Abstract
This paper proposes an adaptive method based on fuzzy logic that utilizes data from phasor measurement units (PMUs) to assess and classify generating-side voltage trajectories. The voltage variable and its associated derivatives are used as the input variables of a fuzzy-logic block. In addition, the voltage trajectory is compared with the pre-selected pilot-bus voltage to make a reliable decision about the voltage operational state. Different types of short-term voltage dynamics are considered in the proposed method. The fuzzy membership functions are determined using a systematic method that considers the current situation of the voltage trajectory. Finally, the voltage status is categorized into four classes to determine appropriate remedial actions. The proposed method is validated on a IEEE 73-bus power system in a MATLAB environment.
DUE to the fast-growing complexity of power systems, whether from a software or hardware perspective, the steady-state operation of power systems is often exposed to different disturbances. In addition, modern power systems are heavily loaded close to their capacity limits due to economic and environmental issues. The increasing penetration of flexible electrical loads into power systems also makes power system dynamics more complex than before. Consequently, the stable operation of power systems is frequently threatened by their low-stability margins. Under these circumstances, the voltage stability (VS) encounters significant challenges. Therefore, it is necessary to have proper knowledge of the VS before entering into an unacceptable operation area. This in turn allows the system operator (SO) to maintain system stability and restore the voltage profile without significant load shedding or generator disconnection.
VS is defined as “the ability of a power system to maintain steady-state voltages close to the nominal value at all buses in the system after being subjected to a disturbance [
Among many VS issues, short-term voltage instability (STVI), fault-induced delayed voltage recovery (FIDVR), and fast voltage collapse are the most harmful phenomena that result from the penetration of fast load dynamics in modern power systems. These phenomena are inherently fast, making their evaluation challenging. STVI is defined as the inability of a power system to deliver the required reactive power due to the fast interaction of the load components when the voltage is at a low level. By contrast, FIDVR refers to the slow recovery of voltage following fault clearance under low-voltage conditions. However, a voltage collapse indicates a significant decrease in voltage in a noticeable area of the power system following a disturbance [
Notably, despite the efficacy of the existing methods in identifying these phenomena, most of them consider only one of the mentioned phenomena. In addition, they make decisions about the voltage status only when they exceed a predefined secure area. Although these principles may lead to accurate identification, they result in expensive remedial actions for only single case of the aforementioned phenomena. Furthermore, the existing methods do not allow for preemptive measures to be taken in a timely manner, as they only identify the issue after they exceeded a predefined area. This often requires the SO to perform severe and costly remedial actions to maintain power system security. Therefore, this paper proposes a new type of voltage classification that enables low-cost preemptive actions to be taken before potential threats increase.
In general, VS assessment methods can be categorized into event-based [
Traditionally, VS is accomplished by power system models. To achieve specific aims, model-based methods require solving relevant sophisticated differential equations using time-domain simulations. Among these methods, P-V and Q-V curves for specified load buses are the most conventional schemes, requiring enormous power flow calculations [
To address the aforementioned drawbacks and considering the major progress in communication infrastructure and wide-area measurement systems (WAMSs), data-driven methods have recently gained attention because of their high speed and accuracy in VS assessments. In general, data-driven methods for VS assessment involve machine-learning and analytical-measurement methods.
Machine-learning methods such as artificial neural networks [
Unlike machine-learning methods, analytical-measurement methods have been developed to derive cognitive indices based on the mathematical equations that govern the phenomena under study. These methods simplify the decision-making process compared with model-based methods [
In another attempt, the trajectory violation index (TVI), which is a model-free assessment index, is introduced in [
In the area of analytical-measurement VS assessment, some studies have examined the methods based on the Thevenin equivalent circuit. The voltage instability predictor is a well-known index that relies on the Thevenin impedance compatibility with the load impedance. This method attempts to determine the maximum load power by comparing the equivalent Thevenin impedance with the load impedance. Although this index is used for long-term voltage instability assessment, it is used in [
In [
Most existing methods focus only on voltage assessment when the voltage is outside a predefined area. This in turn requires numerous corrective actions to address complex situations. In addition, these methods often lack appropriate thresholds, necessitating complex studies to improve the assessment accuracy. This issue is discussed further in the comparison section of this paper.
To address these drawbacks, this paper proposes a fuzzy-logic-based framework to identify the voltage status and classify the voltage condition into the four classes of steady state, alarm, emergency, and high risk. Some existing studies that perform VS assessments, in which the present voltage value is compared with its previous behavior within a specific window, may fail in proper decision making. Hence, the bus voltage is compared with the reference pilot bus voltage to provide a comprehensive perspective based on a strict bus in the proposed method. In addition, the results of the implementation of the proposed method in this paper are involved in the decision-making process.
Although the FIDVR, STVI, and oscillatory conditions are considered in the assessment process, they are independently investigated in previous studies. Notably, unlike some existing methods, the voltage status assessment is performed when the voltage trajectory remains within the allowable range of the North American Electric Reliability Council (NERC) criteria [
The contributions of the paper are as follows.
1) A simple data-driven fuzzy-logic method is proposed to determine the voltage status.
2) The voltage situation is classified into four categories when it lies within the allowable area introduced by the NERC to implement proper measures against the circumstances created.
3) The effects of the FIDVR, STVI, and oscillatory conditions are simultaneously considered in the classification process.
4) The developed assessment process considers the behavior of the non-pilot bus voltage based on the pilot bus.
5) The history of the voltage trajectory is involved in each averaging window, which improves decision making in terms of broad data samples.
The remainder of this paper is organized as follows. Section II provides the proposed methodology. The developed fuzzy-logic method is explained in Section III. Simulation results are assessed in Section IV to confirm the efficacy of the proposed method. Finally, the overall features of the results are summarized in Section V.
Determining the power system voltage status results in proper situational awareness and provides conditions for conducting appropriate corrective and preventive actions. However, maintaining the generating units in an operational state is essential to effectively satisfy the reactive power requirements of the system. Hence, the status of the voltage situation is investigated based on PV bus voltage trajectories in this paper. To this end, the following hypotheses are first considered to simplify the voltage assessment process.
A. Hypotheses
1) The NERC relevant to voltage ride-through in [

Fig. 1 Modified voltage ride-through criterion based on NERC.
2) The voltage magnitude trajectory may exhibit an oscillatory feature due to transient conditions following a severe disturbance. Thus, it can have a destructive effect on fuzzy-logic classification. To alleviate this effect, the averaged voltage in a window length involving 20 samples and taking 0.33 s is used in the fuzzy logic. This measure can reduce the oscillatory effect of a voltage signal with frequency oscillations greater than 3 Hz. This helps remove oscillations with frequencies higher than 3 Hz. This strategy indicates the overall voltage position during the 0.33 s concerning measurement errors and the oscillatory voltages with high frequency during the decision-making process. The averaging-related window length consists of five past samples accompanied by 15 updated samples. The instant of the obtained average value belongs to the latest received corresponding time.
3) The pilot bus in an area is known as the firmest bus in that area. Various criteria can be used to select a pilot bus such as the conventional maximum short-circuit current [
B. Overall Framework

Fig. 2 Overall process of proposed method for assessing voltage status.
Voltage assessment is conducted in three segments, as shown in
The desired voltage trajectory is achieved when it continuously approaches its nominal value. Therefore, the slope of the present voltage magnitude sample with respect to the lower-voltage bound at the previous sample time provides useful information regarding its distance to the lower-voltage bound and its trend toward the normal state. Thus, the slope of the voltage magnitude is included as an input variable in the fuzzy-logic block to obtain better classification results. This input variable is defined based on (1).
(1) |
where is the lower voltage at the segment; is the current variable sample of the non-pilot bus voltage magnitude; and j is the current variable sample. The time variable is considered as the second input to the fuzzy-logic block. This input variable provides information on the variations in the voltage trajectory.
However, assessing the voltage status of the generator buses based on the pilot bus, which is the strongest of the other buses in the area, improves comprehensive situational awareness. The pilot bus provides more reliable countermeasures for the reactive power demand and better response compared with other buses in the area [
(2) |
where is the voltage magnitude of the pilot bus at the previous sample time. The behavior of the is determined by its directional specifications. In addition, the variations in its magnitude are determined based on its previous value. Therefore, the ratio of the absolute value of the obtained at the present sample time to its value in the past sample indicates the magnitude variations, as expressed in (3).
(3) |
Furthermore, the negative or positive signs of RoCoVp at the present instant indicates the direction of the obtained slope, providing additional information for better decision making as the fourth input.
(4) |
The voltage magnitude at the previous sample time provides reliable information for the fuzzy-logic method to generate accurate results. This information assists in properly considering the effects of oscillatory trends on the voltage profile.
As the final input, the , based on its previous voltage magnitude, elucidates the trend of the voltage profile between two consecutive samples. Combining it with other inputs completes the classification. The RoCoV function is derived based on (5).
(5) |

Fig. 3 Overall structure of fuzzy-logic method.
A. Membership Function Design
Accordingly, MF1, which is the membership function block associated with the voltage magnitude position, consists of three trapezoidal membership functions within its specified range.
This membership function determines the area of the voltage magnitude position by considering its slope from the lower-bound value of the previous sample time. The lower bound of the voltage magnitude varies depending on the current segment. For Segments 1-3, this value is set to be 0.65, 0.75, and 1 p.u., respectively. The defined parts of MF1 are categorized into three linguistic values: L (low), M (medium), and H (high).

Fig. 4 Process for determining parameters of MF1.
Notably, the values associated with and vary depending on the current segment. values for all segments are set to be 1.05 p.u.. The values corresponding to are equal to 0.92, 0.95, and 0.975 p.u. in Segments 1-3, respectively.
MF2 is a part of the membership function block associated with the time-variable input. In general, in each segment, MF2 consists of two triangular membership functions. In Segment 1, the L1 linguistic parameter is dedicated to the triangular membership function between s and s. The parameters belong to the second triangular membership function from to s. In Segment 2, the two membership functions take between s and s, respectively. The relevant time parameters in Segment 3 are equal to , s, and s, respectively.

Fig. 5 Distribution principle of membership functions for time variable input.

Fig. 6 Membership function pertaining to .
In this case, Rui denotes the upper bound of , which can be determined using (6) and as the lower bound is written as (7).
(6) |
(7) |
The and are the voltage magnitude boundaries, and refers to the understudy segment. The values for in Segments 1 and 2 and in the first part of Segment 3 are set to be 0.8, 0.9, and 0.95 p.u., respectively.
The values for V2 in Segments 1 and 2 and the first part of Segment 3 are 1, 1.06, and 1.05 p.u., respectively. The upper and lower bounds in the second part of Segment 3 are set to be 1.02 and 0.975 p.u., respectively.
In addition, the variations in voltage magnitude of the pilot bus demonstrate the adaptive nature of the membership function status. As shown in
MF4 and MF5 are relevant for determining the RoCoVp trajectory. Accordingly, MF4 identifies the RoCoVp trend when it declines continuously in two consecutive samples. Thus, when the ratio of current absolute RoCoVp value to the RoCoVp value at the previous sample time is less than -1, it implies that the RoCoVp value has increased, whereas its previous sample has a negative value. MF4 includes two trapezoidal membership functions, as illustrated in

Fig. 7 Characteristics of MF4 as related to Yj.
MF5 specifies the sign of the RoCoVp based on the membership functions, as shown in

Fig. 8 Characteristics of MF5 as related to sign of .
The remaining MFs refer to the behavior of the self-voltage magnitude. As previously mentioned, when the voltage trajectory remains less than 0.8 p.u. for a time duration more than 0.25 s, it indicates the potential high-risk circumstance for the voltage [

Fig. 9 Characteristics of MF6.
In addition, MF7, which is the membership function block associated with RoCoV, consists of three trapezoidal membership functions. As

Fig. 10 Characteristics of MF7.
Finally, MF8 refers to the output variable consisting of two trapezoidal and triangular membership functions.
According to the combination of the input variable effects using the fuzzy-logic block, the output is categorized into four statuses: normal, alarm, emergency, and high risk.

Fig. 11 Characteristics of MF8.
B. Determination of Fuzzy Rules
Based on the existing eight MFs and the numbers of their membership functions, defining extensive rules for the classification intention is then necessary. In general, 1944 rules use a combination of different membership functions. For clarification, the fuzzy rules related to each category output are described in detail.
These fuzzy rule bases are listed in
Row | MF1 | MF2 | MF3 | MF4 | MF5 | MF6 | MF7 | MF8 |
---|---|---|---|---|---|---|---|---|
1 | L | L3 | L | L | L | L | L | H |
2 | H | H2 | H | H | H | M | H | E |
3 | M | L3 | M | H | H | L | M | A |
4 | M | L3 | M | H | H | M | M | N |
5 | L | H3 | L | L | L | M | L | H |
6 | L | H2 | L | L | L | L | L | H |
The second row in
The third row of
Another combination is shown in the fifth row of
The combination of arrays in the sixth row in
If the voltage trajectory exits a predefined framework, it is considered a high-risk situation that may lead to generator disconnection and increase the risk of voltage instability. Investigating the voltage behavior within a predefined framework provides useful information about the transient voltage trend and the capacity of the power system to meet the load requirements after fault clearance. The proposed method considers the generator voltage, indirectly indicating the load bus voltage status for voltage assessment. In some cases, the generator voltage may remain within the predefined area, whereas the load bus voltage may lead to instability, affecting the generator voltage with a time delay. Therefore, detailed information about the generator voltage is essential to predict the future trends of the system and help SOs implement cost-effective measures to maintain system stability.
The most common countermeasures against the undesired voltage profile can range from capacitor banks and flexible alternating current transmission systems to shedding small blocks of loads. The Mamdani method, as a fuzzy inference method, is used for the fuzzy-logic method, and defuzzification is performed using the centroid method.
Following fuzzy-logic decision making, an averaging process is performed on the output variable in a moving window consisting of five samples, as expressed in (8).
(8) |
where is the output of the sample.
This process provides more reliable results based on the voltage conditions. Considering four prior samples with identical weighting coefficients prevents unnecessary decision making and provides comprehensive results. This process results in the decisions that lead to conservative and reliable preemptive actions against the undesired voltage profile.
A. Benchmark System
Different contingencies are applied to a IEEE 73-bus power system to investigate the performance of the proposed method in terms of voltage-status classification. The case study consists of 33 generating units distributed across three areas.

Fig. 12 Single-line diagram of IEEE 73-bus power system.
B. Simulation Results
A three-phase fault with is applied to Line 208-210 at s and lasts for 0.35 s. The fault point distance from bus 208 is 20% of the line length. The proposed method determines the voltage status of bus 207, as shown in

Fig. 13 Assessment results after a three-phase fault with Ω on Line 208-210 for 0.35 s. (a) Averaged and instantaneous outputs of fuzzy-logic controller. (b) Averaged voltage magnitudes of pilot bus 223 and bus 207.
The voltage magnitude trajectory of bus 207 approaches an unstable state after fault clearance. Thus, the voltage classification results indicate a high-risk situation. It can be observed from
By contrast, the proposed method analyzes the voltage magnitude status of bus 202 following a three-phase fault on Line 208-209. The symmetrical fault occurrence with remains on the line for 0.3 s from s at a distance from bus 208 for half of the line length.
The averaged voltage magnitude trajectory exceeds the upper bound in Segment 1 at a specified time and returns to acceptable conditions. In addition, the voltage trajectory in Segment 2 follows an incremental trend for a limited duration. Accordingly, this condition is dedicated to alarm situations under the proposed classification. The voltage then follows a smooth trajectory in a secure form.

Fig. 14 Assessment results after a three-phase fault with Ω on Line 208-209 for 0.3 s. (a) Averaged and instantaneous outputs of fuzzy-logic controller. (b) Averaged voltage magnitudes of pilot bus 223 and bus 202.
Another three-phase fault with from s to s on Line 219-220 exposes the stability of the power system under a threat. The fault occurrence is imposed on the middle line. The average voltage of bus 216, as shown in

Fig. 15 Assessment results after a three-phase fault with Ω on Line 219-220 from s to s. (a) Averaged and instantaneous outputs of fuzzy-logic controller. (b) Averaged voltage magnitudes of pilot bus 223 and bus 216.
However, in these cases, the voltage trajectory may instantaneously cross safe conditions, approaching an undesired boundary, as shown in
At this stage, a three-phase fault with on Line 216-219 from s to s challenges the proposed classification performance. The fault point distance from bus 216 is 20% of the line length. The results show that the voltage magnitude experiences severe oscillations because of the unstable power swing following the fault occurrence, as shown in

Fig. 16 Assessment results after a three-phase fault with Ω on Line 216-219 from s to s. (a) Averaged and instantaneous outputs of fuzzy-logic controller. (b) Averaged voltage magnitudes of pilot bus 223 and bus 216. (c) Instantaneous voltage trajectory of bus 216.
In addition, the voltage trajectory of bus 216 following a three-phase fault with on Line 222-217 is categorized based on the proposed method, as shown in

Fig. 17 Assessment results after a three-phase fault with Ω on Line 222-217 from s to s. (a) Averaged and instantaneous outputs of fuzzy-logic controller. (b) Averaged voltage magnitudes of pilot bus 223 and bus 216.
The voltage profile after the fault clearance at s as shown in
C. Comparison and Discussion
For voltage assessment, the performance of the proposed method is compared with several popular indices, including TVSI, VSRI, TVI, contingency severity index (CSI), and estimated time for voltage recovery (denoted as TR).
The characteristics of these indices are briefly introduced as follows. Additional details can be found in [
TVSI indicates the instances in which the difference between the initial and current values of the voltage profile exceeds a specific threshold. The sum of these differences determines the voltage status after fault clearance up to the time of the STVS evaluation.
VSRI determines the voltage status based on the voltage behavior in a window with a length of several samples. The average voltage value obtained using a moving window is then compared with the most recent voltage sample.
TVI determines the sum of the areas in which the voltage trajectory exceeds the exponential upper and lower boundaries.
CSI uses two indices to obtain the VS status. The first index is related to the duration in which the voltage trajectory remains below a specific value, and the second index indicates the minimum value of the voltage after fault clearance.
Finally, serving as an indicator of load shedding, TR is introduced in the paper. This index is derived from the voltage deviation and estimated time required for voltage restoration to a safe level. Specifically, the index quantifies the time necessary for voltage recovery when the voltage remains less than 0.8 p.u. after fault clearance. If the estimated time exceeds the prespecified time for restoration, load shedding is automatically initiated. The estimated time is determined by the slope of the voltage trajectory, where a negative slope indicates an infinite recovery time and a positive slope allows for an estimation of the recovery time. One can obtain the estimated recovery time, which is calculated as follows.
(9) |
where is the estimated time; is the current sample after the fault occurrence; and is the voltage magnitude at the sample of the time. is then compared with the predetermined time for recovery after fault clearance as follows.
(10) |
where and are the clearance time and time index, respectively. The triggering of load shedding depends on the estimated time being greater than zero, which is necessary to restore the voltage to a secure level.
In this regard, two scenarios are considered to compare the proposed and previous methods.
1) The system operates at 120% of a base load. Then, a three-phase fault with a resistance of 0.001 Ω is applied to Line 216-219. The fault point distance from bus 216 is 20% of the line length that lasts for 0.3 s from s.
2) The power system operates at 110% of the base load. Then, a three-phase fault is applied to Line 216-219 with a property similar to that of Scenario 1.

Fig. 18 Voltage magnitudes of bus 216 in response to Scenarios 1 and 2. (a) Scenario 1. (b) Scenario 2.

Fig. 19 Results in response to Scenario 1. (a) TR profile after applying scenario. (b) TVSI profile for different time intervals. (c) VSRI profile in response to applied scenario over time. (d) TVI profile. (e) CSI profile for different time intervals. (f) Results with proposed method.
In addition, the index is useful only under conditions in which the voltage remains less than 0.8 p.u. for 4 s after a fault occurrence. Finally, the index does not provide classification information about the voltage trajectory when it is greater than 0.8 p.u. under this time duration.
TVSI results, as shown in
In addition, TVSI uses local indices from other locations to generate a global index and therefore cannot be used as a local indicator of VS.
TVI is an index that determines whether the voltage can remain in a predefined area, indicating the time duration at which the voltage surpasses the lower or upper bound. According to
(11) |
where is the lower exponential border for the voltage; is the steady-state voltage; B is the damping factor; and is the end of the evaluation time.
The proposed method is then employed to showcase the response to Scenario 1, as depicted in

Fig. 20 Responses of evaluated indices to Scenario 2. (a) TR profile after applying scenario. (b) TVSI profile for different time intervals. (c) VSRI profile in response to applied scenario over time. (d) TVI profile. (e) CSI profile for different time intervals. (f) Results with proposed method.
Index | Comparison |
---|---|
Voltage trajectories | Voltage trajectories are stable after the fault clearance but follow a risky trend requiring suitable corrective measures to return the voltage to a safe bound. |
TVSI | TVSI is damped over time following a considerable increase after . In this case, it does not present clear information, particularly for a long time. |
VSRI | It oscillates around zero with low magnitudes. It does not present an accurate assessment while the voltage follows a risky trend. |
CSI | Although the voltage tracks a vulnerable trend in the long time interval, the CSI has low values and does not provide accurate information. |
TVI | It has low values over time after the fault clearance while the voltage remains below 0.95 p.u. for a long time, indicating a potential risk. |
TR | The output of this index at initial time results in load shedding, which may not be necessary for early stages of this scenario with respect to the voltage trend. |
Proposed method | The proposed method classifies the applied disturbance to prepare for potential corrective action at low costs. |
Index | Comparison |
---|---|
Predictive-based methods | They need Thevenin equivalent circuit parameters at each load bus and components model as a challenge, especially for emerging time-varying flexible loads. Generally, predictive methods can be only used for long-term stability assessment. |
TVSI | It needs a proper threshold to provide an accurate assessment. It does not present detailed information when the voltage stays in predefined area. The criterion for index calculation changes from one case to another. |
VSRI | It compares the voltage with its past behavior in a specific moving window. The window length determination for averaging is challenging. It needs a proper threshold to assess the voltage assessment. It needs the local information from other locations. If the voltage follows a smooth trend but outside the safe area, it cannot provide an accurate decision. |
CSI | CSI cannot determine voltage risky status when it is higher than 0.8 times of pre-disturbance voltage, especially in long time. It needs for load bus information to provide better decisions. It needs to determine a proper threshold for different time intervals. |
TVI | Parameter definition to specify safe area is challenging to provide a proper trade-off between short- and long-time assessment. It needs to determine a proper threshold for an accurate assessment. It cannot to provide an awareness when the voltage is higher than 0.9 p.u. but close to it for long time. |
TR | Instantaneous values of the voltage are used for decision making. The index performance can be challenging with the border conditions at 0.8 p.u.. During the oscillatory conditions, the risk of the mistakes may increase. |
Proposed method | It provides a classification assessment to prepare low-cost corrective actions when the voltage has a potential risk trend. It focuses on generator buses without the need for load buses. It compares the voltage trajectory with the firmest one in that area, unlike the VSRI index. It provides a reliable decision after the specific time interval using averaging the past results in a moving window. Because it considers the behavior voltage inside the predefined area, it needs a proper time interval to provide reliable awarenes for low-cost corrective actions. It needs to wait for 15 new samples for each new decision making result. |
To clarify the statistics of the applied disturbances in evaluating the performance of the proposed method, we must refer to the 53 states that indicate successful responses to the proposed method.
Parameter | Value |
---|---|
Loading condition (%) (number of scenarios) | 120 (4 scenarios), 115 (7 scenarios), 110 (6 scenarios), 105 (8 scenarios) |
Fault resistance (Ω) | 0.001, 0.1, 10, 20 |
Faulted line location | 20%, 50%, 80% of line length |
Time duration (s) | 0.1, 0.2, 0.3, 0.4 |
Faulted lines |
216-219, 219-220, 220-223, 212-223, 213-223, 204-209, 207-208, 202-201, 222-217, 218-217, 318-317, 322-317, 316-319 |
Determining of the voltage trend when it lies within a pre-specified operation area generates more precise situational awareness and prevents undesirable conditions. Accordingly, the proposed method focuses on this issue and provides a classification method for the generating-side voltage trajectories following severe disturbances. An adaptive fuzzy-logic method is introduced to categorize the voltage status by considering FIDVR, STVI, and oscillation effects. In the proposed method, a fuzzy-logic controller consisting of eight MFs conducts the intended classification. In addition, the membership function parameters are adaptively determined over time.
Simulations are conducted using an IEEE 73-bus power system to confirm the effectiveness of the proposed method.
Accordingly, the proposed method presents a solution that has the following features.
1) The classification method provides more opportunities for operators to take countermeasures against undesirable conditions.
2) The proposed method considers different variables to participate in decision making and to generate comprehensive results.
3) The adaptive process of membership function determination enables the proposed method to be more flexible under current conditions.
4) The fuzzy-logic output, after an averaging process, considers the background decisions and provides reliable results.
5) The voltage behavior is compared with the preselected pilot bus voltage, which provides a reliable assessment for decision making.
The proposed method for voltage-stability analysis utilizes data from two PMU locations, eliminating the need for a complex high-bandwidth communication infrastructure. This method streamlines the analytical process and enhances the accuracy and reliability while providing a cost-effective solution.
References
N. Hatziargyriou, J. Milanovic, C. Rahmann et al., “Definition and classification of power system stability – revisited & extended,” IEEE Transactions on Power Systems, vol. 36, no. 4, pp. 3271-3281, Jul. 2021. [Baidu Scholar]
C. Andersson, J. E. Solem, and B. Eliasson, “Classification of power system stability using support vector machines,” in Proceedings of 2005 IEEE PES General Meeting, San Francisco, USA, Jun. 2016, pp. 650-655. [Baidu Scholar]
A. Borici, J. L. Rueda Torres, and M. Popov, “Comprehensive review of short-term voltage stability evaluation methods in modern power systems,” Energies, vol. 14, no. 14, p. 4076, Jul. 2021. [Baidu Scholar]
Y. Xu, R. Zhang, J. Zhao et al., “Assessing short-term voltage stability of electric power systems by a hierarchical intelligent system,” IEEE Transactions on Neural Networks Learning System, vol. 27, no. 8, pp. 1686-1696, Sept. 2015. [Baidu Scholar]
H. H. Goh, Q. S. Chua, S. W. Lee et al., “Evaluation for voltage stability indices in power system using artificial neural network,” Procedia Engineering, vol. 118, pp. 1127-1136, Sept. 2015. [Baidu Scholar]
B. R. Prusty and D. Jena, “A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach,” Renewable and Sustainable Energy Reviews, vol. 69, pp. 1286-1302, Mar. 2017. [Baidu Scholar]
S. You, Y. Zhao, M. Mandich et al., “A review on artificial intelligence for grid stability assessment,” in Proceedings of 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), Tempe, USA, Nov. 2020, pp. 14-19. [Baidu Scholar]
L. Zhu, C. Lu, I. Kamwa et al., “Spatial-temporal feature learning in smart grids: a case study on short-term voltage stability assessment,” IEEE Transactions on Industrial Informatics, vol. 16, no. 3, pp. 1470-1482, Mar. 2020. [Baidu Scholar]
O. A. Alimi, K. Ouahada, and A. M. Abu-Mahfouz, “A review of machine learning approaches to power system security and stability,” IEEE Access, vol. 8, pp. 113512-113531, Jun. 2020. [Baidu Scholar]
L. Zhu, C. Lu, and Y. Luo, “Time series data-driven batch assessment of power system short-term voltage security,” IEEE Transactions on Industrial Informatics, vol. 16, no. 12, pp. 7306-7317, Dec. 2020. [Baidu Scholar]
K. Ye, J. Zhao, H. Zhang et al., “Data-driven probabilistic voltage risk assessment of miniWECC system with uncertain PVs and wind generations using realistic data,” IEEE Transactions on Power Systems, vol. 37, no. 5, pp. 4121-4124, Jun. 2022. [Baidu Scholar]
Y. Xu, Z. Y. Dong, K. Meng et al., “Multi-objective dynamic VAR planning against short-term voltage instability using a decomposition-based evolutionary algorithm,” IEEE Transactions on Power Systems, vol. 29, no. 6, pp. 2813-2822, Nov. 2014. [Baidu Scholar]
S. Wildenhues, J. L. Rueda, and I. Erlich, “Optimal allocation and sizing of dynamic var sources using heuristic optimization,” IEEE Transactiosn on Power Systems, vol. 30, no. 5, pp. 2538-2546, Oct. 2014. [Baidu Scholar]
M. Aslanian, M. E. Hamedani-Golshan, H. H. Alhelou et al., “Analyzing six indices for online short-term voltage stability monitoring in power systems,” Applied Science, vol. 10, no. 12, p. 4200, Jun. 2020. [Baidu Scholar]
A. Alshareef, R. Shah, N. Mithulananthan et al., “A new global index for short term voltage stability assessment,” IEEE Access, vol. 9, pp. 36114-36124, Feb. 2021. [Baidu Scholar]
M. Glavic, D. Novosel, E. Heredia et al., “Real-time voltage control under stressed conditions, see it fast to keep calm,” IEEE Power Energy Magazine, vol. 10, pp. 43-53, Jun. 2012. [Baidu Scholar]
C. Liu, F. Hu, D. Shi et al., “Measurement-based voltage stability assessment considering generator VAR limits,” IEEE Transactions on Smart Grid, vol. 11, no. 1, pp. 301-311, Jan. 2020. [Baidu Scholar]
H. J. Lee, A. K. Srivastava, V. V. G. Krishnan et al., “Decentralized voltage stability monitoring and control with distributed computing coordination,” IEEE Systems Journal, vol. 16, no. 2, pp. 2251-2260, Jun. 2022. [Baidu Scholar]
H. Yang, N. Li, Z. Sun et al., “Real-time adaptive UVLS by optimized fuzzy controllers for short-term voltage stability control,” IEEE Transactions on Power Systems, vol. 37, no. 2, pp. 1449-1460, Mar. 2022. [Baidu Scholar]
S. M. Halpin, K. A. Harley, R. A. Jones et al., “Slope-permissive under-voltage load shed relay for delayed voltage recovery mitigation,” IEEE Transactions on Power Systems, vol. 23, no. 3, pp. 1211-1216, Aug. 2008. [Baidu Scholar]
North American Electric Reliability Corporation, PRC-024-1. (2021, Jan.). Generator frequency and voltage protective relay settings. [Online]. Available: https://www.nerc.com/pa/Stand/Reliability%20Standards/PRC-024-2.pdf [Baidu Scholar]
Western Electricity Coordination Council, TPL-001-WECC-CRT-3.1. (2016, Aug.). Transient voltage criteria reference document. [Online]. Available: https://www.wecc.org/Reliability/TPL-001-WECC-CRT-3.1.pdf [Baidu Scholar]
H. Golpîra, A. Román-Messina, and H. Bevrani, Renewable Integrated Power System Stability and Control. New York: John Wiley & Sons, 2021. [Baidu Scholar]