Voltage Stability Level Research Articles

Quantitative evaluation of power grid voltage stability level of power system with high proportional power electronics device

Abstract There is an increasing need for long-distance electricity transportation using high voltage direct current (HVDC). By incorporating numerous renewable energy grid integration technologies at the receiving end, an advanced power grid network will be built. The occurrence of short-circuit faults at the receiving end has the potential to trigger commutation failure and voltage dip. Consequently, the exploration of transient voltage stability assessment is pivotal in enhancing the secure and reliable functioning of the receiving electricity grid. To address this challenge, this paper initially delves into the quantitative assessment of the voltage stability status when subjected to a power system with high proportional power electronics device. It also clarifies the dynamic interplay between reactive power and voltage. Subsequently, a suitable quantitative assessment metric for transient voltage stability is formulated. Finally, the transient voltage stability evaluation of a power system with high proportional power electronics device is realized.

A Modified Genetic Algorithm for Optimizing the Placement and Sizing of Distributed Generators in Radial Distribution Systems Including Security Analysis

In this paper, a Modified Genetic Algorithm (MGA) combined with ETAP (Electrical Transient Analyzer Program), is proposed to optimize the placement and sizing of Distributed Generation (DG) units while considering multiple objectives, such as improving voltage profiles, reducing line losses, and managing short-circuit levels. These factors are critical for maintaining power quality, system reliability, and overall stability. The MGA approach is validated through simulations using the IEEE 33-bus distribution system, modeled in both MATLAB and ETAP. The results show significant improvements in voltage stability, loss reduction, and short-circuit level management, enhancing energy management and operational efficiency. A comparative analysis with alternative algorithms, including the Bat Algorithm (BA), Bacterial Foraging Optimization Algorithm (BFOA), and Artificial Immune System (AIS), demonstrates that MGA achieves superior convergence speed and accuracy, making it highly effective for DG placement and power system performance optimization.

Fostering restoration and power delivery efficiency by distributed generators and line switches in electricity distribution network

ABSTRACT The distribution of power is being faced with challenges during and after extreme weather events. This contingent might cause a partial or full power blackout in the distribution territory. Hence, the restoration of the service is one of the key concerns of the utilities. A strategy is adopted to felicitate the power restoration process by the deployment of distributed generators (DGs) and line switches. A fuzzy-based system model is proposed to allocate line switches considering the impact of wind-driven extreme weather and the fault frequency character of the lines. The study further recommends an arrangement of dispatchable DGs in the sections of the distribution grid. A particle swarm optimization-based model is proposed for suitable capacity and location assessment of the DGs to foster the restoration of supply avoiding voltage and frequency disturbances in the developed sections of the grid. The results are further verified with the application of the grasshopper optimization algorithm on the multipurpose composite objective function. The proposed DG allocation approach escalates the network power loss reduction by 95.10%, improvement in average voltage stability level by 6.46%, and loadability margin enhancement by 37.37% when the DGs are operated in grid-connected mode. Moreover, power supply reliability is restored with successive employment of DG units. The proposed approach has been tested on an Indian 28-bus power distribution network. The outcome of the proposed approach is compared with existing DG allocation methods. The experiment confirms the credential of the proposed approach with better value addition in multiple objectives.

Voltage Stability Analysis of Power System with Photovoltaic Power Plant

Photovoltaic power plants usually do not provide reactive power output; hence the application of large photovoltaics in power systems will decrease the voltage stability level of the power system. Capacitor banks can provide reactive power to compensate the photovoltaic plants; therefore, capacitor banks can overcome the reactive power deficiency of photovoltaic plants. However, the effect of capacitor bank installation on the system’s voltage stability is unknown. Therefore, the research aims to investigate whether installing a capacitors bank can restore the level of system voltage stability. The study employs the method of Voltage Stability Margin and transient stability simulation to the IEEE 9 bus system. The IEEE 9 bus system is modified where one generator of the system is replaced with a photovoltaic plant, and a capacitor bank is also installed. The study results show that the modified system voltage stability level is lower than the original system. When the capacity of the capacitor bank is increased to the maximum allowable value, the voltage stability level rises. However, it is still unable to be restored to its original value.

Research on Weak Node Power Flow Calculation and Voltage and Reactive Power Compensation of Off Grid Microgrid

The voltage stability control of off grid microgrid is the key and core issue of power grid stability. Aiming at the problem of voltage stability control of off grid microgrid with unbalanced nodes, the Newton Raphson homotopy algorithm is proposed to calculate the power flow, estimate the reactive power margin of each load node, and adopt reactive power supply droop compensation control for weak nodes to improve the voltage stability level. The simulation verifies the effectiveness of this method.

Design and simulation of reference voltage sources circuit in lasers

AbstractFor the design of reference voltage source circuits in lasers, there is a problem of low accuracy using general design approach, this paper proposes an improved high‐precision voltage source circuit design. Firstly, a suitable reference voltage source chip is selected, then the excitation source circuit with better stability is designed, a high‐order filter is designed for filtering, and finally a compensation circuit is designed to improve the accuracy of the lasers voltage source. The effect of the designed voltage source circuit was verified, and the simulation results showed that the designed voltage source circuit was improved in output voltage accuracy, stability, and noise level, achieving a voltage noise level of 0.978 μV/Hz1/2 at 0.1 mHz at an input voltage of 2V. The validity of the voltage source circuit used for the lasers is verified, providing a high reference value for improving the lasers accuracy in laser spectroscopy.

Optimal Reconfiguration of Power Distribution Network Using Hybrid Firefly and Particle Swarm Optimization Algorithm

Electrical energy has become the most essential requirement for working of today’s modern world. Power distribution networks (PDN) are required for providing power from substations to consumers but are subjected to power loss and voltage drop problems. These problems greatly affect the operational cost and voltage stability level of a PDN. Network reconfiguration (NR) is a cost effective approach to optimize PDN for reduction of power loss and improvement of voltage profile (VP). This paper presents an effective meta-heuristic, population-based algorithm for finding optimal configuration of a PDN. In particular Hybrid Firefly and Particle Swarm Optimization (HFPSO) algorithm is used. The HFPSO algorithm has enhanced exploration and exploitation strategies, and fast convergence rate. MATLAB software is used to implement the algorithm and IEEE 33-bus radial distribution system (RDS) is considered for NR. The results obtained show that active power loss is reduced by 46.35% from original value and minimum voltage is improved to 0.9572p.u. The comparison of obtained results with literature show that HFPSO algorithm has efficiently reduced active power loss and improved VP of the network.

Optimal adjustment of power network structure by considering static voltage stability and Short-Circuit current level of multi-infeed DC systems

Optimal adjustment of power network structure by considering static voltage stability and Short-Circuit current level of multi-infeed DC systems

DNN-Based Distributed Voltage Stability Online Monitoring Method for Large-Scale Power Grids

With the increase of power load demand and the complexity of power grid structure, the problem of voltage stability is becoming more serious, and it is urgent to study the countermeasures. In this paper, a DNN-based distributed voltage stability online monitoring method for large-scale power grids is proposed. Unlike the traditional load margin methods, the proposed method uses a local index load impedance modulus margin (LIMM) index to determine the optimal installation locations of PMUs, which is more efficiently. Moreover, the DNN is applied to learn the nonlinear relationship between the power system operation state and its corresponding LIMM. By this way, the corresponding LIMM value can be predicted through the state variables of nodes from the installed PMUs. This method can greatly improve the calculation speed of LIMM and assess the system voltage stability level in real-time, which help the system operator to judge the operating state and take measures in time. Finally, the proposed method is tested on the 14-bus system and then on the 118-bus system respectively, and the simulation results verify the effectiveness and correctness of the proposed method.

Multi‐stage coordinated dynamic VAR source placement for voltage stability enhancement of wind‐energy power system

Increased wind power penetration and induction loads have deteriorated the voltage stability performance of the power system. This study proposes a multi-stage multi-objective dynamic VAR source placement method for wind energy power system, where three sub-objectives are optimised simultaneously: (i) investment cost and operational control cost; (ii) steady-state voltage stability index; (iii) short-term voltage stability index. This method coordinates the dynamic VAR allocation decisions with preventive and corrective stability controls, including wind power curtailment, modification of the line drop compensation, and load shedding, to improve both steady-state and short-term voltage stability of the system. A robust parameter design technique called Taguchi's Orthogonal Array Testing is used to model the wind power uncertainty. Pareto optimal solutions are obtained for flexible decision-making. The computation burden is mitigated by candidate buses selection and critical contingency identification. The proposed model is demonstrated on the New England 39-bus test system using PSS®E. Compared with conventional approaches, it can achieve higher voltage stability level with less overall cost and moderate wind power curtailment, and at the same time avoid the conservativeness of planning decisions.

Bayesian Learning-Based Multi-Objective Distribution Power Network Reconfiguration

This article proposes a scheme aiming at solving the reconfiguration problem of distribution power network (DPN) with high wind power penetrations. The virtue of the presented scheme lies in balancing the voltage stability and the absorption rate of wind energy. First, the DPN reconfiguration is formulated as a multi-objective optimization problem, where a curtailment strategy is introduced with the assistance of the secure operations of DPN. Thereby, the absorption rate of the generated wind power is maximized and voltage stability level is improved as well. Meanwhile, a modified multi-objective Bayesian learning-based evolutionary algorithm is applied to yield a Pareto front, which is a tradeoff between absorption rate and voltage stability. Afterwards, A technique for order preference by similarity to an ideal solution (TOPSIS) is adopted to determine the dispatching solution by similarity to an ideal solution. Finally, numerical case studies are conducted on a modified IEEE-33 bus system to verify the effectiveness of the proposed scheme.

Robust 2DOF state-feedback PI-controller based on meta-heuristic optimization for automatic voltage regulation system

The Automatic Voltage Regulation (AVR) system which works within the synchronous generator[s] locally is defined as the closed loop control system that keeps the reactive power output at demanded value by adjusting exciter signal. Designing a proper control scheme for the AVR system to provide the desired level of voltage stability is an important research field. Nowadays, classic 1DOF PI-controller which takes into account only the load side disturbance is generally used in the AVR systems. In this study, to improve the robustness of this system towards the relatively severe disturbances caused from both load side and set point side, the 2DOF state feedback PI-controller which is tuned with a meta-heuristic optimization algorithm is proposed. Since only the error signal is minimized by using a simple cost function, this method can be applied simpler as independent to the system parameters, optimal coefficients are computed simpler. The superiority of the proposed controller is proved by applying stability, time-domain, frequency-domain and two different robustness analyses such as instantaneous and continuous disturbance analyses. It is observed from these analyses that the maximum overshoot and settling time obtained from the proposed control structure decrease more than a half. In addition, the immunity towards instantaneous and continuous disturbances significantly improve and the step responses in these cases stay in 2% band. At the end of the study, the implementation proposal related to the new control scheme is presented and interpreted in detail.

Secure and Reliable Distribution Feeder Reconfiguration in the Presence of Static VAR Compensator

This paper presents a multi-objective approach for solving distribution feeder reconfiguration (DFR) problem aiming at optimizing active power of distributed generations (DGs) and locating static VAR compensators (SVCs) in distribution network. To have a positive effect, DGs and SVCs must suitably integrate and coordinate with the distribution system feeder design. Besides the power loss reduction as a main purpose, expansion of distribution systems forces the system operators to obtain an acceptable reliability and the voltage stability level in distribution system. Furthermore, increasing DG penetration in distribution systems pushes system operators to take transient stability of DGs into account. Considering multiple objective functions beside different operational constraints of distribution systems makes the proposed DFR problem a complex optimization problem that needs to be solved by a proper solution methodology. In this connection, teacher learning-based algorithm, a well-known evolutionary algorithm, is employed to solve the proposed problem. The proposed optimization algorithm is coded in DPL environment of DIgSILENT® Power Factory with a detailed dynamic modeling of all electric devices. The effectiveness of the proposed approach is demonstrated using a typical 84-bus test system.

Improvement of Power System Loading Margin with Reducing Network Investment Cost Using SVC

Under emergency conditions to reduce the harms from environmental deterioration, one of the recently focused developments in the power industry is to make the existing transmission networks sufficiently utilize their capability in power transfer. From the detailed analysis and many studies, voltage instability was found to be the main factor responsible for several blackout events. As an index to indicate the level of static voltage stability of a transmission system, the Loading Margin (LM) or Voltage Stability Margin (VSM), represents the maximum power that can be transferred between generators and loads before voltage collapse point achieved is generally measured in system planning. In this paper, under each contingency with high Risk Index (RI) value, the Modal Analysis (MA) technique is used to determine which buses need Static VAR Compensator (SVC) installation, and with maximum LM and minimum SVC installation cost composed into the multi-objective function. The optimal LM enhancement problem is formulated as a multi-objective optimization problem (MOP) and solved by using the fitness sharing multi-objective particle swarm optimization (MOPSO) algorithm for a Pareto front set. The proposed method may be tested on the IEEE 24-bus reliability test system (RTS) and IEEE 14-bus system.

Voltage stability constrained line‐wise optimal power flow

The purpose of optimal power flow (OPF) is to optimise an objective function subject to a set of operating constraints. It remains an active research area because of using the bus-wise power balance equations, which leads to a non-linear solution space, resulting in OPF yielding local optimal solutions, thereby causing significant economic loss. In this study, first, a new line-wise OPF (LWOPF) formulation is proposed. Thereafter, a maximum loadability factor, as a voltage collapse indicator, is derived and combined with LWOPF constraints to form a voltage stability constrained LWOPF (VSCLWOPF) model. As the line-wise power balance equations are based upon the square of voltage magnitudes, it results in significant improvement in the solution space and lower-order terms in all computational steps. The LWOPF and VSCLWOPF formulations, are solved using non-linear optimisation technique, tested on several benchmark and real power systems. Results show that the proposed LWOPF is accurate, provides monotonic convergence, and scales well for large systems. It provides a better solution and is consistently faster, up to twice the speed of MATPOWER, due to reduced computational needs. Results of VSCLWOPF show that, for the same voltage stability level, the solution costs less than that obtained by classical bus-wise OPF.

Distribution Network Reconfiguration Using Binary Particle Swarm Optimization to Minimize Losses and Decrease Voltage Stability Index

Power losses and voltage drop are existing problems in radial distribution networks. This power losses and voltage drop affect the voltage stability level. Reconfiguring the network is a form of approach to improve the quality of electrical power. The network reconfiguration aims to minimize power losses and voltage drop as well as decreasing the Voltage Stability Index (VSI). In this research, network reconfiguration uses binary particle swarm optimization algorithm and Bus Injection to Branch Current-Branch Current to Bus Voltage (BIBC-BCBV) method to analyze the radial system power flow. This scheme was tested on the 33-bus IEEE radial distribution system 12.66 kV. The simulation results show that before reconfiguration, the active power loss is 202.7126 kW and the VSI is 0.20012. After reconfiguration, the active power loss and VSI decreased to 139.5697 kW and 0.14662, respectively. It has decreased the power loss for 31.3136% significantly while the VSI value is closer to zero.

Bus Allocation for Voltage Stabilization in Multi-Machine Power System Using GWO

Today, power systems are being operated under greatly stressed conditions due to rapidly growing demand for electrical energy, penetration of renewable energy sources, large seasonal load variations, and operation in competitive energy market conditions. The main part of this work involves achieving complete system observability and improving voltage stability level simultaneously by placing a minimal number of PMUs. Initially, weak buses (very sensitive to smaller reactive power variations) are identified by using Fast Voltage Stability Index (FVSI) calculation. In this work, the reliability of observing the weak buses is purposely maximized. Suppose any sudden voltage instability problem occurs on the weak bus. In that case,PMUs can immediately communicate to the operator and prevent the outage of the weak bus, even if one of the PMUs fails. PMUs can maintain the FVSI value of the critical lines, not exceeding their maximum limit, by initiating the remedial actions scheme, such as smart islanding, controlling the transformer tap settings, coordinating between automatic corrective devices, etc. In this system, the positioning of PMUs on poor buses should be favoured over other buses. Improved voltage reliability can be accomplished by effective and accurate control of critical lines and vulnerable buses. This is done by a small rise in the amount of PMUs relative to previous results.

Multi‐objective robust dynamic VAR planning in power transmission girds for improving short‐term voltage stability under uncertainties

Modern power transmission grids are facing more and more critical short-term voltage stability problems. This study proposes a novel robust dynamic VAR planning approach for improving the short-term voltage stability level under uncertainties including the peak load level, the maximum proportion of dynamic load, fault clearing time and deviation of the actual capacity of dynamic VAR compensators from rated capacity when contingencies occur. The robust dynamic VAR planning problem is formulated as a multi-objective optimisation model with objectives including the investment cost, the expectation and robustness of the short-term voltage stability level. The complexity of the planning model is firstly reduced by selecting severe contingencies and potential buses, leading to a simplified multi-objective optimisation model. Latin hypercube sampling is then used for the uncertainty quantification. The simplified multi-objective optimisation model is then solved by the combination of a multi-objective evolutionary algorithm called ${\rm \epsilon }$e-NSGAII and extreme learning machine-based surrogate modelling with adaptive training data sampling. This combination significantly reduces the unaffordable computing burden. Simulations are carried on the IEEE 39-bus system, illustrating that the authors proposed methodology is reliable with high computational efficiency, and offering decision-makers planning solutions with high mean performance and strong robustness with respect to the short-term voltage stability level.

Surrogate Modeling-Based Multi-Objective Dynamic VAR Planning Considering Short-Term Voltage Stability and Transient Stability

Transient stability and short-term voltage stability have successively attracted the attention of electric power industry. This paper proposes a novel systematic approach for dynamic VAR planning to improve short-term voltage stability level and transient stability level. The dynamic VAR planning problem is formulated as a multi-objective optimization (MOO) model with objectives including investment cost, short-term voltage stability level, and transient stability level. To reduce the complexity of the proposed MOO model, K-means clustering-based severe contingencies selection and global sensitivity analysis-based potential buses selection are employed, leading to a simplified MOO model. The combination of a surrogate modeling technique called support vector regression and the multi-objective evolutionary algorithm (MOEA) are then used to solve the simplified MOO model, considering both the accuracy of models and the optimization computation cost. This combination makes it feasible to perform multiple runs of MOEAs for weakening the effect of the MOEA's randomness to optimal results and offering more diverse Pareto-optimal solutions for decision makers. Simulations are carried on the IEEE 39-bus system and a real power grid of China, illustrating that our methodology is reliable with high efficiency.

Optimal location strategy for distributed generation to maximize system voltage stability based on line sensitivity factors

This paper presents a combination strategy to determine the optimal location of PV distributed generation units (PV-DGs) in terms of maximizing the power system voltage stability level. The voltage collapse power indices (VCPIs) is chosen to access the voltage stability level of a system. To eliminate the need of iterations, a new line power flow calculation method based on the line sensitivity factors (LSFs) is developed. It could precisely compute out VCPI without executing AC power flow program. Combined with the economic optimization software HOMER to determine the sizes and quantities of PV-DGs, the optimal buses to connect PV-DGs are selected by minimizing the sum of VCPIs. The proposed location strategy is validated by multiple IEEE test systems. The numerical simulation results demonstrate that the proposed method is accurate on VCPI calculations and has the decreased computation time compared with the Newton-Raphson power flow method. Through the continuous power flow results, it is verified that the optimal DG configuration selected by the proposed strategy could maximize the overall voltage stability margin of the system.