13 node is solved using sequence three-phase power flow algorithm and the RDAP software. The solution of the IEEE 13 node feeder is given in Table 2. The result from the developed program closely match with RDAP result without PV DG grid-connected as shown in Table 2 for Colum 2 and 3. The other Colum shows that PV DG connected have improved voltage profile of IEEE 13 node system. The PV DG sizes also give effect on voltage improvement. However, for single-phase PV DG model does not always guarantee voltage improvement such as for phase b of using model 3 have been decreased as shown in Fig.3 for phase b. The dummy nodes have voltages equal to the upstream nodes voltage since the current flow through the dummy lines is zero for all phases in the program. The missing phase in unbalanced lateral showed empty in the result of Table 2 and Fig. 3, because no actual voltage node available here.

TABLE 2 THREE PHASE VOLTAGE PROFILE

Node RDAP

Without PV DG

Without PV DG Model 1 Model 2 Model 3 Model 4

634 Ppv=0 Ppv=0 Ppv=876.2 Ppv=270 Ppv=240(A) Ppv=189

672 Ppv=0 Ppv=0 Ppv=442.9 Ppv=272 Ppv=0 Ppv=378

650 1 1 1 1 1 1 632 0.9559 0.9557 0.9647 0.9597 0.9644 0.96 633 0.9528 0.9524 0.9641 0.9573 0.9653 0.9573 634 0.9271 0.9267 0.9585 0.9381 0.9621 0.9362 645 - - - - - - 646 - - - - - - 671 0.9232 0.9226 0.9346 0.9285 0.9313 0.9294 672 0.9232 0.9226 0.944 0.9344 0.9313 0.9375 680 0.9232 0.9226 0.9346 0.9285 0.9313 0.9294 684 0.9214 0.9209 0.9329 0.9267 0.9295 0.9277 611 - - - - - - 652 0.9154 0.915 0.9269 0.9208 0.9236 0.9217 692 0.9232 0.9226 0.9346 0.9285 0.9313 0.9294 675 0.9161 0.9154 0.9276 0.9214 0.9242 0.9223

The system losses are evaluated without and with PV

models connected. The effect of proposed PV DG model on line losses is given in Table 3 for all cases. The result shows that the losses are reduced when the total size of PV DG increased from 240 kW to 1319.1 kW. Therefore, the PV DG size give more effect in network loss reduction.

.

Figure 3. Three-phase voltage profile for 13 node test feeder.

TABLE 3 SYSTEM LOOSES

PV Models Ppv (kW)

Losses (kW)

Without PV 0 119.6 Model 1 1319.1 82.32 Model 2 542 94.79 Model 3 240 109.18 Model 4 567 94.54

The simulation results presented that the integration of PV DG into an existing distribution network can improve the voltage profile as well as reduces the total system losses. Among the PV DG models, model 1 which act as PQ node have better performance relate to voltage profile and loss reduction. However, for single-phase PV DG model does not always have a voltage improvement.

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VI. CONCLUSION The paper has presented grid-connected PV DG model as

three-phase source for three-phase distribution load flow and analyzed their effect when they are connected in distribution networks. In this paper, the PV DG was modeled as PQ node with Q limit and as PQ node with have five different type of P calculation. The model was tested and analyzed using a 13 node IEEE distribution feeder. The simulation results show that the integration of grid-connected PV into an existing distribution network can improve the voltage profile as well as reduces the total system losses. However, for single-phase PV DG model does not always guarantee voltage improvement.

REFERENCES [1] Marcelo Gradella Villalva, Jonas Rafael Gazoli, and Ernesto Ruppert

Filho, "Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays',IEEE Transaction on Power Electronic, Vol. 24, No. 5, May 2009

[2] Renewable Energy Policy Network for the 21st Century, “Renewables Global Status Report 2009 Update”, REN21, 2009

[3] Zekai Sen, Solar energy in progress and future research trends, Progress in Energy and Combustion Science, Volume 30, Issue 4, 2004, Pages 367-416

[4] D. Das, R Esmaili, L. Xu, and D Nichols,” An Optimal Design of a Grid Connected Hybrid Wind/Photovoltaic/Fuel Cell System for Distributed Energy Production”, 2005

[5] M. R. Patel,”Wind and Solar Power System”, CRC Press, Boca Raton, Florida, 1999

[6] S. Conti, and S. Raiti,” Probabilistic load flow using Monte Carlo

techniques for distribution networks with photovoltaic generators,” Journal of Solar Energy, February 2007

[7] Gay, C.F., Rumberg, J.E., Wilson, J.H., AM/PM-All-Day module performance measurements. In: Proceedings of the 16th IEEE Photovoltaic Specialists Conference, San Diego, CA, USA., 1982.

[8] Gagliano, S., Raiti, S., Tina, G., Hybrid solar/wind power system probabilistic modelling for long-term performance assessment. Journal of Solar Energy 80 (5), 578–588. 2006

[9] M. Abdel-Akher, K. M. Nor, and A. H. Abdul Rashid, “Improved Three-Phase Power-Flow Methods Using Sequence Components”, IEEE Transaction on Power System Vol.20, no 3, pp. 1389-1397, Aug 2005

[10] Syafii Ghazali, Khalid M Nor and Mamdouh Abdel-Akher “Parallel Sequence Decoupled Full Newton Raphson Three-Phase Power Flow”, IEEE International Conference TenCon, Singapore, Dec 2009.

[11] Syafii, K. M. Nor, and M. Abdel-Akher, “Analysis of Three Phase Distribution Networks with Distributed Generation”, Proc of IEEE International Power and Energy Conference (PECon), Malaysia, Dec 2008.

[12] M. Abdel-Akher, and K. M. Nor, Fault Analysis of Multiphase Distribution Systems Using Symmetrical Components, IEEE Transactions on Power Delivery, Vol 25, Oct 2010.

[13] K. M. Nor, H. Mokhlis, and T. A. Ghani, "Reusability techniques in load flow analysis computer program", IEEE Tran. on power system, vol. 19, no. 4, pp. 1754-1762, Nov. 2004

[14] W. H. Kersting, “Radial distribution test feeders”, PES winter meeting, vol. 2, no. 28, pp. 908-912, Jan. 28/Feb. 1, 2001: Available:http://ewh.ieee.org/soc/pes/dsacom/test feeders.html

[15] Radial Distribution Analysis Program (RDAP), which can be downloaded from http://www.zianet.com/whpower/

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