Online monitoring of voltage stability margin using PMU measurements

Received Apr 15, 2019 Revised Oct 11, 2019 Accepted Oct 20, 2019 With the growing smart grid concept it becomes important to monitor health of the power system at regular intervals for its secure and reliable operation. Phasor Measurement Units (PMUs) may play a vital role in this regard. This paper presents voltage stability monitoring in real time framework using synchrophasor measurements obtained by PMUs. Proposed approach estimates real power loading margin as well as reactive power loading margin of most critical bus using PMU data. As system operating conditions keep on changing, loading margin as well as critical bus information is updated at regular intervals using fresh PMU measurements. Simulations have been carried out using Power System Analysis Toolbox (PSAT) software. Accuracy of proposed Wide Area Monitoring System (WAMS) based estimation of voltage stability margin has been tested by comparing results with loading margin obtained by continuation power flow method (an offline approach for accurate estimation of voltage stability margin) under same set of operating conditions. Case studies performed on IEEE 14-bus system, New England 39-bus system and a practical 246-bus Indian power system validate effectiveness of proposed approach of online monitoring of loading margin.


INTRODUCTION
Voltage stability has been considered as an important threat against secure operation of power system [1]. Several incidences of voltage instability initiated grid failures have been observed in different parts of the world [2]. Various approaches for offline estimation of voltage stability have been well documented [3]. Offline assessment of voltage stability is quite useful in advance planning of preventive and corrective measures against instability. However, secure operation of a system in real time framework requires its online monitoring against instability. A forecasting-aided state estimation has been proposed for online monitoring of voltage stability [4]. Online assessment of voltage stability margin based on available reactive power reserve has been suggested [5]. Yiwei Qiu et. al. proposed parametric polynomial approximation of static voltage stability region boundaries based on Galerkin method and, suggested real time determination of left and right eigen vectors associated with zero eigen value at the estimated saddlenode-bifurcation space for online monitoring and control of voltage stability [6].
With advancement in wide-area monitoring system (WAMS) technology, online monitoring of voltage stability through time stamped measurements by Phasor Measurement Units (PMUs) seems possible. In comparison to Supervisory Control and Data Acquisition (SCADA) System the utilization of PMUs shows improved decision making and operation [7,8]. Many researchers proposed online monitoring of voltage stability margin by obtaining Thevenin's equivalence of network across a critical load bus based on real time 1157 measurements by PMUs. Online estimation of voltage stability margin through matching of critical load impedance with PMU measurements based Thevenin's impedance of the rest of the network has been proposed [9][10][11][12]. Representation of whole network connected across a critical load bus may be suitable for voltage stability monitoring of radial networks. However, interconnected power system may have a critical area comprising of a set of critical load buses prone to voltage collapse. Thevenin's equivalent of critical load area based on PMU measurements at its surrounding buses has been proposed [13,14]. All the buses in the critical load area have been merged to replace these by a fictitious load bus. A critical load area is fed by multiple tie-lines, in general. Some of these may have over flows that may lead to voltage instability in the area. Replacing all the buses in the area with a single equivalent bus merges all the tie-lines too into a fictitious equivalent tie-line. Therefore, tie-lines of original network having overflows and hence being responsible for instability cannot be detected. In order to address this issue, online monitoring of voltage stability margin of a load area based on tie-line flows has been proposed [15]. Tie-line flows have been obtained through phasor measurements performed by PMUs placed at boundary buses of the critical load area. However, critical load areas are dependent upon operating conditions and topology of the network. Change of network topology due to occurrence of contingencies may lead to emergence of new critical load areas where PMUs are not placed. Distributed linear algorithm has been proposed for online computation of voltage stability proximity indices (VCPI) based on local phasor measurements performed at all the load buses [16]. PMU measurements based online monitoring of critical buses using Q-V (reactive power-voltage magnitude) and P-Ө (real power-voltage angle) sensitivities has been proposed [17]. However, assumption of Q-Ө and P-V decoupling are not valid near nose point. A normalized P-index has been proposed for online monitoring of voltage stability using phasor measurements [18]. However, P-index has been developed assuming constant power factor under increased demand which is not valid for real time systems.
Online monitoring of voltage stability based on Thevenin's equivalent of the network [9][10][11][12][13][14][15], as well as sensitivity based real time estimation of voltage stability margin [16][17][18] may fail to produce satisfactory results in case of large disturbances due to highly non-linear behavior of power systems. An Artificial Neural Network (ANN) based monitoring of voltage stability based on phasor measurements has been proposed [19]. Proper training of ANN is still a challenge. Enhanced-Online-Random-Forest (EORF) model has been proposed based on voltage phasor measurements for online monitoring of voltage stability [20]. EORF model updates voltage stability information under change in operating conditions/network topology using fresh PMU measurements at important load buses. EORF model may lead sometimes to erroneous estimation of voltage stability margin due to non-consideration of voltage phasor information of remaining buses. A general method to adjust loads at the receiving end has been applied to determine the proximity to voltage collapse [21]. Here, it is concluded that the intermediate load adjustment improves the accuracy of the indices. In this the PMUs are not placed optimally in the system. In most of the research the statistical information obtained from PMUs has not actionably used to improve the voltage stability. In [22], the new method has been suggested that gauges and improves the voltage stability of a system using statistical data obtained from PMUs.
In this paper, real time determination of nose curve of all the load buses based on three successive PMU measurements and pseudo-measurements is performed. Minimum out of maximum loadability of all the load buses has been considered as the loading margin of the system. Voltage stability information is updated with new PMU measurements obtained. Thus, proposed approach is capable of monitoring voltage stability of real time systems as change in system operating conditions and network topology is considered by updated PMU measurements performed at regular intervals. PMUs have been optimally placed in the system based on result of binary integer linear programming ensuring full network observability even in case of loss of few PMUs under contingencies [23]. Paper is structured as follows: Section II presents methodology proposed for online monitoring of voltage stability margin using PMU measurements based quadratic fitting of nose curves. Section III validates effectiveness of proposed approach based on case studies performed on standard IEEE 14-bus system, New England 39-bus system and a practical 246-bus Indian system representing power network of nine states and union territories of India. Section IV concludes summarizing important contributions of the proposed work.

METHODOLOGY
Proposed approach of online monitoring of voltage stability margin using phasor measurements is presented: Real power demand ( where, 1i b , 2i b and 3i b are constants.
At the nose point of Q-V curve, where, nq i V = voltage magnitude of bus-i at the nose point of Q-V curve shown in Figure 2. From (5) and (7), where, i n D Q = Reactive power demand of bus-i at the nose point of Q-V curve shown in Figure 2. Constants 1i a , 2i a and 3i a were obtained by solution of equations: where, Figure 1 and in Figure 2 correspond to voltage magnitude of bus-i at operating points 1, 2 and 3, respectively, and Evaluated constants 1i a , 2i a and 3i a were used to find real power loading margin of bus-i using (4). Constants 1i b , 2i b and 3i b are obtained by solution of equations: where, Figure 2 correspond to reactive power demand of bus-i at operating points 1, 2 and 3, respectively. Evaluated constants 1i b , 2i b and 3i b were used to find reactive power loading margin of bus-i using (8). Constants a1i, a2i, a3i, b1i, b2i and b3i for each of the load buses were evaluated using voltage magnitude, real power demand and reactive power demand obtained by PMU measurements/pseudo measurements performed at operating points 1, 2 and 3, respectively. Evaluated constants predict real power loading margin as well as reactive power loading margin of each bus using (4) and (8), respectively. Minimum out of maximum real power loadability of all the load buses present in the system is considered as real power loading margin of the system, and corresponding bus was considered as the most critical bus based on real power loading margin. Minimum out of maximum reactive power loadability of all the load buses present in the system was considered as reactive power loading margin of the system, and corresponding bus was considered as the most critical bus based on reactive power loading margin criterion. A flow chart for finding loading margin as well as most critical bus based on PMU measurements is shown in Figure 3. Since, loading margin of a real time system keeps on changing with change in operating conditions; it is proposed to update loading margin as well as most critical bus information based on new PMU measurements obtained, at regular intervals. Flowchart shown in Figure 3 assumes very high initial loading margin of 10,000 MW and 10,000 MVAR, respectively, keeping in mind such values to be higher than loading margin of any of the load buses present in the system, and keeps on reducing these till real power loading margin as well as reactive power loading margin of the most critical bus are obtained. Pseudo measurements were performed using following network observability rules: a. If voltage and current phasor at one end of a branch are known, voltage phasor at the other end of the branch can be calculated using Ohm's law. b. If voltage phasors at both the ends of a branch are known, branch current can be calculated c. If there exists a zero-injection bus with all branch currents known except for one, the unknown branch current can be calculated using Kirchhoff's Current Law (KCL).

CASE STUDIES
Proposed approach of online monitoring of voltage stability margin was tested on IEEE 14-bus system, New England 39-bus system and 246-bus Northern Region Power Grid (NRPG) system of India with the help of Power System Analysis Toolbox (PSAT) software [24]. Simulation results obtained on three systems are presented below:

IEEE 14-Bus System
IEEE 14-bus system consists of two synchronous generators (at bus numbers 1 and 2), three synchronous condensers (at bus number 3, 6 and 8) and 20 transmission lines including three transformers [25]. This system has a zero-injection bus at bus number 7. PMUs were placed at bus numbers 2, 4, 5, 6 and 9 based on results of binary integer linear programming [23] ensuring full network observability even in case of loss of few PMUs. Voltage magnitude, real power demand and reactive power demand of all the load buses were obtained at three operating points (viz. points 1, 2 and 3, respectively) using combination of PMU measurements and pseudo measurements for the system intact case. Constants a1i, a2i and a3i were calculated using (9), (10) and (11) for each of the load buses. Evaluated constants were used to find nose point real power demand ( Measured voltage magnitude and real power demand of the most critical bus at the three operating points, calculated using proposed approach and real power loadability based most critical bus number have been shown in Table 1 for the system intact case and few critical contingency cases. In order to validate real power loading margin obtained by proposed approach, real power demand versus voltage magnitude curve (P-V curve) of most critical bus was plotted using continuation power flow (CPF) method [26] for the system intact case and all the single line outage cases. For obtaining P-V curve of the most critical bus using CPF method, its real power demand was varied as per following: where, = fraction of real power demand increase at bus-j Real power loading margin ( ) of the most critical bus obtained by CPF method (real power demand at the nose point of its P-V curve) have also been shown in Table 1 for the system intact case and few critical contingency cases. It is observed from Table 1 that real power loading margin obtained by proposed approach closely matches with real power loading margin found by continuation power flow method.   Constants b1i, b2i and b3i were calculated for each of the load buses using (12), (13) and (14) for the system intact case and all the single line outage cases using PMU measurements/pseudo measurements. Q value was considered as most critical bus requiring attention as for as reactive power loading margin is concerned. In order to validate reactive power loading margin obtained by proposed approach, reactive power demand versus voltage magnitude curve (Q-V curve) of the most critical bus was obtained by CPF method for the system intact case and all the single line outage cases. For obtaining Q-V curve of the most critical bus using CPF method, its reactive power demand was varied using: where, = fraction of reactive power demand increase at bus-j Measured voltage magnitude and reactive power demand of most critical bus at three operating points, reactive power loading margin ( ) obtained by proposed approach as well as by CPF method have been shown in Table 2 1163 loadability based most critical bus number has also been shown in Table 2 for all these cases. It is observed from

New England 39-Bus System
The New England 39-Bus System has 10 generators and 46 transmission lines with 12 zero-injection buses at bus numbers 1, 2, 5, 6, 9, 10, 11, 13, 14, 17, 19 and 22 [27]. Binary integer linear programming was used to optimally place PMUs in the system ensuring full network observability even in case of loss of few PMUs [23]. It results PMU placement at bus numbers 4, 8, 12, 16, 18, 20, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38 and 39. Real power loading margin was calculated as per flow chart shown in Figure 3 for the system intact case and all the single line outage cases, as in case of IEEE 14-bus system. Measured voltage magnitude and real power demand of the most critical bus at the three operating points, calculated using proposed approach and real power loadability based most critical bus number have been shown in Table 3 for the system intact case and few critical contingency cases. In order to validate real power loadability obtained by proposed approach, real power demand versus voltage magnitude curve (P-V curve) of most critical bus was plotted using continuation power flow (CPF) method [26] for the system intact case and all the single line outage cases. For obtaining P-V curve of the most critical bus, its real power demand was varied as per (15). Real power loading margin ( ) of the most critical bus obtained by CPF 1164 method (real power demand at the nose point of its P-V curve) have also been shown in Table 3 for the system intact case and few critical contingency cases. It is observed from Table 3 that real power loading margin obtained by proposed approach closely matches with real power loading margin found by continuation power flow method.  P-V curve of bus 20 (most critical bus) obtained by proposed quadratic fitting of nose curves using PMU measurements/pseudo measurements obtained at three operating points as well as continuation power flow based P-V curve of same bus have been shown in Figure 6 for the outage of line 29-38. It is observed from Figure 6 that nose point real power loadability obtained by proposed approach closely matches with real power loading margin of the bus obtained by continuation power flow method. Reactive power loading margin ( ) was calculated as per flow chart shown in Figure 3 for the system intact case and all the single line outage cases, as in case of IEEE 14-bus system. In order to validate reactive power loading margin obtained by proposed approach, reactive power demand versus voltage magnitude curve (Q-V curve) of the most critical bus was also obtained by CPF method for the system intact case and all the single line outage cases. For obtaining Q-V curve of the most critical bus, its reactive power demand was varied as per (16). Measured voltage magnitude and reactive power demand of most critical bus at three operating points, reactive power loading margin ( ) obtained by proposed approach as well as by CPF method have been shown in Table 4, for the system intact case and few critical contingency cases. Reactive power loadability based most critical bus number has also been shown in Table 4 for all these cases. It is observed from Table 4

NRPG 246-Bus System
The 246-bus Northern Regional Power Grid (NRPG) system covers power network of seven states (Jammu and Kashmir, Himachal Pradesh, Punjab, Haryana, Rajasthan, Uttarakhand and Uttar Pradesh) and two union territories (Chandigarh and New Delhi) of India x Ma D P was calculated for the system as per flow chart shown in Figure 3 for the system intact case and all the single line outage cases, as in case of IEEE 14-bus system and New England 39-bus system. Measured voltage magnitude and real power demand of the most critical bus at the three operating points, real power loadability based most critical bus number and calculated using proposed approach have been shown in Table 5 for the system intact case and few critical contingency cases. In order to validate real power loading margin obtained by proposed approach, real power demand versus voltage magnitude curve (P-V curve) of most critical bus was plotted using continuation power flow (CPF) method [26] for the system intact case and all the single line outage cases. CPF based P-V curve was obtained by varying real power demand at the bus as per (15). Real power loading margin ( ) of the most critical bus obtained by CPF method (real power demand at the nose point of its P-V curve) have also been shown in Table 5 for the system intact case and few critical contingency cases. It is observed from Table 5 that real power loading margin obtained by proposed approach closely matches with real power loading margin found by continuation power flow method. 25 1166 P-V curve of bus 174 (most critical bus) obtained by proposed quadratic fitting of nose curves using PMU measurements/pseudo measurements at three operating points as well as continuation power flow based P-V curve of same bus have been shown in Figure 8 for the outage of line 194-198. It is observed from Figure 8 that nose point real power loadability obtained by proposed approach closely matches with real power loading margin of the bus obtained by continuation power flow method.
was calculated for the system intact case and all the single line outage cases, as in case of IEEE 14-bus system and New England 39-bus system. In order to validate reactive power loading margin obtained by proposed approach, reactive power demand versus voltage magnitude curve (Q-V curve) of the most critical bus was also obtained by CPF method for the system intact case and all the single line outage cases. CPF based Q-V curve was obtained by varying reactive power demand at the bus as per (16). Measured voltage magnitude and reactive power demand of most critical bus at three operating points, reactive power loading margin ( ) obtained by proposed approach as well as by CPF method have been shown in Table 6, for the system intact case and few critical contingency cases. Reactive power loadability based most critical bus number has also been shown in Table 6 for all these cases. It is observed from Q-V curve of bus 158 (most critical bus) obtained by proposed quadratic curve fitting of nose curves using PMU measurements/pseudo measurements at three operating points as well as CPF based Q-V curve of same bus have been shown in Figure9 for the outage of line 156-158. It is observed from Figure 9 that nose point reactive power loadability of bus 158 obtained by proposed approach closely matches with CPF based nose point reactive power demand.

CONCLUSION
Online monitoring of voltage stability margin using PMU measurements has been proposed in this work. Proposed approach estimates voltage stability margin based on measurements obtained at three operating points. Due to highly dynamic nature of power systems, voltage stability margin keeps on changing. Therefore, proposed approach suggests computation of updated voltage stability margin at regular intervals based on new PMU measurements obtained. Change in operating scenario has been simulated in PSAT software considering different single line outage cases. Accuracy of proposed approach has been validated by comparing voltage stability margin obtained by proposed approach with margin estimated using continuation power flow method under same set of operating conditions. Case studies performed on three test systems show that real power loading margin as well as reactive power loading margin of the system obtained by proposed approach closely matches with loading margin obtained by continuation power flow method. 12 Proposed Approach CPF