Steady-state Voltage Stability Research Articles

SDP-Based Optimal Power Flow With Steady-State Voltage Stability Constraints

This paper proposes a voltage stability-constrained optimal power flow (VSC-OPF) model based on semidefinite programming (SDP) relaxation. The minimum singular value of the power flow Jacobian is used as a steady-state voltage stability index, which is incorporated into the SDP formulation. To model an ADP constraint for voltage stability, an auxiliary matrix based on the power flow Jacobian is constructed, and this auxiliary matrix can be reformulated as a function of the semidefinite variable matrix defined for SDP relaxation. The resulting SDP-based VSC-OPF model is formulated and solved via the solver SDPT3 and the toolbox YALMIP. Extensive simulations on IEEE test systems validate the effectiveness of the proposed model.

Modified affine arithmetic based continuation power flow analysis for voltage stability assessment under uncertainty

Continuation power flow (CPF) analysis has been used in the literature to determine the voltage collapse point from active power versus voltage curves (PV curves) for steady-state voltage stability assessment. Affine arithmetic-based (AA) CPF analysis to determine PV curve bounds under uncertainty in power generation was introduced in the literature to overcome the problem of large computational time with Monte Carlo (MC) simulations, by getting a faster solution with a reasonably good accuracy. However, AA operations lead to more noise terms and hence overestimation of bounds. In the present work, a modified AA (modAA)-based CPF analysis is proposed to determine PV curve bounds by considering uncertainties associated with active and reactive power injections at all buses in the system. The proposed method reduces the overestimation caused by the AA operations and gives more accurate solution bounds. The proposed modAA-based CPF analysis is tested on 5-bus test case, IEEE 57, European 1354 and Polish 2383-bus systems. The simulation results with the proposed method are compared with MC simulations and AA-based CPF analysis to show the efficacy of the proposed method.

Online Voltage Stability Assessment for Load Areas Based on the Holomorphic Embedding Method

This paper proposes an online steady-state voltage stability assessment scheme to evaluate the proximity to voltage collapse at each bus of a load area. Using a non-iterative holomorphic embedding method (HEM) with a proposed physical germ solution, an accurate loading limit at each load bus can be calculated based on online state estimation on the entire load area and a measurement-based equivalent for the external system. The HEM employs a power series to calculate an accurate P – V curve at each load bus and accordingly evaluates the voltage stability margin considering load variations in the next period. An adaptive two-stage Pade approximant method is proposed to improve the convergence of the power series for accurate determination of the nose point on the P – V curve with moderate computational burden. The proposed method is first illustrated in detail on a four-bus test system and then demonstrated on a load area of the Northeast Power Coordinating Council 48-geneartor 140-bus power system.

Fast Stability Scanning for Future Grid Scenario Analysis

Future grid scenario analysis requires a major departure from conventional power system planning, where only a handful of most critical conditions is typically analyzed. To capture the inter-seasonal variations in renewable generation of a future grid scenario necessitates the use of computationally intensive time-series analysis. In this paper, we propose a planning framework for fast stability scanning of future grid scenarios using a novel feature selection algorithm and a novel self-adaptive PSO-k-means clustering algorithm. To achieve the computational speed-up, the stability analysis is performed only on small number of representative cluster centroids instead of on the full set of operating conditions. As a case study, we perform small-signal stability and steady-state voltage stability scanning of a simplified model of the Australian National Electricity Market with significant penetration of renewable generation. The simulation results show the effectiveness of the proposed approach. Compared to an exhaustive time series scanning, the proposed framework reduced the computational burden up to ten times, with an acceptable level of accuracy.

Hierarchical and Distributed Monitoring of Voltage Stability in Distribution Networks

We consider the problem of quantifying and assessing the steady-state voltage stability in radial distribution networks. Our approach to the voltage stability problem is based on a local, approximate, and yet highly accurate characterization of the determinant of the Jacobian of the power flow equations parameterized according to the branch-flow model. The proposed determinant approximation allows us to construct a voltage stability index that can be computed in a fully distributed or in a hierarchical fashion, resulting in a scalable approach to the assessment of steady-state voltage stability. Finally, we provide upper bounds for the approximation error and we numerically validate the quality and the robustness of the proposed approximation with the IEEE 123-bus test feeder.

Analysis into the Impacts of Short Circuit Capacity and X/R Ratio on Voltage Stability in Wind Power Plants

The voltage stability of a distribution network connected Wind Power Plant (WPP) is dictated by the Short Circuit Capacity (SCC), Short Circuit Ratio (SCR), and short circuit impedance angle ratio at a given Point of Common Coupling (X/RPCC). This paper presents a comprehensive analytical study into the interconnection of WPPs to distribution networks through detailed power-voltage (PV), reactive power-voltage (QV), and SCR-voltage analysis studies. Analysis studies have been carried out using Induction Generator (IG) and Doubly-Fed Induction Generator (DFIG) WPP models connected to IEEE standard distribution systems. The study has shown that for small X/RPCC ratios, DFIG-based WPPs suffer from Power Quality (PQ) concerns. In the case of IG-based WPPs, PQ requirements can hardly be satisfied when wind power penetration is high for both large and small X/RPCC values. Analytical models, developed using QV analysis, have shown that voltage variations in response changes in wind reactive power at large X/RPCC buses is approximately two times greater than those with a small X/RPCC ratio. This research will guide decisions on the selection of feasible networks and WPP interconnection buses where steady-state voltage stability requirements can be best satisfied.

Effective Demand Side Scheme for PHEVs Operation Considering Voltage Stability of Power Distribution Systems

Abstract This paper presents a new technique for a controlled charging/discharging of the PHEV’s battery considering the network status on a real-time basis. A control strategy is developed to secure the operation of power system irrespective of the number of vehicles and their connection place. The proposed control strategy utilizes an improved normalized steady-state voltage stability index that is easy to compute in the distribution management systems. A fuzzy logic controller (FLC) is used for evaluating the battery level of charging/discharging of individual PHEV connected to the distribution network. The controller is a part of the smart charger which uses the battery state of charge and the stability index as input variables. Based on the FLC output, the interface converter of a PHEV decides the desired charging/discharging levels of the battery. The developed controller ensures the secure operation of the distribution system during charging since only empty batteries will have a high priority to charge. A time domain, as well as 24-hour time-series simulations, are used to test the proposed control method. The results show that the developed control method guarantees secure operation, whatever the number and location of PHEVs connected to the studied system.

Fuzzy logic approach for reactive power coordination in grid connected wind farms to improve steady state voltage stability

This study presents a fuzzy logic approach for reactive power coordination in grid connected wind farms with different types of wind generator units to improve steady state voltage stability of power systems. The load bus voltage deviation is minimised by changing the reactive power controllers according to their sensitivity using fuzzy set theory. The proposed approach uses only few controllers of high sensitivity to achieve the desired objectives. The 297-bus and 417-bus equivalent grid connected wind systems are considered to present the simulation results. To prove the effectiveness of the proposed approach, a comparative analysis is carried out with the conventional linear programming based reactive power optimisation technique. Results demonstrated that the proposed approach is more effective in improving the system performance as compared with the conventional existing technique.

A Steady State Voltage Stability Analysis of Wind Power Centralized System

It is significant to research the voltage stability of the wind power centralized system (WPCS) for the effective development of the large scale clustering wind energy resources. A steady state voltage stability analysis of the WPCS by employing the PV curve and model analysis is proposed to reveal the voltage stability influence from different aspects. The PV curve is utilized to trace and indicate the voltage collapse point of the WPCS when the small disturbance of wind power is increased gradually. Then the steady state voltage instability modes of the WPCS are analyzed by calculating the bus participation factors of the minimum eigenvalue model at the collapse point. The simulation results of an actual WPCS in North China show that the static state voltage instability mode of the WPCS is closely related to the operating features and control strategies of different reactive power sources. In addition, the implementation of the doubly-fed induction generator wind turbine generator voltage control is beneficial to improve the WPCS voltage stability.

Evaluation of Steady State Voltage Stability Margin of a Power System Using Search Group Algorithm

Evaluation of Steady State Voltage Stability Margin of a Power System Using Search Group Algorithm

Sensitivity Model of L Index for Steady-state Voltage Stability of Wind Power Systems with Doubly Fed Induction Generators

There is increasing concern for the steady-state voltage stability of power systems with wind power integration. Simplification to wind turbine generators or transmission systems yields inaccurate judgment to steady-state voltage stability. In this article, a detailed configuration of doubly fed induction generators under maximum power-point tracking mode is provided and solved together with power flow equations to derive the L indices of load buses. The sensitivities of L to the bus powers and tap changers are newly proposed to quantify the effect of control measures on steady-state voltage stability. The former does not ignore the line resistance as the existing sensitivity model of the B index; the latter considers the derivatives of the admittance matrix to the tap changer. The numerical results show that the doubly fed induction generators and wind speeds have a notable effect on the steady-state voltage stability. Active load shedding may improve or decrease the steady-state voltage stability, while reactive load shedding improves the steady-state voltage stability. The tap changers may yield opposite effects on different load buses. Compared with the continual power flow, the sensitivity model describes the control measures for steady-state voltage stability with desirable accuracy.

Singular Value Sensitivity Based Optimal Control of Embedded VSC-HVDC for Steady-State Voltage Stability Enhancement

In this paper, we propose a novel control algorithm for improving steady-state (quasi-static) voltage stability by use of an embedded voltage source converter (VSC) based high voltage direct current (HVDC) system. In this paper, the terms “steady-state” and “quasi-static” are used interchangeably. By embedded HVDC, we refer to a meshed AC system with all HVDC terminals connected within the same AC grid. The sensitivity between VSC control input and the voltage stability margin is introduced. Based on this sensitivity, the proposed control algorithm jointly satisfies system-wide voltage stability margin as well as local voltage magnitude requirements. The proposed approach is to first migrate the entire system to have sufficient voltage stability margin, and then to correct any voltage magnitude violation while keeping that stability margin. A contour-based visualization of the VSC capability space for maintaining system voltage stability is introduced, which can effectively illustrate how the singular value sensitivity (SVS) based control achieves both the local and global voltage stability requirements. The efficacy of the proposed algorithm is shown via case studies on a 6-bus and 118-bus system with and without static VAR compensation.

Matpower CPF Program Improvement and Steady-State Voltage Stability Analysis

In steady-state voltage stability analysis, Continuation power flow (CPF) method is widely used for it can track power flow solution at the critical voltage point. The existing matpower CPF program can only simulate PV curve of a single bus when load increases at one certain bus. In this paper, original CPF program will be modified to be more flexible and in line with the actual situation. Several indices will be proposed to discuss how to determine the first crash bus (namely the system vulnerabilities) when load increases at multiple buses. Simulation results of a regional power grid in northern China verify the validity and practicability of the proposed method.

Coordinated tuning of PSS and TCSC to improve Hopf Bifurcation margin in multimachine power system by a modified Bacteria Foraging Algorithm

Abstract Recent research works have reported the effects of rotor angle dynamics of generators on bifurcation related system instability. This study intends to verify the possible influence of the Power System Stabilizers (PSS) and the Thyristor Controlled Series Capacitors (TCSC), on instabilities related to the Hopf Bifurcation (HB). Recently proposed optimization algorithm known as Bacteria Foraging Algorithm (BFA) in its modified version is applied in this study to tune the controller parameters of nine numbers of PSS and two numbers of TCSC present in the 10 machine New England power system. The main objective of this work is to maximize the margin of loading in the same system before the occurrence of the HB. Moreover, the formulation of a properly designed objective function is also an important issue that affects the final result. The objective function, that is formulated only to improve the overall damping in power system, may not be sufficient to avoid the HB under stressed operating condition. Therefore, this study proposes to reformulate an eigenvalue based objective function to improve the extent of loading before the HB could occur in the system. A coordinated control of the TCSC with those of the PSS may enable the controllers to delay the point of HB, compared to the case when the PSS alone were operating in the system. At the outset, the control parameter settings of several transformer taps and PV-bus voltages of nine generators were optimized to improve the steady state Voltage Stability Limit (VSL) of the system. At these settings, the damping controller parameters are tuned to improve the loadability before the point of HB. Similar approach is adopted when the TCSCs were operating coordinately with the PSS. At the end, small perturbation cases were simulated in the system to verify the performance of designed controllers in time domain analysis. The results further establish the efficacy of the controllers

Coordination of Reactive Power in Grid-Connected Wind Farms for Voltage Stability Enhancement

This paper studies the feasibility of utilizing the reactive power of grid-connected variable-speed wind generators to enhance the steady-state voltage stability margin of the system. Allowing wind generators to work at maximum reactive power limit may cause the system to operate near the steady-state stability limit, which is undesirable. This necessitates proper coordination of reactive power output of wind generators with other reactive power controllers in the grid. This paper presents a trust region framework for coordinating reactive output of wind generators with other reactive sources for voltage stability enhancement. Case studies on 418-bus equivalent system of Indian southern grid indicates the effectiveness of proposed methodology in enhancing the steady-state voltage stability margin.

A Study on Integrated Performance of Tap-Changing Transformer and SVC in Association with Power System Voltage Stability

Abstract—Electricity market activities and a growing demand for electricity have led to heavily stressed power systems. This requires operation of the networks closer to their stability limits. Power system operation is affected by stability related problems, leading to unpredictable system behavior. Voltage stability refers to the ability of a power system to sustain appropriate voltage levels through large and small disturbances. Steady-state voltage stability is concerned with limits on the existence of steady-state operating points for the network. FACTS devices can be utilized to increase the transmission capacity, the stability margin and dynamic behavior or serve to ensure improved power quality. Their main capabilities are reactive power compensation, voltage control and power flow control. Among the FACTS controllers, Static Var Compensator (SVC) provides fast acting dynamic reactive compensation for voltage support during contingency events. In this paper, voltage stability assessment with appropriate representations of tap-changer transformers and SVC is investigated. Integrating both of these devices is the main topic of this paper. Effect of the presence of tap-changing transformers on static VAR compensator controller parameters and ratings necessary to stabilize load voltages at certain values are highlighted. The interrelation between transformer off nominal tap ratios and the SVC controller gains and droop slopes and the SVC rating are found. P-V curves are constructed to calculate loadability margins.

Coordination between SC and SVC for Voltage Stability Improvement

At any point of time, a power system operating condition should be stable, meeting various operational criteria and it should also be secure in the event of any credible contingency. Present day power systems are being operated closer to their stability limits due to economic and environmental constraints. Maintaining a stable and secure operation of a power system is therefore a very important and challenging issue. Voltage instability has been given much attention by power system researchers and planners in recent years, and is being regarded as one of the major sources of power system insecurity. Voltage instability phenomena are the ones in which the receiving end voltage decreases well below its normal value and does not come back even after setting restoring mechanisms such as VAR compensators, or continues to oscillate for lack of damping against the disturbances. Reactive power limit of power system is one of the major causes of voltage instability. This paper investigates the effects of coordinated series capacitors (SC) with static VAR compensators (SVC) on steady-state voltage stability of a power system. Also, the influence of the presence of series capacitor on static VAR compensator controller parameters and ratings required to stabilize load voltages at certain values are highlighted. Keywords—Static VAR Compensator (SVC), Series Capacitor (SC), voltage stability, reactive power.

Assessment of reactive power contribution of photovoltaic energy systems on voltage profile and stability of distribution systems

This paper studies the impact of large-scale photovoltaic (PV) generation, up to 50% penetration level, on distribution system voltage regulation and voltage stability. The system voltage profiles are computed using power-flow calculations with load variation of a 24-h time scale. The steady-state voltage stability is examined at different times of the day using a developed continuation power-flow method with demand as continuation parameter and up to the maximum loading conditions. The load-flow analysis, implemented for both voltage regulation and voltage stability analysis, is performed by using the forward/backward sweep method. The secant predictor technique is developed for predicting the node voltages which are then corrected using the load flow solver. Three models of the PV interface inverter are implemented in this study with full set of data representing environmental conditions. The voltage profiles are regulated using the PV interface inverters, where the available inverter capacity is utilized for regulating the system node voltages. The most possible scenarios of system voltage collapse are investigated at different times of the study period. The developed methods and models are used to assess the performance of a 33-bus radial distribution feeder which operates with a high level of PV penetration. The results show that the PV interface inverters operate for reactive power support in distribution system resulting in improved voltage profile, secure power systems operation, and increasing the lifetime of the online tap changing transformers due to minimizing the total number of switching operations.

Voltage Stability Analysis in the Albanian Power System

With the new social-economical developments and the free moving of the population, the electricity consumption in Albania has changed significantly. The main problem facing by Albania Electric Power System is that the power demand is increasing rapidly whereas the supply growth is constrained by reduced capital availability. Many failures have been occured in Albanian power systems due to voltage instability, in the past few years. This paper mainly concern steady state voltage stability by capability checking of Albanian power system to maintain the voltage profile in the presence of active/reactive load variations. Voltage stability analysis was performed by utilizing voltage stability tools in NEPLAN software. The paper discusses the results of different methods in comparison of investments impact in the voltage stability. The results have shown that in heavily loaded power system of Albania the voltage stability problems cannot be met with the existing transfer capabilities, even with shunt compensation. New transmission capacities are necessary to improve the voltage stability.

A Power Flow Method Using a New Bus Type for Computing Steady-State Voltage Stability Margins

In steady-state voltage stability analysis, it is well-known that as the load is increased toward the maximum loading condition, the conventional Newton-Raphson power flow Jacobian matrix becomes increasingly ill-conditioned. As a result, the power flow fails to converge before reaching the maximum loading condition. To circumvent this singularity problem, continuation power flow methods have been developed. In these methods, the size of the Jacobian matrix is increased by one, and the Jacobian matrix becomes non-singular with a suitable choice of the continuation parameter. In this paper, we propose a new method to directly eliminate the singularity by reformulating the power flow problem. The central idea is to introduce an AQ bus in which the bus angle and the reactive power consumption of a load bus are specified. For steady-state voltage stability analysis, the voltage angle at the load bus can be varied to control power transfer to the load, rather than specifying the load power itself. For an AQ bus, the power flow formulation consists of only the reactive power equation, thus reducing the size of the Jacobian matrix by one. This reduced Jacobian matrix is nonsingular at the critical voltage point. We illustrate the method and its application to steady-state voltage stability using two example systems.