System Static Voltage Stability Research Articles

The static voltage stability analysis of photovoltaic energy storage systems based on NPU algorithm

Although the data-driven static voltage stability problems have been widely studied, most of the classical algorithms focus more on improving the accuracy of the system prediction, ignoring the error classification errors generated during the prediction process. Furthermore, current research ignores the utilization of data-driven voltage stability assessment of energy storage systems. Therefore, this paper proposes a static voltage stability assessment method for photovoltaic energy storage systems based on considering the error classification constraint algorithm using Neyman-Pearson umbrella algorithms. Firstly, the Spearman Correlation Coefficient is employed in the feature selection phase. Secondly, an updated voltage stability assessment (VSA) model is proposed. Compared with the existing data-driven prediction of system static voltage stability in the literature, it can realize voltage stability assessment more quickly. Furthermore, on the basis of rapid voltage stability assessment, the umbrella NP classifier can also effectively limit the first-class error and attenuate the effect of error classification by mirroring the control of the number of cycle splits and the type I classification error threshold. Finally, the simulation and experimental results show that the effectiveness and robustness of the scheme proposed in this paper in grid-connected photovoltaic energy farms.

Static voltage stability considering reactive power limit of salient synchronous generator and active power loss of exciter

With increasing load, it is difficult to maintain power system static voltage stability (SVS). The existing SVS analysis based on the reactive power limit (RPL) of the non-salient synchronous generator (SG) and ignoring the exciter’s loss is inaccurate. This paper proposes an SVS model with exact description to the SG. The novelties are: (1) Seeing that the SVS is deteriorated when the SG reaches the RPL, a solution to the RPL of the salient SG with different reactances along the direct and quadrature axis is newly proposed. (2) The active power loss of the exciter of the SG is newly included in the power flow and the SVS analysis. (3) By deriving the sensitivity of the L index with respect to the load, an index is newly defined to quantify the dependency of the SVS on the RPL. The simulation results show that the RPL of the salient SG considering the stator resistance is narrower. The active power loss of the exciter has more obvious impact on the power flow under heavier loading conditions. When the proposed index is positive, the RPL instead of the L index is more critical to maintain the SVS.

Static Voltage Stability Assessment Considering Impacts of Ambient Conditions on Overhead Transmission Lines

The static voltage stability assessment model is effective in analyzing system stability states. However, the electrothermal coupling relationship dependent on practical current-carrying and ambient conditions is generally ignored for models concerning overhead transmission lines, thereby introducing certain analysis errors. Therefore, this article proposes a unified power flow model which allows for the electrothermal coupling effect characterized by the balance of heat absorption and dissipation for overhead conductors. Moreover, the meteorological and geographic information around the transmission lines is involved as variables in the power flow calculation. Then, the Newton iteration formulations are restated and the improved power flow model is solved by continuously adjusting the variables and updating an extended Jacobian matrix. Then, the extended matrix corresponding to the final power flow solutions is used to establish the improved <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> sensitivity and modal analysis methods, which allows one to evaluate system static voltage stability considering variations of ambient factors. Consequently, based on an IEEE 14-bus test system, the results obtained by the traditional model and the improved model are contrastively analyzed in different scenarios, which are substantially different from each other. The results illustrate that the consideration of ambient conditions around the transmission line will cause remarkedly impacts on the static voltage stability assessment results.

System static voltage stability analysis considering load characteristics of electrolytic aluminum

The load characteristics have a significant impact on the static voltage stability analysis of the power grid. Wenshan power grid has a large amount of relatively centralized electrolytic aluminum load, accounting for 65% of the total local load. Due to the different load characteristics of electrolytic aluminum shown in the big closed-loop feedback current stabilizing state, the detailed load characteristics of electrolytic aluminum must be considered when analyzing the static voltage stability of the Wenshan power grid. Firstly, based on the actual production process of electrolytic aluminum, an accurate load characteristic model of electrolytic aluminum under the big closed-loop feedback current stabilizing state is built; secondly, a static voltage stability analysis model on account of the electrolytic aluminum load characteristic is established, and solving this model can obtain the generalized Jacobi matrix J and reduced dimensional Jacobi matrix J1 which considers comprehensively the influence of system active and reactive power on the static voltage stability, based on the singular value decomposition theory, the static voltage stability margins MSV-J and MSV-J1 decomposed from the matrix J and J1 respectively can be obtained to describe the stability degree of system static voltage accurately. And the effect of adjusting the current stabilizing device on the load characteristics of electrolytic aluminum and the static voltage stability of the system is also studied. Finally, the influence of load characteristics of electrolytic aluminum on the system static voltage stability is analyzed by some examples, and the results indicate that the static voltage stability margin indexes MSV-J and MSV-J1 can well describe the static voltage stability of the grid.

Online Static Voltage Stability Monitoring for Power Systems Using PMU Data

A new online static voltage stability monitoring method for power systems is proposed by using phasor measurement unit (PMU) data in this paper. This approach uses the real-time power, voltage, and phase angle data collected by the PMU to estimate the power flow Jacobian matrix of the system, and then the static voltage stability is monitored via the minimum singular values (MSVs) of the power flow Jacobian matrix. The novelty of the approach lies in the fact that it only utilizes PMU data for implementing online monitoring of the power system static voltage stability, independent of the physical model and its parameters. The application results on the IEEE 57-bus test system verify the effectiveness of the proposed approach.

Research on power system static voltage stability considering geomagnetic disturbances effect

AbstractThe reactive power losses caused by the power grid Geomagnetically Induced Current (GIC) severely disturb the static voltage stability of power systems, and may even trigger voltage collapses. In this paper, the 1 V/km uniform induced geoelectric field is adopted to analyze how greatly geomagnetic disturbance (GMD) can influence the static voltage stability of power systems, given the features of GMD disasters hitting the power grids of China. Considering the GIC reactive power losses, a method that combines second‐order sensitivity adaptive variable step size and local curve fitting is put forth to calculate the critical point of the active power and voltage nodes (PV) curve. With the increment ratio of the curve slope set at discretion, the method enables the curve to approach its critical point with great strides, a design managing to reduce the quantity of power flow calculations remarkably. By taking into account the reactive power violation of PV nodes in the acquisition of load increment step size, the method calculates the critical point of the PV curve in a much more accurate way. The method applied to the Northwest 750 kV power grid, the calculation results suggest that the 1 V/km induced geoelectric field markedly undermines the static voltage stability, thus posing grave threats to the above grid.

A Chaos Disturbed Beetle Antennae Search Algorithm for a Multiobjective Distribution Network Reconfiguration Considering the Variation of Load and DG

As the distributed generation (DG) in a power supply and the user load demand constantly change in an actual distribution network, multiobjective optimal network reconfiguration considering variations in load and DG has become a major concern, which is important and required to make system operations safe and economical. The aim is to minimize the sum of the active power loss, the sum of the load balancing index and the sum of the maximum node voltage deviation index simultaneously during the reconfiguration period. Here, this article proposes a new Chaos Disturbed Beetle Antennae Search (CDBAS) algorithm to reduce the computational time and solve the multiobjective optimal problem of network reconfiguration. To adopt the Chaos Disturbed Beetle Antennae Search algorithm for solving this multiobjective problem, grey target decision-making technology is used to rank the beetles. Additionally, to the enhance the system static voltage stability and voltage quality, a grey target decision-making model is established to achieve a layer relationship between each index and the switching operation index. The plausibility and effectiveness of the presented methodology is verified on the modified IEEE 33, 69 and 118-Bus Test Radial Distribution Network. Finally, compared with other research methods in the literature, the CDBAS algorithm outperforms other algorithms and produces a quality decision solution.

Global Approximation of Static Voltage Stability Region Boundaries Considering Generator Reactive Power Limits

Power system static voltage stability region boundary (SVSRB) is a complicated hypersurface in parameter space. Due to inequality constraints such as generator reactive power limits, different critical points on the SVSRB may be related to different groups of active constraints and can be associated with different types of loadability limit, which makes it difficult to approximate the whole SVSRB at once or assemble many local approximations of the SVSRB. To overcome the difficulty, this paper proposes an approach for globally approximating the whole SVSRB considering generator reactive power limits at one go. First, a parametric optimization model incorporating all inequality constraints is formulated to describe the SVSRB, where the optimal solutions are the critical points on the SVSRB. The optimality condition, i.e., parametric Karush–Kuhn–Tucker conditions (KKT conditions), is also derived. Then, by applying the Galerkin method to the parametric KKT conditions in an interior-point-method-like manner, the whole SVSRB is approximated and represented using a single polynomial expression. Case studies in a 10-bus system and IEEE 300-bus system verify the effectiveness and accuracy of the proposed method.

Fuzzy Load-Shedding Strategy Considering Photovoltaic Output Fluctuation Characteristics and Static Voltage Stability

Based on the equilibrium point equations of a classic three-node system integrated with a large-scale photovoltaic cell (PV) power plant, the impact of PV output fluctuation on the saddle-node bifurcation (SNB) was derived and analyzed. When PV runs in a unity power factor and the PV output active power Ppv is not too large (several hundred MW and below), the PV output fluctuation has little effect on the SNB point position and load margin index, so that the load margin index can be calculated online using the SNB point at Ppv = 0 pu. On the other hand, the local reactive power compensation in the load center can effectively raise the load bus voltage and make the voltage stability problem become more concealed; the traditional under-voltage load-shedding (UVLS) strategy only carries out load shedding when the bus voltage amplitude is below the specified value and cannot effectively maintain the system static voltage stability in some occasions. In this paper, a fuzzy load-shedding strategy considering the impact of PV output fluctuations for the large-scale PV grid-connected system was designed, taking the load bus voltage amplitude and load margin index as fuzzy input variables, and the load-shedding command as a fuzzy output variable. Nine fuzzy IF-THEN rules were extracted for the fuzzy controller and the corresponding practical calculation method of load-shedding quantity was put forward. The simulation results of the classic three-node system and IEEE 14-bus system, both with a 100 MW PV power plant, verified the effectiveness of the fuzzy load-shedding controller whose input variable load margin index was calculated using the SNB point when the PV active power output was 0. The designed fuzzy load-shedding strategy can compensate for the defect—that the traditional UVLS strategy cannot effectively guarantee the system static voltage stability—and it can be widely used in power grids integrated with PV power plants whose scales are at a level of several hundred MW and below.

Impact of large‐scale photovoltaic generation integration structure on static voltage stability in China's Qinghai province network

Large-scale photovoltaic (PV) generations are integrated into China's Qinghai province network and challenging the system stability. This study focuses on static voltage stability analysis of Qinghai grid in consideration of high-penetration PV generation. The test system is based on the practical network structure of Qinghai grid. Different practical PV integration structures are, respectively, studied by discussing the influences of transmission line length, output power of PV plant and reactive power compensation capacity on system static voltage stability. The authors also compared different PV integration structures to study the effect of topology on static voltage stability. Simulation results are performed in the practical network structure of Qinghai grid. The analysis results can be used to provide guidance for system modification and thereby improve the system operation stability.

Involvement of cost savings and voltage stability indices in optimal capacitor allocation in radial distribution networks using artificial bee colony algorithm

This article applies the artificial bee colony algorithm to define and allocate static shunt capacitors along radial distribution networks. The objective function is adapted to maximise net yearly savings and to enhance the overall system static voltage stability index with weighting and magnifying factors. Load variations have been considered to optimally size the fixed and switched capacitors required. Nodes with higher loss sensitivity factors and lower voltage stability indices are initially identified for capacitor allocations. The proposed algorithm ascertains optimal sizing and placement, and takes the final decision for optimum locations among the number of buses nominated. The realised numerical results are compared with those found by other recent heuristic methods and show that the proposed method is capable of producing high-quality solutions and validated its viability and applicability.

Multi-objective Capacitor Allocations in Distribution Networks using Artificial Bee Colony Algorithm

This article addresses an efficient heuristic-based approach to assign static shunt capacitors along radial distribution networks using the artificial bee colony algorithm. The objective function is adapted to enhance the overall system static voltage stability index and to achieve maximum net yearly savings. Load variations have been considered to optimally scope the fixed and switched capacitors required. The numerical results are compared with those obtained using recent heuristic methods and show that the proposed approach is capable of generating high-grade solutions and validated viability.

Artificial Bee Colony Algorithm to Allocate Fixed and Switched Static Shunt Capacitors in Radial Distribution Networks

This article introduces an efficient heuristic-based approach to assign static shunt capacitors along radial distribution networks using the artificial bee colony algorithm. The objective function is adapted to enhance the overall system static voltage stability index and to achieve maximum net yearly savings. Load variations have been considered to optimally scope the fixed and switched capacitors required. The numerical results are compared with those obtained using recent heuristic methods and show that the proposed approach is capable of generating high-grade solutions and validated viability.

Research on Impacts of FACTS on Static Voltage Stability Characteristics of AC/DC Power System

Based on the improved Continuation Power Flow algorithm, this paper investigates the impacts of FACTS on static voltage stability characteristics of AC/DC hybrid power system. This paper introduces the steady-state model of different FACTS devices, and the power flow mathematical model is established about AC/DC power system with FACTS devices. The impacts of FACTS devices with various capacities in different locations on static voltage stability are compared and analyzed. The calculation results of a four-machine two regions AC/DC power system show that FACTS are able to improve the voltage stability and the installation of SVC shunt compensation can possess a better effect to improve the system static voltage stability limit than TCSC series compensation.

Research on Wind Farm and Energy Storage System Integration on Power System

Based on power system static voltage stability constraints, by theoretical analysis, calculation method of injection power for each node in power system is given. Compared with power flow simulation, results show that this method can be used to obtain nodes with relative large injection power, and calculation accuracy in a certain extent depends on the accuracy of power system Thevenin equivalent impedance. In addition, the application of energy storage systems to improve wind farm power injection is analyzed preliminarily. Simulation results show that locations of energy storage system in power system have impacts on the improvement of wind farm power injection.

An economical generation direction for power system static voltage stability

This paper proposes an economical generation direction for static voltage stability. The proposed generation direction minimizes the total operating cost at any loading level, up to the point of collapse. The proposed approach, named as EGD approach, is based on the economic load dispatch with load flow. Two alternative methods to identify the economic generation direction are proposed. Economical generation direction is used in the continuation power flow process to obtain the static voltage stability margin. Static voltage stability margin with economical generation direction is compared with the margins resulting from other existing generation directions in the modified IEEE 14-bus test system under various system operating conditions. Cost of providing loading margin as well as PV curves and losses under different generation directions resulting from various generation direction approaches are also studied and compared. The proposed approach provides an alternative way for utilities to obtain the lowest total operating cost with voltage stability constraint by using any existing commercial software.

Optimal static voltage stability improvement using a numerically stable SLP algorithm, for real time applications

A numerically stable sequential Primal–Dual LP algorithm for the reactive power optimisation (RPO) is presented in this article. The algorithm minimises the voltage stability index C 2 [1] of all the load buses to improve the system static voltage stability. Real time requirements such as numerical stability, identification of the most effective subset of controllers for curtailing the number of controllers and their movement can be handled effectively by the proposed algorithm. The algorithm has a natural characteristic of selecting the most effective subset of controllers (and hence curtailing insignificant controllers) for improving the objective. Comparison with transmission loss minimisation objective indicates that the most effective subset of controllers and their solution identified by the static voltage stability improvement objective is not the same as that of the transmission loss minimisation objective. The proposed algorithm is suitable for real time application for the improvement of the system static voltage stability.