Abstract Keywords: Voltage stability, VMPI, generator output control, static capacitor control, photovoltaic powe

Atsushi Enomoto

Kimihiko Shimomura

Nobuyuki Ariyoshi

Satoshi Osaki

Shinichi Iwamoto

Shunsuke Aida

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International Journal of Smart Grid and Clean Energy  
 
 
Generator output and static capacitor control considering 
voltage stability for large penetration of photovoltaic power 
Atsushi Enomoto
a
, Shunsuke Aida
a*
, Shinichi Iwamoto
a 
Satoshi Osaki
b
, Nobuyuki Ariyoshi
b
, Kimihiko Shimomura
b
 
a WASEDA University, 3-4-1 Okubo Shinjuku-ku, Tokyo 169-8555, Japan 
b CHUBU Electric Power Company, Japan 
 
Abstract 
  
 
 
 
  
 
 
 
Keywords: Voltage stability, VMPI, generator output control, static capacitor control, photovoltaic power  
1. Introduction 
Since power system loads are located further away from power plants and have become more unevenly 
distributed in recent years, it has also become more difficult to maintain voltage stability in power 
systems. Therefore, proper voltage ranges are determined in order to prevent voltage instability and to 
protect power devices. In our previous studies of a voltage stability control scheme, we proposed a 
voltage stability index, the voltage margin proximity index (VMPI), that could easily yield the voltage 
stability margin [1], [2]. In the later stages of the study, to prevent voltage instability phenomena caused 
by contingency or voltage collapse caused by heavy loads, we proposed a static voltage stability 
preventive control scheme and an emergency voltage stability control scheme both based on VMPI [3]-
[5].  
Recently, however, clean energy such as photovoltaic power generation (PV) or wind power 
generation, is penetrating into the Japanese power system following the enforcement of the Renewable 
Portfolio Standard (RPS) law and the feed-in tariff (FIT) policy. If a large number of PV penetrates into 
the power system, voltage values increase, since load demand is decreased due to the active power 
outputs of the PV. Especially, for decreasing power demand in the spring (Japanese Golden Week) and 
summer (Japanese Religious Holidays), it is considered that the voltage rise will be remarkable. In this 
paper, we therefore focus our attention on the upper voltage limits for a large penetration of PV. We 
propose a smart generator output and static capacitor control for the large penetration of PV. For the 
generator output control we propose to use the optimal power flow in terms of minimizing bus voltage 
deviations from the prescribed values. In addition, if voltage value violates the voltage upper limit, we 
consider static capacitors as control equipment against high voltages, and propose a static capacitor 
 
* Manuscript received May 15, 2013; revised July 29, 2013. 
Corresponding author. Tel.: -5286-3184; E-mail address: iwamoto.lab.pwrs@gmail.com. +81 3
In Japan, the introduction of large capacity of clean energy such as PV (photovoltaic power generation) is planned to 
reduce environmental burdens. The Japanese government has set the target of 53 GW of PV by 2030. However, large 
penetration of PV will cause several problems in power systems. One of these problems is that voltage values 
increase with the amount of PV penetration. Thus, we focus our attention on the upper voltage limit for a large 
penetration of PV in terms of voltage stability. In this paper, we consider a smart generator output and static capacitor 
control for the large penetration of PV. For the generator output control we propose to use the optimal power flow in 
terms of minimizing bus voltage deviations from the prescribed values. Simulations are run using the IEEJ WEST 10-
machine O/V system model to confirm the validity of the proposed method.
58 International Journal of Smart Grid and Clean Energy, vol. 3, no. 1, January 2014 
control method by using VMPI. Simulations are run using IEEJ (the Institute of Electrical Engineers of 
Japan) WEST 10-machine O/V system model [6] to confirm the validity of the proposed method.  
generators, and that the power factor of the PV is constant at 1.0. In addition, we focus our attention on a 
static analysis of voltage stability, and thus dynamics are not considered here.  
2. Voltage Stability Index  
2.1. Voltage stability index VMPI 
VMPI is an index that evaluates the voltage margin from the operating point to the boundaries of the 
proper voltage range, especially the upper voltage limit. The concept behind VMPI is shown in Fig.1. 
VMPI is calculated based on the angle between vectors at the upper voltage limit (yU) and at the operating 
point (ys). VMPI is classified into two types; one based on the voltage space and the other on the specified 
space. In this paper, we use the latter, which is superior to the former in terms of its linearity. 
 
Fig. 1. Concept behind voltage stability index VMPI. 
 
The vector at the operating point is specified by the initial value: 
sy = [e  f  PGen  VGen
2  
 PLoad  QLoad  ]
T
.
  
(1) 
The specified value at the upper voltage limit is obtained by an optimal power flow (OPF) calculation 
using the following formulae. 
Objective function:  
Minimize f = kc  (2) 
Equality constraints: 
Generator buses   PGen = kc∙PGen, VGen =VGen, (3) 
Load buses          P Load = kc∙PLoad, QLoad=kc ∙QLoad (4) 
Slack bus             e = e,   f = f (5) 
Inequality constraints: 
Voltage limits                  Vmin < VLoad < Vmax  (6) 
Reactive power limits      QGen min < Q Gen < QGen max  (7) 
where 
e : real part of voltage kc : load multiplier  
f  :   imaginary part of voltage Vmin : lower voltage limit 
PGen : active power of generator Vmax : upper voltage limit  
VGen : voltage of generator  Qi : reactive power at generator i 
PLoad : active power of load QGen_min : lower reactive power limit of generator 
QLoad : reactive power of load QGen_max : upper reactive power limit of generator 
sU yy   
U 
y S 
y VMPI 
output control means control of only active power from In this paper, we assume that generator 
when it is within the proper voltage range,  point is the operating vector at The specified
 Atsushi Enomoto et al.:Generator output and static capacitor control considering voltage stability for large penetration…  59 
sU yy  VMPI 
follows: 
1
1
cos ,      
cos ,   
t
s U
U s
s U
t
s U
U s
s U
y y
y y
y y
VMPI
y y
y y
y y







 

 

  (8) 
2.2. VMPI sensitivity 
VMPI sensitivity VMPIs  of a voltage control device is represented by  
0VMPIIVMPVMPIs   (9) 
where VMPI
0
 is the value of VMPI before the switch and VMPI  is the value of VMPI after the switch. 
Fig. 2 shows VMPI variation, that is, VMPI sensitivity when the static capacitors (buses 6, 7 and 16) 
are controlled for the IEEJ WEST 10-machine O/V system model. In Fig. 3, it is established that the 
behaviour of VMPI is linearly dependent on the amount of control of the static capacitor. A similar 
linearity is also found when the other buses are controlled. Because there is linearity between VMPI and 
the control variable of the control devices, we can calculate the required control variables by using VMPI 
sensitivity. 
 
Fig. 2. VMPI sensitivity. 
 
Fig. 3. IEEJ WEST 10- machine O/V system model. 
G1 G10
G2 G3 G4 G5 G6 G7 G8 9
18 1
2 3 4 5 6 7 8
9
10 11 12 13 14 15 16 17
19 20 21 22 23 24 25 26
27
 
 
G1 G10
G2 G3 G4 G5 G6 G7 G8 G9
18 1
2 3 4 5 6 7 8
9
10 11 12 13 14 15 16 17
19 20 21 22 23 24 25 26
27
 
 
when  below  voltage limit. Using these properties, is defined as it fallsand is the upper
by switching one of the voltage control device units. VMPI sensitivity shows the variation obtained 
60 International Journal of Smart Grid and Clean Energy, vol. 3, no. 1, January 2014 
3. Relationship between VMPI and Penetration of PV 
relationship between VMPI and the penetration of PV in order to show the 
influence on the voltage stability when a large number of PV penetrate the power system model. We use 
the IEEJ WEST 10-machine O/V system model shown in Fig. 3 to run simulations. 
The assumptions of the simulations are as follows: 
1) PV is installed to all load buses, and the power output is proportional to each load demand. 
2) Reductions in the generator active power outputs are the same as the total power of the PV. 
3) The active power outputs are controlled for all generators, and reductions are proportional to each 
generator’s original active power output. 
In Fig. 4, when the installed PV a  [p.u.], VMPI is below zero, and it is confirmed that the 
voltage value deviates from the proper voltage range of 1.05 [p.u.]. 
 
Fig. 4. Variation in VMPI for increasing penetration of PV. 
4. Generator Output Control Method Regarding Each Load Bus Voltage (Proposed Method) 
As stated previously, if we do not control the static capacitors with respect to the voltage, then the 
voltage values deviate from the proper voltage range when the level of installed PV reaches about 13 
[p.u.]. Therefore, if a large number of PVs are to be installed in the power system, it is possible that the 
voltage values will deviate from the proper voltage range. Thus, in this section, a generator output control 
method is stated which uses VMPI for a large penetration of PV.  
In the previous section, the active power output reductions are proportional to each generator’s original 
active power output. However, this control method is not effective generator output control in terms of 
the voltage stability. Therefore, for the generator output control we propose to use the optimal power flow 
in terms of minimizing bus voltage deviations from the prescribed values.  
Formulation of minimizing bus voltage deviations OPF 
Objective function: 
Minimize function = Σ｜Vref  - VLoad｜ (10) 
Equality constraints: 
Generator buses   VGen =VGen (11) 
Load buses          P Load =PLoad , QLoad= QLoad (12) 
Slack bus             eSlack = eSlack,  fSlack = f Slack (13) 
Inequality constraints: 
Voltage limits                  Vmin < VLoad < Vmax (14) 
Active power limits         PGen min < PGen < PGen max (15) 
Reactive power limits      QGen min < Q Gen < QGen max (16) 
We demonstrate the 
re at about 13
 Atsushi Enomoto et al.:Generator output and static capacitor control considering voltage stability for large penetration…  61 
where 
Vref : reference voltage  Vmin : lower voltage limit 
VLoad : voltage at loads Vmax : upper voltage limit  
e : real part of voltage PGen : active power of generator 
f  :   imaginary part of voltage QGen : reactive power of generator 
PGen : active power of generator PGen_min : lower active power limit of generator 
VGen : voltage of generator  PGen_max : upper active power limit of generator 
PLoad : active power of load QGen_min : lower reactive power limit of generator 
QLoad : reactive power of load QGen_max : upper reactive power limit of generator 
Also, it is considered that the voltage value violates the voltage upper limit only using the generator 
output control. Therefore, we control the static capacitor if the voltage value deviates from the voltage 
upper limit. In this paper, the flowchart of PV penetration is shown in Fig. 5. At first, we install 1 [p.u.] 
PV and determine the generator output by calculating the OPF. Then, we measure the voltage value at 
each load bus. If any of the bus voltage values are above 1.03 [p.u.] (for example), we have to perform 
voltage control. If all the load bus voltage values are below 1.03 [p.u.], we can install PV up to 30 [p.u.], 
which is the target value. 
Fig. 6 shows a flowchart of static capacitor control. In Fig. 6, if any of the load bus voltage values are 
above 1.03 [p.u.], we calculate the VMPI sensitivity and make a bus number ranking in descending order 
of VMPI sensitivity. Finally, we reduce, by 0.05 [p.u.], the static capacitor installed at the bus with the 
highest ranking. 
 
                                 
Fig. 5. Flowchart of PV penetration.                                             Fig. 6. Flowchart of the static capacitors control. 
5. Simulation 
In this section, a simulation is run to confirm the validity of the proposed method. In this simulation, 
the IEEJ WEST 10-machine O/V system model is used.  
Assumptions in simulations are as follows. 
1) PV is installed at all load buses, and the power output is proportional to each load demand. 
2) The total generator active power outputs are equal to the total PV power outputs. 
3) All generators are controlled and the reductions are proportional to generator’s original active 
power outputs. 
4) Control devices are only the static capacitors installed at the load buses. 
62 International Journal of Smart Grid and Clean Energy, vol. 3, no. 1, January 2014 
Fig. 7 shows the relationship between VMPI and the penetration of PV when the proposed method are 
carried out and Fig. 8 shows the voltage value at each load bus after voltage control has been carried out 
when the installed PV are at 30 [p.u.]. 
If we do not control the voltage, PV can be installed only to a maximum of 13 [p.u.]. But, by using the 
proposed method, we can install PV up to 30 [p.u.], which is our target. And Fig. 7 and Fig. 8 show the 
voltage value at each load bus after voltage control has been carried out. It is confirmed that the load bus 
voltages are within the proper voltage range. 
Also, Table 1 shows the amount of each generator output control until 30 [p.u.] of PV are installed 
every 5 [p.u.]. Table 2 shows the static capacitors installed on each bus, which are used for voltage 
control until 30 [p.u.] of PV are installed. Method1 is that all generators are controlled and reductions are 
proportional to each generator’s original active power output. Method2 is that all generators are 
controlled by proposed method. It was confirmed that amount of the static capacitor control is less than 
the method1 when we determine the generator output using the proposed method.  
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
Penetration of PV[p.u.]
V
M
P
I[
d
eg
]
 
 Variation of VMPI for penetration of PV. 
0.97
0.98
0.99
1
1.01
1.02
1.03
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Load Bus No.
V
o
lt
a
g
e
s 
[p
.u
.]
 
 Voltage value after the control. 
Table 1. Amount of generator control 
Generator 5[p.u.] 10[p.u.] 15[p.u.] 20[p.u.] 25[p.u.] 30[p.u.] 
G1 -3.51  -3.51  -3.51  -3.51  -3.51  -3.51  
G2 -2.24  -2.24  -2.24  -2.24  -2.24  -2.21  
G3 1.24  -1.24  -2.34  -2.34  -2.34  -2.34  
G4 2.51  0.27  -1.67  -0.78  -0.05  -0.35  
G5 -2.20  -2.38  2.11  3.45  0.53  -2.16  
G6 3.96  3.04  1.96  1.26  -3.24  -1.04  
G7 -1.62  1.70  1.25  -1.06  -0.17  -2.26  
G8 -1.40  -1.40  -1.40  -1.40  -1.40  -1.40  
G9 3.67  -1.14  -1.85  -3.24  -3.24  -3.24  
G10 -5.20  -5.73  -7.02  -7.37  -9.12  -10.36  
Fig. 7.
Fig. 8.
 Atsushi Enomoto et al.:Generator output and static capacitor control considering voltage stability for large penetration…  63 
Table 2. Amount of static capacitor control 
Bus No. Initial value [p.u.] Amount of control [p.u.] (Method 1) Amount of control [p.u.] (Method 2) 
3 0.35 -0.10 -0.05 
4 0.35 -0.10 0.00 
5 0.35 -0.10 0.00 
6 0.4 -0.15 0.00 
7 0.65 -0.25 0.00 
8 0.4 -0.15 0.00 
9 3.5 -0.05 0.00 
16 0.3 -0.10 0.00 
6. Conclusion 
Recently, clean energy such as PV has attracted attention because of the threat posed by serious 
environmental and energy problems. Thus, in this paper, we have focused our attention on wide-scale 
penetration of PV, with an emphasis on upper voltage limit considerations, and have shown the 
relationship between VMPI and PV penetration. Moreover, we have proposed a smart control method by 
using the optimal power flow in terms of minimizing bus voltage deviations from the prescribed values 
for a large penetration of PV. Finally, to verify the effectiveness of the proposed method, we have run 
simulations using the IEEJ WEST 10 machines O/V system model. As a result, it is confirmed that load 
bus voltages are within the proper voltage range in a small amount of static capacitor control by using the 
proposed method. 
References 
[1] Kataoka Y, Watanabe M, Iwamoto S. A new voltage stability index considering voltage limits. In: Proc. of IEEE PES PSCE 
'06, 2006: 1878–1883. 
[2] Tamura Y, Sakemoto K, Tayama Y. Voltage instability proximity index (VIPI) based on multiple load flow solutions in ill-
conditioned power systems. In: Proc. of the 27th IEEE Conference on Dicision and Control, 1988:2114-2119. 
[3] Kataoka Y, Watanabe M, Iwamoto S. Voltage stability preventive control using VMPI sensitivities. Presented at: IEEJ 
Proceedings of the 18th Annual Conference of Power & Energy Society, 2006 (in Japanese). 
[4] Sakaeda S, Watanabe M, Iwamoto S. Fast voltage stability preventive control using ellipse-approximate P-V curves. Presented 
at: 2008 IEEE PES General Meeting, 2008.  
[5] Tanaka H, Tokumitsu K, Iwamoto S, Kobayashi R, Hirano D, Takeuchi A. Development of the emergency voltage control 
scheme using VMPI. Presented at:  2009 IEEE PES General Meeting, 2009. 
[6] Standing Special Committee of Power System Model Standardization. Standard Model of Power Systems. Technical Report of 
 IEE of Japan, No. 754, 1999.


International Journal of Smart Grid and Clean Energy Generator output and static capacitor control considering voltage stability for large penetration of photovoltaic power

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International Journal of Smart Grid and Clean Energy Generator output and static capacitor control considering voltage stability for large penetration of photovoltaic power

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