- Email: [email protected]
A Study on the Optimal Operation Method of Voltage Regulator at Distribution Substation
Cops ri"ht
©
I F.·\( : Powe r Ss·stem s a"d
\OLl .\(;F KU;U ..\TIO:\ .\:\J) C():\TKOI.
PO\H'r Plant COIltl"ol. Seoul. Korea , I ~H~~.
A STUDY ON THE OPTIMAL OPERATION METHOD OF VOLTAGE REGULATOR AT DISTRIBUTION SUBSTATION J.
H. Kim, D. Rho and
KiQl
POll'er Sn/fllI DH 'isioll. Korm E/nlrolf(/iIlU/ogy Rnrar(/i Iw/i/II/f. P.o. Bux 20. C /i (III/fll 'OIl. K orra
Abstract. In order to deliver the suitable voltage to as many customers as possible. optimal supply voltage should be decided by the effective operation of voltage regulator at distribution substation. Bank LDC method is currently used in many utilities in order to control the supply voltage. This method uses an imaginary standard fee4er to represent the total feeder characteristics. Compared with the actual system, the determination of load center with the imaginary standard feeder becomes very difficult considering random load characteristics. In this paper the optimal operation method of voltage regulator at substation is developed on the basis of statistical analysis of the voltage measurement data at customer sites. This accommodates the highest and the lowest voltage conditions not only to maintain customer voltage within the required range but to keep it closer to the nominal volta~e. And the optimal operation method of multiple voltage regulators is also suggested. Keywords. Voltage Regulator, Line Drop Compensator(LDC), Step Voltage Regulator(SVR), Voltage Compensation Rate. INTRODUCTION M.Tr at the distribution substation has ULTC (Under Load Tap Changer) function and can regulate every feeder voltage at the same bank. Fig. I shows a typical one line diagram.
As a result of the development of the industry and the improvement of the living standards, home electric equipments and computer facilities are rapidly increasing. It requires the better quality in service more than ever before. To maintain the customer voltage within the allowable limit( 101 ± 6V), the optimal operation method of voltage regulator at distribution substation and primary feeders needs to be developed.
Primary Feeden (Three Phase)
In this research the worst conditioned primary feeder from one bank is selected, and then two point voltages - the first customer and the last customer of a feeder - are measured and used for the analysis. In order to keep customer voltage closer to the nominal voltage, sending voltage at distribution substation has to be decided by optimal compensation rate of voltage regulator within specified limits. According to the relation between this optimal sending voltage and hourly load current of the Main Transformer (M.Tr), computer program by the Least Squares Method is developed such as to find the load center and LDC (Line Drop Compensator) setting value.
Voltage Regulator
154 kv
22.9kv
Sev~
P. Tr 100v
First CustOmer VI(t)
This program avoids the complicate calculation work related to feeder configuration and random load variation and also can remove the cause of computation errors.
Condition Feeder
P.Tr
lOOv
Last Customer V2(t)
Fig. I Voltage Compensation by M.Tr( LDC Method) As for the worst conditioned feeder that has the biggest voltage drop and severe voltage fluctuation, if all customer voltages throughout this feeder are to be held within the specified limits and have the reasonable voltage distribution, then customer voltage of any other feeder from the same bank must be reasonable condition within the permitted limits. Fig.1 shows that VI(t) is the highest customer voltage supplied by voltage regulator and V2(t) is the lowest voltage.
The optimal operation by multiple voltage regulator is also described in this paper. The optimal compensation rate of each regulator is calculated by the Newton Iteration Method, and then convergence characteristic of this method is improved. This operational method of voltage regulator has a capability to feedback the customer voltage condition through measured data back to substation. With the randomly varying load, this method can be used for the ON-LINE voltage control based on MICRO-computer and can be used a part of Distribution Automation.
Usually ULTC has the voltage compensation limit as a ± 10%, and is required to maintain the customer voltage within the permitted upper and lower limits. Suppose that the sending voltage at substation M.Tr is raised by controlling ULTC until one customer voltage reaches at its upper limit first. Then the first customer voltage is set to upper voltage limit. By the same way, if the sending voltage is lowered step by step by ULTC control, customer reaching at the lower limit first is set to lower voltage limit. These upper and lower voltage limits var.v with the change of time.
OPTIMAL OPERATION METHOD OF VOLTAGE REGULATOR Optimal Voltaj;e Compensation by M Tr
jOI
502
H. Kim. D. Rho aml.J. Killl
But, the voltage of flrst and last customer sites can be ccnvened into one voltage value calculated at flrst customer site and then simplifled as the following two equations.
-
where V3(t) is the measured voltage of the flrst customer at the back side of SVR V4(t) is the measured voltage of the last customer at _ the back side of SVR, V3(t) is conversion value of the upper limit at the flrst customer, and Y3(t) is conversion value of the lower limit at the flrst customer.
-
VI(t) = V
(I)
Yl(t) = YVl(t)/V2(t)
(2)
where _ V is the upper limit of allowable voltage (l07V), Y is the lower limit of allowable voltage (95V), VI(t) is the measured voltage of the flrst customer, Y2(t) is the measured voltage of the last customer, Vl(t) is the conversion value of the upper limit at the flrst customer, YI(t) is the conversion value of the lower limit at the first customer, and t is time interval (30 minute). To calculate the most reasonable voltage compensation rate of ULTC, the objective function can be formulated as equation (3) below. This function shows the squared value of difference between the upper, lower voltage limit and flrst customer voltage decided by the optimal ULTC compensation. This means that customer voltages have maximum margin from the upper, lower limit while keeping closer to the nominal voltage. By minimizing this equation, the desired voltage distribution can be obtained. -
2
J = ( Vl(t) - Vl(t) Xmtr!Rmtr} + ( Vl(t) Xmtr/Rmtr - Yl(t)}
2
(3)
where J is the objective function, Rmtr is ULTC voltage compensation rate at the measuring time, and Xmtr is the optimal voltage compensation rate by ULTC. Now the problem is how to flnd the optimal Xmtr value. The condition for the minimum value of equation (3) is dJ / dXmtr = O. Therefore, Xmtr can be written as :
Primary Feeders (Throe Phase ) VOltage Regulator VOltager Regulator(SVR)
154 kv
22.9kv
P. Tr 100v
First
CuStomer VI (t)
P. Tr 100v
Last Customer V2(t)
First Customer
Last Customer
V3( t)
V4(t)
Fig. 2 Voltage Compensation by the Multiple Voltage Regulators Now, the problem is how to make the load voltage distribution most reasonable state by controlling the ULTC of M.Tr and SVR. The voltage compensation by UL TC of M.Tr has effects on both Sides of the SVR. In this case it seems reasonable that Yl(t) and V3{!) have maximum margin from each voltage limit Vl(t), Yl(t), V3(t), Y3(t), and their values are kept to be closer to the nominal voltage. Considered both the voltage drops of primary feeder from substation to SVR and the internal voltage drop of SVR, the flrst customer voltage, V3(t), can be written in equation (8). Vdrop(t) = VI(t) - V3(t) Tap.vr / (Vn.vr R.vr)
(8)
where dJ/dXmtr = 2(2Vl(t) Xmtr/Rmtr - Vl(t) - Yl(t)} Xmtr
= Rmtr ( Vl(t) + Yl(t) } /2Vl(t) Volta~e
Compensation by Multiple Volta~e
=0
(4) (5)
Re~lators
In radial transmission system, serially interconnected voltage control system needs mutual cooperation for its perfect control. Transmission substation ULTC and distribution substation ULTC are the first co-ordination case for voltage regulation . And distribution substation ULTC and voltage regulator installed at the feeder(Step Voltage Regulator : SVR) is the second case. In this paper we deal with the second case only. In order to serve the better quality, the distribution voltage is first regulated by substation ULTC and then controlled by SVR secondly. The proper location of SVR is another imponant problem, but we assume here the proper location and concentrate on the operation co-ordination between ULTC and SVR only.
Vdrop is voltage drop of primary feeder and internal SVR, Vn.vr is SVR nominal voltage, Tap.vr is SVR tap voltage at the measuring time, and Rvr IS SVR voltage compensation rate at the measuringtime. If the voltage compensation rate of M.Tr, Rmtr, is changed to Xmtr and the voltage compensation rate of SVR, Rvr, is changed to Xvr, then the first customer voltage, V3(t) , is changed to V3X(t) . The relationship of these variables can be written as equation (9). V3X(t) = (Vl(t) Xmtr / Rmtr - Vdrop(t» Vn.vr Xvr / Tap.vr
(9) where
x vr is the optimal voltage compensation rate of the SVR.
As explained earlier, the highest voltage from substation to SVR is Vl(t) and the lowest one V2(t) as shown in Fig. 2. And V3(t) and V4(t) are the highest and the lowest voltages from SVR to the feeder end, respectively. V3(t) can be represented as the following two equations.
V3(t) Y3(t)
=V = Y V3(t) / V4(t)
(6)
(7)
Substituting Vdrop(t) in equation (8) into equation (9), V3X(t) becomes : V3X(t)
=V3(t) Xvr!Rvr + (Xmtr!Rmtr -I) Vl(t) Vn.vr (Xvr/ Tap.vr)
(10)
T.hus, by adding equations related with customer voltage distribution at the back side of SVR as well as the terms related with SV.R coordination, the objective function can be expanded as equation (11)
Voltage Regulator at Distribution Substation
J
2 2 = (VI(t) - VI(t) Xmtr!Rmtr) + (VI(t)Xmtr!Rmtr - VI(t)}
503
Asswnptioo Initial Value : Ra
+ (V3(t) - V3(t) Xvr/Rvr - [Xmtr/Rmtr - IjVI(t)Vn.vr 2
Xvr rrap.vr} + (V3(t) Xvr/Rvr + [Xmtr!Rmtr -ljVI(t) 2
2
Vn.vrXvrrrap.vr - V3(t) } + K {Xmtr - Xvr} (11) In equation (11), K is a weighting factor which is decided by the coordination level between voltage regulators. Necessary and sufficient conditions to minimize the objective function, J, are :
l
a::" j
VJ
o
(12)
oXvr Fig. 3 flowchart of Iterative Calculation for Voltage Compensation Rates at M.Tr and SVR
and
Calculation of the Qptimal LDC Settin~ value (13)
equation(13) is positive definite for the solution of equation (12). So, optimal voltage compensation rate, Xmtr and Xvr, can be found by using the Newton Iteration Method shown as follows :
Load center voltage and LDC setting value can be obtained from the statistical analysis of the interrelation between the optimal sending voltage and total load current of M.Tr at substation.
LDC setting is operating with the same value for a long periods once fixed, and the compensated sending voltage by LDC setting has to be identified with the calculated optimal sending voltage. Optimal sending voltage is described as shown in equation (16), and optimal LDC setting is obtained by solving this equation for Vo and Z. Vop(t)
[ xmtr] Xvr
= Vo + Z I(t)
(16)
where k+1
This method shows that the convergence in the near optimal solution region is fast and stable. However it may not be stable in the other region. It seems desirable to choose the initial value closer to the optimal solution, if possible. In this research, to prevent the solution in unstable condition if a
new solution obtained by equation (14) is greater than an old solution, this new one is ignored and equation (15) is then introduced. This equation implies that the objective function moves to the decreasing direction at the rate of 0.5%.
Vop(t) is the optimal sending voltage at the voltage regulator, Vo is load center voltage, Z is LDC setting value related to voltage drop( R, X), and I(t) is total load current at time t. Due to the load current variation at substation and receiving voltage fluctuation from the transmission system, it is difficult to maintain the same optimal sending voltage as shown in equation (16). Optimal sending voltages can't usually provide a linear equation. However, they show a wide distribution characteristic as shown in Fig. 4.
Yap
Xmtr Xvr
where,
1 k+1
Xmtr Xvr
1k
-
VJ 0.OO51VJl (15)
I V J I = [ (oJ / oXmtr) 2 +
(oJ / oXvr) 2]112
The flowchart of the iterative calculation described above is shown in Fig. 3.
I (M.Tr current)
Fig. 4 Distribution Characteristic of Optimal Sending Voltage at the Voltage Regulator
504
H. Kim. D. Rho and
Therefore, the solution of optimal LDC setting value is equivalent to fmding coefficient of the first order equation. It is desirable to minimize the difference between the optimal sending voltage at voltage regulator and the first order equation. The Least Squares Method is now introduced in order to fmd the optimal LDC setting value. The squared summation of difference is written as follows : n
L [ Vop(k) - Vo - Z I(k) ]
q
2
(17)
k=l
J.
Kim
BONGD UI' S,l S # 1 t·.H r ":.:U RRErIT {Wmr UlaG . •""'jju,.. r,~
~I ~ '·. '. -_ _ ___ It,"" m +-_____________ -.j.'. .
~ 1
~.~·~~·~B,B-.~:~'~·~--i--· -~\_ _\\.~~:
n is the total number of time interval. Minimizing q in Equation (17), Vo and Z can be obtained as : n
\ '1
I
/..-tf<\~
7 u
>DD
::f~'
where
I D'
!
la n
' 3 l a ' 1 111 1! :!D ::1 ::: :!J :!+
1:: 1:1 H
TIME INTEI1VAL
oq / oVo = -2 L
(18)
[Vop(k) - Vo - Z I(k)] = 0 k=1
a
+
SATURDAY
SUNDAY
0 MONDAY
Fig. 5 Hourly Load Current of M.Tr
n
= -2
I
:oo+I_______ ~ ~ .... 1.JJ4..-F . ---~-~~;
[5
oq / 0 Z
/i . '~
I
L [I(k) (Vop(k) - Vo - ZI(k)] = 0
(19)
k=1 Then, Vo and Z can be written as follows : n
Vo = [
n
k=1 Z =[
k=1
f
n
2
L I(k) Vop(k) - Z L (I(k))
]/
L I(k)
i
f
(20)
k=1
I
I(k) Vop(k) - n I(k) Vop(k)] / [ ( I(k) )2 k=1 k=1 k=1 k=1 n
-n
L
2
(I(k)) ]
(21)
k=1 The calculated values by using the above equations have to be converted into LDC setting value according to the ratio of PT and er of voltage regulator.
>
~:~+-I --------------------~ -------11 ----------...-------1~ -,--~___,..___.----'c--____,..___il
:::. 1+---
,,. +-.
:w .. "".... ···"·>"
. ""1
~ ~ ========::::=:=j! : 1 t::::
11
!I
1D 11
1:: 1J
' " 1~
111 1:'
,. 1! :0
~l
:: ::1
:+
TIME INTERVAL
APPLICATION AND COMPARISON The simulated result by using the optimal operation program of voltage regulator developed in this paper is compared with the measurement data obtained by using the existing method. To test the efficiency of the proposed approach, the voltage data measured at DONGSAN DIL for 3 days is analyzed. Input Data Hourly load current and PT voltage of M.Tr at substation and measured voltage of the last customer are used as input data of the optimal operation program. Fig. 5 through Fig. 7 show each input data.
o SATURDAY
11l
11 0
::: E===========! i. .. ' 01
'"
1 1)1
I
B
111:1
,
10:
I
101
••
I
lOO
:.
...
. ,4
-
•
i
s·
.
'.
.' '. .,.' I
.B" .'-
•
t.....~ .,'
hi ' .
" "" !
.. I "
TIME INTERVAL
Application Result I:l
By using the developed method in this paper, the optimal sending voltage at the substation is calculated and shown in Fig. 8. The sending voltage of this figure is converted by value PT ratio (22900/110 V).
MONDAY
'" ,,. '" I!,
b
Fig. 7 shows that the last customer voltage stays higher than the nominal voltage even though it is within the allowable limit 101± 6%.
o
SUNDAY
Fig. 6 The Measured PT Voltage Distribution ( Sending Voltage)
108 •
Fig. 5 shows that M.Tr load represents characteristic of commercial area with residential load, and that Saturday's load is peak during the week.
T
SATURDAY
T SUNDAY
0 MONDAY
Fig. 7 The Measured Voltage Distribution of the Last Customer
.
I
\ 'ollage Regulator at Distribution Substation
BONGCdJf< S/S ;, 1
OPTI~tA.L
SEIJDIN G VO LT.AG E
Results Comparison
:::~---------I
The operation criteria of voltage regulator is usually decided by the voltage condition of customer, and also related to the number of operation count of ULTC tap.
'" .;..---------------------1
8 §
'" +I - - - - -/-i-,
...f · \.
11\
l:'\
•
,
101
• .> •
.-..;,_...,.,----,l+-_~.:_.'____:____: ./~'\,. -
'. \ i/ '. • • \a +-----,___..-..--.,. . ,........................ __ • • • • -4-_.,-,0-<'--_+--'--,, "
>
110
I (/
F . '/
:~ 1: :: ,
:2
l
..
505
.. .
Fig. 10 obtained by the average of Fig. 7 and Fig. 9 respectively shows that the simulation result by using proposed method is to maintain more reasonable voltage state and to be kept closer to the nominal voltage(101 V) than the results by using current voltage drop calcJIlation method. ~.m'·;URED
COMFARISON EXFECTED &:
,
"
r e ! la
11
12 13 14 '.5 10 1:' 111 11 20 :1 22 13 , .
TIME INTERVAL
+
c SATURDAY
>
~ MONDAY
SUNDAY
1
::~Lf ~'" l 03
0
~
I
.8"""S'-
'8 _
:,:,:. +!----~-"7'-..__::-'..:.......--..:.::o-'""""..:::. "~ !
-.:----,:.~::...
"I
~. ~
•.,. . -.• ..; .
Table 1 5hows the LDC setting value and load center voltage by the developed method in this paper.
. 1
C
~
Compa:ison Results
Load Center Voltage
IIOV
llOV
R
3.0 V
2.5 V
X
5.0V
5.4 V
( 22900/11 OV)
LDC Setting Value
3
..
3
11
l
"
!
la 11
1~
13 H
"
.
I
lit V' 111 U
'D 21 Z2 ::!3 H
TIME INTERVAL MEASURED VOLTAGE EXPECTED VOLTAGE
+
Fig. 10 Comparison Between the Measured Voltage and Simulation Result at the Last Customer
Application Result
Existing Method
2
,/ ~ '
, ,, " , I
:,:, I
Table 1 Application Result of the LDC Setting Value
---:1
---..... - .-.
b
- ""t"""
,
t
0
D.
ty..
Fig. 8 Optimal Sending Voltage Qistribution at M.Tr
VOLTAGE
Table 2 also shows that the number of operation count of ULTC tap is improved. Table 2 Comparison of the Number of ULTC Tap Operation
According to the calculated LDC setting value~ the expected voltage profile of the last customer is shown In Fig. 9.
Saturday
Sunday
Monday
16
II
24
15
11
23
the Counter by the Exist- ing Method
the CoUnter by theSimu-lation Result
DF En EC' \iOL TAGE OF {WfIt ..
L.~·;T ,:·U:;:r l)~,1 EP
U.OI :.~U .... ~·
"' 11 .-+.-------------------~ I
'"" '~------------------~ -t--------------------, 11' +----~--------------~
, ,,+-------------------~ , .,+----~--------------~
:; ,lQe~======================================~ .. +-------------------~ ,s a l a:"
~
tiI
~
o >
I Q!! • •
!
,::~., !~·· Ic. :..:..: :..l! .•.~:-::., 10+
:-;, ~ .•• ·.: .:4 i
<:-
The proposed method in this paper which uses the computer program based on the statistical analysis of the measured voltage data proved to be reasonable and effective. Moreover, this method with the extent use of computer can be easily implemented and effectively used in real system operation. And this operational method can be used for the ON-LINE voltage control based on MICRO-computer considering random load characteristics, we will study this project in the future.
'''n 1 ,____~~~'_·____:.B_a~·_._·_'~~~.-,~_ _~ ~t
"+~'===========~================~,~.========~
" I • ,,~~-------------------I
:
l
..
:I
11
~
11
!
,0
11
12 13 , .. 1:1
, D , 1 111 I! 10
TIME INTERVAL ,:) SATURDAY
+
SUNDAY
:~
o MONDAY
Fig. 9 The Expected Voltage Distribution at the Last Customer
:: :3 ,..
REFERENCES [I] Voltage Regulator Application on Rural Distribution Systems ,R.E.A. (1973), REA Bulletin 169-27. [2] Chao-Shun Chen (1982). The Effect of Voltage Control to the Efficiency and Operation of Electric Distribution System, University of Texas at Arllington. [3] Denouzous, Spams, Mason (1974). Systems, Network, Computations ; Multivariable Methods, McGrow-Hill.
©
I F.·\( : Powe r Ss·stem s a"d
\OLl .\(;F KU;U ..\TIO:\ .\:\J) C():\TKOI.
PO\H'r Plant COIltl"ol. Seoul. Korea , I ~H~~.
A STUDY ON THE OPTIMAL OPERATION METHOD OF VOLTAGE REGULATOR AT DISTRIBUTION SUBSTATION J.
H. Kim, D. Rho and
KiQl
POll'er Sn/fllI DH 'isioll. Korm E/nlrolf(/iIlU/ogy Rnrar(/i Iw/i/II/f. P.o. Bux 20. C /i (III/fll 'OIl. K orra
Abstract. In order to deliver the suitable voltage to as many customers as possible. optimal supply voltage should be decided by the effective operation of voltage regulator at distribution substation. Bank LDC method is currently used in many utilities in order to control the supply voltage. This method uses an imaginary standard fee4er to represent the total feeder characteristics. Compared with the actual system, the determination of load center with the imaginary standard feeder becomes very difficult considering random load characteristics. In this paper the optimal operation method of voltage regulator at substation is developed on the basis of statistical analysis of the voltage measurement data at customer sites. This accommodates the highest and the lowest voltage conditions not only to maintain customer voltage within the required range but to keep it closer to the nominal volta~e. And the optimal operation method of multiple voltage regulators is also suggested. Keywords. Voltage Regulator, Line Drop Compensator(LDC), Step Voltage Regulator(SVR), Voltage Compensation Rate. INTRODUCTION M.Tr at the distribution substation has ULTC (Under Load Tap Changer) function and can regulate every feeder voltage at the same bank. Fig. I shows a typical one line diagram.
As a result of the development of the industry and the improvement of the living standards, home electric equipments and computer facilities are rapidly increasing. It requires the better quality in service more than ever before. To maintain the customer voltage within the allowable limit( 101 ± 6V), the optimal operation method of voltage regulator at distribution substation and primary feeders needs to be developed.
Primary Feeden (Three Phase)
In this research the worst conditioned primary feeder from one bank is selected, and then two point voltages - the first customer and the last customer of a feeder - are measured and used for the analysis. In order to keep customer voltage closer to the nominal voltage, sending voltage at distribution substation has to be decided by optimal compensation rate of voltage regulator within specified limits. According to the relation between this optimal sending voltage and hourly load current of the Main Transformer (M.Tr), computer program by the Least Squares Method is developed such as to find the load center and LDC (Line Drop Compensator) setting value.
Voltage Regulator
154 kv
22.9kv
Sev~
P. Tr 100v
First CustOmer VI(t)
This program avoids the complicate calculation work related to feeder configuration and random load variation and also can remove the cause of computation errors.
Condition Feeder
P.Tr
lOOv
Last Customer V2(t)
Fig. I Voltage Compensation by M.Tr( LDC Method) As for the worst conditioned feeder that has the biggest voltage drop and severe voltage fluctuation, if all customer voltages throughout this feeder are to be held within the specified limits and have the reasonable voltage distribution, then customer voltage of any other feeder from the same bank must be reasonable condition within the permitted limits. Fig.1 shows that VI(t) is the highest customer voltage supplied by voltage regulator and V2(t) is the lowest voltage.
The optimal operation by multiple voltage regulator is also described in this paper. The optimal compensation rate of each regulator is calculated by the Newton Iteration Method, and then convergence characteristic of this method is improved. This operational method of voltage regulator has a capability to feedback the customer voltage condition through measured data back to substation. With the randomly varying load, this method can be used for the ON-LINE voltage control based on MICRO-computer and can be used a part of Distribution Automation.
Usually ULTC has the voltage compensation limit as a ± 10%, and is required to maintain the customer voltage within the permitted upper and lower limits. Suppose that the sending voltage at substation M.Tr is raised by controlling ULTC until one customer voltage reaches at its upper limit first. Then the first customer voltage is set to upper voltage limit. By the same way, if the sending voltage is lowered step by step by ULTC control, customer reaching at the lower limit first is set to lower voltage limit. These upper and lower voltage limits var.v with the change of time.
OPTIMAL OPERATION METHOD OF VOLTAGE REGULATOR Optimal Voltaj;e Compensation by M Tr
jOI
502
H. Kim. D. Rho aml.J. Killl
But, the voltage of flrst and last customer sites can be ccnvened into one voltage value calculated at flrst customer site and then simplifled as the following two equations.
-
where V3(t) is the measured voltage of the flrst customer at the back side of SVR V4(t) is the measured voltage of the last customer at _ the back side of SVR, V3(t) is conversion value of the upper limit at the flrst customer, and Y3(t) is conversion value of the lower limit at the flrst customer.
-
VI(t) = V
(I)
Yl(t) = YVl(t)/V2(t)
(2)
where _ V is the upper limit of allowable voltage (l07V), Y is the lower limit of allowable voltage (95V), VI(t) is the measured voltage of the flrst customer, Y2(t) is the measured voltage of the last customer, Vl(t) is the conversion value of the upper limit at the flrst customer, YI(t) is the conversion value of the lower limit at the first customer, and t is time interval (30 minute). To calculate the most reasonable voltage compensation rate of ULTC, the objective function can be formulated as equation (3) below. This function shows the squared value of difference between the upper, lower voltage limit and flrst customer voltage decided by the optimal ULTC compensation. This means that customer voltages have maximum margin from the upper, lower limit while keeping closer to the nominal voltage. By minimizing this equation, the desired voltage distribution can be obtained. -
2
J = ( Vl(t) - Vl(t) Xmtr!Rmtr} + ( Vl(t) Xmtr/Rmtr - Yl(t)}
2
(3)
where J is the objective function, Rmtr is ULTC voltage compensation rate at the measuring time, and Xmtr is the optimal voltage compensation rate by ULTC. Now the problem is how to flnd the optimal Xmtr value. The condition for the minimum value of equation (3) is dJ / dXmtr = O. Therefore, Xmtr can be written as :
Primary Feeders (Throe Phase ) VOltage Regulator VOltager Regulator(SVR)
154 kv
22.9kv
P. Tr 100v
First
CuStomer VI (t)
P. Tr 100v
Last Customer V2(t)
First Customer
Last Customer
V3( t)
V4(t)
Fig. 2 Voltage Compensation by the Multiple Voltage Regulators Now, the problem is how to make the load voltage distribution most reasonable state by controlling the ULTC of M.Tr and SVR. The voltage compensation by UL TC of M.Tr has effects on both Sides of the SVR. In this case it seems reasonable that Yl(t) and V3{!) have maximum margin from each voltage limit Vl(t), Yl(t), V3(t), Y3(t), and their values are kept to be closer to the nominal voltage. Considered both the voltage drops of primary feeder from substation to SVR and the internal voltage drop of SVR, the flrst customer voltage, V3(t), can be written in equation (8). Vdrop(t) = VI(t) - V3(t) Tap.vr / (Vn.vr R.vr)
(8)
where dJ/dXmtr = 2(2Vl(t) Xmtr/Rmtr - Vl(t) - Yl(t)} Xmtr
= Rmtr ( Vl(t) + Yl(t) } /2Vl(t) Volta~e
Compensation by Multiple Volta~e
=0
(4) (5)
Re~lators
In radial transmission system, serially interconnected voltage control system needs mutual cooperation for its perfect control. Transmission substation ULTC and distribution substation ULTC are the first co-ordination case for voltage regulation . And distribution substation ULTC and voltage regulator installed at the feeder(Step Voltage Regulator : SVR) is the second case. In this paper we deal with the second case only. In order to serve the better quality, the distribution voltage is first regulated by substation ULTC and then controlled by SVR secondly. The proper location of SVR is another imponant problem, but we assume here the proper location and concentrate on the operation co-ordination between ULTC and SVR only.
Vdrop is voltage drop of primary feeder and internal SVR, Vn.vr is SVR nominal voltage, Tap.vr is SVR tap voltage at the measuring time, and Rvr IS SVR voltage compensation rate at the measuringtime. If the voltage compensation rate of M.Tr, Rmtr, is changed to Xmtr and the voltage compensation rate of SVR, Rvr, is changed to Xvr, then the first customer voltage, V3(t) , is changed to V3X(t) . The relationship of these variables can be written as equation (9). V3X(t) = (Vl(t) Xmtr / Rmtr - Vdrop(t» Vn.vr Xvr / Tap.vr
(9) where
x vr is the optimal voltage compensation rate of the SVR.
As explained earlier, the highest voltage from substation to SVR is Vl(t) and the lowest one V2(t) as shown in Fig. 2. And V3(t) and V4(t) are the highest and the lowest voltages from SVR to the feeder end, respectively. V3(t) can be represented as the following two equations.
V3(t) Y3(t)
=V = Y V3(t) / V4(t)
(6)
(7)
Substituting Vdrop(t) in equation (8) into equation (9), V3X(t) becomes : V3X(t)
=V3(t) Xvr!Rvr + (Xmtr!Rmtr -I) Vl(t) Vn.vr (Xvr/ Tap.vr)
(10)
T.hus, by adding equations related with customer voltage distribution at the back side of SVR as well as the terms related with SV.R coordination, the objective function can be expanded as equation (11)
Voltage Regulator at Distribution Substation
J
2 2 = (VI(t) - VI(t) Xmtr!Rmtr) + (VI(t)Xmtr!Rmtr - VI(t)}
503
Asswnptioo Initial Value : Ra
+ (V3(t) - V3(t) Xvr/Rvr - [Xmtr/Rmtr - IjVI(t)Vn.vr 2
Xvr rrap.vr} + (V3(t) Xvr/Rvr + [Xmtr!Rmtr -ljVI(t) 2
2
Vn.vrXvrrrap.vr - V3(t) } + K {Xmtr - Xvr} (11) In equation (11), K is a weighting factor which is decided by the coordination level between voltage regulators. Necessary and sufficient conditions to minimize the objective function, J, are :
l
a::" j
VJ
o
(12)
oXvr Fig. 3 flowchart of Iterative Calculation for Voltage Compensation Rates at M.Tr and SVR
and
Calculation of the Qptimal LDC Settin~ value (13)
equation(13) is positive definite for the solution of equation (12). So, optimal voltage compensation rate, Xmtr and Xvr, can be found by using the Newton Iteration Method shown as follows :
Load center voltage and LDC setting value can be obtained from the statistical analysis of the interrelation between the optimal sending voltage and total load current of M.Tr at substation.
LDC setting is operating with the same value for a long periods once fixed, and the compensated sending voltage by LDC setting has to be identified with the calculated optimal sending voltage. Optimal sending voltage is described as shown in equation (16), and optimal LDC setting is obtained by solving this equation for Vo and Z. Vop(t)
[ xmtr] Xvr
= Vo + Z I(t)
(16)
where k+1
This method shows that the convergence in the near optimal solution region is fast and stable. However it may not be stable in the other region. It seems desirable to choose the initial value closer to the optimal solution, if possible. In this research, to prevent the solution in unstable condition if a
new solution obtained by equation (14) is greater than an old solution, this new one is ignored and equation (15) is then introduced. This equation implies that the objective function moves to the decreasing direction at the rate of 0.5%.
Vop(t) is the optimal sending voltage at the voltage regulator, Vo is load center voltage, Z is LDC setting value related to voltage drop( R, X), and I(t) is total load current at time t. Due to the load current variation at substation and receiving voltage fluctuation from the transmission system, it is difficult to maintain the same optimal sending voltage as shown in equation (16). Optimal sending voltages can't usually provide a linear equation. However, they show a wide distribution characteristic as shown in Fig. 4.
Yap
Xmtr Xvr
where,
1 k+1
Xmtr Xvr
1k
-
VJ 0.OO51VJl (15)
I V J I = [ (oJ / oXmtr) 2 +
(oJ / oXvr) 2]112
The flowchart of the iterative calculation described above is shown in Fig. 3.
I (M.Tr current)
Fig. 4 Distribution Characteristic of Optimal Sending Voltage at the Voltage Regulator
504
H. Kim. D. Rho and
Therefore, the solution of optimal LDC setting value is equivalent to fmding coefficient of the first order equation. It is desirable to minimize the difference between the optimal sending voltage at voltage regulator and the first order equation. The Least Squares Method is now introduced in order to fmd the optimal LDC setting value. The squared summation of difference is written as follows : n
L [ Vop(k) - Vo - Z I(k) ]
q
2
(17)
k=l
J.
Kim
BONGD UI' S,l S # 1 t·.H r ":.:U RRErIT {Wmr UlaG . •""'jju,.. r,~
~I ~ '·. '. -_ _ ___ It,"" m +-_____________ -.j.'. .
~ 1
~.~·~~·~B,B-.~:~'~·~--i--· -~\_ _\\.~~:
n is the total number of time interval. Minimizing q in Equation (17), Vo and Z can be obtained as : n
\ '1
I
/..-tf<\~
7 u
>DD
::f~'
where
I D'
!
la n
' 3 l a ' 1 111 1! :!D ::1 ::: :!J :!+
1:: 1:1 H
TIME INTEI1VAL
oq / oVo = -2 L
(18)
[Vop(k) - Vo - Z I(k)] = 0 k=1
a
+
SATURDAY
SUNDAY
0 MONDAY
Fig. 5 Hourly Load Current of M.Tr
n
= -2
I
:oo+I_______ ~ ~ .... 1.JJ4..-F . ---~-~~;
[5
oq / 0 Z
/i . '~
I
L [I(k) (Vop(k) - Vo - ZI(k)] = 0
(19)
k=1 Then, Vo and Z can be written as follows : n
Vo = [
n
k=1 Z =[
k=1
f
n
2
L I(k) Vop(k) - Z L (I(k))
]/
L I(k)
i
f
(20)
k=1
I
I(k) Vop(k) - n I(k) Vop(k)] / [ ( I(k) )2 k=1 k=1 k=1 k=1 n
-n
L
2
(I(k)) ]
(21)
k=1 The calculated values by using the above equations have to be converted into LDC setting value according to the ratio of PT and er of voltage regulator.
>
~:~+-I --------------------~ -------11 ----------...-------1~ -,--~___,..___.----'c--____,..___il
:::. 1+---
,,. +-.
:w .. "".... ···"·>"
. ""1
~ ~ ========::::=:=j! : 1 t::::
11
!I
1D 11
1:: 1J
' " 1~
111 1:'
,. 1! :0
~l
:: ::1
:+
TIME INTERVAL
APPLICATION AND COMPARISON The simulated result by using the optimal operation program of voltage regulator developed in this paper is compared with the measurement data obtained by using the existing method. To test the efficiency of the proposed approach, the voltage data measured at DONGSAN DIL for 3 days is analyzed. Input Data Hourly load current and PT voltage of M.Tr at substation and measured voltage of the last customer are used as input data of the optimal operation program. Fig. 5 through Fig. 7 show each input data.
o SATURDAY
11l
11 0
::: E===========! i. .. ' 01
'"
1 1)1
I
B
111:1
,
10:
I
101
••
I
lOO
:.
...
. ,4
-
•
i
s·
.
'.
.' '. .,.' I
.B" .'-
•
t.....~ .,'
hi ' .
" "" !
.. I "
TIME INTERVAL
Application Result I:l
By using the developed method in this paper, the optimal sending voltage at the substation is calculated and shown in Fig. 8. The sending voltage of this figure is converted by value PT ratio (22900/110 V).
MONDAY
'" ,,. '" I!,
b
Fig. 7 shows that the last customer voltage stays higher than the nominal voltage even though it is within the allowable limit 101± 6%.
o
SUNDAY
Fig. 6 The Measured PT Voltage Distribution ( Sending Voltage)
108 •
Fig. 5 shows that M.Tr load represents characteristic of commercial area with residential load, and that Saturday's load is peak during the week.
T
SATURDAY
T SUNDAY
0 MONDAY
Fig. 7 The Measured Voltage Distribution of the Last Customer
.
I
\ 'ollage Regulator at Distribution Substation
BONGCdJf< S/S ;, 1
OPTI~tA.L
SEIJDIN G VO LT.AG E
Results Comparison
:::~---------I
The operation criteria of voltage regulator is usually decided by the voltage condition of customer, and also related to the number of operation count of ULTC tap.
'" .;..---------------------1
8 §
'" +I - - - - -/-i-,
...f · \.
11\
l:'\
•
,
101
• .> •
.-..;,_...,.,----,l+-_~.:_.'____:____: ./~'\,. -
'. \ i/ '. • • \a +-----,___..-..--.,. . ,........................ __ • • • • -4-_.,-,0-<'--_+--'--,, "
>
110
I (/
F . '/
:~ 1: :: ,
:2
l
..
505
.. .
Fig. 10 obtained by the average of Fig. 7 and Fig. 9 respectively shows that the simulation result by using proposed method is to maintain more reasonable voltage state and to be kept closer to the nominal voltage(101 V) than the results by using current voltage drop calcJIlation method. ~.m'·;URED
COMFARISON EXFECTED &:
,
"
r e ! la
11
12 13 14 '.5 10 1:' 111 11 20 :1 22 13 , .
TIME INTERVAL
+
c SATURDAY
>
~ MONDAY
SUNDAY
1
::~Lf ~'" l 03
0
~
I
.8"""S'-
'8 _
:,:,:. +!----~-"7'-..__::-'..:.......--..:.::o-'""""..:::. "~ !
-.:----,:.~::...
"I
~. ~
•.,. . -.• ..; .
Table 1 5hows the LDC setting value and load center voltage by the developed method in this paper.
. 1
C
~
Compa:ison Results
Load Center Voltage
IIOV
llOV
R
3.0 V
2.5 V
X
5.0V
5.4 V
( 22900/11 OV)
LDC Setting Value
3
..
3
11
l
"
!
la 11
1~
13 H
"
.
I
lit V' 111 U
'D 21 Z2 ::!3 H
TIME INTERVAL MEASURED VOLTAGE EXPECTED VOLTAGE
+
Fig. 10 Comparison Between the Measured Voltage and Simulation Result at the Last Customer
Application Result
Existing Method
2
,/ ~ '
, ,, " , I
:,:, I
Table 1 Application Result of the LDC Setting Value
---:1
---..... - .-.
b
- ""t"""
,
t
0
D.
ty..
Fig. 8 Optimal Sending Voltage Qistribution at M.Tr
VOLTAGE
Table 2 also shows that the number of operation count of ULTC tap is improved. Table 2 Comparison of the Number of ULTC Tap Operation
According to the calculated LDC setting value~ the expected voltage profile of the last customer is shown In Fig. 9.
Saturday
Sunday
Monday
16
II
24
15
11
23
the Counter by the Exist- ing Method
the CoUnter by theSimu-lation Result
DF En EC' \iOL TAGE OF {WfIt ..
L.~·;T ,:·U:;:r l)~,1 EP
U.OI :.~U .... ~·
"' 11 .-+.-------------------~ I
'"" '~------------------~ -t--------------------, 11' +----~--------------~
, ,,+-------------------~ , .,+----~--------------~
:; ,lQe~======================================~ .. +-------------------~ ,s a l a:"
~
tiI
~
o >
I Q!! • •
!
,::~., !~·· Ic. :..:..: :..l! .•.~:-::., 10+
:-;, ~ .•• ·.: .:4 i
<:-
The proposed method in this paper which uses the computer program based on the statistical analysis of the measured voltage data proved to be reasonable and effective. Moreover, this method with the extent use of computer can be easily implemented and effectively used in real system operation. And this operational method can be used for the ON-LINE voltage control based on MICRO-computer considering random load characteristics, we will study this project in the future.
'''n 1 ,____~~~'_·____:.B_a~·_._·_'~~~.-,~_ _~ ~t
"+~'===========~================~,~.========~
" I • ,,~~-------------------I
:
l
..
:I
11
~
11
!
,0
11
12 13 , .. 1:1
, D , 1 111 I! 10
TIME INTERVAL ,:) SATURDAY
+
SUNDAY
:~
o MONDAY
Fig. 9 The Expected Voltage Distribution at the Last Customer
:: :3 ,..
REFERENCES [I] Voltage Regulator Application on Rural Distribution Systems ,R.E.A. (1973), REA Bulletin 169-27. [2] Chao-Shun Chen (1982). The Effect of Voltage Control to the Efficiency and Operation of Electric Distribution System, University of Texas at Arllington. [3] Denouzous, Spams, Mason (1974). Systems, Network, Computations ; Multivariable Methods, McGrow-Hill.