Steady-state Voltage Stability Research Articles

Probabilistic steady-state and short-term voltage stability assessment considering correlated system uncertainties

As correlated uncertainties in power grids become more prevalent, modeling of stochastic dependencies is becoming increasingly necessary. Independent probability distributions disregard these correlated uncertainties, potentially leading to significant errors, underscoring the necessity of dependence structures. This paper presents a probabilistic approach for modeling uncertain system parameters with their inherent correlations. The proposed approach is validated through various aspects of system voltage measures, including voltage profile and static and dynamic voltage stability. In total, nine alternative sampling generation techniques are employed, and their accuracy is measured based on real-world data using root mean square error (RMSE) and coefficient of determination (R2) criteria. The result suggests that multivariate (Gaussian and Student's) copula techniques accurately represent the real system data, consistently achieving high accuracy rates of 98 % for voltage profiles, 97 % for static voltage stability, and 93 % for dynamic voltage stability. In contrast, the independent sampling technique failed to follow the real-world system data for the different aspects of system voltage measures.

Performance Analysis of Microgrid Using Wind Power Based on Steady-State Voltage Stability

This investigation is done for augmentation of steady-state voltage stability in microgrid with doubly fed induction wind generator for the growing need of DG systems in distribution and transmission network. A poor stability in voltage reduces the efficiency of the distributed generation system (DGs). Double Fed Induction Generator (DFIG) is a type of induction generator interconnected into microgrid and it acting an essential role during the performance of microgrid in distributed generation systems of distribution network. The performance characteristics of microgrid with DFIG is analyzed and improved by control strategy. The PI (proportional and integral) control strategy of microgrid with DFIG rooted in double-fed induction generator (DFIG) in pitch angle control in the energy storage system (ESS). The performance analysis microgrid with DFIG is implemented by means of simulink platform in MATLAB software. The outcome was evaluated in this article in favor of steady-state voltage stability enhancement in microgrid with DFIG. This work is done for the achievement of a stable operation microgrid in DG system against disturbances in wind. The proposed work is intended to produce 1.58 MW of reactive power without controller and 0.48 MW, 0.36 MW, and 0.32 MW of power with P, PI, and PID (Proportional–Integral–Derivative) controller with PAC.

Steady-state voltage stability assessment of new energy power systems with multi-quadrant power modes

The “source–load” attributes of the nodes in a new energy power system are complex and diverse due to a large amount of new energy access. The node power (active and reactive power) in the system can offer a changing mode, which causes several serious challenges to the security of steady-state voltage stability. Aiming at the steady-state voltage stability problem in the system with multi-quadrant power modes, this paper reveals the mechanism of voltage evolution by voltage analytical expressions and the geometric characteristics of voltage components. Then, the indexes of voltage rise and drop are put forward by using a normalized voltage sensitivity. The voltage stability index is formulated based on the characteristics of voltage–power change. These indexes are used for steady-state voltage safety and stability assessment. Through the analysis of results that simulated by the IEEE-14 node power system and the coupled system in which the traditional power supply and new energy are connected to the same point of interconnection in Liaoning province, the results have proved that these indicators can be used to evaluate the steady-state voltage stability under multi-quadrant power modes. It is of great significance to guide the operation of voltage security in the power system with new energy.

Construction of Power Supply Stability Control Model for Wind Connected Power Grid

There are many problems in the power supply stability control of wind power generation system, such as large fluctuations, poor control effect and so on. Therefore, a new stability control model of wind power grid connected is designed. Determine the DC grid connection mode when the wind farm is connected, convert the DC power into AC power through the converter station, and transmit it to the final AC system to realize the grid connection of wind power and power grid; According to the determined wind power access mode, calculate the mechanical operation power, mechanical torque and wind energy utilization coefficient collected by the wind turbine, complete the best collection of wind energy, and determine the shafting according to the mass block model of the wind turbine and generator, so as to realize the research on the mathematical model of wind power generation. By analyzing the power flow direction of the stator and rotor of the wind turbine generator set, the unstable state of the power supply voltage of the wind turbine generator set after grid connection is determined. The PV curve method is used to calculate the steady-state voltage stability of grid connected wind turbines, and a power supply stability control model based on the voltage stability of grid connected wind turbines is established. The nonlinear objective function method is used to optimize the critical point of power supply stability, calculate the maximum load and maximum power of the system, establish the static power supply and transient power supply stability model after wind power grid connection, and realize the power supply stability control research of grid connected wind power through the analysis of power supply characteristics. The experimental results show that the model is closer to the stability of the actual power supply in the test of improving the stability of the power supply, ensuring the quality of power supply, while the test results of the other two methods have large fluctuations. In the analysis of the change of power supply after grid connection, the experimental results obtained by the model are very close to the actual data values. Therefore, this method can effectively improve the performance of power system.

Data-Driven Joint Voltage Stability Assessment Considering Load Uncertainty: A Variational Bayes Inference Integrated With Multi-CNNs

Few studies have focused on assessing the transient and steady-state voltage stability status of dynamic systems simultaneously. This motivated us to propose a new concept referred to as joint voltage stability assessment (JVSA). Towards this end, this paper proposes a novel data-driven JVSA method considering load uncertainty. It combines multiple convolutional neural networks (multi-CNNs) and a novel variational Bayes (VB) inference for better JVSA accuracy. First, the multi-CNN model is utilized to fast estimate the maximum voltage deviations during the transient and steady-state process. Uncertain load scenarios and system topology under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -1 contingency with are chosen as inputs of each CNN model. Second, estimated voltage deviations are put into the VB inference to automatically infer the transient and steady-state voltage stability status. To validate its effectiveness, numerical simulations are performed on the modified WECC 179-bus system by comparing with benchmark algorithms. It is demonstrated that the proposed data-driven JVSA method is more accurate and faster than the conventional VSA method.

Voltage Stability Analysis of IEEE118 Bus System with Wind Penetration

The increased penetration of renewable energy sources affects the voltage stability of the system. This article provides steady state voltage stability analysis with wind penetration. The standard IEEE 118 bus system is used for the analysis. The system is modelled in PSSE software and NR-Power flow method is used to perform the power flow studies with various levels of wind penetration. From the load flow studies voltage profile at load buses is analysed through PV curves. System is further studied with reactive power compensation provided at wind generator terminals. All cases are analysed for voltage stability with respect to increase in loading of the system.

An efficient multi-objective based squirrel search optimization for optimal placement of FACTS devices

The adoption of a new transmission line is extremely complex because of its socio-economic problems such as environmental clearances. Thus, there is a prominence of better utility over available transmission infrastructure. The Flexible Alternating Current Transmission System (FACTS) devices can offer transmission capability enhancement, power compensation, and stability as well as voltage improvement. However, the FACTS devices have a higher penetration impact of wind generation for the dynamic stability of power networks. In this work, an efficient Intellectual Control system has been proposed to stabilize the FACTS devices placement. The Squirrel Search Optimization is adapted with an intellectual control system to enhance the steady-state voltage stability of FACTS devices. The proposed system has been evaluated with the assist of IEEE 14 and 26 standard bus systems to handle the multi-objective functions like cost, reduction in power loss, reducing risks, and maximizing user’s benefit. These multi-objective functions facilitate to attain the optimal placement and load flows at various sites. The simulation can be carried out with MATLAB/SIMULINK environment and the results manifest that the proposed system outperforms well when compared with existing approaches.

Optimal Power Flow Considering Global Voltage Stability Based on a Hybrid Modern Heuristic Technique

Integrating large renewable energy to grid complicates power systems’ steady-state operation which leads to the high risk of voltage instability due to its intermittent and stochastic properties. The steady-state voltage stability margin (VSM) can be measured by the smallest singular value (SSV) of the load flow Jacobian matrix. Unlike other voltage stability indices such as L-index which shows the probability of voltage collapse for a particular bus, namely, local stability index, SSV represents the global voltage stability and the smaller the value is, the riskier the whole system's stability is. Voltage stability constrained-optimal power flow (VSC-OPF) is an effective tool to stabilize system voltage. Yet VSC-OPF is a highly non-linear and non-convex problem because of AC power flow and implicit SSV constraints. Such challenge is tackled, in this work, by a novel hybrid heuristic method, differential evolutionary particle swarm optimization (DEEPSO) which can easily formulate explicit constraints and objective functions to obtain near-optimal solutions efficiently. Several case studies are conducted on the IEEE 30-bus system, and they demonstrate the effectiveness of the hybrid technique and presents some insights on voltage profiles under various system operating condition.

On Steady-State Voltage Stability Analysis Performance in MATLAB Environment

Nowadays, electric power systems have been often operated close to their limits due to increased electric power consumptions, vast installments of renewable power sources and deliberated power market policies. This poses a serious threat to stable network operation and control. Therefore, voltage stability is currently one of key topics worldwide for preventing related black-out and islanding scenarios. In this paper, modelling and simulations of steady-state voltage stability problems in MATLAB environment are performed using author-developed computational tool implementing both conventional and more advanced numerical approaches. Their performance is compared with Simulink-based library Power System Analysis Toolbox (PSAT) in terms of solution accuracy, CPU time, and possible limitations. Their use for both real-time and off-line monitoring and assessment of system's voltage stability are also discussed.

Theorems to explore the nature of cyber attacks on power system voltage stability

Abstract Smart electric grids are practising flexible, reliable and robust operations during delivery and consumption of power. However, these grids are highly vulnerable to a wide range of cyber attacks due to the deployment of an extensive communication network. In this paper, the nature of cyber attack on given power system based on proposed cyber attack models and theorems is analysed by utilizing steady state voltage stability (L index). Further, a cyber attack factor is introduced which may mislead the bus voltage stability virtually. The proposed cyber attack models and theorems are validated by executing cyber attacks on WSCC 9 bus and IEEE 14 bus test systems by using Siemens PSS/E and MATLAB softwares. Through the proposed theorems, the paper exposes and quantifies the threat of cyber attacks in the electric power grid. The simulation results reveal that the proposed cyber attack models may misrepresent the bus voltage stability, thereby misleading the energy management centre (EMC) operator into taking incorrect countermeasures. The above incorrect actions may force voltage instability which further leads to major interruptions in the electric power supply and possible cascading failure of the electric power grid. Moreover, the proposed theorems and rigorous simulations presented in the paper support the EMC operator in intelligently identifying a cyber attack, thereby enabling development of appropriate corrective actions during such cyber attacks on the smart electric grid. Thus, the concept of proposed methodology could best assist the power system operator to build detection algorithms for discrimination of cyber attacks from electrical faults towards strong electric grid resilience character.

Study of Voltage in Stability in Power Systems Using Catastrophe Theory. (Dept. E)

Catastrophe theory is a mathematical technique for the qualitative analysis of system equations, defining the jump phenomena and sudden changes caused by smooth changes in the system parameters. This theory has been applied previously to the study of steady state stability of power system. This paper presents a new technique in the area of power system stability studies to describe steady-state voltage stability in terms of one of the catastrophe manifolds to which the power system can be fitted.

Probability analysis of steady-state voltage stability considering correlated stochastic variables

The penetration of renewable generation, such as photovoltaic and wind power in power networks will significantly impact the system’s stability in future, due to randomness and intermittency in the natural environment. Moreover, the correlations between renewable generation may enhance the impact on power system's stability. In this paper, cumulant-based maximum entropy method (CMEM) combined with Nataf Transform (NT) is proposed to analyze the steady-state voltage stability problem considering correlations and uncertainties of power injections and consumptions. The proposed methodology is tested on the IEEE 30-node and IEEE 57-node test systems. Taking the results of Monte Carlo method (MCM) as the experimental control group, this paper compares the proposed method with series expansion method (SEM), discusses and analyzes their calculation results and speed under different scenarios, and the results of the comparison prove the validity, accuracy and rapidity of the CMEM.

Machine Learning Enabled Steady-State Security Predictor as Deployed for Distribution Feeder Reconfiguration

The distribution network is reconfigured by modifying the topology arrangement of the network feeders. Because the voltage stability of the distribution networks can differ within a range following network reconfiguration, the calculation of steady-state voltage stability plays a significant role in real-time feeder reconfiguration. Examining the state of security and estimating it for the next operational configuration is crucial for making real-time decisions. Online security evaluation needs minimal complexity and computing time. Standard methods of assessing the distribution network’s steady-state voltage stability can be insufficient for online and real-time environments due to their high complexity and long computing period. This study proposes a machine learning (ML) approach for classifying configuration states and adopts the decision tree technique to interpret the online applications in the feeder reconfiguration. For the classification, the single line equivalent L-index voltage stability and switching configurations of the feeders are employed as training information for the ML models. A modified IEEE 14-bus and 30-bus test systems verifies the feasibility of the suggested solution. Once trained, the proposed system provides a quick and accurate classification for unknown configurations of the specific security state in 0.3 seconds.

Load Flow and Transient Stability Analyses for an Integrated Solar Combined Cycle Station in Iraqi Southern by Using ETAP

Analyses of a power system are important for designing and operating phase execution monitoring and to ensure reliable grid operations by sufficient protection projects settings. In this paper, electrical model of a 340 MW integrated solar combined cycle (ISCC) located in the south of Iraq, is developed by Electrical Transient Analyzer Program (ETAP) and load flow, voltage stability and short circuit analyses are performed. Impact of power grid voltage instability on system buses of the power plant is estimated. Using load flow analysis that use Newton-Raphson algorithm, buses operating at under voltage due to power grid voltage instability are specified and their voltages are improved according to given voltage limitation that are based on buses criticality with regard to loads. On-load tap changers and reactive power compensation are used to improve steady state voltage stability. Optimal position for capacitor banks placement and number of capacitor banks are proposed by using optimal capacitor placement module of ETAP. The use of modern technology and advance planning have a big impact on reducing losses. The article shows that the lack of planning is one of the main causes of energy losses. The parameters of the module also indicate the voltage limits, bus voltage and ratings of available capacitor banks. The voltage limit is set at 95% ≤ V ≤ 110%, and it is global for all buses

Steady State Voltage Stability Estimation by Using Local Bus Parameters

In this study, an estimation approach based on local bus measurements of voltage, current and phase angle is presented to assess voltage stability at any of the system load bus. For this purpose, Thevenin equivalent circuit parameters of the IEEE 30-bus standard test system are estimated by using local measurements from Bus k which is selected to be evaluated in terms of voltage stability. Estimated Thevenin equivalent circuit parameters are used to calculate critical voltage values and voltage stability margin values of Bus k online for the voltage stability assessment. In conclusion, the voltage stability margin results of the proposed approach are compared with three different Thevenin equivalent based voltage stability estimation approaches. Simulation results show that the proposed approach successfully estimates the voltage stability margins of any load bus in the system. From the perspective of voltage stability, estimated voltage stability margins can be used to assess the loading levels of any load bus, to define critical busses and to make decision for load shedding.

Survey about impact voltage instability and transient stability for a power system with an integrated solar combined cycle plant in Iraq by using ETAP

The Analyses for power systems are more necessary for the designing, operating phase execution control and to make sure safe network operations by sufficient protection project settings. In this article, we have prepared a sufficient scientific survey about the electrical model of a 340 MW integrated solar combined cycle system (ISCCS) located in the Iraqi southern, is developed and simulation by a program called Electrical Transient Analyzer Program (ETAP) and carry out throw this program the load flow, voltage stability and short circuit analyses for this power plant with part of the national grid in Al-Basra city in an industrial region. The effect of voltage instability for the grid on system buses (load buses) of the power system is estimated. By using load flow analysis as a case study by using the Newton-Raphson algorithm, when the load buses operating at down voltage because of instability voltage of the power grid are specified and their voltages are should to improved according to given voltage limitations that are depended on buses criticality with regard to loads. The appliance on-load tap changers of the transformer and reactive power compensation are used to improve steady-state voltage stability for any instability system. The method of the optimal position for capacitor banks placement is meaning the number of capacitor banks is proposed to adding to the weak buses by using the optimal capacitor placement module of ETAP. Energy is actually required for the expansion of our country. To sustain the generation of electric power at an adequate level power system supplies power to different types of loads that are located far away from the generating plants using transmission lines.

Probabilistic Steady State Voltage Stability Assessment Method for Correlated Wind Energy and Solar Photovoltaic Integrated Power Systems

Herein, a novel method for the assessment of steady state probabilistic voltage stability margins (PVSMs) in power systems considering generation and load demand uncertainty is investigated. The steady state VSM in an uncertain environment is jointly analyzed through continuous power flow (CPF) and the three point estimation method (3PEM). The statistical distribution of the VSM is obtained using Cornish–Fisher (CF) expansion series. Results are compared with the benchmark Monte Carlo simulation method. Probabilistic models of grid‐connected wind and solar photovoltaic energy sources are utilized in this study. For identification of weak/strong buses and contingency ranking of transmission lines, a steady state voltage stability index, the L‐index, is utilized. The validation of the proposed method is analyzed through IEEE 24 bus and 118 bus test systems. For a realistic study of the system, correlations among wind speeds, solar power outputs, and load demands are considered with various static load models, i.e., constant impedance (CZ), constant current (CI), constant power (CP), and ZIP. Moreover, the concept of relative electrical distance (RED) is applied for selecting the conventional generators for power balancing. The results reveal that factors such as load characteristics and correlations have significant effects on PVSM.

An Interactive Partitioning Algorithm-Based Electrical Power Crisis Management for Service Restoration with Existing Black-Start Resources Considering Load Priority

This article explores a new clustering-based solution for power systems that would be restored by post-outage power supply. The suggested solution has divided the overall network into separate clusters in such a way that each cluster has at least one ‘black-start unit,’ which can restart its own generation. The proposed algorithm manages a variety of restrictions when creating clusters, such as black-start generation capability, supply–demand balancing, and load priority, and attempts to minimize the active and reactive power difference between black-start unit and cluster loads as well as minimize power losses. This paper focuses on the standby available sources in a network to act like ‘black-start units,’ while their neighboring high-priority loads as defined by the supply provider were called cluster participants. K-means neighbor clustering algorithm was used to form the clusters, and, before validating each cluster, the steady-state voltage stability of the clusters was tested using equivalent network L-index value analysis technique. Two separate case studies were performed on the modified distribution IEEE 33-bus system and New England electrical transmission system with 39 buses to demonstrate the efficacy of the proposed algorithm. The results of the simulation show that each cluster was consistently able to maintain reasonable voltage stability with minimum power imbalance between available BSU and loads.

Optimal converter control for PV-fed DC and AC interconnection by using hybrid artificial neural networks

Abstract Optimal control of power converters to avoid voltage instability in cases such as system loading or faults is one of the most studied nonlinear problems that affect energy quality in power systems. The optimization problem related to converter control becomes more difficult with the inclusion of renewable energy systems while trying to fulfill power system constraints and providing an adequate amount of energy. In this paper, a simple approach based on artificial neural networks (ANNs) has been proposed and applied to photovoltaic-fed high-voltage DC and high-voltage AC systems interconnection consisting of PI-controlled power converters. By using the proposed method, converter control parameters are optimized for different cases to improve steady-state and dynamic voltage stability while also avoiding any kind of system faults. In order to implement hybrid control methodology by using ANN and PI control, the network should be well trained with samples including not only global best values but also the whole possible system characteristic. For this reason, a novel optimization algorithm, differential search algorithm, is used to sample solution space and train ANN by using random and localized samples. Obtained and presented results of the proposed approach show that due to robust and fast response, ANNs can be successfully used to overcome nonlinear security and optimization problems concerning power system stability.

Augmented system for detecting the steady‐state voltage stability margin

This work provides an augmented system (AS), constructed based on a modified tangent vector Index, i.e. the full derivative of the uncontrollable parameter with respect to the voltage magnitude of critical bus of the system, to directly detect steady-state voltage stability margin (SSVSM). The Newton iteration produced by the AS is illustrated to be able to approach the equilibrium manifold until converging to the saddle node bifurcation, given that the initial point is approaching to the corresponding branch. With the special searching direction, limit induced dynamic bifurcations or limit induced static bifurcation that appear along the equilibrium manifold are able to be located with expected precision by the proposed corrections. Several cases in a 2000-bus synthetic grid exemplify the effectiveness and high efficiency of the algorithm, compared with standard continuation power flow and the predicter-corrector primal dual interior point algorithm for detecting the SSVSM.