Voltage Stability Constraints Research Articles

Multi-Period Optimal Transmission Switching with Voltage Stability and Security Constraints by the Minimum Number of Actions

Due to the ever-growing load demand and the deregulation of the electricity market, power systems often run near the stability boundaries, which deteriorates system voltage stability and raises voltage issues for the stable operations of power systems. Transmission switching (TS) has been applied to improve economic benefits and security operations for many applications. In this paper, a multi-period voltage stability-constrained problem (MP-VSTS) is established, intending to improve voltage security and the stability of a power system. Considering the online application of transmission switching, the minimum number of switching actions is taken as the objective function of the proposed MP-VSTS problem, which extends the TS application for real industries. The proposed model provides the switching lines for the upcoming period and the state of power systems for several successive periods. To overcome the solving difficulties of the proposed model, a two-stage approach is presented, which balances speed and accuracy. Numerical studies on the IEEE 118- and 662-bus power systems have demonstrated the proposed approach’s performance.

Security-constrained unit commitment model considering frequency and voltage stabilities with multiresource participation

The rapidly increasing proportion of renewable energy sources has led to a reduction in the relative share of synchronous units, which has resulted in a decline in the inertia of the power system and a decrease in its voltage support capacity. This has led to several issues related to the frequency and voltage stabilities of the power system. To ensure these frequency and voltage stabilities, it is necessary to maintain a number of synchronous units online in the day-ahead generation schedule. First, the dynamic frequency change process after a power system fault is discussed, and a linear expression is derived for the frequency stability constraints involving energy storage systems and wind turbines. Second, the short-circuit capacity of the bus is characterized to describe the strength of voltage support, and the minimum short-circuit capacity requirement of the bus is solved based on the transient voltage recovery problem after clearance of the short-circuit faults. The total short-circuit capacity provided by the unit to the bus is then calculated through the network reactance matrix to establish the voltage stability constraint. Subsequently, the security-constrained unit commitment model considering frequency and voltage stabilities (FVS-SCUC) is established. Finally, the effectiveness of the proposed model is demonstrated through a numerical simulation of the IEEE-39 system comprising storage and wind turbines. The model ensures the frequency and voltage securities of the system, and the renewable energy output is improved upon considering energy storage. Thus, the overall system cost was reduced by nearly 30% by considering the frequency regulation effects of the energy storage system and wind turbine as well as the voltage regulation effects of the energy storage system.

Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method

Optimal planning and design of microgrids are priorities in the electrification of off-grid areas. Indeed, in one of the Sustainable Development Goals (SDG 7), the UN recommends universal access to electricity for all at the lowest cost. Several optimization methods with different strategies have been proposed in the literature as ways to achieve this goal. This paper proposes a microgrid installation and planning model based on a combination of several techniques. The programming language Python 3.10 was used in conjunction with machine learning techniques such as unsupervised learning based on K-means clustering and deterministic optimization methods based on mixed linear programming. These methods were complemented by the open-source spatial method for optimal electrification planning: onsset. Four levels of study were carried out. The first level consisted of simulating the model obtained with a cluster, which is considered based on the elbow and k-means clustering method as a case study. The second level involved sizing the microgrid with a capacity of 40 kW and optimizing all the resources available on site. The example of the different resources in the Togo case was considered. At the third level, the work consisted of proposing an optimal connection model for the microgrid based on voltage stability constraints and considering, above all, the capacity limit of the source substation. Finally, the fourth level involved a planning study of electrification strategies based mainly on microgrids according to the study scenario. The results of the first level of study enabled us to obtain an optimal location for the centroid of the cluster under consideration, according to the different load positions of this cluster. Then, the results of the second level of study were used to highlight the optimal resources obtained and proposed by the optimization model formulated based on the various technology costs, such as investment, maintenance, and operating costs, which were based on the technical limits of the various technologies. In these results, solar systems account for 80% of the maximum load considered, compared to 7.5% for wind systems and 12.5% for battery systems. Next, an optimal microgrid connection model was proposed based on the constraints of a voltage stability limit estimated to be 10% of the maximum voltage drop. The results obtained for the third level of study enabled us to present selective results for load nodes in relation to the source station node. Finally, the last results made it possible to plan electrification using different network technologies and systems in the short and long term. The case study of Togo was taken into account. The various results obtained from the different techniques provide the necessary leads for a feasibility study for optimal electrification of off-grid areas using microgrid systems.

Impedance analysis of voltage prediction compensation scheme for DC-link oscillation suppression in cascade drive system

The dc-link voltage oscillation caused by the negative impedance characteristic of the constant power load is a significant issue in the series LC branch-permanent magnet synchronous motor (PMSM) cascade system. To this end, this paper proposes a voltage prediction compensation (VPC) strategy to suppress the dc-link voltage oscillation by adding a voltage stability constraint term to the finite control set model predictive current control (FCS-MPCC). First, the linearized q-axis reference voltage is obtained by taking the derivation of the cost function of the VPC, thereby deriving the input impedance of the inverter-permanent magnet motor system. Then, the impedance matching criterion and Nyquist stability criterion are used to theoretically prove that the proposed strategy can effectively improve system stability, and the robustness of the proposed method to changes in motor parameters is analyzed. Finally, experimental verification was conducted on a 1 kW motor platform. The results show that when the motor is running under rated working conditions, after adding the stability constraint, the dc-link voltage fluctuation drops from 40 V to 7 V; the q-axis current pulsation rate also drops to 3.8 %. Theoretical analysis and experimental results show that the VPC strategy can effectively suppress the dc-link voltage oscillation of the cascade drive system.

Nodal price-based demand response management via orderly time-of-use strategy for an unbalanced isolated microgrid considering voltage stability constraints

This paper scrutinizes the compatibility of voltage stability criteria with price-based demand response management (DRM) for a large-scale isolated microgrid considering severe dependency of constant-impedance loads (CILs) on nodal voltage magnitude. Meanwhile, a hybrid nodal pricing (HNP) scheme is developed to determine clearing prices for resources and time-of-use (TOU) tariffs for price-responsive loads. The proposed framework is composed of three ingredients including two optimization molds with the objective of actual net profit and recast operation expense sequentially solved in an iterative process together with one pay-off module. The energy schedules, unbalanced voltages and nodal prices are determined considering intermittency of renewable resources, unbalances, circuit limitations, and reactive power requirements. Two bus and line voltage stability indices as well as voltage profile management criterion are used to prevent voltage instability. Thus, load profile is corrected such that voltage stability can be upheld as well. The proposed method is implemented via a modified CIGRE benchmark. The simulation results demonstrate that load factor improves at least 4.30% under desirable stability margins. Moreover, total energy loss and line voltage unbalance rate (LVUR) decrease at least 1.02% and 10.03% respectively.

Influence of Load Models and DG Operational Power Factor on Optimization of Shunt Capacitor Placement in Distribution Grids Considering Voltage Stability

The paper proposes a mathematical model of mixed-integer nonlinear programming (MINLP) to optimize the location and size of shunt capacitors in power distribution grids with distributed generation (DG), considering voltage stability constraints. At the same time, the paper also analyzes the influence of the load models, such as voltage-dependence load (ZIP load) and constant power load, together with DG’s operating power factor on the optimal solution. The objective function of the proposed optimization formulation is minimizing the total expenses, including the capital investment of capacitors and the expense incurred by network energy loss. This MINLP model includes constraints in the current and critical loading conditions, such as the system of power flow equations, nodal voltage limits, branch thermal limits, capacitor-related constraints, and restrictions of minimum security level. The proposed optimization model was evaluated on a modified IEEE 33-node distribution grid using the KNITRO commercial solver with the GAMS programming language. The calculation results show that the voltage stability constraints, load models, and operational power factor of the DG units have an essential influence on the optimal position and capacity of the shunt capacitors.

Voltage Stability Constrained Economic Dispatch for Multi-Infeed HVDC Power Systems

Multi-infeed LCC-HVDC decreases voltage stability margins due to its current source nature. Moreover, the high penetration of variable renewable energy makes it difficult to reserve enough margins for all periods. Therefore, voltage stability constraints need to be considered in the scheduling stage. However, the challenge is that the voltage stability margin is not analytic with respect to state variables. We propose a sparse support vector machine to extract the nonlinear voltage stability rule. To embed the rule into economic dispatch (ED), we apply a convex reformulating technique to the rule and then formulate a voltage stability constrained ED (VSCED) model by semi-definite programming. The model is tested on a modified IEEE-14 system and a real-world system from Jiangsu Province, China; and it is compared with other typical data-driven-based models in the Jiangsu system. The numerical experiments suggest that the stability margins can be effectively reserved above the required threshold within an acceptable computation time by the proposed VSCED model, which outperforms the other models.

Learning Multiple Convex Voltage Stability Constraints for Unit Commitment

Learning Multiple Convex Voltage Stability Constraints for Unit Commitment

Emergency Control Strategy for Electrolytic Aluminum Load Considering the Load's Transient Overcurrent Characteristics and Transient Voltage Stability Constraints

Emergency Control Strategy for Electrolytic Aluminum Load Considering the Load's Transient Overcurrent Characteristics and Transient Voltage Stability Constraints

Coordinated Optimization for Multi-Infeed LCC-HVDCs Transient Control Considering Short-Term Voltage Stability of Receiving-End Grid

With local synchronous generators in receiving-end grids being replaced by multi-infeed line-commutated converter-based (LCC) high-voltage direct currents (HVDCs), the dynamic voltage supportability of the power grid decreases. Moreover, the reactive power consumption of LCC-HVDCs during the recovery process brings risks to voltage stability. Hence, the transient control of LCC-HVDCs should be optimized coordinately to support short-term voltage stability under credible contingencies. In this paper, the dynamic reactive power characteristics between AC/DC systems are derived mathematically. Based on the coupling mechanism among the voltage-dependent current order limiter (VDCOL), AC dynamic voltage, and HVDC power recovery, an “autonomous-synergic” optimization strategy incorporating short-term voltage stability constraints is proposed for multi-infeed LCC-HVDCs. To handle the problem of large-scale differential-algebraic equations (DAEs), the optimization is iteratively solved based on time-domain simulation (TDS) and trajectory sensitivities. The stability is quantified by an indicator and the trajectory sensitivity analysis is utilized to relax stability constraints. The effectiveness and feasibility of the proposed methods are verified with a benchmark system and a real system in China. The short-term voltage stability under all credible contingencies can be guaranteed, while the total power recovery of LCC-HVDCs is improved.

Asymmetrically Reciprocal Effects and Congestion Management in TSO-DSO Coordination Through Feasibility Regularizer

TSO-DSO coordination together with flexibility service pave the way for the grids to make the most of distributed energy resources while maintaining system secure operations. In T-D coordination, stemming from the diversity of distribution systems including sizes and renewable levels, vulnerable distribution systems may be placed in unfavorable working conditions under the same coordination with TSO. Also, the variance of coupling points affects transmission and distribution systems differently. This work proposes to formalize such heterogeneous effects, called “asymmetric reciprocal effects” (AREs), for the first time. AREs can be characterized through flexibility services and incorporated in T-D coordination to limit improper couplings that push the weaker DSO to its feasibility boundaries associated with long-term voltage stability and operational constraints including voltage and thermal thresholds. An advanced flexibility region construction technique is developed by leveraging the latest feasibility certificate using Kantorovich fixed-point theorem. AREs are then quantified using feasibility regularizers measuring the variations of feasibility regions of TSO and DSO due to coupling point fluctuation. A scalable approach based on statistics is also developed for AREs metrics. Simulation results of one-shot and 24 h optimal dispatch on single-TSO-multi-DSO model are presented to illustrate the concept and how AREs contribute to TSO-DSO coordination.

Voltage Stability Constrained Unit Commitment in Power Systems With High Penetration of Inverter-Based Generators

With the increasing penetration of renewable energy sources, power system operation has to be adapted to ensure the system stability and security while considering the distinguished feature of the Inverter-Based Generator (IBG) interfaced generators. The static voltage stability which is mainly compromised by heavy loading conditions in conventional power systems, faces new challenges due to the large scale integration of IBG units. This paper investigates the static voltage stability problem in high IBG-penetrated system. The analytic criterion that ensures the voltage stability at the IBG buses are derived with the interaction of different IBGs being considered. Based on this, an optimal system scheduling model is proposed to minimize the overall system operation cost while maintaining the voltage stability during normal operation through dynamically optimizing the active and reactive power output from IBGs. The highly nonlinear voltage stability constraints are effectively converted into Second-Order Cone (SOC) form, leading to an overall Mixed-Integer SOC Programming (MISOCP), together with the SOC reformulation of AC power flow and frequency constraints. The effectiveness of the proposed model and the impact of various factors on voltage stability are demonstrated in thorough case studies.

Operating Wind Power Plants Under Weak Grid Conditions Considering Voltage Stability Constraints

This article analyzes the power transfer limit ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_max</i> ) of wind power plants (WPPs) under the weak grid condition. It is pointed out that the impact of different grid parameters and grid configurations on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_max</i> cannot be fully reflected by the short-circuit ratio (SCR), but can be readily captured by voltage sensitivity (∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> /∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> ). Hence, ∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> /∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> turns out to be a more appropriate metric for the assessment of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_max</i> compared with the SCR. Based on this insight, the voltage control of the WPP is suggested to be implemented at the bus with the highest ∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> /∂ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> to maximize the power transfer capability. Moreover, a dynamic voltage control is further added at the turbine level to improve the disturbance rejection capability of the WPP as well as its dynamic robustness against grid strength variations. Finally, simulation and field test results are given to demonstrate the theoretical analysis and the effectiveness of the proposed control method.

DC-Link Voltage Constraint Strategy for DC Power Supply Film-Capacitor Drive System Based on Improved Model Predictive Control

DC-link voltage oscillation is a common problem that needs special attention in dc power supply film-capacitor drive systems. For this problem, an improved model predictive control method is presented in this article, which achieves system stability control by adding voltage stability constraint of dc-link in the cost function. First, the discrete predictive equations of motor current and LC filter voltage for permanent magnet synchronous motor are derived in this article. The system stability is proved by analyzing the system damping with voltage constraint in the meantime. The weight factor of the cost function based on exponential function is designed to accelerate the suppression of dc-link voltage oscillation in the dynamic process. Second, a full-order observer is designed for observing the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter inductor current, which is designed to reduce hardware costs. Third, an improved control set method is proposed to improve the steady-state performance of each control item in the cost function. Finally, a hardware platform based on DSP is built to verify the validity of the stability constraint scheme proposed in this article.

Data‐model driven rescheduling considering both rotor angle stability and transient voltage stability constraints

Facing the problem of workforce and time costs caused by the rescheduling of large-scale power grids with renewable energy penetration, and the lack of parallel control research on rotor angle instability and transient voltage instability, a rescheduling method based on trajectory sensitivity and deep reinforcement learning (DRL) is proposed to meet the requirements of rotor angle stability and transient voltage stability at the same time. By introducing the process of rescheduling to meet the transient stability constraint, the Markov decision-making process of rescheduling is first constructed. Then, a simple dominant instability type identification method is proposed according to the occurrence time, location, voltage pattern, and position of the oscillation centre. Moreover, a rescheduling strategy is formulated based on the dominant instability mode identification, trajectory sensitivity calculation, actionable device selection, action amount computation, and action of the device. Next, according to the improved distributed distributive deep deterministic policy gradients (D4PG), a DRL model is established to map the action to actionable generator pairs and capacitors/reactors, so as to realize parallel rescheduling of rotor angle instability and transient voltage instability. Finally, the improved New England 39-bus system and an actual power grid are used to verify the effectiveness and advantages of the method.

A Method for Evaluating the Maximum Capacity of Grid-Connected Wind Farms Considering Multiple Stability Constraints

Boosting the capacity of grid-connected wind farms will greatly contribute to increasing the share of sustainable energy in the global generation mix. It is imperative to study the way to quantitatively assess the maximum capacity of grid-connected wind farms in combination with power system stability characteristics. In this work, a method to evaluate the maximum capacity of grid-connected wind farms considering the joint constraints of frequency and voltage stability is proposed based on the global intrinsic property of frequency stability and the local characteristic of voltage stability. Firstly, the maximum capacity of grid-connected wind farms in the power grid with high wind power penetration is assessed globally based on the frequency stability constraints, and then locally considering the voltage stability constraints of each local power grid. Further on, a quantitative method to evaluate the capacity of grid-connected wind farms is proposed based on the correlation between the local static voltage stability margin and the local capacity of grid-connected wind farms, as well as the global constraint of the maximum capacity of grid-connected wind farms. Finally, the effectiveness of the proposed method is verified by the simulation results of an actual regional power grid.

Multi-Time-Scale Optimal Scheduling in Active Distribution Network with Voltage Stability Constraints

The uncertainty associated with loads and renewable-energy sources affects active distribution networks in terms of the operation and voltage stability on different time scales. To address this problem, a multi-time-scale voltage stability constrained optimal scheduling framework is proposed, which includes a day-ahead model with a coarse-grained time resolution and an intra-day model with a fine-grained time resolution. The day-ahead economic-scheduling model maps out a scheme to operate different types of devices with the aim of minimizing the network losses. Following the scheme, the intra-day corrective-adjustment model based on model predictive control is proposed to regulate the flexible devices, such as the energy storage systems and the photovoltaic converters. In particular, the proposed optimal scheduling framework embeds a voltage stability constraint which is constructed by using a novel index, defined based on the Distflow model Jacobian. As the index at each bus is a linear function of the locally measurable power flow variables, the proposed constraint does not introduce additional computational burdens. Simulation results demonstrate the necessity and effectiveness of the proposed multi-time-scale voltage stability constrained optimal scheduling model. The results also show that the variation trend of the proposed index is consistent with that of the commonly used voltage stability index.

The Impact of Voltage Stability Constraint L-Index on Power System Optimization Base on Interior Point Algorithm by Considering the Integration of Renewable Energy

Renewable energy (RE) generation including wind and solar farms has experienced significant growth due to the challenge of climate and energy crisis. High penetration of RE affects system stability and generation cost optimization. In this paper, voltage stability L-index is proposed as the constraint of the primal-dual interior point method for optimal power flow by considering the integration of wind and photovoltaic cell power on system. L-index is used in this study to indicate the voltage security while renewable energy is prefixed into power system to build a new (REL-OPF) formulation that can consider the voltage stability margin and generation cost of the power grid. Weibull and Beta probability density functions are applied to determine the outputs of wind and photovoltaic power generation respectively. This model has the advantage that there is no need to calculate the critical point and could obtain the demanded voltage security level by adjusting the upper limits of indicator L constraints. The optimal solution can concurrently satisfy both the voltage security and the economical demand for power systems. The overall problem is simulated under coding written in MATLAB environment. The results obtained from regulating the upper limit of voltage stability constraint on IEEE30-bus has shown that the attention of RE generations into the system leads the fuel cost objective to decrease randomly as well as enlarge the distance of stability to a critical point with faster convergence.

Short-Term Voltage Stability-Constrained Unit Commitment for Receiving-End Grid With Multi-Infeed HVDCs

With the increasing development of AC/DC hybrid power systems, local synchronous generators in receiving-end grids are being replaced by high-voltage direct current (HVDC) power. The risk of short-term voltage instability exists because of the decline in dynamic reactive power resources from generators, the presence of high-proportioned induction motors and the demand for vast reactive power of HVDC under AC faults. In this situation, unit commitment (UC) should take short-term voltage stability into account. Hence, crucial generators can be retained to provide sufficient dynamic reactive power. This paper proposes a UC model incorporating short-term voltage stability constraints (SVSCUC). Furthermore, a decomposition-based solution approach is presented, which involves an alternate iterative solving of UC and differential-algebraic equations (DAEs). Time-domain simulation (TDS) is utilized to quantify the stability with an indicator. Linear stable cuts are formulated through trajectory sensitivity analysis and added into the UC. The UC is decomposed into a master problem based on mixed-integer linear programming (MILP) and subproblems. The SVSCUC is illustrated using benchmark systems and a real system in eastern China. The results show the effectiveness and efficiency of the proposed methods. Violations of short-term voltage stability for credible contingencies are eliminated under the commitment of SVSCUC.

Security-Constrained generation and transmission expansion planning based on optimal bidding in the energy and reserve markets

The increasing growth of power system demand causes different challenges for the network operation and security situation. Therefore, this paper presents security-constrained generation and transmission expansion planning (SCGTEP) according to a strategic bidding model in the energy and reserve markets. This method includes a bi-level optimization problem, where its upper level refers to the transmission company (TransCo) and generation company (GenCo) economic model. This level minimizes the difference between TransCos and GenCos costs and revenues in the energy and reserve markets subjected to allowed investment budget for transmission lines and generation units. Moreover, the lower level problem considers the energy and reserve market-clearing model based on AC security-constrained optimal power flow. In other words, this problem minimizes the summation of network operation and security costs limited to the linearized AC optimal power flow equations, reserve formulation of generation units, load shedding model due to N – 1 contingency, and linearized voltage stability constraints. In the next step, the single-level SCGTEP is achieved using the Karush-Kuhn-Tucker, and it is solved by the Benders decomposition approach to obtain an optimal solution at a low calculation time. This strategy includes the uncertainties of load, renewable generation power, and the availability of the network equipment, hence, scenario-based stochastic programming is used in this paper to model uncertain parameters. The proposed SCGTEP is tested on the 6-bus and 118-bus IEEE networks in the GAMS software. According to the obtained numerical results, the proposed strategy can be simultaneously improved operation and security indices about 34.5% and 100%, respectively, compared to the power flow analysis based on the optimal location of generation units and transmission lines. Also, GenCos and TransCos can clear their investment cost after 5 years with participation in the electricity market.