Voltage Stability Margin Of System Research Articles

The Effect Pso/Abc, Abc/Bfo, Pso/Bfo and Cs/Bfo Hybrid Techniques on Power System Buses for Voltage Stability Margin Improvement

This paper presents and investigates new approaches inspired by nature to determine the optimal placement of UPFC for enhancing voltage stability margin of power system network. Voltage collapse phenomenon has remained an operational problem yet to be solved by power system engineers. To improve the voltage stability of the power system network, new optimisation techniques viz: PSO/ABC, ABC/BFO, PSO/BFO AND CS/BFO hybrids are investigated for their performance on power system buses for voltage stability improvement. The performance of the proposed hybrid methods are examined on the practical Nigerian 56 - bus network for voltage stability improvement. The simulation results has shown that ABC/BFO technique is better than BFO/PSO by 3.44 in improving voltage stability of margin of power system, gives additional improvement of 4.07, totalling 7.51% and lastly BFO/CS technique improved voltage stability margin of power system further by 5% totalling 12.51%. Also this research revealed that the smaller the gamma value the better the UPFC contribution to voltage stability enhancement. BFO/CS technique yielded the smallest gamma values of 0. 74532 and 0.830913 in both Nigerian practical network and IEEE – 14 bus network as shown in the analysis.

Static voltage stability margin prediction considering new energy uncertainty based on graph attention networks and long short‐term memory networks

AbstractThe existing static voltage stability margin evaluation methods cannot meet the actual demand of current power grid well in terms of calculation speed and accuracy. Thus, this paper proposes a static voltage stability margin prediction method based on a graph attention network (GAT) and a long short‐term memory network (LSTM) to predict the static voltage stability margin of a power system accurately, fast, and effectively, considering new energy uncertainty. First, an innovative machine learning framework named the GAT‐LSTM is designed to extract highly representative power grid operation features considering the spatial‐temporal correlation of the power grid operation. Then, a static voltage stability margin prediction method based on the GAT‐LSTM is developed. Particularly, considering the influence of new energy power uncertainty, two loss functions of certainty and uncertainty are used in the proposed method to predict the voltage stability margin and voltage fluctuation range. Finally, the IEEE39‐bus power system and a practical power system are employed to verify the proposed method. The results show that the computational speed of the proposed method is greatly improved compared to the traditional methods not based on machine learning; the computation results are more accurate and reliable than the existing machine learning methods. Compared with the existing methods, the proposed method has higher scalability and applicability.

Coupled single-port method based voltage stability assessment with inverter-based generators

With the increase of inverter-based generators in the power system, the proportion of traditional generators is decreasing, and their voltage support ability to the power system is weakening, the power system operation is approaching to its voltage stability limit. It is of great significance to study on-line analysis of power system voltage stability under different control manners of inverter-based generators. Firstly, impedance matching theory and coupled single-port circuit theory are introduced. Secondly, coupled single-port method based voltage stability assessment method with inverter-based generators is proposed. Then, use the impedance matching condition and proposed method to analyze the influence of inverter-based generators on voltage stability in different control manners. The proposed method can reveal the voltage stability margin of power system with inverter-based generators in the current running state, and is suitable as an on-line voltage stability approach to evaluate the proximity of voltage collapse in real time. The various scenario simulations experiment validate the effectiveness and accuracy of the proposed method. Meanwhile, experimental analysis results show that different control manners of inverter-based generators not only affect voltage stability margin but also change the weakest bus of power system.

A composite voltage stability index for integrated energy systems based on L-index and the minimum eigenvalue of reduced Jacobian matrix

The closer interdependency of subsystems in integrated energy systems (IESs) and the continuous increase of electricity/gas/heat loads have brought great challenges to the stable operation of IESs. In response to the static voltage stability problem of IESs, this paper proposes a composite voltage stability index (CVSI) based on the minimum eigenvalue of a reduced Jacobian matrix and the known L-index. First, a unified multi-energy flow model for integrated electrical, natural gas and heating system is established, which comprises the steady-state modeling of each energy subsystem and coupling components in IESs. Then, an integrated multi-energy flow calculation method based on the Newton–Raphson algorithm is developed to solve the unified steady-state model of IESs. On the basis, the unified Jacobian matrix after multi-energy flow convergence can be obtained. Moreover, a reduced Jacobian matrix considering the impacts of multi-energy state variables on the reactive power of electrical power system (EPS) is constructed. Afterward, the CVSI is proposed, which combines the minimum eigenvalue of the constructed reduced Jacobian matrix and the L-index derived from bus voltage calculation formula. The proposed CVSI takes both the voltage stability margin of whole system and the voltage stability of electrical buses into consideration. Finally, numerical simulations are exploited to verify the effectiveness and applicability of the proposed voltage stability index.

Probabilistic Load Shedding Scheme for Power System Voltage Stability Enhancement Using Discrete Group Search Optimization Algorithm

This paper presents a discrete heuristic algorithm to improve voltage stability margins of the power system, during under frequency conditions. Discrete group search optimization algorithm is proposed for the first time in this work and applied to a load shedding problem. Sometimes, after initial frequency drop following severe disturbances, the system frequency might return to its acceptable value, however, the system might become unstable due to voltage problems. This paper proposes discrete group search optimization algorithm to solve the load shedding problem as well as returning system frequency to the acceptable range. The objective of proposed method is to enhance voltage stability margins of the power system. Furthermore, in the paper the load uncertainty as the most critical source of uncertainty in power system is handled using point estimation approach. The proposed method is implemented on the modified IEEE 14-Bus test system as well as 39 bus New England Network to demonstrate its applicability and effectiveness. The performance of discrete group search optimization method is also compared with several methods in terms of enhancing voltage stability margins. The results confirm that the proposed method provides a considerable enhancement in the power system voltage stability margin.

Examining Impact of Distribution System Characteristics on Transmission Security Assessment of Future Power Systems

The nature and characteristics of distribution systems are changing continuously with the increased penetration of distributed energy resources. With this, the need for examining the transmission and distribution (T&D) interaction while assessing the voltage security has become significant. In much of the analysis and practices reported so far, voltage security assessment studies are performed separately for T&D systems. Thus, a transmission system operator (TSO) is oblivious to the operations and controls taking place at the distribution system (DS) level. Some of the recent studies examine the impact of an active DS on the voltage security assessment of future power systems. However, the effect of various factors like voltage dependency of loads, reactive power capability of renewable energy sources (RES), location of distributed generation units, and network losses on the voltage stability margin (VSM) of transmission system has not been reported comprehensively so far. This paper first theoretically examines the impact of these factors on VSM. Then, to get the more realistic results for VSM, continuation power flow (CPF) is performed in a coordinated fashion including both T&D systems. The simulations show that considering losses, load characteristics dependency on voltage and reactive power limits of RES in a DS for transmission voltage security assessment studies lead to a more rational outcome than when neglected.

A decomposition and coordination algorithm for SVSM interval of integrated transmission and distribution networks considering the uncertainty of renewable energy

The uncertain power output of renewable energy stations (RESs) will result in the uncertain fluctuation of the static voltage stability margin (SVSM) of a power system with centralized and distributed RESs integrated to the transmission network (TN) and distribution networks (DNs), respectively. A decomposition and coordination calculation (DCC) method is proposed to determine the SVSM interval of integrated transmission and distribution networks (ITDNs) using intervals to describe the uncertain RES outputs. First, based on the polynomial approximation expressions of the injected power of the boundary bus with respect to its voltage and the load growth parameter of each DN, the DCC of continuation power flow between TN and DNs is executed to obtain the central value of the SVSM interval of ITDNs. Next, the affine interval algorithm is used to calculate the SVSM fluctuation interval caused by the uncertain RES output intervals. The block bordered-diagonal form and Gaussian elimination method are used to execute the DCC of the first-order sensitivities of SVSM with respect to RES outputs, and alternating iterations between TN and each DN are used to execute the DCC for optimizing the contractive noise symbol intervals. The proposed DCC method can efficiently calculate the SVSM interval of ITDNs in which lots of DNs are integrated with distributed RESs. Test results on two ITDNs, one composed of modified IEEE systems and the other an actual 2285-bus power grid, demonstrate the correctness and efficiency of the proposed method compared with the centralized algorithm and the Monte Carlo method.

Nonparametric preventive/corrective voltage stability enhancement of active distribution systems with integrated electric vehicles charging facilities

The increasing penetration of electric vehicles (EVs) and renewable energy resources (RESs) have raised concerns about the voltage instability in distribution power systems. Thus, some probabilistic algorithms are needed by decision-makers to quickly yet accurately evaluate the voltage stability margin in smart distribution systems. This paper proposes a nonparametric preventive control to mitigate the risk of voltage instability in the active distribution systems consisting of EVs and RESs. First, a framework is developed to evaluate EVs' degree of participation in preventive control by estimating potential achievable power capacity (PAPC). To estimate the probability density function (PDF) of the system voltage stability margin, Bernstein density estimator (BDE) is utilized due to its capability to handle the boundary effect. Finally, a preventive/corrective control model based on the model predictive control (MPC) is developed considering the dynamic behavior of EVs and RESs. The capability of the proposed algorithm is tested on the modified IEEE 33-node system.

Impact of Wind Farms on Power System Voltage Stability (Dept.E)

Steady state analysis of wind turbine generating units (WTGUs) interconnected with the grid is needed as the use of WTGU are getting more popular and many new systems are being planted. In this paper, probabilistic voltage stability algorithm of WTGUs interconnected with the utility grid is developed via power Moy analysis where these units are modeled as P-Q bus(es) by detecting the collapse p oint on the Q-V curves. The developed algorithm also facilitates the computation of both the real and reactive power output of the fixed speed pitch regulated wind turbine at a specific site, wind turbine characteristics, wind speed and terminal voltage. The probabilistic nature of wind is considered by introducing the expected voltage stability margin is an index that combines both of the voltage stability and the wind distribution in one index. The proposed algorithm is implemented and applied on the IEEE 26-bus, voltage stability margin (VSM), and expected voltage stability margin (EYSM) are calculated at each wind speed. The accumulation of the EVSM over a specific period, can be considered as the system voltage stability margin which is a single value that can be compared with the voltage stability margin of the all-conventional power system.

PMU-Based Distributed Non-Iterative Algorithm for Real-Time Voltage Stability Monitoring

The Phasor measurement unit (PMU) measurements are mandatory to monitor the power system's voltage stability margin in an online manner. Monitoring is key to the secure operation of the grid. Traditionally, online monitoring of voltage stability using synchrophasors required a centralized communication architecture, which leads to high investment cost and cyber-security concerns. The increasing importance of cyber-security and low investment cost have recently led to the development of distributed algorithms for online monitoring of the grid that are inherently less prone to malicious attacks. In this work, a novel distributed non-iterative voltage stability index (VSI) is proposed by recasting the power flow equations as circles. The online computations of VSI are simultaneously performed by the processors embedded at each bus in the smart grid with the help of PMUs and communication of voltage phasors between neighboring buses. The distributed nature of the index enables the real-time identification of the critical bus of the system with minimal communication infrastructure. The effectiveness of the proposed distributed index is demonstrated on IEEE test systems and contrasted with existing methods to show the benefits of the proposed method in speed, interpretability, identification of outage location, and low sensitivity to noisy measurements.

Static voltage stability margin calculation of power systems with high wind power penetration based on the interval optimisation method

Calculation of the static voltage stability margin (SVSM) of a power system with high wind-power penetration requires consideration of the uncertain fluctuation of wind farms' (WFs') output. Using interval numbers to describe the uncertain WF output fluctuation and based on the interval optimisation theory, a new SVSM interval calculation method is proposed. The method establishes two bi-level optimal power flow (OPF) models to calculate the SVSM interval, including a min–min model for the upper bound and a max–min model for the lower bound. Through the dual theory of convex programming, the max–min model is transformed into a max–max model, which is solved by transforming it into a one-layer optimisation model. Using correlation angles to describe the correlation of different WF output intervals and using linear transformation to decorrelate them into independent intervals, two bi-level OPF models of calculating the SVSM interval considering different WFs' correlation are established. Take the IEEE-39 bus system and an actual 964-bus provincial power grid as examples, compared with the Monte-Carlo method and the continuous power flow and affine interval integrated method, the results indicate the proposed method obtains more accurate SVSM interval and has better calculation efficiency.

Multi-Objective Optimal Control Approach for Static Voltage Stability of Power System Considering Interval Uncertainty of the Wind Farm Output

The static voltage stability margin (SVSM) of a power system considering the uncertain fluctuation range of wind farm (WF) output can be described as an interval value called the SVSM interval. A multi-objective optimal control model for SVS of a power system considering the interval uncertainty of WF output is proposed. The objective functions of the model are to increase the central value and reduce the fluctuation range of the SVSM interval, and the decision variables are the active power output and terminal voltage of generators and the switching capacity of shunt capacitors. Thus, it is a multi-layer optimization model. A parametric approximation (PA) method is used to obtain the approximate functional relationship between the optimal objective function values and the decision variables of the inner-layer and mid-layer optimization models and convert the optimization model into a single-layer bi-objective optimization model. A method for obtaining the continuous Pareto frontier of the bi-objective optimization model is proposed based on the normalized normal constraint and PA methods, and the compromise optimal solution calculated from the continuous Pareto frontier is used as the optimal control scheme. Two methods for improving the calculation efficiency of the PA method are also proposed. Finally, results from experimentation on the IEEE 39-bus system and an actual provincial power grid demonstrate the effectiveness of the proposed method.

Investigation of Relevant Distribution System Representation With DG for Voltage Stability Margin Assessment

This paper emphasizes the importance of including unbalanced distribution systems for voltage stability studies in power systems. The paper aims to: discuss the various simulation methods for power system analysis; highlight the need for modeling unbalanced distribution system for accurate load margin assessment; demonstrate the influence of net-load unbalance (NLU) on voltage stability margin (VSM). We also share a TD these are not guaranteed to proliferate in a balanced manner and uncertainty resulting due to these DERs is well acknowledged. These uncertainties cannot be captured or visualized without representing the distribution system in detail along with the transmission system. We show the impact of proliferation of DERs in various 3-phase proportions on voltage stability margin through T&D co-simulation. We also study the impact of volt/VAR control on voltage stability margin. This analysis is only possible by representing the distribution system in detail through T&D co-simulation. Higher percentage of net-load unbalance (NLU) in distribution system aggravates the voltage stability margin of the distribution system, which can further negatively influence the overall voltage stability margin of the system.

SVSM calculation of power system with high wind‐power penetration

Calculation of the static voltage stability margin (SVSM) of power system with high wind-power penetration must consider the uncertain fluctuation of power output from wind farms (WFs). On the basis of a continuous power flow (CPF) and improved affine interval (IAI) algorithm that considers quadratic terms, a new method to calculate the SVSM interval of a power system that considers the uncertain fluctuation intervals of WF output is proposed. Considering the high penetration of wind power, the power variation of the active load, and wind-power fluctuation are assigned by all conventional generators, except the swing generator in the CPF calculation model. In the proposed IAI algorithm, the non-linear second-order sensitivities are considered to obtain a more accurate SVSM interval. With the correlation of different WF output intervals described by relative angles, as well as the independent intervals obtained by decorrelation of the correlated WF output intervals, the SVSM interval is calculated by the CPF and IAI algorithms. Take the IEEE 39-bus system and an actual 964-bus provincial power grid as examples, and compared with Monte Carlo method, the results show that the SVSM interval calculated by the proposed method is more accurate, and the computation time is significantly reduced.

A Continuation Power Flow Model of Multi-Area AC/DC Interconnected Bulk Systems Incorporating Voltage Source Converter-Based Multi-Terminal DC Networks and Its Decoupling Algorithm

Existing continuation power flow (CPF) models mainly focus on the regional independent systems, which are not suitable for multi-area AC/DC interconnected systems because the market trading behaviors and security control for power allocation of tie-lines are ignored. This study presents a novel CPF model and its decoupling algorithm for multi-area AC/DC interconnected systems incorporating a voltage source converter (VSC)-based multi-terminal direct current (MTDC) network. This CPF model includes the following unique features: (1) In view of the bilateral power trading contracts among regional subsystems, the nonlinear constraint equations of directional trading active power via interface are derived, and the multi-balancing machine strategy is introduced to realize the active power balance of each subsystem. (2) An accurate simulation method for the security control behaviors of the power allocation in tie-lines is proposed, which includes a specific selection strategy for automatic generation control units and a generation re-dispatch strategy. These two strategies work together to prevent the serious overload in tie-lines during load growth and improve the voltage stability margin of the interconnected bulk systems. (3) The switching characteristic of reactive power control behaviors of VSC stations is simulated in the CPF calculation. In the end, a novel decoupling CPF algorithm based on bi-directional iteration is presented to realize the decomposition and coordination calculation. This decoupling algorithm preserves the precision and convergence of integrated CPF algorithms, and it has an apparent advantage on the calculation speed. Furthermore, this decoupling algorithm also can easily reflects the effects of the control mode changes of VSC stations to the voltage stability margin of AC system. Case studies and comparative analysis on the IEEE two-area RTS-96 system indicate the effectiveness and validity of the proposed CPF model and corresponding decoupling algorithm.

Optimum Interconnected Islanded Microgrids Operation with High Levels of Renewable Energy

ABSTRACTThis paper aims to study the optimal probabilistic energy efficiency horizon of active distribution networks with high penetration of wind power generation considering a variety of possible islanded microgrid (IMG) zones. The penetration of renewable power sources such as wind turbines (WTs) and the load variations can create challenges in the active distribution system that will significantly affect system modeling, power flow algorithm, voltage stability index and system planning. In this regard, an appropriate model for IMGs is suggested, which aims to estimate the voltage stability margin of a two-bus system based on both saddle-node and limited induced bifurcations. Furthermore, a new concept, named reduced IMG network (RIN), is well explored to generalize the proposed index to n-bus islanded MGs using a developed power flow algorithm. The simulated frame work indicates a two-stage probabilistic planning algorithm that considers the variability in load and generation. The proposed algorithm improve voltage stability index and minimize the IMG customers’ interruption. This improvement allow for a time delay in renewing MGs. The performance and effectiveness of the proposed method are tested and verified through the IEEE 33-bus test system across different case studies.

Searching severest VSM basing on CCPF among multiple dispatch centres

It is important to search voltage stability margin (VSM) of an interconnected power system in order to determine secure operation constraints. Traditionally, centralised continuation power flow (CPF) is used, which may fail to model the varied load growth directions of different regional power grids. In this study, a distributed VSM searching method is proposed grounding on a coordinated CPF (CCPF) performed by neighbouring dispatch centres. First, a distributed power flow model for VSM is established, which considers the automatic allocation of network loss. Then, a critical bus of the power system is used to indicate the system-level voltage stability. It is chosen according to the sensitivity of the minimum singular value of Jacobi matrix to nodal voltage amplitudes, and the sensitivity of boundary power injection to nodal voltage amplitudes. Moreover, the gradient of critical bus voltage amplitude to regional loading parameters is computed, which is set as the load growth direction for the current step. The severest VSM is obtained by solving the CCPF iteratively along the worst load growth direction. Tests on IEEE 118 bus system and a real power grid of China validate the proposed method in the enhancement of the security for interconnected power systems.

A Method to Estimate Power System Voltage Stability Margins Using Time-Series From Dynamic Simulations With Sequential Load Perturbations

In this paper, a methodology to assess power system voltage stability margins from time-series data is presented. The proposed method obtains time-series from dynamic simulations subject to sequential load changes that are then used as an input to a voltage stability estimation method. After a contingency is applied, load perturbations aim to move the system through different loading levels. This approach allows estimating voltage stability margins from time-series without any information or numerical quantities of the mathematical model of the system other than the simulation’s output. This is useful for dynamic security assessment systems that only have transient simulators for their workflows and still require to estimate the voltage stability margins. The proposed method is used to quantify the severity of the contingencies using a three-layer index. The proposed approach is illustrated using a simple two-bus system and then tested using time-domain simulations of the Nordic-44 Bus test system.

Probability assessment for power system voltage stability margin with renewable energy source using slice sampling

Summary With the prevalence of renewable energy source in power system, it is necessary to appraise the voltage stability of the integration system by probabilistic methods. The traditional Markov Chain Monte Carlo (MCMC) simulation could show great calculation precision for the probabilistic assessment, but it is always involved with complicated sampling iterations because of the Gibbs sampling method currently used in MCMC simulation. Instead of Gibbs sampling method, this paper presents the application of slice sampling in MCMC simulation for the voltage stability probabilistic assessment of the power system with renewable source. Firstly, the probabilistic models of renewable source generation are constructed. Then, the sample space of renewable source outputs is obtained by slice sampling, and the samples from the sample space are calculated by power flow. Finally, the voltage stability margin is obtained by the result of the power flow calculation, and the probabilistic assessment of the voltage stability is implemented. Furthermore, the MCMC simulations using Gibbs sampling and slice sampling are compared by Gelman-Rubin diagnostic and Kullback-Leibler divergence tests on IEEE 14-bus system and IEEE 39-bus system, respectively. The results show that the slice sampling method is simpler and more efficient than Gibbs sampling method in the voltage stability probabilistic assessment.

Simple and efficient method for steady‐state voltage stability analysis of islanded microgrids with considering wind turbine generation and frequency deviation

Distribution grids are being transformed from passive to active networks. The active distribution systems are constructed through the implementation of microgrids (MGs) which are characterised as ‘the building blocks of smart grids’. This type of network eases the integration of distributed generation into power networks and makes it possible to define a new index for voltage stability. The penetration of renewable power sources such as wind turbines can create new challenges in this system that will affect voltage stability index (VSI). In this study, an improved indicator is proposed to estimate the voltage stability margin of a two-bus system based on both saddle node and limited induced bifurcations considering different types of load model. The catastrophe theory is used to define this new VSI of an islanded MG (IMG), called as cat_VSIIMG. A new concept, named reduced IMG network, is also used to generalise the proposed index to n-bus IMGs by splitting these networks. The cat_VSIIMG, which is validated by a verified continuation power flow method for IMGs is called the maximum loadability margin of IMG. The performance and effectiveness of the proposed method are demonstrated on 33-bus and 69-bus test systems for different types of load model.