中英文资料翻译
原文:
A SPECIAL PROTECTION SCHEME FOR VOLTAGE
STABILITY PREVENTION
Abstract
Voltage instability is closely related to the maximum load-ability of a transmission network. The energy flows on the transmission system depend on the network topology, generation and loads, and on the availability of sources that can generate reactive power. One of the methods used for this purpose is the Voltage Instability Predictor (VIP). This relay measures voltages at a substation bus and currents in the circuit connected to the bus. From these measurements, it estimates the Thévenin?s equivalent of the network feeding the substation and the impedance of the load being supplied from the substation. This paper describes an extension to the VIP technique in which measurements from adjoining system buses and anticipated change of load are taken into consideration as well.
Keywords: Maximum load ability; Voltage instability; VIP algorithm.
1. Introduction
Deregulation has forced electric utilities to make better use of the available transmission facilities of their power system. This has resulted in increased power transfers, reduced transmission margins and diminished voltage security margins.
To operate a power system with an adequate security margin, it is essential to estimate the maximum permissible loading of the system using information about the current operation point. The maximum loading of a system is not a fixed quantity but depends on various factors, such as network topology, availability of reactive power reserves and their location etc. Determining the maximum permissible loading, within the voltage stability limit, has become a very important issue in power system operation and planning studies. The conventional P-V or V- Q curves are usually used as a tool for assessing voltage stability and hence for finding the maximum loading at the verge of voltage collapse [1]. These curves are generated by running a large number of load flow cases using, conventional methods. While such procedures can be automated, they are time-consuming and do not readily provide information useful in gaining insight into the cause of stability problems [2].
To overcome the above disadvantages several techniques have been proposed in the literature, such as bifurication theory [3], energy method [4], eigen value method [5],
multiple load flow solutions method [6] etc.
Reference [7] proposed a simple method, which does not require off-line simulation and training. The Voltage Indicator Predictor (VIP) method in [7] is based on local measurements (voltage and current) and produces an estimate of the strength / weakness of the transmission system connected to the bus, and compares it with the local demand. The closer the local demand is to the estimated transmission capacity, the more imminent is the voltage instability. The main disadvantage of this method is in the estimation of the Thévenin?s equivalent, which is obtained from two measurements at different times. For a more exact estimation, one requires two different load measurements.
This paper proposes an algorithm to improve the robustness of the VIP algorithm by including additional measurements from surrounding load buses and also taking into consideration local load changes at neighboring buses.
2. Proposed Methodology
The VIP algorithm proposed in this paper uses voltage and current measurements on the load buses and assumes that the impedance of interconnecting lines (Z12,Z13) are known, as shown in (Figure 1). The current flowing from the generator bus to the load bus is used to estimate Thévenin?s equivalent for the system in that direction. Similarly the current flowing from other load bus (Figure 2) is used to estimate Thévenin?s equivalent from other direction. This results in following equations (Figure 3). Note that the current coming from the second load bus over the transmission line was kept out of estimation in original (VIP) algorithm.
V(Z?Zth1)?V2(Z12)?Eth1(Zth1) [1] 1L1V(Z?Zth2)?V1(Z12)?Eth2(Zth2) [2] 2L2E(Z)?V1(Zth1)?IE1 [3] th1th1E(Z)?V2(Zth2)?IE2 [4] th2th2Where IE1 and IE2 are currents coming from Thévenin buses no.1 and 2. Equation (1)-(4) can be combined into a matrix form:
?1?1?ZL1?1?Z12?1?Zth1?1?V?Z12?Zth10?1???-1?1?1?1?1?Z12ZL2?Z12?Zth20?Zth2??V2???? ??*??1?1?Zth10Zth10???Eth1????1?1??E0?Zth20Zth2??th2???1?1?1?1?1?1?1?1?1?1?1?1?0??0???[5] ?IE1????IE2?Using the first 2 rows in the system Equations (1)-(4), the voltage on buses number 1 and 2 can be found as shown in Equation (6) below. From Equation (6) we
can see that the voltage is a function of impedances. Note that the method assumes that all Thévenin?s parameters are constant at the time of estimation.
?1?1?1?1??Eth1Zth1?1??Z12?V1??ZL1?Zth1?Z12? [6] ?????*??1?1?1?1?1V?Z12ZL2?Zth2?Z12??2??????Eth2Zth2??
?1Where, y1?ZL1 y12?Z12 and y2?ZL2
The system equivalent seen from bus no.1 is shown in Figure 3. Figure 4(a) shows the relationship between load admittances (y1 and y2) and voltage at bus no.1. Power delivered to bus no.1 is (S1) and it is a function of
(ZL1,ZL2).S1?V1*yL1 [7] Equation 7 is plotted in figure 4 (b) as a ?landscape? and the maximum loading point depends on where the system trajectory ?goes over the hill?.
2?1?1?1
Fig. 1. 3-Bus system connections Fig. 2. 1-Bus model
Fig. 3. System equivalent as seen by the proposed VIP relay on bus #1 (2-bus model)
(a)Voltage Profile (b) Power Profile
Fig. 4. Voltage and power profiles for bus #1
2.1. On-Line Tracking of Thévenin’s Parameters
Thévenin?s parameters are the main factors that decide the maximum loading of the load bus and hence we can detect the voltage collapse. In Figure3, Eth can be expressed by the following equation:
Eth?Vload?ZthI [8]
V and I are directly available from measurements at the local bus. Equation (8) can be expressed in the matrix form as shown below.
?Vr??Eth(r)??0??E(i)?th? ?????Vi??Rth?????0X???th??1?0??0??00?IrIi.?000?? [9] 1?Ii.Ir??000? B= A X [10] The unknown parameters can be estimated from the following equation:
TT AAX?AB [11]
Note that all of the above quantities are functions of time and are calculated on a sliding window of discrete data samples of finite, preferably short length. There are additional requirements to make the estimation feasible:
? There must be a significant change in load impedance in the data window of at least two set of Measurements.
? For small changes in Thévenin?s parameters within a particular data window, the algorithm can estimate properly but if a sudden large change occurs then the process of estimation is postponed until the next data window comes in.
? The monitoring device based on the above principle can be used to impose a limit on the loading at each bus, and sheds load when the limit is exceeded. It can also be used to enhance existing voltage controllers. Coordinated control can
also be obtained if communication is available.
Once we have the time sequence of voltage and current we can estimate unknowns by using parameter estimation algorithms, such as Ka lm an Filtering approach described [6].
stability margin (VSM) due to impedances can be expressed as (VSMZ); where subscript z denotes the impedance.Therefore we have:
VSMZ?ZLoad?Zthev [12]
ZLoad The above equation assumes that both load impedances (Z1, Z2) are decreasing at a steady rate, so the power delivered to bus 1 will increase according to Equation (7). However once it reaches the point of collapse power starts to decrease again.
Now assume that both loads are functions of time. The maximum critical loading point is then given by Equation(13):
ds1?0 [13] dtExpressing voltage stability margin due to load apparent power as ( VSMS), we S1have:
Critical?SCritical?SLoad VSMS? [14] CriticalSNote that both VSMZ and VSMS are normalized quantities and their values decrease as the load increases.
At the voltage collapse point, both the margins reduce to zero and the corresponding load is considered as the maximum permissible loading.
Fig. 5. VIP algorithm
2.2. Voltage Stability Margins and the Maximum Permissible Loading
System reaches the maximum load point when the condition: Zload?Zthevis
satisfied (Figure5).Therefore the voltage stability boundary can be defined by a circle
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