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A New Concept of Voltage-Collapse Protection Based on Local Phasors Gregor Verbiˇc, Student Member, IEEE, and Ferdinand Gubina, Member, IEEE

Abstract—A new algorithm for protection against voltage collapse is proposed. The algorithm makes use of the magnitudes and angles of the local phasors (i.e., bus voltages and load currents). The change in an apparent power-line flow during a time interval is exploited for computing the voltage-collapse criterion. The criterion is based on the fact that the line losses in the vicinity of the voltage collapse increase faster than the delivery of the apparent power and, at the voltage-collapse point, the losses consume all of the increased power. The selected criterion equals 0 when a voltage collapse occurs. The proposed algorithm could be easily implemented in a numerical relay. The information obtained by the relay can be used at two levels–for the coordinated system-wide control action or for automatic action on the local level. The algorithm is simple and computationally very fast. It was tested on the IEEE 118-bus test system. Index Terms—Local phasors, power system dynamic stability, power system protection, voltage collapse.



EREGULATION has forced electric utilities to make better use of the available transmission facilities of their power systems. This has resulted in increased power transfers, reduced transmission margins and, at the same time, diminished voltage-security margins. Together with ever-present disturbances, this may in certain cases result in voltage stability problems, with a serious consequence of a voltage collapse. As a result, voltage instability is becoming one of the main limiting constraints; together with the rotor-angle stability it is of great concern to power system operators. This is evident from the attention paid to the many major system collapses that have occurred around the world due to voltage instability [1], [9]–[11]. A voltage collapse is basically a dynamic phenomenon with rather slow dynamics and a time domain ranging from a few seconds to some minutes, or more. Owing to its quasi-static character, it has mostly been static methods that were proposed for its analysis. Most of the available methods utilize the system’s Jacobian matrix [1], [2], [9]–[11], [13] by exploiting either its sensitivity or its eigenvalue behavior to determine its closeness to singularity. This represents a computational burden for real-time voltage-stability estimation. The main idea of certain proposed local methods [3], [4], [12] is based on findings which suggest that local phasors (i.e., bus voltages and line currents), contain enough information to deManuscript received November 22, 2002. The authors are with the University of Ljubljana, Faculty of Electrical Engineering, Ljubljana 1000, Slovenia (e-mail: Digital Object Identifier 10.1109/TPWRD.2004.824763

tect parts of the system that are prone to voltage collapse. These methods have proved to be efficient with regard to computational time, and because of their speed, they are applicable in online protection schemes. Despite all of these facts, the number of proposed local methods is relatively few. Two methods proposed by Strmˇcnik and Gubina [3], [12] are based on power system decomposition. With this method, the power system is decomposed into several radial transmission networks, starting at the reactive-power source bus and ending at a reactive-power drain bus, which are then transformed into exact two-bus substitutes. Since the analytical proof for the maximum stable power transfer for the two-bus network is available, the stability of the power transfer along each transmission path can be reliably assessed. The proposed voltage-collapse assessment should combine both the voltage-collapse proximity indicator and the involved generator maximum reactive-power reserve indicator. Using two indicators means that a determination of the protection activation threshold is not straightforward. The other weak point of this approach is that it does not take into account the electrical distance of reactive power sources from the affected load bus when calculating the generators’ reactive-power reserve. The method is also too conservative in some cases. The method proposed by Vu et al. [5] is based on a comparison of the Thevenin equivalent as seen from the load bus and the apparent impedance of the load. The assessment of the distance to voltage instability is based on the fact that the two impedances are equal at the point of voltage collapse. The main disadvantage of this method is in the estimation of the Thevenin equivalent, which is obtained from two measurements at different times. For a more exact estimation, one would require two different load measurements. Yabe et al. [6] proposed the use of artificial intelligence. Several system conditions are simulated in order to generate the patterns that are used for the training of the neural-fuzzy system. In real-time operation, the true measurements are compared to known patterns from which the proximity to the voltage collapse is inferred. The method requires offline training, which is slow, and it has to be rerun after every topological modification of the system. Despite the number of studies, many questions still remain unanswered, and only a few studies have resulted in the implementation of protection schemes against voltage collapse. The most common application used today is undervoltage load shedding [7], [8]. The main problem is that the voltage, on its own, is often a poor indicator of voltage instability. The fixed set point may result in unnecessary shedding or may fail to recognize instability.

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Therefore, a voltage-stability index that is simple for an application in an online protection scheme is of vital importance for a reliable and secure operation of a power system. It determines how far from voltage collapse the system is, and can be used for activating predefined protective measures at the most critical buses in the system. II. THEORETICAL BACKGROUND In order to achieve a desired power-system voltage profile during operation, it is necessary to have both a sufficient amount and an appropriate allocation of reactive power in a power system. Voltage instability can, thus, be caused either by an inability of reactive-power sources to produce enough reactive power to supply a load bus or by inability of power lines to transmit the required reactive power to it. In a load node, lack of reactive power results in a voltage decrease, which can, in the worst case, lead to voltage instability. When the system becomes increasingly stressed, the line losses start to grow rapidly in the vicinity of the voltage collapse. At the collapse point, the loss-increasing ratios , , , and go to infinity. This fact provides the theoretical background for the power-loss-sensitivity method [13]. It can be proved that the voltage-collapse condition using the power-loss-sensitivity method is identical to that of the Jacobian method. In the vicinity of a voltage collapse, the stressed lines become big reactive power consumers and they begin limiting the reactive power supply to a load node. That can result in a demand for a higher reactive-power flow on other lines, resulting in an unstable process on the lines connected to the affected node. With the increased loading of other lines, they may reach the point of instability, and the process leads to a chain reaction that is difficult to stop. In the final step, all of the connected lines fail to supply the desired reactive power to the affected load node, which is the starting point of its voltage instability. A protective relay requires computation of the S difference criterion (SDC), which uses consecutive measurements of the apparent power in a line’s relay point. In the vicinity of the voltage instability point, all of the increase in the power flow at the sending end supplies the transmission losses. As a result, an increase in the apparent power flow at the sending end of the line no longer yields an increase in the received power. That means at the line’s relay point when the voltage instability that occurs. It has been shown that this condition also coincides with the singularity of the system’s Jacobian matrix [13]. The apparent power supplied at the receiving end can be written as (1) An increase in the apparent-power loading in the time interval between and is defined as follows:

Fig. 1.

Critical zone when the protective relay should operate.

can be neglected, since it repreThe term sents a very small value. In the vicinity of the voltage collapse, all increase in the apparent-power supply at the sending end of the line no longer yields an increase in the power at the receiving end (3) Equation (3) can be rewritten as follows:

(4) Expression (3) equals zero when (5) (6) However, the condition in (5) is also fulfilled when the system variables (i.e., the voltages and currents), do not change significantly, or at all, during a given time interval. This common situation in the normal operating state is not critical for voltage stability and it should be disregarded. Voltage instability is reached when the magnitude ratio equals 1 and the phase equals at the same time. shift The SDC is defined as the absolute value of expression (4) as follows: (7) At the point of the voltage collapse, when , the SDC equals 0. The relay should operate when the SDC is smaller than the predefined threshold. The critical zone when the protective relay should operate is shown in Fig. 1. In this case, the activation threshold was set to 0.2. III. RELAY ALGORITHM


The SDC was used in the protection algorithm, which samples local phasors of bus voltage and line current at each line’s relay point. The algorithm is simple enough for implementation in a numerical relay.



Fig. 2. Flowchart of the proposed algorithm.

As discussed previously, there might be exceptional operating cases, and the algorithm parameters must be appropriately determined to make the algorithm applicable in the online protection scheme. The algorithm uses cyclic measurement samples on the line’s relay point. In the first step, the voltage and current phasors are measured and their values are stored. Based on the last two consecutive measurements, the difference between currents and voltages at the last two time intervals is then calculated in order to check whether the operational state changed in the selected time interval. With increased loading, both node voltages and line currents change, especially when the system is close to voltage instability. Therefore, use of only one of the two conditions ( or ) proved to be satisfactory. During normal operation, bus voltages lie somewhere between 0.9 and 1.1 p.u. Line currents normally exhibit a faster and broader range of change. In our case, only the current change was used. Determination of the critical threshold depends on the sampling frequency (i.e., the sampling time interval ). It is clear that the use of a shorter sampling time would produce smaller values for . The minimum was set to 0.01 p.u. When the condition threshold is fulfilled, the SDC is calculated. Otherwise, the SDC is set to 1. One can argue that if the SDC is not calculated in several steps, the load can change considerably from the initial state.

However, when the system is close to maximum loading, the and are fulfilled at conditions every step. If we take into account the voltage and current changes from the previous moments, the calculated SDC values would differ only when the loading does not change much. Since such operational states are not critical, neglecting the and when is smaller voltage and current changes is, therefore, justifiable. than the threshold Instead of voltage and current changes, one could use the . The problem in this case change of the apparent power flow because the loading is how to set a minimum threshold of different lines in the system can be quite diverse. One could use the relative change instead of the absolute one, which would then bring about problems with very small apparent power flows close to 0. In the next step, the algorithm detects whether a line is a source or a consumer of reactive power. Because of the shunt capacity, the line is a source of reactive power in the case of a small load under its natural loading. Such operational states are not critical regarding voltage collapse. In the case of heavy loading, the line reacts as a consumer of reactive power. Therefore, only when the line is a consumer of reactive power, the SDC is calculated in the following step. When the calculated , a warning SDC is smaller than the predefined threshold signal is sent to the control center. If the SDC is smaller than , a triggering signal is sent to predefined dethe threshold vices close to the affected node. The flowchart of the proposed algorithm is shown in Fig. 2.


Information obtained by the voltage-instability relay can be used at two levels with two different settings. The higher SDC is used for the coordinated system-wide control threshold is meant for automatic action, while the lowest setting action on the local level. Therefore, information obtained by the relay is first sent to the control center where the reported SDCs are analyzed and coordinated actions are issued. If the coordinated measures are not sufficient and the SDCs further decrease the relays at lines where the SDC reaches the threshold operate automatically by doing the following: • blocking the tap changers of predefined nearest transformers; • sending a triggering signal to the selected generators to increase the production of reactive power; • activating the nearest compensating devices; • load shedding of the selected consumers. The relay thus presents a line of defense at the local level and supports the system-wide protection against voltage collapse.

Fig. 3. IEEE-118 test system, load increase at all buses SDC



IV. TEST RESULTS The new protection algorithm was tested on the meshed IEEE 118-bus (IEEE-118) test system by increasing the active and reactive loads at selected buses. The increased generation was distributed evenly among the selected generators in the system according to their base-case production. Several loading scenarios were observed. In each case, the loading was progressively increased until the power-flow program failed to converge. It is well known that a purely static load (e.g., a constant impedance or a constant current load, cannot cause voltage instability, so at least a part of the load must be dynamic) [i.e., the load must exhibit some sort of self-restoring characteristic]. In this paper, the load will, therefore, be assumed to be primarily constant apparent power. Although the loads in the models are not considered as voltage dependent, their potential voltage dependency would reflect the measured values of voltage and current phasors, which affect the SDC as well. The generators’ reactive power production was limited in all cases. In this paper, we present the test results obtained on the IEEE 118-bus test system. The total demand of the base case is approximately 4242 MW and 1438 Mvar. For each test case, the minimum SDC in the system at each time is plotted versus the system loading (Figs. 3 and 5). Figs. 4 and 6 present the SDC for every bus in the system at the point of maximum loading. The most critical lines and buses are listed in Tables I and II. The lines were chosen where the SDC lies under, or just above, 0.2. In this way, the most at-risk parts of the system can be identified. Due to the local character of the voltage instability, this information is crucial. Moreover, it also enables the operator to locate where in the system the protective measures are required. A. Loads Increase at All Buses In the first scenario, the load was increased at all buses in the system simultaneously. Fig. 3 presents the minimum SDC in the system. In order to determine the most critical buses in the system, the SDC is plotted for every bus in the system at the point of maximum loading (Fig. 4). We can identify three critical areas:

Fig. 4. IEEE-118 test system, load increase at all buses, SDC for all buses in the system.

Fig. 5.

IEEE-118 test system, load increase at buses 54–60, SDC


from bus 1 to bus 39, from bus 46 to bus 56, and buses 71 and 73. Table I presents the SDC values for the most critical lines and buses in the system. B. Load Increase at Selected Buses (54–60) The procedure is repeated for the second loading scenario, where the load was increased proportionally at selected buses (i.e., buses 54–60). The minimum SDC values in the system at each time are presented in Fig. 5.





Fig. 7. IEEE-118 test system, load increase at buses 54–60, shunt VAR compensation at buses 54, 55, 56, and 59, SDC .

Fig. 6. IEEE-118 test system, load increase at buses 54–60, SDC for all buses in the system.

We can see that limitations in the reactive-power generation cause sudden changes to the SDC value when the limits are reached, since node-type switching from PV to PQ occurs when the load continues to increase. These changes are often followed by a steeper decline in the SDC value. As expected, the most endangered buses lie in the area from bus 54 to bus 60 (Fig. 6). Table II presents the SDC values for the most critical lines and buses in the system. V. REMEDIAL ACTIONS Many different preventive and corrective remedial measures have been proposed for power-system voltage-stability enhancement. The most common measures include the following: shunt reactor disconnection, shunt capacitor connection, shunt VAR compensation by means of SVCs and synchronous condensers, starting of gas turbines, low-priority load disconnection, and shedding of low-priority load. Load shedding and shunt VAR compensation are among the most commonly used remedial actions. In order to ensure the effectiveness of the

remedial measures, the most critical buses in the system have to be identified. The purpose of this paper is not to determine the magnitude of the protective measures but to study their effect on the voltage-stability margin. In order to do so, we studied and simulated load shedding and shunt VAR compensation, which would be triggered by the voltage-instability relay. The timing of the activation of the protective measures was determined on the basis of the value of the SDC. The threshold magnitude was set to 0.2. Simulations were performed on the IEEE-118 test system. The load was increased at selected buses in the system simultaneously. Candidate nodes for protective measures were those with the lowest SDCs. A. VAR Shunt Compensation First, one tries to avoid voltage instability by means of the shunt VAR compensation. In order to do this, 10, 25, and 50 Mvar is installed at buses 54, 55, 56, and 59. This makes, all together, 40, 100, and 200 Mvar of VAR support. The minimum SDCs for the system are plotted in Fig. 7. We can see that after the compensation, the voltage-stability margin is increased. B. Load Shedding at Selected Buses Next, one tries to shed some load at the buses 54 to 60. The results for 5%, 10%, and 20% load shedding are presented in Fig. 8.


Fig. 8. IEEE-118 test system, load increase at buses 54 to 60, load shedding at buses 54 to 60, SDC .

We can observe similar results as in the previous case. Since the loading continues to increase, a voltage collapse is inevitable. VI. CONCLUSION The proposed algorithm for protection against voltage instability uses only local data (i.e., voltage and current phasors measurement in the relay point of each selected line). The relay-operating criterion is based on the fact that in the vicinity of the voltage collapse, the entire increase in apparent power loading is due to the supply of transmission losses. Due to its computational simplicity, the algorithm is easy to implement in a numerical relay. The information obtained by the relay can be used for blocking the tap changers, as a triggering signal of voltage increase at the selected nearest generators or of compensating devices, and for load shedding activation at the node. In addition, the signal may be transmitted to the control center where coordinated system-wide control action can be undertaken. It presents a line of defense at the local level as well as supporting the system-wide protection against voltage collapse. The proposed method was successfully tested on the meshed IEEE 118-bus test system. Load shedding and shunt VAR compensation were studied as possible protective measures for different loading scenarios. They proved to be an efficient countermeasure for avoiding voltage collapse.

[2] P. A. Löf, G. Anderson, and D. J. Hill, “Voltage stability indices for stressed power systems,” IEEE Trans. Power Syst., vol. 8, pp. 326–335, Feb. 1993. [3] F. Gubina and B. Strmˇcnik, “A simple approach to voltage stability assessment in radial networks,” IEEE Trans. Power Syst., vol. 12, pp. 1121–1128, Aug. 1997. [4] G. Verbiˇc and F. Gubina, “A new concept of voltage security assessment based on local phasors,” Electrotech. Rev., vol. 69, no. 1, 2002. [5] K. Vu, M. M. Begoviˇc, D. Novosel, and M. M. Saha, “Use of local measurements to estimate voltage-stability margin,” IEEE Trans. Power Syst., vol. 14, pp. 1029–1035, Aug. 1999. [6] K. Yabe, J. Koda, K. Yoshida, K. H. Chiang, P. S. Khedkar, D. J. Leonard, and N. W. Miller, “Conceptual designs of AI-based systems for local prediction of voltage collapse,” IEEE Trans. Power Syst., vol. 11, Feb. 1996. [7] C. W. Taylor, “Concepts of undervoltage load shedding for voltage stability,” IEEE Trans. Power Delivery, vol. 7, pp. 480–488, Apr. 1992. [8] S. Arnborg, G. Andersson, D. J. Hill, and I. A. Hiskens, “On undervoltage load shedding in power systems,” Int. J. Elect. Power Energy Syst., vol. 19, no. 2, Feb. 1997. [9] P. Kundur, Power System Stability and Control: McGraw-Hill, 1994. [10] T. Van Cutsem and C. Vournas, Voltage Stability of Electric Power Systems. Norwell, MA: Kluwer, 1998. [11] Voltage Stability Assessment Procedures and Guides, IEEE/Power Eng. Soc., Power system stability subcommittee, 1999. [12] F. Gubina, D. Grgiˇc, and B. Strmˇcnik, “An alternative approach to voltage instability assessment,” in Proc. CIGRE 1998 Session, Paris, France, Aug. 1998. [13] Y.-H. Moon, H.-S. Ryu, and J.-G. Lee, “Uniqueness of static voltage stability analysis in power systems,” in Proc. IEEE Power Eng. Soc. Summer Meeting, Vancouver, BC, Canada, 2001.

Gregor Verbiˇc (S’98) was born in 1971 in Slovenia. He received the M.Sc. degree from the University of Ljubljana in 2000, where he is also pursuing the Ph.D. degree. After graduation, he was with Korona Power Engineering for three years. In 1998, he accepted a Teaching Assistant position with the Faculty of Electrical Engineering at the University of Ljubljana. His research interests include power system operation, dynamics, and control.

Ferdinand Gubina (M’73) was born in 1939 in Slovenia. He received the Diploma Engineer, M.Sc., and Dr.Sc. degrees from the University of Ljubljana, Ljubljana, Slovenia, in 1963, 1969, and 1972, respectively. Currently, he is Full Professor at the University of Ljubljana, where he has been since 1988. In 1970, he was a Teaching Associate with The Ohio State University, Columbus, for one year. From 1963, he was with the “Milan Vidmar” Electroinstitute, Ljubljana, where he was heading the Power System Operation

REFERENCES [1] C. Barbier and J. P. Barret, “An analysis of phenomena of voltage collapse on a transmission system,” ELECTRA, July 1980.


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