STUDIES IN THE OLTC EFFECTS ON VOLTAGE COLLAPSE USING LOCAL LOAD BUS DATA M. Bahadornejad and G. Ledwich School of Electrical and Electronic Systems Engineering Queensland University of Technology (QUT) Australia Email:
[email protected]
Abstract It is known that following a major disturbance, on-load tap changers (OLTC) may lead a power system to a voltage collapse. The aim of this paper is on-line estimation of the time distance to such a voltage collapse. It is shown that local load bus measured voltage and current phasors can be used to anticipate a voltage collapse for a system consisting constant impedance load behind a tap changer, and also, to estimate the time to the collapse. Two different methods are introduced. The first method is based on the comparison of the magnitudes of the system and load impedances. In the second method the estimated changes in the load power due to the OLTC operations are used to estimate the time to collapse. The proposed methods are confirmed by simulation. 1.
INTRODUCTION
In the last two decades, power systems have been loaded much more heavily than was usual in the past. As a consequence, many power systems around the world have experienced voltage instability or voltage collapse problems [1]. Loads are the driving force of voltage instability, and for this reason this phenomenon has also been called load instability [1]. Voltage instability stems from the attempt of load dynamics to restore power consumption beyond the capability of the combined transmission and generation system [2]. There are some kinds of loads with constant demands. In these loads following a drop in the supply voltage, the load power consumption is firstly decreased but then is restored to its initial value, load demand. So far three mechanisms of load recovery have been well-known: Induction motors (in seconds), on-load tap changer (OLTC) controlled loads (in minutes) and constant energy heating loads (in tens of minutes or a few hours) [3]. Many of the voltage collapse incidents have been caused by the attempt of the OLTC to restore the load side voltage to its setpoint value. These tap changes decrease the load impedance, seen from the bulk power delivery bus, and in the case of a major disturbance in the supply system, it may become equal in magnitude to the impedance of the equivalent system feeding the bus. Any further tap changes beyond this point will have reverse effect causing decreases in the load voltage and power. The proposed voltage instability predictor by Vu et. al [4] is based on the above well known fact. In references [5-9], reverse control action of OLTC in
association with voltage collapse has been investigated. It is shown theoretically that the critical condition for occurrence of reverse action coincides with the power matching condition under which the power consumed by load is maximized. In other words, the power matching condition is nothing but the voltage collapse condition. This fact suggests that the reverse action of tap changer is closely related to the voltage collapse. There are, however, exceptions such as a feeder serving almost exclusively heavily loaded induction motors [5]. In [6], using the continuous and also discrete models of tap changer, the long term mechanisms of voltage collapse has been investigated. Based on dynamic interaction considerations between loads and transformers, a tap locking strategy is proposed which ensures that voltage collapse will not occur. Yorino et. al. in [7] have investigated the sensitivity of load voltage to tap position with both load exact characteristics and constant power load and have concluded that it can be used to assess the occurrence of reverse control action . In [8] Hong and Wang have presented an approach for estimating voltage stability region concluding the stability region of OLTCs. In [9] it is shown that in addition to restoring the load, OLTC also extends the system power transfer capacity and the voltage instability will occur if system can not balance the amount of extended power transfer limit and the amount of restored load by the same tap changer. To stop the evolution of an unstable scenario before its conclusion to a voltage collapse, the time to identify the instability is a critical aspect. Many emergency control measures are based on extensive off-line studies.
This paper is a part of a research work for on-line estimation of the time distance to a possible voltage collapse. It will be shown that local load bus measured voltage and current phasors can be used to identify a voltage collapse for a system consisting of a constant impedance load behind a tap changer and to estimate the time to such a collapse. 2.
effect causing decreases in the load voltage and power (Figures 3b &3c).
THEORY
Consider a simple model system shown in Figure 1, where the constant impedance load is supplied through an OLTC. The Tap ratio is shown by n. E and Z s are the supply system Thevenin equivalent voltage and impedance, respectively. At time T, a major disturbance causes a significant sudden increase in Z s (Fig. 2a). This change in the system impedance, in turn, will cause significant sudden drops in Vp ,Vs and P , the load primary and secondary
voltages and real power, respectively. E
G
Zs
Ip
Vp
n:1
Vs ZL
P+jQ
Figure 1. Simple system with OLTC
OLTC attempts to restore the load side voltage to its setpoint value by decreasing the tap ratio, n. These tap changes decrease the load impedance, seen from the primary side (Figure. 2a). Tap changes will stop in two cases: Vs reaches its set point value, and/or, Tap reaches its limit.
Figure 2. Changes in impedances, tap ratio, voltages and power
It is possible that the load impedance becomes equal in magnitude to the impedance of the equivalent system feeding the bus (Figure 3a). In this case any further tap changes beyond this point will have reverse
Figure 3. Changes in impedances, Load voltage and power
Thus, in the critical point of impedance matching, the load voltage and power, Vs and P , will be on their maximum values. Also, the changes in the real power due to tapping in the two sides of the critical point will have different signs. Thus, each of the following approaches may be used to identify the remaining time to a possible collapse: 2.1 Time to collapse estimation using impedance matching
This approach is based on the comparison of magnitudes of the load primary side view impedance and system Thevenin impedance. 2.1.1
System Thevenin impedance computation
System Thevenin impedance can be estimated using changes in the load side. In this case the load impedance has a fix value, however, the changes in the tap ratio cause changes in the load impedance, seen from the primary side. The changes in the primary side load impedance cause changes in the primary side voltage and current. Using the first changes, due to the first taping, post-fault Z s may be estimated using Equation (1) [10]. ∆V p Zs = − (1) ∆I p The above method for the system impedance estimation will fail if there are random changes in system Thevenin. In fact there are system changes causing changes in E. For this case the ratio of the cross-correlations of the voltage and current random changes with respect to the load admittance random changes can be used to estimate the system impedance [10]. Zs =
−Ε [∆ VP ∆ Y ] Ε [∆ I P ∆ Y ]
(2)
2.1.2
Time to collapse estimation
For a constant impedance load and two successive tap ratios one can write: ni +12 Z L
2
2
n n − ∆n ∆n = 1 − = = i +1 = i 2 Z Pi n n ni ni Z L i i
Z Pi +1
2
(3) where ni is the tap ratio after ith tapping and ∆ n is the size of each tap step and: Z Pi = ni 2 Z L =
VPi I Pi
(4)
Putting i=0 in equation (3) and using equation (4) the initial tap ratio can be computed. Also it can be shown that after the ith tapping the value of Z p will be: 2 ∆ n Z p i ≅ Z p 0 1 − 2 ∆ n i − (i − 1) (5) no no 2 where Zp 0 and no are the initial values of the primary
side view load impedance and tap ratio, respectively. Z pi = Z S in Equation (5) we can Putting compute icr , the required numbers of tapings for making load impedance equal in magnitude to the system impedance. The critical tap ratio will be: ncr = no −i cr ∆ n
(6)
The tap changing logic at time instant ti is as following:
n + ∆ n if V >V o + d and n < n s s i max i o ni +1 = ni − ∆ n if Vs nmin n otherwise i
Now it should be checked to see whether ncr will exceed the tap limit or not. If yes, the collapse will not happen. But if the answer is no, then other quantities should be checked. Using icr and no the magnitude of Vs for n = ncr may be computed and checked to see whether it exceeds the reference value or not. If yes, collapse will not happen, otherwise, system will experience a voltage collapse. It can easily be shown that: Z Z +Z n (8) (Vs )i = (V s )o * o * Pi * s Po ni Z Po Z s + Z Pi Where i is the number of tap changes and Z Pi is defined by equation (5).
Where d and Vs o are half of the OLTC dead band and load voltage reference value, respectively. There are two modes of OLTC operation. In sequential mode tap changes starts after an initial fixed time delay and continues at constant time intervals until the secondary side voltage error is brought back inside the OLTC deadband, or until the tap limit is reached. The initial time delay is in the range of 30-60 sec and the subsequent taping time intervals are usually around 10 sec. The voltage error dead band is usually in the range of ± 1%-2%. In non-sequential mode of operation there is no distinction between first and subsequent taps and all time delays are given by the same formula [3].
is the post-fault
In an alternative method one may compute the amount of the load power (apparent, active or reactive) and compare it to its predisturbance value. For a constant impedance load:
(P )i (P )o (P )o
2
(V s ) i (9) = (V ) s o is the post-fault load real power and before the
OLTC operation. In the following subsection another method will be introduced that is based on the changes in the load power due to the OLTC operation. 2.2
(7)
(V s )o
secondary voltage and before the OLTC operation. Putting i = i cr in equation (8) the secondary voltage at critical point can be computed.
Time to collapse estimation using load power changes
At the voltage collapse point the load power is in its peak value. Therefore the changes in the power prior to this point are positive and after that point the changes are negative. Therefore, the tap ratio related to the sign changing point of the load power changes will identify the time of voltage collapse. Using a least-square based method the value of the third change is estimated using the values of the first and second changes in load power. Recursively, the subsequent changes are estimated using each pair of the changes until the point that the value of the power change becomes zero or negative. It can be shown that for the algebraic equation (10) y = xθ an estimation for θ can readily be as following:
(
θˆ = X T X
)−1 X TY
(11)
θ = [α β ]T can be estimated Putting: Y (1) = [∆P4 ∆P3 ]T
and
∆P3 ∆P2 X (1) = ∆P2 ∆P1
in equation (11), and then
Y (2 ) = [∆P5 ∆P4 ]T can be
by successively changing the tap ratio. Now let: Z s(post fault) = k*Z s(prefault) .The system and load impedances and load real power for three different values of k are shown in Figures 5, 6 and 7.
∆P4 ∆P3 in equation (9). ∆P3 ∆P2
computed putting X(2 ) =
∆Pi is the change in load active power due to the ith
tapping. This one-step ahead computation uses the estimated power changes to estimate a new point and it continues until the estimation of the jth point that ∆Pj becomes negative. If at the (j-1)th point of tapping the tap ratio exceeds the OLTC limit, collapse will not happen, otherwise, using the estimated power changes the amount of the load power at this point should be computed and be compared to the load pre-disturbance power. If the estimated power exceeds the predisturbance power collapse will not happen, because this means that secondary voltage will reach to its reference value prior to this point of tapping and tapping process will stop. 3
Figure 5. (a): System and load impedances, (b): Load real power, k=2
SIMULATION
The proposed methods are applied to the system shown in Figure 1. The load admittance is modelled as a constant impedance load plus a small randomly changing component (Figure 4). OLTC quantities are set to the values shown in Table 1. The time interval for all tap changes is assumed to be 10 sec. Considering the values of no , dn and nmin in Table 1; the tap limit will be reached by ten successive tap changes.
Figure 6. (a): System and load impedances, (b): Load real power, k=2.5
Figure 4. Simulation of load admittance Table 1. OLTC tap initial ratio, step size, lower limit, time delay and dead band.
no 1
∆n %
1.5
n min 0.85
∆T (sec)
d%
10
±2
At the time instance T= 10 sec there is a significant increase in the system impedance, and this in turn, causes sudden drops in the secondary voltage and load power. OLTC starts to restore load voltage and power
Figure 7. (a): Changes in the system and load impedances, (b): changes in load real power, k=3
Equation (2) was used to estimate post-fault system impedance. Tap initial ratio and the number of taps to collapse were estimated using equations (3) and (5), respectively. The results are shown in Table 2. The
estimated numbers of taps have been rounded to their next integer numbers. Table 2. Actual and estimated system impedance, initial tap ratio and taps to collapse for different values of k in Z s(post fault) = k*Z s(prefault)
Z s (pu)
k A* 2
0.1+0.4i
2.5
0.125+0.5i
3
0.15+0.6i
n o (pu) E**
A
E
sixth tap change. Thus, in this case the fifth tap change is the critical point. The values of the power changes at the first five tap changes are added to the post-fault (before OLTC operation) power value to compute the load power at the critical tap ratio. The result is as following: P
Taps to collapse
0.1+0.4i
1 0.9999
15
0.125+0.5i
1 1.0005
10
0.15+0.6i
1 0.9994
5
n = n cr
= 0.542 < 1.08 = P
n = no
Thus tap operation will continue and voltage will collapse.
*Actual value **Estimated value
As it can be seen from Table 2, estimated values for the system impedance are the same as the actual values and the estimated initial tap ratios are very close to the actual value. In the first case (k=2) collapse will not happen because as it was stated before OLTC limit will be reached by 10 tap changes. In the second case (k=2.5) also collapse will not happen because in this case the critical tap ratio is equal to the tap limit and OLTC operation will be stopped.
Figure 8. Comparison of estimated and actual values of power changes due to tapping, k=2
In the third case (k=3) the estimated taps to collapse is less than 10. Now it should be checked to see whether OLTC operation will stop before the critical point or not. Equation (9) is used to compute the load real power in the critical point. The result is as following: P
n = ncr
= 0.541 < 1.08 = P
n = no
Thus tap operation will continue and voltage will collapse. The above method of voltage collapse identification is based on the estimated tap initial position. The size of a tap step is usually in the range of 0.5%-1.5%. So, any error in estimation of the tap initial ratio may result in an incorrect value of n o , and therefore, untrue identification of voltage collapse.
Figure 9. Comparison of estimated and actual values of power changes due to tapping, k=2.5
Now we use equations (10) and (11) to identify the voltage collapse. The sizes of the actual and estimated changes in power for different values of k are shown in Figures 8, 9 and 10. As it can be seen the estimated and actual values are close together. Estimated power changes show that the power changes due to tapping for k=2 and k=2.5 are still positive at tenth tapping ( n = n min ). This means that in these cases collapse will not happen. But for k=3 the sign of the power change becomes negative at the
Figure 10. Comparison of estimated and actual values of power changes due to tapping, k=3
In this method, for identification of a voltage collapse one should wait until the time of the fourth change in power. Therefore, it will be useful just in the cases that there is left a lot of time to collapse.
[3]
Van Cutsem, T. and C.D. Vournas, "Voltage stability of electric power systems". 1998 Boston,USA: Kluwer Academic Publisher.
[4]
Vu, K., et al., “Use of local measurements to estimate voltage stability margin”. IEEE transactions on power systems, 1997. 14(3) pp 1029-1035
[5]
Vournas, C.D. "On the role of LTC s in emergency and preventive voltage stability control". in IEEE/PES Power System Stability Controls Subcommittee Meeting. 2002. New York, USA.
[6]
Popovic, D., I.A. Hiskens, and D.J. Hill, "Investigations of load-tap changer interaction” Electric Power & Energy Systems, 1996. 18(2) pp 81-97
[7]
It was also shown that the estimated changes in the load power due to the OLTC operations can used to estimate the time to collapse. This method is useful in the cases that there is left at least five tapping to collapse.
Yorino, N., A. Funahashi, and H. Sasaki, "On reverse control action of on-load tap changers”. Electric Power & Energy Systems, 1997. 19(8) pp 541-548
[8]
Hong, Y.-Y. and H.-Y. Wang, "Investigation of the voltage stability region involving on-load tap changers". Electric Power Systems Research 1995. 32: p. 45-54
The proposed methods were confirmed by the simulation results.
[9]
Zhu, T. X., S. K. Tso and K. L. Lo, “An investigation into the OLTC effects on voltage collapse”, IEEE Transactions on power systems, 2000. 15: pp 515-521
[10]
Bahadornejad, M. and G. Ledwich, “Studies in system Thevenin impedance estimation from normal operational data”, Accepted for presentation in the 6th International Power Engineering Conference, IPEC 2003, 22-24 May 2003, Singapore
Simulation results shown in Figures 5, 6 and 7 confirm the above achieved results by the both proposed methods in this paper. 4
CONCLUSIONS
Based on the measured data in the local load bus two methods were introduced to identify a possible voltage collapse and to estimate the time to such a collapse. It was shown that by the comparison of the system impedance to the estimated primary side view load impedance the number of the required tapping for a collapse can be identified at the first tapping time. This method is based on the estimation of the initial tap ratio and because of the small tap steps any error in the estimation will cause incorrect estimation of time.
5
REFERENCES
[1]
Taylor, C.W.,"Power system voltage stability". 1994, New York: McGraw-Hill.
[2]
Van Cutsem, T., “Voltage instability: Phenomena, countermeasures and analysis Methods”. Proceedings of the IEEE, 2000. 88(2): pp 208-227.
