A Comprehensive Dynamic and Transient Voltage Stability Study by Digital Simulation Techniques

In this paper, digital simulation techniques for dynamic and transient voltage performance studies, using accurate load and synchronous generator models have been proposed. Particular attention has been paid to the induction motor load model. Accurate models of voltage supporting devices including OLTC transformer are derived. The system of differential equations based on the above models are converted into linear algebraic equations by use of the trapezoidal approximation formula. These are then written as difference equations to facilitate computational programming. For various contingencies a numerical iterative technique is used to obtain a simulation of the system voltage and angle profile. Various contingency tests on a 9-bus sample system and a 22-bus system prove the applicability of the package.

Chaos quantum particle swarm optimization for reactive power optimization considering voltage stability

The reactive power optimization considering voltage stability is an effective method to improve voltage stablity margin and decrease network losses,but it is a complex combinatorial optimization problem involving nonlinear functions having multiple local minima and nonlinear and discontinuous constraints. To deal with the problem,quantum particle swarm optimization (QPSO) is firstly introduced in this paper,and according to QPSO,chaotic quantum particle swarm optimization (CQPSO) is presented,which makes use of the randomness,regularity and ergodicity of chaotic variables to improve the quantum particle swarm optimization algorithm. When the swarm is trapped in local minima,a smaller searching space chaos optimization is used to guide the swarm jumping out the local minima. So it can avoid the premature phenomenon and to trap in a local minima of QPSO. The feasibility and efficiency of the proposed algorithm are verified by the results of calculation and simulation for IEEE 14-buses and IEEE 30-buses systems.

Impact of Wind Integration on Transient Voltage Stability in Regional Grid

With the increasing development of wind power,the scale of wind farms and unit capacity of wind turbines are getting larger and larger,and the impact of wind integration on power systems cannot be ignored.However,in most cases,the areas with a plenty of wind resources do not have strong grid structures.Furthermore,the characteristics of wind power dictate that wind turbines need to absorb reactive power during operation.Because of the strong correlation between voltage stability and systems' reactive power,the impacts of wind integration on voltage stability has become an important issue.Based on the power system simulation software DIgSILENT and combined analysis of actual practice,this paper investigates the impacts of two types of wind farms on voltage stability:namely a type of wind farms which are constituted by constant speed wind turbines based on common induction generators(IG) and another type of wind farms which are constituted by VSCF wind turbines based on doubly-fed induction generators(DFIG).Through investigation the critical fault clearing time is presented for different outputs of wind farms.Moreover,the impacts of static var compensator(SVC) and static synchronous compensator(STATCOM) on transient voltage stability in IG-based wind farms are studied to improve the security and stability of the Jiangsu power grid after the integration of large scale wind power.

Analysis of grid-connected voltage stability of FSCWT based on bifurcation theory

This paper studies on the change mechanisms of the voltage stability caused by the grid connection of front-end speed-controlled wind turbines(FSCWT)integrating into power system.First of all,the differential algebraic equations describing the dynamic characteristics of wind turbines are illustrated.Then,under the guidance of IEEE3 node system model,the influence of the angular velocity of wind turbines,the reactive power and the active power at load bus on the voltage stability of grid-connection has been analyzed by using bifurcation theory.Finally,the method of linear-state feedback control has been applied to the original system in accordance with the bifurcation phenomenon of grid-connected voltage caused by the increase in the active power at load bus.Research shows that voltage at the grid-connected point would be changed with the fluctuation of turbines angular velocity.And increasing its reactive power can enhance voltage at the grid-connected point;problem of bifurcation at the grid-connected point can be delayed when increasing the gain k s of feedback controller within a certain range.

A New Proximity Indicator for Assessment of Voltage Stability and Critical Loadability Point

This paper presents a newly developed proximity indicator for voltage stability assessment which can be used to predict critical real system load and voltages at various load buses at critical loading point.The proximity indicator varies almost parabolic with total real load demand and reaches orthogonally to real load axis.This relation has been utilized to predict critical loading point.It has been shown that two operating points are needed for estimating critical point and proper selection of operating points and variation of proximity indicator near collapse point highly affect the accuracy of estimation.Simulation is based on load flow equations and system real and reactive loadings have been increased in proportion with base case scenario for IEEE 14 and IEEE 25 bus test systems to demonstrate the behaviour of proposed proximity indicator.CPF has been used as benchmark to check the accuracy of estimation.

Study on Impact of Wind Turbines on Static Voltage Stability of Power System

The static voltage stability of the power system integrating wind farms adopting different kinds of wind turbines is analyzed. Through the simulation of one certain local power grid in Xinjiang Uygur Autonomous Region, the PV curves at the point of common coupling (PCC), key buses and important substations are plotted; the variation of voltage as well as the limit and margin of static stability are analyzed. It is resulted from the simulation that the limit of static voltage at weak nodes is lower, and the static voltage of the power system with wind farms adopting doubly-fed induction generators (DFIG) is more stable than that with wind farms adopting common asynchronous generators.

Improving Voltage Stability of Power System by Optimal Location of FACTS Devices Using Bio-Inspired Algorithms

Power system operations can be optimized using power electronics based FACTS devices. The location of these devices at appropriate transmission line plays a major role in their performance. In this paper, two bio-inspired algorithms are used to optimally locate two FACTS devices: UPFC and STATCOM, so as to reduce the voltage collapse and real power losses. Particle swarm optimization and BAT algorithms are chosen as their behaviour is similar. VCPI index is used as a metric to calculate the voltage collapse scenario of the power system. The algorithm is tested on two benchmark power systems: IEEE 118 and the Indian UPSEB 75 bus system. Performance metrics are compared with the system without FACTS devices. Application of PSO and BAT algorithms to optimally locate the FACTS devices reduces the VCPI index and real power losses in the system.

Investigation of Connecting Wind Turbine to Radial Distribution System on Voltage Stability Using SI Index and λ - V Curves

The growth of wind energy penetration level in distribution system raises the concern about its impact on the operation of the power system, especially voltage stability and power loss. Among the major concerns, this paper studied the impact of connecting wind Turbine (WT) in radial distribution system with different penetration levels and different power factor (lead and lag) on power system voltage stability and power loss reduction. Load flow calculation was carried out using forward-backward sweep method. The analysis proceeds on 9- and 33-bus radial distribution systems. Results show that voltage stability enhancement and power loss reduction should be considered as WT installation objective.

Overcoming the Na-ion conductivity bottleneck for the cost-competitive chloride solid electrolytes

Chloride solid electrolytes possess multiple advantages for the construction of safe,energy-dense allsolid-state sodium batteries,but presently the chlorides with sufficiently high cost-competitiveness for commercialization almost all exhibit low Na-ion conductivities of around 10^(-5)S cm^(-1)or lower.Here,we report a chloride solid electrolyte,Na_(2.7)ZFCl_(5.3)O_(0.7),which reaches a Na-ion conductivity of 2.29×10^(-4)S cm^(-1)at 25℃without involving overly expensive raw materials such as rare-earth chlorides or Na_(2)S.In addition to the efficient ion transport,Na_(2.7)ZrCl_(5.3)O_(0.7)also shows an excellent deformability surpassing that of the widely studied Na_(3)PS_(4),Na_(3)SbS_(4),and Na_(2)ZrCl_(6)solid electrolytes.The combination of these advantages allows the all-solid-state cell based on Na_(2.7)ZrCl_(5.3)O_(0.7)and NaCrO_(2)to realize stable room-temperature cycling at a much higher specific current than those based on other non-viscoelastic chloride solid electrolytes in literature(120 mA g^(-1)vs.12-55 mA g^(-1));after 100 cycles at such a high rate,the Na_(2.7)ZFCl_(5.3)O_(0.7)-based cell can still deliver a discharge capacity of 80 mAh g^(-1)at25℃.

Identification of the Worst-case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

Day-ahead Voltage-stability-constrained Network Topology Optimization with Uncertainties

A day-ahead voltage-stability-constrained network topology optimization(DVNTO)problem is proposed to find the day-ahead topology schemes with the minimum number of operations(including line switching and bus-bar splitting)while ensuring the sufficient hourly voltage stability margin and the engineering operation requirement of power systems.The AC continuation power flow and the uncertainty from both renewable energy sources and loads are incorporated into the formulation.The proposed DVNTO problem is a stochastic,largescale,nonlinear integer programming problem.To solve it tractably,a tailored three-stage solution methodology,including a scenario generation and reduction stage,a dynamic period partition stage,and a topology identification stage,is presented.First,to address the challenges posed by uncertainties,a novel problem-specified scenario reduction process is proposed to obtain the representative scenarios.Then,to obtain the minimum number of necessary operations to alter the network topologies for the next 24-hour horizon,a dynamic period partition strategy is presented to partition the hours into several periods according to the hourly voltage information based on the voltage stability problem.Finally,a topology identification stage is performed to identify the final network topology scheme.The effectiveness and robustness of the proposed three-stage solution methodology under different loading conditions and the effectiveness of the proposed partition strategy are evaluated on the IEEE 118-bus and 3120-bus power systems.

Convolution Neural Network-based Load Model Parameter Selection Considering Short-term Voltage Stability

The recently proposed ambient signal-based load modeling approach offers an important and effective idea to study the time-varying and distributed characteristics of power loads.Meanwhile,it also brings new problems.Since the load model parameters of power loads can be obtained in real-time for each load bus,the numerous identified parameters make parameter application difficult.In order to obtain the parameters suitable for off-line applications,load model parameter selection(LMPS)is first introduced in this paper.Meanwhile,the convolution neural network(CNN)is adopted to achieve the selection purpose from the perspective of short-term voltage stability.To begin with,the field phasor measurement unit(PMU)data from China Southern Power Grid are obtained for load model parameter identification,and the identification results of different substations during different times indicate the necessity of LMPS.Meanwhile,the simulation case of Guangdong Power Grid shows the process of LMPS,and the results from the CNNbased LMPS confirm its effectiveness.

Power Flow Analytical Solutions and Multi-dimensional Voltage Stability Boundaries Based on Multivariate Quotient-difference Method

This paper proposes a novel Multivariate Quotient-Difference(MQD)method to obtain the approximate analytical solution for AC power flow equations.Therefore,in the online environment,the power flow solutions covering different operating conditions can be directly obtained by plugging values into multiple symbolic variables,such that the power injections and consumptions of selected buses or areas can be independently adjusted.This method first derives a power flow solution through a Multivariate Power Series(MPS).Next,the MQD method is applied to transform the obtained MPS to a Multivariate Pad´e Approximants(MPA)to expand the Radius of Convergence(ROC),so that the accuracy of the derived analytical solution can be significantly increased.In addition,the hypersurface of the voltage stability boundary can be identified by an analytical formula obtained from the coefficients of MPA.This direct method for power flow solutions and voltage stability boundaries is fast for many online applications,since such analytical solutions can be derived offline and evaluated online by only plugging values into the symbolic variables according to the actual operating conditions.The proposed method is validated in detail on New England 39-bus and IEEE 118-bus systems with independent load variations in multi-regions.

Optimal Location and Sizing ofMulti-Resource Distributed Generator Based onMulti-Objective Artificial Bee Colony Algorithm

Distribution generation(DG)technology based on a variety of renewable energy technologies has developed rapidly.A large number of multi-type DG are connected to the distribution network(DN),resulting in a decline in the stability of DN operation.It is urgent to find a method that can effectively connect multi-energy DG to DN.photovoltaic(PV),wind power generation(WPG),fuel cell(FC),and micro gas turbine(MGT)are considered in this paper.A multi-objective optimization model was established based on the life cycle cost(LCC)of DG,voltage quality,voltage fluctuation,system network loss,power deviation of the tie-line,DG pollution emission index,and meteorological index weight of DN.Multi-objective artificial bee colony algorithm(MOABC)was used to determine the optimal location and capacity of the four kinds of DG access DN,and compared with the other three heuristic algorithms.Simulation tests based on IEEE 33 test node and IEEE 69 test node show that in IEEE 33 test node,the total voltage deviation,voltage fluctuation,and system network loss of DN decreased by 49.67%,7.47%and 48.12%,respectively,compared with that without DG configuration.In the IEEE 69 test node,the total voltage deviation,voltage fluctuation and system network loss of DN in the MOABC configuration scheme decreased by 54.98%,35.93%and 75.17%,respectively,compared with that without DG configuration,indicating that MOABC can reasonably plan the capacity and location of DG.Achieve the maximum trade-off between DG economy and DN operation stability.

A novel collapse prediction index for voltage stability analysis and contingency ranking in power systems

Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed condi-tions.To prevent voltage collapse caused by such instability,accurate voltage collapse prediction is necessary for power system planning and operation.This paper proposes a novel collapse prediction index(NCPI)to assess the volt-age stability conditions of the power system and the critical conditions of lines.The effectiveness and applicability of the proposed index are investigated on the IEEE 30-bus and IEEE 118-bus systems and compared with the well-known existing indices(Lmn,FVSI,LQP,NLSI,and VSLI)under several power system operations to validate its practicability and versatility.The study also presents the sensitivity assumptions of existing indices and analyzes their impact on voltage collapse prediction.The application results under intensive case studies prove that the proposed index NCPI adapts to several operating power conditions.The results show the superiority of the proposed index in accurately estimating the maximum load-ability and predicting the critical lines,weak buses,and weak areas in medium and large networks during various power load operations and contingencies.A line interruption or generation unit outage in a power system can also lead to voltage collapse,and this is a contingency in the power system.Line and generation unit outage contingencies are examined to identify the lines and generators that significantly impact system stability in the event of an outage.The contingencies are also ranked to identify the most severe outages that significantly cause voltage collapse because of the outage of line or generator.

Machine Learning Accelerated Real-Time Model Predictive Control for Power Systems

This paper presents a machine-learning-based speedup strategy for real-time implementation of model-predictive-control(MPC)in emergency voltage stabilization of power systems.Despite success in various applications,real-time implementation of MPC in power systems has not been successful due to the online control computation time required for large-sized complex systems,and in power systems,the computation time exceeds the available decision time used in practice by a large extent.This long-standing problem is addressed here by developing a novel MPC-based framework that i)computes an optimal strategy for nominal loads in an offline setting and adapts it for real-time scenarios by successive online control corrections at each control instant utilizing the latest measurements,and ii)employs a machine-learning based approach for the prediction of voltage trajectory and its sensitivity to control inputs,thereby accelerating the overall control computation by multiple times.Additionally,a realistic control coordination scheme among static var compensators(SVC),load-shedding(LS),and load tap-changers(LTC)is presented that incorporates the practical delayed actions of the LTCs.The performance of the proposed scheme is validated for IEEE 9-bus and 39-bus systems,with±20%variations in nominal loading conditions together with contingencies.We show that our proposed methodology speeds up the online computation by 20-fold,bringing it down to a practically feasible value(fraction of a second),making the MPC real-time and feasible for power system control for the first time.

An Adaptive Many-objective Robust Optimization Model of Dynamic Reactive Power Sources for Voltage Stability Enhancement

The deployment of dynamic reactive power sourcecan effectively improve the voltage performance after a disturbance for a power system with increasing wind power penetration level and ubiquitous induction loads.To improve the voltage stability of the power system,this paper proposes an adaptive many-objective robust optimization model to deal with thedeployment issue of dynamic reactive power sources.Firstly,two metrics are adopted to assess the voltage stability of the system at two different stages,and one metric is proposed to assess the tie-line reactive power flow.Then,a robustness index isdeveloped to assess the sensitivity of a solution when subjectedto operational uncertainties,using the estimation of acceptablesensitivity region(ASR)and D-vine Copula.Five objectives areoptimized simultaneously:①total equipment investment;②adaptive short-term voltage stability evaluation;③tie-line power flow evaluation;④prioritized steady-state voltage stabilityevaluation;and⑤robustness evaluation.Finally,an anglebased adaptive many-objective evolutionary algorithm(MaOEA)is developed with two improvements designed for the application in a practical engineering problem:①adaptive mutationrate;and②elimination procedure without a requirement for athreshold value.The proposed model is verified on a modifiedNordic 74-bus system and a real-world power system.Numerical results demonstrate the effectiveness and efficiency of theproposed model.

Optimization of the Placement and Size of Photovoltaic Source

This paper presents a new optimization study of the placement and size of a photovoltaic source(PVS)in a distribution grid,based on annual records of meteorological parameters(irradiance,temperature).Based on the recorded data,the production output as well as the daily average power(24-h vector)of the PVS is extracted over the year.When a power vector is available,it can be used as an input when searching for the optimal size of the PVS.This allows to take into account the constraint of the variation of the power generated by this source considering the variation of the power consumed by the electrical loads during the whole day.A multi-objective fitness function has been considered.The latter minimizes the active losses and maximizes the voltage stability index during the day,while considering the constraints of the system,that is,the security,technical,geographical,and meteorological constraints.This problem was solved using the Non-dominated Sorting Genetic Algorithm NSGA-II optimization technique under MATLAB 2021.It was applied to the distribution network of Ghardaïa of 59 nodes.

Research on Reactive Power Optimization of Offshore Wind Farms Based on Improved Particle Swarm Optimization

The lack of reactive power in offshore wind farms will affect the voltage stability and power transmission quality of wind farms.To improve the voltage stability and reactive power economy of wind farms,the improved particle swarmoptimization is used to optimize the reactive power planning in wind farms.First,the power flow of offshore wind farms is modeled,analyzed and calculated.To improve the global search ability and local optimization ability of particle swarm optimization,the improved particle swarm optimization adopts the adaptive inertia weight and asynchronous learning factor.Taking the minimum active power loss of the offshore wind farms as the objective function,the installation location of the reactive power compensation device is compared according to the node voltage amplitude and the actual engineering needs.Finally,a reactive power optimizationmodel based on Static Var Compensator is established inMATLAB to consider the optimal compensation capacity,network loss,convergence speed and voltage amplitude enhancement effect of SVC.Comparing the compensation methods in several different locations,the compensation scheme with the best reactive power optimization effect is determined.Meanwhile,the optimization results of the standard particle swarm optimization and the improved particle swarm optimization are compared to verify the superiority of the proposed improved algorithm.

Investigating the Effects of Slack Bus Selection in Load Flow Studies: A Comparative Analysis of Robust and Weak Grids

Load flow studies play a critical role in the analysis of power systems. They enable the computation of voltage, current, and power flows in a power system. They provide valuable insights into the steady-state performance of the power system under different operating conditions. Choosing a slack bus is a vital step in conducting load flow simulations. A slack bus is a PV bus that includes a generator and is used to balance real and reactive power during load flow studies. Many studies have been conducted on the selection of slack buses in load flow analysis. However, varied conclusions regarding the impact on system losses and power flows were obtained during these studies. Therefore, using the IEEE-14 bus test system, this study investigated the effects of slack bus selection in strong and weak grids by alternating slack buses among PV buses and observing the effects on bus voltage magnitude, bus voltage phase angle, total power flows, and active and reactive power losses. The study noted that the effect of slack bus selection on these system quantities is contingent upon the voltage stability of the grid. Whereas in a robust grid, system losses and power flows remained constant irrespective of the choice of slack bus, a weak grid experienced some variations in these system quantities under similar circumstances. The simulation results led to the conclusion that, to a large extent, the voltage stability of the grid plays a significant role in determining the degree to which slack bus selection affects system losses and other quantities in load flow studies.