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Abstract-- With the deregulation of the electric power industry and the advancement of new technologies, the attention of the utilities has been drawn towards adapting Distributed Generation (DG) into their existing infrastructure. In this paper photovoltaic (PV) systems are modeled to study the effects of their interconnection in a distribution system. The system is a combination of the PV array, DC-DC boost converter with Maximum Power Point Tracking (MPPT) control and DC-AC inverter. With increasing penetration of PV, reverse power may flow on the grid which is associated with voltage rise that may lead to violation of various standards. The impact depends upon the size and location of the PV system. Studies are conducted on the real time data obtained from DTE Energy utility. Voltages of the feeder, two way flow of power and the voltage regulation under various levels of PV penetration are analyzed for an IEEE test system utilizing unbalanced power flow solution.

Index Terms— Distributed generation, Photovoltaic (PV) cells,

Grid connected PV systems, MPPT control, penetration, OpenDSS, Distribution Power flow.

I. INTRODUCTION he deployment of DG does bring ample technological and environmental benefits to the traditional distribution

networks. The appropriate sizing and placement of DG systems which generate power locally to fulfill consumer demands, helps to reduce power losses and avoid transmission and distribution system expansion. These systems connected to a distribution system have the potential to improve the system voltage stability and power quality. The environmental benefits include reduction of both carbon footprint and emission of pollutant gases. The connection of a DG to a distribution network is achieved through interfaces such as asynchronous generators and power electronic convertors. Among all the various DG technologies, solar photovoltaic are fastest growing. Their annual growth rate in the power market is estimated to be about 25-35% [1]. Until a few years back, PV were mainly used for off grid applications like rural electrification, water pumping and heating while most of the newly installed PV is used in the distribution grid. The increasing penetration of PV into the grid has given rise to potential problems relating to voltage regulation and stability

1Lane Department of Electrical Engineering and Computer Science, West

Virginia University, Morgantown, WV, 26505-6109 USA (email: Sarika.Khushalani-Solanki@mail.wvu.edu)

of the grid. To mitigate these problems, changes must be made to utility interface requirements and rate structures, to obtain the maximum benefit from these systems. Grid connected PV systems have the following typical characteristics [2].

1) The PV systems along with the inverter are connected in parallel to the grid and the load is served only when the grid is available. The energy produced by the PV system decreases the apparent load, excess energy flows into the grid.

2) The PV system usually produces power at unity power factor and the utility must undertake all the VAR requirements.

3) IEEE 1547 standards on DG interconnection with the grid require that there must be no direct communication or control between the inverter and the utility. Hence when the grid voltage/frequency deviates from the boundaries, the inverter must disconnect itself from the grid until normal conditions resume.

4) Grid connected PV systems have differential pricing schemes. For residential and small commercial systems, the interconnection is typically net-metered at a flat rate. For large commercial systems, time of use rates may apply with the cost of energy being higher during periods of peak demand.

5) Geographical factors influence the efficiency of grid connected PV systems by restricting the PV production to coincide with the times when it is most economical for the utilities to use.

6) A desirable feature for the PV systems is that efficient storage is designed, such that the system can operate independent of the grid.

Many previous works have investigated different aspects related to PV systems, including the energy production and economics [3] and [4]. Another widely addressed topic is that of power converter configurations for PV systems. References [5] and [6] provide comprehensive surveys on different single-phase and three-phase converter circuits for PV applications. In addition, a fair amount of the technical literature has dealt with the integration of PV systems into

Vaidyanath Ramachandran1, Student Member, IEEE, Sarika Khushalani Solanki1, Member, IEEE, and Jignesh Solanki1, Member, IEEE

Steady State Analysis of Three Phase Unbalanced Distribution Systems with Interconnection of

Photovoltaic Cells

T

978-1-61284-788-7/11/$26.00 ©2011 IEEE

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distribution networks. The majority of this body of the literature has focused on single-phase PV systems, with an emphasis on their harmonic interactions with the distribution networks [7] and [8]. The reverse power flow problem in a grid connected PV system causes a voltage rise on a power distribution line [9]–[11], in particular, in the case of intensive grid connection, voltage may exceed the upper tolerance limit at the point of common coupling (PCC). To analyze some of these aspects, a PV system is modeled and interfaced with a distribution circuit. In Section II, the photovoltaic system model is explained in detail. Section III analyses the power flow algorithm used for radial distribution systems with the inclusion of a distributed generator. In Section IV, real time data obtained from utility and its significant features are presented. Section V presents the study results and analyzes the impact of different PV penetration scenarios.

II. PHOTOVOLTAIC SYSTEM MODELING An individual PV module can be represented as a diode circuit [12], in conjunction with series and parallel resistances Rs and Rp respectively. PV cells have very distinctive V-I characteristics with respect to the change in the load impedance, solar irradiance and temperature.

Fig 1: PV cell circuit model Any increase in the solar insolation causes the short circuit current of the PV cell to increase, but it has very less impact on the open circuit voltage. However, an increase in the temperature leads to a small increase in the short circuit current and a small decrease in the open circuit voltage. Fig.1 shows the equivalent circuit model for a single PV cell. Mathematically, the current and voltage characteristics for the PV module are expressed by the equations (1), (2) and (3).

0=−−− PVP

DDSC I

RVII (1)

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−= 1* T

D

OD VV

eII (2)

PVSDPV IRVV *−= (3)

Fig 2(a): Schematic of Grid connected PV system Fig 2(b): DC-DC Boost Converter Model; 2(c): DC-AC Inverter Model

A schematic of a grid connected PV system is shown in the Fig.2 (a). The PV system is a combination of many PV modules that are connected in series and parallel (by wiring them together) to obtain a suitable power point rating. Vpv is the DC output voltage of the PV system which is then boosted and converted to AC voltage by the inverter. To achieve the highest efficiency a Maximum Power point Tracking (MPPT) system is implemented [13]. This tracking system adjusts the inverter reference signal and thereby the DC voltage at the output of the solar array. A good MPPT technique must make a tradeoff between cost and efficiency. Some of the techniques used are the open circuit voltage method, the incremental conductance method, the ripple-based method and the perturbation and observation (P&O) technique. The technique used in this paper is based on (P&O) algorithm, where at each cycle the voltage and current of the PV array are measured and the output power is compared with the value obtained in the previous cycle. The feedback from the MPPT controller adjusts the value of voltage accordingly. To boost the value of the voltage fed into the inverter, a DC – DC boost converter is used as shown in Fig. 2(b). The voltage conversion ratio of the boost converter is given by Equation (4), where D is the duty cycle. The boost converter in this paper is assumed to be lossless and hence it works as an ideal DC-DC transformer whose step ratio is electronically adjustable by changing the duty cycle.

DVVDM

G

OUT

−==

11)( (4)

The output of the inverter depends upon the solar irradiance and is affected by the temperature of the cells. The DC - AC inverter model used is shown in Fig. 2(c). The inverter operates as an AC current-controlled voltage source inverter which is synchronized with the phase of the line voltage automatically through a current-controlling reference signal that is synchronized with the line. This technique allows the

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inverter to control its power factor, real power, and reactive power. The inverter adjusts its reactive power to the line reactive power or reactive current demand signal. Real and reactive power accuracy is controlled to within +/-2% of the rated demand. If the voltage or frequency (or both) of the line strays from its specified range, the inverter stops and disconnects itself from the line and the PV arrays. The typical inverter efficiency range [14] is between 90-95% and depends on the power levels in the circuit. At lower power levels, the efficiency drops due to switching and other fixed losses while at higher power levels, conduction losses dominate. The grid connected PV system model as described above was incorporated in MATLAB and the parameters used for simulation of PV system are as shown in Table 1. These parameters are measured for the solar panel at standard test conditions of 1 KW/m2 at 25 ° C, and ASTM E-892 spectral irradiance standards [15]. The V-I and P-V relations obtained from the PV model are highly nonlinear and depend on the solar irradiance incident on the PV array as shown in Fig. 3(a) and Fig. 3(b) respectively.

TABLE I TYPICAL DATA SHEET PARAMETERS

Parameter Value

Short Circuit Current (ISC) 5.45 A Open Circuit Voltage (VOC) 22.2 V Rated Current at MPP (IR) 4.95 A Rated Voltage at MPP(VR) 17.2 V

Thermal Voltage (VT) 0.026 V

Fig. 3 (a): V-I characteristics for Insolation ranging from 0.25 KW/m2 to 1 KW/m2 ; (b): P-V characteristics for Insolation ranging from 0.25 KW/m2 to 1 KW/m2

III. POWER FLOW IN RADIAL SYSTEMS WITH DG A distribution system typically has a radial topological structure which means that its analysis is unlike that of a transmission system. The lines in a distribution network have higher (R/X) ratios. This makes the distribution system ill- conditioned and hence the fast decoupled Newton method is not suitable for power flow solutions. The constant power demand assumption does not hold good for a distribution system because the system bus voltages are not constant. Hence the load flow algorithm becomes non-linear and iterative methods must be employed for solving it [16]. Steady state voltages at all buses in the system, real and reactive power flows in cables, transformers and loads, power losses and reactive power generated or absorbed constitute the results of the load flow algorithm. In this paper OpenDSS is used to obtain the power flow solution. OpenDSS is a comprehensive

electrical power system tool for electric utility distribution systems developed by EPRI [17]. The applications of OpenDSS include distribution planning and analysis, general multiphase AC circuit analysis, distributed generation interconnection analysis, annual load and generation profiles. Power flows can be performed in various modes, including a snapshot in time, daily and yearly power flow. OpenDSS provides many new analysis modes to meet future needs related to grid modernization efforts. Apart from performing load flow, advanced load models and distributed energy resources can be designed and managed in OpenDSS and calculations can be performed over an entire year to evaluate reduced losses and demand response. OpenDSS can run as a standalone platform and the solution engine can be implemented from an in process COM server to be driven from other software interfaces. Dynamically Linked Libraries (DLLs) can be defined for user developed models that plug into the OpenDSS program. One of the most commonly used models [18] for a power electronic based DG like a PV system is the constant power factor model. This paper utilizes the trigger angles of the power electronic circuitry to control the output reactive power. The specified values include real power output and the power factor of the generator at the node connecting PV system to a distribution grid. Based on the solar irradiance the real power output of the solar panel changes continuously, while the MPPT control strives to extract maximum power from the PV system. The necessary steps for incorporating the DG into the power flow are given below.

1) With the specified real power and power factor and the reactive power initialized to zero, a load flow is run.

2) The MPPT control as discussed in Section II, is used to keep the PV system at maximum power. The output power from the PV system is compared with the internal power reference of the controller. This power difference when divided by the terminal voltage of the inverter AC side produces the real current demand.

3) Reactive power control as discussed in Section II is used to maintain the voltage a constant. The output voltage of the PV with the system is compared with the grid voltage. The inverter control algorithm generates a resulting error signal which is used to produce the reactive power demand. This demand may be limited due to the internal presence of a hard limiter in the inverter.

4) If the load flow has converged, a check is performed to verify that the voltage magnitude mismatch at the generator node is below a specified tolerance.

ε<Δ−Δ=Δ calculatedispecifiedii VVV ,, (5)

5) If the voltage mismatch lies between the specified tolerances, the node voltage has converged to the specified value. If not, then the reactive power compensation necessary to maintain the specified voltage must be calculated, and added to the original compensation (if any) at the generator node.

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IV. DATA ANALYSIS Real time data for this study is obtained from the DTE Solar Currents #2 PV facility in Southfield, Michigan and the PV facility in Southern California (Fountain Valley # 1). The voluminous amount of data for the past few years is segregated, and parameters of interest namely average insolation in (kWh/m2) and the System efficiency (%) are calculated, and they are represented in Fig. 7 and Fig. 8 respectively. The monthly average insolation is calculated based on the daily insolation data. The system efficiency is calculated as the ratio of effective power output to the insolation received. It is noticed that the insolation patterns remain similar over the years, but vary with geographic locations. The system efficiency over the years is noticed to follow the same pattern, except for a slight decline in some cases. The system efficiency depends on a lot of factors like inverter operation and efficiency. Also, the efficiency calculations may be incorrect due to estimated insolation values from erroneous readings in the data logger.

Fig 7: Trends of Insolation and System Efficiency at the Fountain Valley California Site

Fig 8: Trends of Insolation and System Efficiency at the Southfield, Michigan Site

V. TEST RESULTS The IEEE 13 node feeder, shown in Fig. 9 is chosen to conduct the simulation study [19]. Based on the insolation trends over the years from the data above, typical insolation profiles are created and the peak insolation of 7kW/m2 is chosen for varying PV penetration levels from 10 % to 50 %.

646 645 632 633 634

650

692 675611 684

652

671

680PV System

Fig 9: IEEE 13 node feeder

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Table II shows the power flow results for system with 10 percent PV penetration. The PV system is connected to load end of the feeder at node 680. The PV output corresponds to 320 kW at an insolation level of 7 kW/m2. At this insolation level, each individual module produces a maximum power of 105 W as per our design specifications. Hence to achieve a power output of 320 kW, 3045 individual PV modules are necessary. Similarly, the penetration levels of the PV are increased to 1600 kW corresponding to 50 % penetration.

TABLE II

POWER FLOW RESULTS FOR THE IEEE 13 NODE FEEDERS WITH 10 % PV PENETRATION

Bus Va

(kV) Ang. (deg)

Vb (kV)

Ang. (deg)

Vc (kV)

Ang. (deg)

Base KV

Source 66.388 30 66.389 -90 66.38 150 115

650 2.4014 0 2.4015 -120 2.401 120 4.16

RG 60 2.5212 0 2.4914 -120 2.521 120 4.16

633 2.4373 -2.3 2.4367 -120.7 2.417 118.3 0.48

634 0.2745 -3 0.2759 -121.2 0.273 117.8 4.16

671 2.3857 -4.6 2.4447 -120.3 2.342 117.1 4.16

645 2.4194 -120.8 2.418 118.3 4.16

646 2.4153 -120.9 2.413 118.4 4.16

692 2.3857 -4.6 2.4447 -120.3 2.342 117.1 4.16

675 2.3703 -4.8 2.4501 -120.5 2.338 117.1 4.16

611 2.333 116.9 4.16

652 2.3676 -4.5 4.16

670 2.4258 -3 2.4404 -120.5 2.393 117.8 4.16

632 2.4445 -2.3 2.4418 -120.7 2.423 118.3 4.16

680 2.3899 -4.3 2.4502 -120 2.344 117.4 4.16

684 2.3811 -4.6 2.338 117 4.16 The following Fig. 10(a), 10(b) and 10(c) represent the variations of voltages from the substation to the feeder at varying PV penetrations. It can be noticed from the graphs that the tail end of the regulation zone of the feeder is forced to a higher voltage due to a large PV system located near the end of the feeder.

Fig 10 (a): Variation of Phase A voltages from substation to the end of the feeder with varying levels of PV penetration

Fig 10 (b): Variation of Phase B voltages from substation to the end of the feeder with varying levels of PV penetration

Fig 10(c): Variation of Phase C voltages from substation to the end of the

feeder with varying levels of PV penetration

VI. CONCLUSIONS The high penetration of PV into the system throws up

some interesting implications for the utilities. − Larger power flow into a distribution system, (which

is designed for one way power flow) may impact system regulation and protection. One of the major factors affecting voltage regulation is the reverse power flow. Since a significant amount of power is introduced at the lower end of the radial line, the line loading appears low to the voltage regulator which implies that the tap settings under the current scenario become irrelevant with the penetration of PV.

− The injection of power downstream from a fuse will not be detected because the traditional fuses are not designed with those capabilities. The larger the number of PV with inverters in the system, the greater the chances of islanding during which the PV continues to supply local loads after a utility fault. If the detection of islanding by the protection relays is not proper, then the inverters may remain on-line and pose serious threats to the equipment and to personnel.

− If the utility has sagging voltage levels due to the high demand conditions, inverters must be disconnected. Since the loads remain on-line, the utility may see an increase in demand, aggravating the chances of a blackout.

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Significant efforts are required in terms of mitigating these effects for the successful integration of PV to the grid. One of the key conclusions is that the DG assets must be coordinated with the utility to enhance the performance of the distribution grid. As the levels of PV penetration rise in the distribution grid, the DG interconnection requirements must be tailored to allow the utilities to maximize the performance from these inherent assets. As a future work, the authors will study the performance of PV systems with storage capabilities and the interaction of PV systems with other DG’s in the grid for an efficient demand dispatch.

VII. ACKNOWLEDGEMENTS The authors gratefully acknowledge the contributions of

Ganesh Ananthasubramaniam and Haukur Asgeirsson at DTE Energy and for providing real time data from their PV systems and their valuable inputs in this regard. The authors would also like to thank Roger Dugan, EPRI for providing a training workshop on OpenDSS software.

VIII. REFERENCES [1] Y.Liu, J. Bebic, B. Kroposki, J. de Bedout and W. Ren,

“Distribution System Voltage Performance Analysis for High-Penetration PV,” IEEE Energy 2030 Conference, Nov, 2008.

[2] “Solar Energy Grid Integration Systems”, US Department of Energy, Energy efficiency and Renewable Energy, Sandia National laboratories, Oct 2007.

[3] J. J. Bzura, “The New England electric photovoltaic systems research and demonstration project,” IEEE Trans. Energy Convers., vol. 5, no.2, pp. 284–289, Jun. 1990.

[4] I. Abouzahr and R. Ramakumar, “An approach to assess the performance of utility-interactive photovoltaic systems,” IEEE Trans. Energy Convers., vol. 8, no. 2, pp. 145–153, Jun. 1993.

[5] H. Haeberlin, “Evolution of inverters for grid connected PV systems from 1989 to 2000,” in Proc. Photovoltaic Solar Energy Conf., 2001, pp. 426–430.

[6] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galvan, R. C. P. Guisado, M. A. M. Prats, J. I. Leon, and N. Moreno-Alfonso, “Power electronic systems for the grid integration of renewable energy sources: A survey,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1002–1016, Aug. 2006.

[7] J. H. R. Enslin and P. J. M. Heskes, “Harmonic interaction between a large number of distributed power inverters and the distribution network,” IEEE Trans. Power Electron., vol. 19, no. 6, pp. 1586–1593, Nov. 2004.

[8] M. C. Benhabib, J. M. A. Myrzik, and J. L. Duarte, “Harmonic effects caused by large scale PV installations in LV network,” presented at the Int. Conf. Electrical Power Quality and Utilization, Barcelona, Spain, Oct. 2007, 6 pages.

[9] G. R. Oapos and M. A. Redfern, “Voltage control problems on modern distribution systems,” in Proc. IEEE Power Eng. Soc. Gen. Meeting, Jun. 6–10, 2004, vol. 1, pp. 662–667.

[10] H. Laukamp, M. Thoma, T. Meyer, and T. Erge, “Impact of a large capacity of distributed PV production on the

low voltage grid,” in Proc. 19th Eur. Photovoltaic. Sol. Energy Conf., Jun. 2004, pp. 2808–2812.

[11] A. Woyte, V. V. Thong, R. Belmans, and J. Nijs, “Voltage fluctuations on distribution level introduced by photovoltaic systems,” IEEE Trans. Energy Convers., vol. 21, no. 1, pp. 202–209, Mar. 2006.

[12] “PV Module/ Simulink Models”, ECEN 2060, University of Colorado at Boulder, Spring 2008.

[13] Yun Tiam Tan, Daniel S. Kirschen and Nicholas Jenkins, “A model of PV generation suitable for stability analysis”, IEEE Transactions on Energy Conversion, Dec. 2004.

[14] R.W.Erickson and D.Maksimovic, “Fundamentals of Power Electronics”, 2nd ed., Springer 2000,

[15] Felix A. Farret and M. Godoy Simoes, “Integration of Alternative Sources of Energy”, John Wiley and sons, 2006.

[16] S. Khushalani and N. Schulz, “Unbalanced Distribution Power Flow with Distributed Generation”, IEEE PES, Transmission and Distribution Conference and Exhibition, 2005/2006

[17] Open DSS Manual, Electric Power Research Institute, Jul 2010.

[18] Jen-Hao Teng, “Integration of distributed generators into distribution three-phase load flow analysis”, IEEE Power Tech, Russia, Jun 2005.

[19] Radial Distribution Test Feeders, http://www.ewh.ieee.org/soc/pes/dsacom/testfeeders.html.

IX. BIOGRAPHIES Vaidyanath Ramachandran graduated from SASTRA University, India, with Bachelors in Electrical and Electronics Engineering. He was involved in a research team on Fuel cells at Fachhoschule Sudwestphalen, Soest, Germany. Currently, he is working towards his Masters in Electrical Engineering at West Virginia University, Morgantown, USA. His research interests include Smart Grids, Computer Applications to Power System Analysis, Distribution System Automation and Distributed Generation.

Sarika Khushalani Solanki received B.E. from Nagpur University, India and M.E. degree from Mumbai University, India in 1998 and 2000 respectively. She received the Ph.D. degree in Electrical and Computer Engineering from Mississippi State University, USA in 2006. She was involved in research activities at IIT Bombay, India. She is currently an Assistant Professor in Lane Department of Computer Science and Electrical Engineering at West Virginia University, Morgantown, WV, since August 2009. Prior to that, she worked for Open Systems International Inc, Minneapolis, MN as a Senior Engineer for three years. Her research interests are Smart Grid, computer applications in power system analysis and power system control. She is a Honda Fellowship Award recipient at MSU as well as student poster competition award recipient in 13th Intelligent Systems Application in Power Conference, 2005 and IEEE PES Transmission and Distribution Conference and Exposition, 2006. Jignesh Solanki received B.E. from V.N.I.T, Nagpur, India and M.E. degree from Mumbai University, India in 1998 and

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2000 respectively. He received the Ph.D. degree in Electrical and Computer Engineering from Mississippi State University, USA in 2006. He was involved in research activities at IIT Bombay, India. He has been Research Assistant Professor in Lane Department of Computer Science and Electrical Engineering at West Virginia University, Morgantown, WV, since August 2009. Prior to that, he worked for Open Systems International Inc, Minneapolis, MN as a Senior Engineer for three years. His research interests are smart grid, multi-agent applications in power system and power system control. He received IEEE multi-agent systems working group award in 2008 and is a member of IEEE since 2002.