Impact of a Large Penetration of Photovoltaic Generation on Voltage Stability of Power System

Nguyen Hoang Viet a a Department of Electrical Engineering, The University of Tokyo, Bunkyo-ku, Tokyo, 113-8656, Japan

vietnguyen@syl.t.u-tokyo.ac.jp

Abstract — This paper focuses on the grid-connected photovoltaic (PV) systems and their impact on the voltage stability of the power system. The modeling of the PV systems for the voltage stability analysis is presented. The impact of a large penetration of PV generation on the voltage stability is examined through numerical simulations conducted on the IEEJ West 10-machine test system. Several of interesting aspects are presented and discussed.

Keywords — Photovoltaic (PV) generation, Renewable energy, PV system modeling, Distribution network, Voltage stability.

I. INTRODUCTION

In recent years, it can be witnessed a rapid development of renewable energy, e.g. wind power, photovoltaic (PV), etc. throughout the world. The main motivations behind this fast-growing development are the rising environmental concerns, i.e. greenhouse gas emission, and carbon footprint reduction, and the increase in the fuel cost used for the electricity production. For instance, by 2002, worldwide production of photovoltaic had approached 600 MW per year and increased by over 40% per year [1]. Japanese government also set out a target to install the PV systems of 53 GW by 2030. The PV modules can become a part of building whereas wind power and other types of renewable energy based generation cannot. Therefore, certain characteristics make the PV generation worthwhile to be considered in planning and operation of the electricity network.

The PV installation target set by the Japanese government led to a substantial increase of research and development works in the area of the PV systems in Japan. The research mainly examines the impact of a large penetration of the PV system on the system security and reliability. This paper is also a part of the previously mentioned research to examine the impact of a large penetration of PV generation on the voltage stability.

The voltage stability of a power system refers to its ability to properly maintain steady, acceptable voltage levels at all buses in the network at all times, even after being subjected to a disturbance or contingency. A power system may enter a condition of voltage instability when the system is subjected to a sudden increase in load demand or a change in operating conditions, or a disturbance (loss of generation, loss of major transformer,

etc.). The voltage stability phenomena may occur in both transmission systems and distribution systems. Therefore, it is necessary to analyze voltage stability for planning and operation of transmission and distribution systems, especially when the distributed generation such as PV system is rapidly developed all over the world.

In general, a PV system can either operate in stand-alone system or in grid-connected system. The stand-alone system must have some means of storing energy, which can be used later to supply the load during the periods of low or no power output. The storage unit is one of the technical components that needs the most development. There is a great need for the development of better battery management principles, adaptation of the existing battery technologies to the charging and discharging requirement in the PV system and the development of completely new and better suited storage units. For the grid-connected PV system, the inverter interfacing the PV system to power grid is the key to power quality, because it transforms the direct-current (DC) power produced by the PV array into alternating-current (AC) power that matches utility power requirements. If the system is affected by a large disturbance, protection scheme may cause the PV system to be suddenly disconnected or the inverters may be shut down because it cannot handle this perturbation. In this case, disconnecting a number of PV systems during the disturbance can impose a significant impact on voltage stability of the power system. Otherwise, although the PV system can ride through the disturbance, its output power mainly determined by inverter’s controller may not effective in helping the power generation to meet the demand. Therefore, it is important to carefully examine such impact.

This paper is organized in the following sequences. Section 2 describes a brief background on the PV system and presents the proposed modeling of the PV system for the short-term voltage stability analysis. Section 3 presents numerical examples, results and discussion carried out on the IEEJ West 10-machine test system. Finally, Section 4 concludes the paper.

II. GRID-CONNECTED PV SYSTEM

The section begins with a brief background on grid-connected PV system. Then it moves on to the proposed

modeling of the PV system for the short-term stability analysis.

A. Background

A grid-connected PV system delivers DC power to a power conditioning unit (PCU) that converts DC to AC and sends power to utility grid as depicted in Fig. 1. In PCU, the DC/DC converter is used for controlling DC power produced by the PV system to reach to maximum power point (MPP). The DC/AC inverter not only transforms the DC power into AC power that matches utility power requirements but also is used for the active and reactive power control in the system.

B. PV System Modeling

In the steady state, the amount of electric power generated by the PV system is always changing with weather conditions. Its characteristic will be shifted as insolation or PV cell temperature changes [2]. In this paper, the PV system for the short-term voltage stability analysis is developed with the assumption that environmental condition cannot change immediately. The PV system is composed of 2 main parts: DC/AC inverter with its control system and DC side of this inverter.

1. DC side of the inverter To get highest power efficiency from PV array, a device called maximum power point tracker (MPPT) is introduced to keep the operating point of PV generation near the knee of its I-V curve. A DC/DC converter which is capable of raising or lowering a DC voltage can be used as a heart of a MPPT. For a 100% efficient MPPT, changing the duty cycle D (0<D<1) of converter switches will redraw the I-V curves of PV [2]. These are described in Figs. 2 and 3.

On the assumption that MPPT operation responds to only environmental condition of the PV arrays, the I-V curve of PV will not be changed during the transient state. Therefore, using a given I-V curve, the output power Ppv from PV arrays is determined from the voltage Vdc_link of DC side. Value of Vdc_link not only impacts on Ppv but also decides the output voltage of the DC/AC inverter through its pulse width modulation (PWM) operation. From the block diagram of the inverter’s DC side shown in Fig. 4, the Vdc_link can be calculated on the assumption that Pdc = Pac due to using an inverter with a power conversion efficiency of 100%. It also easily incorporates the inverter efficiency into the model by multiplying the Pdc and Pac by appropriate efficiency coefficients.

2. DC/AC inverter PV system is usually controlled to keep both the active power and reactive power at the reference set points. Currently, PV systems are designed to operate at unity power factor because this condition will produce the most real power and energy. This limitation is a matter of agreement, not a technical one; many inverters have the capability of providing reactive power to the grid in addition to the active power generated by their PV arrays. The diagram of constant power controlled inverter is depicted in Fig. 5. In the figure, the power system parameters such as the currents and the voltages of the inverter’s AC side are measured, transformed into the dq0 frame and used for calculating the value of the power output of the inverter. This power is compared with the setting value in a power regulator to make a set of current references. These currents are inputted to an automatic current regulator (ACR). The output signals of ACR will control inverter operation.

By using the model in the rotating dq frame, the PV system modeling will be simplified [3]-[4]. The angle velocity ω of dq frame is chosen the same one of the terminal voltage of the inverter; as a result, the Vq of the

Fig. 1. Grid-connected PV system.

Fig. 2. Voltage and current of PV.

Fig. 3. I-V curves of PV.

Fig. 4. Block diagram of the inverter’s DC side.

PV terminal voltage becomes 0 and Vd equals to the terminal voltage magnitude. This transformation is shown in Fig. 6. The power supplied from the PV system to the grid can be achieved by controlling the inverter using the current reference signals,

d d q q d dP I V I V I V (1)

d q q d q dQ I V I V I V (2)

These equations are used for power regulator shown in Fig. 7 to determine the reference value Idref and Iqref of the current regulator input. The active and reactive power deviations from the reference set points are sent to the PI controllers. The outputs of these PI controllers are the reference current signals which are later inputted to the voltage source inverter.

From Fig. 5, it can be seen in the voltage source inverter that the reference currents are used for the inverter terminal voltage control. Fig. 8 shows an equivalent circuit connecting the inverter with the grid. The mathematical model of this circuit is given by,

abcabc abc

diL Ri v

dt (3)

where vabc = vabc - vG; vabc, vG are the terminal voltage of the inverter and the voltage of the grid; R and L are the resistance and inductance of the filter respectively.

By using rotating frame transformation, the way to control Id and Iq currents at the output terminal of the PV system is more simple [5]-[7]. The parameters of inverter can be expressed as,

1dq d q

i RL i i vdt L L

(4)

1qd q d

i RL i i vdt L L

(5)

To transform these equations to Laplace domain, the cross-coupling of d and q components using for automatic current regulator (ACR) is described in Fig. 9 implementing the derivative of

( )sL R j L I V (6)

where I = Id + Iq and V= Vd +j Vq

C. Disconnection of PV System

The PV system may have to be disconnected when its terminal voltage drops below the specified threshold voltage, e.g. 70% of the nominal voltage. This disconnection is mainly done to protect the inverter. However, it also impacts on the transient state of the power system. The capability of the PV system to ride through the faults is determined by low voltage ride through (LVRT) characteristic. The requirement of this LVRT varies from system to system depending on the grid code. The influence of LVRT characteristics of high-penetration PV generation on the transient stability is presented [8]. In this paper, LVRT1 as shown in Fig. 10

Fig. 5. Diagram of constant-power-controlled inverter.

Fig. 7. Modeling of power regulator.

Fig. 8. The inverter’s interface.

Fig. 9. Cross-coupling control of current regulator.

Fig. 6. Geometric interpretation of dq0 transformation.

is applied for the PV system. It can be seen that LVRT1 is relatively so strict that the impact of the PV disconnection on the system voltage stability can be manifested.

III. NUMERICAL EXAMPLE

A. Study System

The simulation is conducted on the IEEJ West 10-machine test system. The diagram is depicted in Fig. 11. The system has the total generation capacity of 110 GW. The total system demand is 107 GW. The lumped PV systems are installed at 6.6kV buses as shown in Fig. 11. Both of induction motor load and constant impedance load are connected to the system at 275kV and 66kV. Figure 12 describes the structure of an equivalent branch from 500kV to 6.6kV in the system.

To examine the impact of a large PV penetration on the

system voltage stability, 4 study cases are conducted as summarized in the following.

Case 1: 10.7 GW PV system is installed (accounting for 10% of the total system demand).

Case 2: 21.4 GW PV system is installed (accounting for 20% of the total system demand).

Case 3: 32.1 GW PV system is installed (accounting for 30% of the total system demand).

Case 4: 42.8 GW PV system is installed (accounting for 40% of the total system demand).

The disturbance here in this analysis is a three-phase to ground fault at a bus of the transmission network. The clearing time is varied depending on the purposes of each test.

B. The role of Vdc_link in Short-Term Voltage Stability

From the analysis in Section 2, it can be realized clearly that the Vdc_link value is very important in the operation of PV generation. Vdc_link changing represents interaction between AC side and DC side of the inverter. It is really necessary to consider the fluctuation of Vdc_link in analyzing transient state of the power system, especially for short-term voltage stability. Once a fault happens near by the PV system, the AC power Pac of the inverter will fluctuate, making Vdc_link change and react to the inverter terminal voltage by PWM operation.

Simulation results in Fig. 13 are the voltages of every

bus in the power system when a fault occurs at bus 2 and the clearing time is 0.07 sec. These two cases have the same generation and load condition: the total PV generation accounts for 10% of total system demand, every load includes induction motor at 80% and constant impedance at 20% of the total load. However, the difference is Vdc_link assumtion: in the first one, Vdc_link values are determined based on constitution of the inverter’s DC side; in the second one, Vdc_link is always kept at constant value during the fault.

Fig. 10. Low voltage ride through characteristics of PV.

Fig. 11. IEEJ West 10-machine system.

Fig. 12. Equivalent branch in IEEJ system.

0 5 10 15 20 25 30 35 400

0.2

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ltag

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Fig. 13. Power system voltage.

The figures show that Vdc_link change makes the power system voltages fluctuate more significantly. As a result, there are PV systems disconnected from the grid at ten buses in the second case whereas the other case has disconnected PV systems at six buses.

The simulation results indicated an important role of Vdc_link as well as the DC side modeling of the inverter of the PV generation in short-term voltage stability analysis.

C. The Influence of Load Characteristics on Short-Term Voltage Stability

Load dynamic response is a key mechanism of power system voltage stability driving the dynamic evolution of voltage and, in extreme case, leading to voltage collapse. Induction motor load is an important component in power system voltage stability assessment [9]. The influence of induction motor on short-term voltage stability has been focused by a lot of researchers for long time ago. However, rapid development of PV generation in distribution networks is making the power system change.

The responses of the power system should be different from conventional one before installing a large penetration of PV generation if the system has a disturbance.

The results shown in Fig. 14 are relative to 3 types of load models varying power percentage of induction motor(M) and constant impedance (Z):

Model 1 - M: 60%, Z: 40%. Model 2 - M: 80%, Z: 20%. Model 3 - M: 100%, Z: 0%. Under the same condition: the fault at bus 6 is cleared

after 0.05 sec and PV generation accounts for 30% of the total system demand, the fluctuation of power system voltage depends on the rate of induction motor in the grid. 100% load having induction motor characteristic can make the voltage collapse as seen from Fig. 14.

It seems that installing PV generation at distribution

network has not enhanced voltage stability in this case. It can be explained by control scheme of the inverter. Up to now, operation at unity power factor makes PV systems

0 5 10 15 20 25 30 35 400

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Fig. 14. Power system voltage.

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Fig. 15. Power system voltage.

generate maximum power output. However, capability to supply positive and negative reactive power of the inverter is an advantage and it is needed to be developed.

The simulation results in Fig. 15 show the different responses of the power system under the same disturbance condition. The fluctuation of the voltage is increased when larger PV penetration levels are installed. Losing a larger of power due to disconnecting a high penetration level of PV generation has significant impact not only on short-term voltage stability but also on transient stability. In some cases, it is difficult to determine that dynamic behavior of PV generation makes the power system lose transient stability or voltage stability. However, to improve LVRT as well as controller of the PV systems may solve the power system stability enhancement problem.

IV. CONCLUSION

This paper presents the modeling of the grid-connected PV system for the short-term voltage stability analysis. In modeling of the dynamic behavior of the PV system in the transient state, it is usually supposed that Vdc_link is constant. However, to analyze the short-term voltage stability, Vdc_link has a significant impact on the results that cannot be neglected. In addition, the penetration level and the LVRT characteristics of the PV system also influence the system voltage stability if a fault happens. A large penetration of PV generation operating at unity power factor can make the power stability critical under the disturbance condition. It is necessary to do research in detail on finding an appropriate low voltage ride through characteristic of the PV system, as well as control schemes to improve the power system stability under the complicated operating condition with dynamic induction motor load, battery energy storage system, etc.

ACKNOWLEDGEMENT

The author wishes to acknowledge the assistance and support of the preparing group for the student sessions of the SNU-UT Joint Seminar 2011.

REFERENCES

[1] Mukund R. Patel, Wind and Solar Power System, CRC Press, 1999.

[2] Gilbert M. Masters, Renewable and Efficient Electric Power Systems, John Wiley & Sons, 2004.

[3] P. Kundur, Power System Stability and Control, McGraw-Hill, 1994.

[4] Marian P. Kazmierkowski and Luigi Malesani, “Current Control Techniques for Three-Phase Voltage-Source PWM Converter: A Survey,” IEEE Trans. on Industrial Electronics, vol. 45, no. 5, pp. 691-703, 1998

[5] Jose R. Espinoza, Geza Joos and Luis Moran, “Decoupled Control of the Active and Reactive Power in Three-Phase PWM Rectifiers based on Non-Linear Control Strategies,” Proc. 30th Annual IEEE Power Electronics Specialists Conference, vol. 1, pp. 131-136, 1999.

[6] Jong-Woo Choi and Seung-Ki Sul, “Fast Current Controller in 3-Phase AC/DC Boost Converter Using d-q Axis Cross-Coupling,” Proc. 27th Annual IEEE Power Electronics Specialists Conference, vol. 1, pp. 177-182, 1996.

[7] D.N. Zmood, D.G. Holmes, G.H. Bode, “Frequency-Domain Analysis of Three-Phase Linear Current Regulators,” IEEE Trans. on Industry Applications, vol. 37, no. 2, pp. 601-610, 2001.

[8] Nguyen Hoang Viet and Akihiko Yokoyama, “Impact of fault ride-through characteristics of high-penetration photovoltaic generation on transient stability,” 2010 International Conference on Power System Technology, pp. 1-7, 2010.

[9] H.Ohtsuki, A.Yokoyama, Y.Sekine: “Verification and Expansion of Transient Analysis of Voltage Collapse Using Induction Motor Load Model,” Trans. of IEEJ, vol. 112-B, no. 8, pp. 677–684, 1992.