This paper deals with the modified modeling of PV system based on the PSCAD/EMTDC and optimal control method of customer voltages in real distribution system interconnected with the photovoltaic (PV) systems. In order to analyze voltage variation characteristics, the specific modeling of PV system which contains the theory of dq transformation, currentcontrol algorithm and sinusoidal PWM method is being required. However, the conventional modeling of PV system can only perform the modeling of smallscale active power of less than 60 [kW]. Therefore, this paper presents a modified modeling that can perform the largescale active power of more than 1 [MW]. And also, this paper proposes the optimal operation method of step voltage regulator (SVR) in order to solve the voltage variation problem when the PV systems are interconnected with the distribution feeders. From the simulation results, it is confirmed that this paper is effective tool for voltage analysis in distribution system with PV systems.
1. Introduction
As power systems have been deregulated and decentralized according to the technology development of smallscale distributed generators, PV systems have been actively interconnected and operated in distribution systems. Therefore, many power quality problems such as voltage variations, flicker and harmonic may be occurred, when PV systems are interconnected in distribution system
[1

6]
. In order to analyze power quality problems like voltage variation characteristics, a specific modeling of PV system considering the theory of dq transformation, currentcontrol algorithm and sinusoidal PWM method is being required. However, the conventional modeling method of PV system can only deal with the modeling of smallscale active power of less than 60[kW]
[7

8]
. Therefore, this paper presents a modified modeling that can perform the largescale active power of more than 1[MW]. In additions, this paper proposes the optimal operation method of the step voltage regulator(SVR) which is located at primary feeder for line voltage control, in order to overcome the voltage variation problem when PV systems are interconnected in distribution system. The case study results show that this paper is effective tool for voltage analysis and regulation in real distribution system interconnected with PV systems.
2. Modeling for real distribution system
 2.1 Distribution system modeling
A single line diagram of real distribution system as depicted in
Fig. 1
is usually being used in power utilities, in order to analyze voltage characteristics of low voltage customers. To simplify the complex diagram, this paper divides 6 sections by major points such as circuit breakers, cable size, cable length and branch configurations. And it is assumed that the PV system is located at the end section of real distribution system.
Single line diagram of distribution system with PV system
Therefore, the simplified diagram as shown in
Fig. 2
can be obtained from the real distribution system.
Simplified diagram of distribution system
In order to perform the load modeling of single line diagram, the real values of each section can be obtained from the relationship between estimation value and measured value as follows.
Where,
I
_{(n)}
and
i
_{(n)}
are the real and estimated currents of n section,
I
_{(SS)}
is the measured (real) total current of the main transformer, and
i
_{(SUM)}
is the estimated total current of main transformer.
 2.2 Concept of SVR operation method
This paper adapts a SVR which is installed at primary feeder to compensate the voltage variations.
Fig. 3
is the configuration of LDC method of SVR. The decision problem of optimal sending voltages is to find the optimal setting values (
V_{ce}
,
Z_{eq}
) of LDC method in order to deliver suitable voltages to as many customers as possible as shown in reference
[4]
. It firstly determines the ideal optimal sending voltages which can be expressed by the optimal compensation rates of SVR, and then obtains optimal setting values by statistical analysis according to the relationship between ideal optimal sending voltages and total load currents.
Concepts for LDC methods
Optimal sending voltages have a general relationship with LDC setting values as shown in Eq. (2). Therefore, the optimal setting values can be calculated by solving the equation for
V_{ce}
and
Z_{eq}
.
where,
V_{semd}
is optimal sending voltage,
V_{ce}
is load center voltage,
Z_{eq}
is equivalent impedance, and
I_{bank}
is total load currents of main transformer.
Solving the equation for
V_{ce}
and
Z_{eq}
in Eq. (2) cannot provide a linear function and has wide distribution characteristic as depicted in
Fig. 4
. Therefore, the solution of optimal LDC setting values is equivalent to finding coefficients of the first order equation of Eq. (2). It is desirable to minimize the differences between optimal sending voltages and the first order equation. The Least Square method is now introduced in order to find optimal LDC setting values. The squared summation of differences is formulated as:
Distribution characteristics of optimal sending voltages of M.tr
where, q is error function and T is total number of time interval.
By minimizing q in Eq. (3),
V_{ce}
and
Z_{eq}
can be obtained as :
In additions, SVR with the ±10% voltage compensation ability are generally composed of 17 tap positions having the each interval of 1.25%. By considering the relationship between sending voltage and nominal voltage (13,200V, phase voltage), each tap position can be formulated by Eq. (6).
where,
T_{p}
is tap position,
V_{send}
is sending voltage,
V_{n}
is nominal voltage,
T_{s}
is reference tap number, and
T_{int}
is tap interval (1.25%).
3. PV Modeling Based on the PSCAD/EMTDC
 3.1 Concept for current control algorithm
The configuration of the control block diagram in PV systems can be generally expressed as depicted in
Fig. 5
. This paper categorizes 4 steps to simplify the diagram.
Control block diagram of PV system

[Step 1]The 3phase voltage and current of distribution system are converted into 2phase voltage and current of the dq stationary coordinate by using the dq transformation method. And then 2phase voltage and current are transformed into DC voltage and current of the dq synchronizing coordinate to easily control the desired voltage and current.

[Step 2]To obtain the reference value for desired current, the DC current of [Step 1] is controlled by the PI controller as shown in Eq. (7) and Eq. (8). In this process, the decoupling control of active and reactive power of PV system can be performed separately.

where,Vqefbis voltage of q axis,Vdefbis voltage of d axis,is PI controllerIqrefis the reference current,IqeandIdeare output current of invertor which is converted to q axis and d axis,ωLis internal reactance for feedforward Compensation, and Vmis instantaneous voltage of distribution system.

[Step 3]The DC voltage compensated by PI controller of [Step 2] is reversely converted into 3phase AC current and voltage by inverse dq transformation method, where PLL (Phase Locked Loop) circuit is used to synchronize the voltage of distribution system.

[Step 4]In order to control the 6 PWM signals, the converted 3phase AC voltage of [Step 3] is compared with the comparator with the triangle waveform. The IGBT (Insulated Gate Bipolar Transistor) devices are driven by the 6 PWM signals, and then the DC voltage and current of PV system can be converted into the AC voltage and current of distribution system.
Furthermore, instantaneous active power (P) and reactive power (Q) in balanced 3phase system can be expressed as shown in Eq. (9) with the concept of the dq axis variables. Because the
V_{q}
with synchronous speed (ω) in the dq coordinate method is equal to the magnitude of instantaneous voltage and
V_{d}
is zero, Eq. (10) can be obtained from Eq. (9).
Where,
V_{d}
,
V_{q}
are output voltages of daxis and qaxis,
I_{d}
,
I_{q}
are output currents of daxis and qaxis, and 
V
_{0}
 is the magnitude of instantaneous voltage.
Therefore, It is clear that the instantaneous active power (P) is proportional to the magnitude of instantaneous voltage (
V
_{0}
) and the current of qaxis (
I_{q}
) in same phase, and also that the instantaneous reactive power (Q) is proportional to the magnitude of instantaneous voltage (
V
_{0}
) and the current of daxis (
I_{d}
) with 90 degree phase difference.
 3.2 Modified modeling of PV system
The conventional modeling of PV system as shown in ref.
[7

8]
can only deal with the smallscale active power of less than 60 [kW]. To overcome this problem, this paper adapts the Eq. (11) and Eq. (12) to compensate the process which converts DC voltage of the PI controller into 3phase voltage. Specifically, V
_{d}
and V
_{q}
from the current control algorithm are transformed to 6 PWM signal in order to operate IGBT device and then 3phase voltage is obtained by dp coordinate method.
In other words, Eq. (11) and Eq. (12) which make each phase synchronize depending on magnitude variations of V
_{d}
and V
_{q}
, were introduced at current control algorithm and then these equations are compensated for the process of PI controller to control a desired current value of large scale active power.
Where, Ø is desired phase angle of grid and V
_{t}
is desired voltage of distribution system.
 3.3 Modified modeling based on the PSCAD/EMTDC
 3.3.1 dq transformation modeling
By using PSCAD / EMTDC, the dq transformation modeling to convert 3phase AC current into DC current is designed as shown in
Fig. 6
. Also, the inverse dq transformation modeling to convert DC voltage into 3phase AC voltage is implemented in
Fig. 7
.
Simulation of dq transformation
Modeling of dqabc transformation
 3.3.2 Current control algorithm modeling
By using PSCAD/EMTDC, the detailed current control algorithm modeling by using Eq. (7) to Eq. (8) is designed as shown in
Fig. 8
.
Modeling of current control algorithm
Reference current modeling
And then, the reference currents (
I_{qref}
,
I_{dref}
) modeling to obtain the desired active power and reactive power based on the Eq. (10) is implemented as shown in
Fig. 8
.
 3.3.3 Gridconnected inverter modeling
Fig. 10
is the modeling of gridconnected inverter to convert DC voltage into 3 phase AC voltage using the IGBT devices and the modeling for sinusoidal PWM to produce the 3phase AC sine waveform with 120 phase difference.
Modeling for gridconnected inverter
4. Modeling of SVR operation method
In order to determine optimal sending voltage, optimal setting values of LDC method should be calculated by the statistical analysis according to the relationship between ideal optimal sending voltages and total load currents as shown in Eq. (2). Based on the concept, the modeling of LDC method is implemented by PSCAD/EMTDC as shown in
Fig. 11
.
Modeling of LDC method
Using the tap changing concept of SVR in the Eq. (3), the tap control modeling with the bandwidth of 50% and time delay of 120 seconds is implemented as shown in
Fig. 12
, and also, the tap changing modeling is in
Fig. 13
. Where,
Fig. 13 (a)
is the modeling of tap up control and
Fig. 13 (b)
is the modeling of tap down control.
Tap Control modeling
Tap changing modeling
5. Case Studies
 5.1 Verification of PSCSD/EMTDC modeling
To control the desired active power and reactive power of PV system, it is critical to obtain the value of reference current at the PSCAD/EMTDC modeling. Based on the Eq. (10), the relationship between reference current and active and reactive power can be expressed by Eq. (13).
Where, I
_{ref−q}
and I
_{ref−d}
are reference current of daxis and qaxis, P and Q is desired active and reactive power, and
V_{d}
and
V_{q}
are output voltages of daxis and qaxis. .
 5.1.1 Characteristic of largescale active power
To obtain largescale active power of 1 [MW], the reference current ( I
_{ref−q}
) can be calculated by Eq. (13), where the qaxis power system voltage of
V_{q}
is assumed as 0.310[kV].
By performing the PSCAD/EMTDC simulation with the reference current, it is verified that the active power of 1 [MW] can be obtained as shown in
Fig. 14
.
Characteristic of 1MW active power
 5.1.2 Characteristic of largescale reactive power
To control the largescale reactive power of 1 [MVAR], the reference current ( I
_{ref−d}
) can be obtained by Eq. (13), where the daxis power system voltage of
V_{d}
is assumed as 0.102 [kV].
By performing the PSCAD/EMTDC simulation with the reference current, it is verified that the reactive power of 1 [MVAR] can be obtained as shown in
Fig. 15
.
Characteristic of 1MVAR reactive power
 5.2 Analysis of customer voltage variation
 5.2.1 Simulation conditions
Based on the model distribution system of
Fig. 1
, distribution parameter and section data of primary feeder are assumed as
Table 1
and
Table 2
, respectively. The turn ratio of pole transformer (P.tr) is considered as 13200V/230V and also voltage drops at the first and last customers of secondary feeder are considered as 2% and 8% of rated voltage (220V). Under these assumptions, the PSCAD/EMTDC modeling of distribution system interconnected with PV system can be expressed as shown in
Fig. 16
.
Distribution system parameter
Distribution system parameter
Section data of primary feeder
Section data of primary feeder
Modeling of distribution system with PV system
 5.2.2 Characteristics of customer voltage variation
With the most severe conditions, it is assumed that offpeak load, middle load and peak load of one primary feeder (D/L) are 1.5 [MW], 5 [MW], and 10 [MW], respectively.
Fig. 17
is the simulation results of primary voltage variation at each section based on the 13,200 [V] of phase voltage, when PV system is not interconnected.
Voltage variation of primary feeder without PV
Table 3
is the customer voltage characteristic of secondary feeder from section 1 to 6, which is calculated from the
Fig. 16
. During the offpeak load of 1.5 [MW], it is clear that the voltage variation of customers is very small and reasonable characteristics. And also, in the peak load of 10 [MW], the customer voltages have reasonable conditions. Therefore, when the PV system is not interconnected with distribution system, it is confirmed that all of customer voltages of each section can be maintained within the allowable limits (220[V]±6%).
Customer voltage variation without PV
Customer voltage variation without PV
However,
Fig. 18
is the voltage variation characteristics of primary feeder at each section when PV system of 3 [MW] is located at section 6. Compared to the
Fig. 17
, it is clear that the overvoltage phenomena at all of sections in primary feeder are occurred by the reverse power flow of PV system. And also, the overvoltage characteristic at the offpeak load of 1.5 [MW] is much bigger than the peak load of 10 [MW], because the reverse power flow of PV system at offpeak load can influence the bigger impact to distribution system than the peak load.
Voltage variation of primary feeder with PV system of 3 [MW]
From the
Fig. 18
, the customer voltage characteristic of secondary feeder from section 1 to 6 is obtained as shown in
Table 4
. It is clear that some customer voltages of section 6 at the offpeak load cannot be maintained within allowable limits with the overvoltage phenomena by the reverse power flow of PV system. Therefore, it is clearly expected that severe voltage quality problems may be occurred if the largescale PV system is located at the end section of primary feeder.
Customer voltage variation with PV system of 3 [MW]
Customer voltage variation with PV system of 3 [MW]
 5.2.3 Voltage compensation with SVR
In order to improve voltage quality problem like overvoltage phenomena from the installation of PV systems as mentioned earlier, this paper adopts that SVR to control the primary feeder is installed at the section 3. Among the various operation method of SVR, this paper shows the comparison result between fixed method and LDC method as shown in
Table 5
. Where, the fixed method is widely used in power utility in Korea, which is operated by fixed sending voltage of 13200[V] based on the phase voltage. It could have possibility of customer voltage problems for the rapid voltage variation. To overcome these problems, this paper presents LDC method which can control the sending voltage of SVR depending on the load variation. Compared to
Table 4
without SVR, it is clear that all of customer voltages can be maintained within the allowable limits according to the voltage control method (LDC method) of SVR. Therefore, it is confirmed that the operation of SVR can make the customer voltage of distribution system with PV system keep better voltage conditions.
Customer voltage conditions with SVR
Customer voltage conditions with SVR
6. Conclusions
This paper has proposed the modified modeling of PV system based on the PSCAD/EMTDC and optimal control method of customer voltages in real distribution system interconnected with the PV systems. The main results are summarized as follows.

(1) It is confirmed that the overvoltage phenomena in primary feeder is occurred by the reverse power flow of PV system. And also, the overvoltage phenomena at the offpeak load is much bigger than the peak load, because the reverse power flow of PV system at offpeak load can influence the bigger impact to distribution system than the peak load.

(2) When the PV system is interconnected with distribution system, some customer voltages cannot be maintained within allowable limits (220[V]±6%). Therefore, it is clear that severe voltage quality problems may be occurred if the largescale PV system is located at the end section of primary feeder.

(3) With the optimal control method of SVR, it is clear that all of customer voltages can be maintained within the allowable limits compared to customer voltages without SVR. Therefore, it is confirmed that the operation of SVR can is practical tool for the better voltage conditions in distribution system interconnected with PV system.
Acknowledgements
This work was supported by the Power Generation & Electricity Delivery Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20131020400720)
BIO
ByungKi Kim He received the B.S. degree and M.S. degree in Electrical Engineering from Korea University of Technology and Education, CheonAn, South Korea, in 2008 and 2012. And he is currently pursuing the Ph.D. degree at KOREATECH, CheonAn, South Korea. He is interested in renewable energy resources and new power distribution systems.
Sungsik Choi He received B.S degree in information and communication engineering from Korea University of Technology and education. And he is currently pursuing the M.S degree at KOREATECH, CheonAn, South Korea. He is interested in renewable energy resources.
YongPeel Wang He received the B.S., M.E. and Ph. D degree in Electrical Engineering from DongA University, Busan, South Korea, in 1992, 1994 and 1998, respectively. He was a postdoctoral fellow from 19992001 at Canterbury University, New Zealand and a lecturer from 20012008 at DongA university. He has been working as a Senior ReSearcher at Electrical Industry Research Institute of Korea since 2009. His research interests include operation of power distribution systems, HVDC power systems, electromagnetic transient, and power quality.
EungSang Kim He received the B.S. degree from Seoul Industrial University, Korea, in 1988 and the M.S. and Ph.D. degrees in Electrical Engineering from Soongsil University, Korea, in 1991 and 1997, respectively. Since 1991, he has been with the Department of Power Distribution System at the Korea Electric Research Institute (KERI), Korea, where he is currently a Principal Researcher and serves as a member of Smart Grid Project Planning committee in Korea. His interests are new and renewable energy system designs and developments of wind power, photovoltaic and fuel cell energy conversion systems.
DaeSeok Rho He received the B.S. degree and M.S. degree in Electrical Engineering from Korea University, Seoul, South Korea, in 1985 and 1987, respectively. He earned a Ph.D. degree in Electrical Engineering from Hokkaido University, Sapporo, Japan in 1997. He has been working as a professor at Korea University of Technology and Education since 1999. His research interests include operation of power distribution systems, dispersed storage and generation systems and power quality.
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