Transient Stability Constraints Research Articles

Operational electricity cost reduction using real-time simulators

Ensuring the safe and cost-effective electricity transmission to consumers, along with the efficient and sustainable operation of power systems, has long been a primary objective for power system managers and operators. However, achieving optimal performance in a modern power system requires timely planning and operational optimal routines to be run within the realm of real-time simulation programs, and sometimes, the divergence becomes a problem with these developed routines. Despite extensive research aimed at advancing these objectives, the growing complexity of networks and their constraints has often led to the oversight of simultaneously considering both technical and economic aspects during operation. In this paper, an innovative real-time framework is introduced to reduce the operational costs of a power system swiftly. This framework addresses various nonlinear constraints, such as transmission losses, generation-consumption balance, power device limitations, and transient stability constraints, across various operational scenarios within a real-time simulator. This novel approach leverages scattered search and intentional contingencies within the network to pinpoint the optimal operating point, taking into account various network dynamics, including Automatic Voltage Regulators (AVR), governors, and tap of the transformers. The proposed method offers a fast and robust approach to identifying the most effective operating conditions for a power system. It incorporates considerations for sudden contingencies and extends capabilities through parallel simulations. It not only facilitates pre-determined preventive actions but also enables the adjustment of control parameters during post-contingency periods, such as fine-tuning of the active and reactive power generation of generators and adjusting the tap settings of transformers within power networks. Since the network simulation can be executed on distributed computers, referred to as ’Global,’ it is possible to achieve global network optimization. This approach allows for the consideration of grid networks, including renewable energy sources with models distributed through PCs. Also, it accounts for the induction motor losses within all factories involved in the global simulation. The results obtained from simulating the proposed method on a commercial real-time simulator demonstrate the superior effectiveness of the proposed framework compared to the existing methodologies, highlighting its potential to enhance the operational efficiency and economic viability of power systems.

Power System Transient Stability Preventive Control via Aptenodytes Forsteri Optimization with an Improved Transient Stability Assessment Model

Transient stability preventive control (TSPC), a method to efficiently withstand the severe contingencies in a power system, is mathematically a transient stability constrained optimal power flow (TSC-OPF) issue, attempting to maintain the economical and secure dispatch of a power system via generation rescheduling. The traditional TSC-OPF issue incorporated with differential-algebraic equations (DAE) is time consumption and difficult to solve. Therefore, this paper proposes a new TSPC method driven by a naturally inspired optimization algorithm integrated with transient stability assessment. To avoid solving complex DAE, the stacking ensemble multilayer perceptron (SEMLP) is used in this research as a transient stability assessment (TSA) model and integrated into the optimization algorithm to replace transient stability constraints. Therefore, less time is spent on challenging calculations. Simultaneously, sensitivity analysis (SA) based on this TSA model determines the adjustment direction of the controllable generators set. The results of this SA can be utilized as prior knowledge for subsequent optimization algorithms, thus further reducing the time consumption process. In addition, a naturally inspired algorithm, Aptenodytes Forsteri Optimization (AFO), is introduced to find the best operating point with a near-optimal operational cost while ensuring power system stability. The accuracy and effectiveness of the method are verified on the IEEE 39-bus system and the IEEE 300-bus system. After the implementation of the proposed TSPC method, both systems can ensure transient stability under a given contingency. The test experiment using AFO driven by SEMLP and SA on the IEEE 39-bus system is completed in about 35 s, which is one-tenth of the time required by the time domain simulation method.

A Double‐Layer Optimization Method for Cascading Failure Prevention Considering Transient Stability

In recent years, in order to reduce the damage from the blackout accident, the demand of the power system for its basic resistance ability has gradually increased. Therefore, this paper proposes a double‐layer optimization method for the prevention of cascading failure of the power system that takes into account the transient stability constraint for cascading trips that directly lead to the accident. In terms of models, the paper reconstructs an outer model for optimizing the safety margin based on the inner model that solves the safety margin of cascading failure prevention. In terms of algorithms, the paper uses the Extended Particle Swarm Optimization (EPSO) algorithm with higher precision and accuracy to solve the inner model and innovatively introduced the Practical Dynamic Security Region (PDSR), which uses PSASP software for offline calculation and online application, as a dynamic analysis method to quickly realize transient stability constraint to solve the outer model. Three evaluation indexes of the preventive optimization effect can be obtained by this method; dispatchers can plan more flexible and reliable optimal dispatching schemes through these indexes, to comprehensively improve the safety margin of cascading failure prevention in the current operating state and enhance the risk resistance ability of the power grid. This paper has used MATLAB and PSASP to perform simulation analysis using the IEEE39 node system as a test example to verify the effectiveness and superiority of the proposed model and algorithm.

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

Transient Stability-Constrained Unit Commitment Using Input Convex Neural Network.

This article proposes a transient stability-constrained unit commitment (TSC-UC) model using input convex neural networks (ICNNs). An ICNN is trained to learn the transient function that maps prefault operation conditions (e.g., generator power output) to the transient stability index (TSI), which can be further utilized to identify the transient status (e.g., stable or unstable). Transient stability evaluation is conducted using the learned ICNN, without discretizing differential-algebraic equations (DAEs) or interacting with the time-domain simulation tools. Based on the convexity of ICNNs, the trained ICNN is exactly encoded as a linear programming (LP) model and integrated into conventional UC models to form a TSC-UC model. To impose transient stability constraints and expedite the solution process, the proposed TSC-UC model is decomposed into a UC master problem and two subproblems (i.e., network feasibility check subproblems and transient stability check subproblems). The decomposed problem is then iteratively solved using the Benders decomposition. Simulation tests are conducted in the New England 39-bus test system and IEEE 118-bus test system to verify the validity of the proposed approach.

Analytic Deep Learning and Stepwise Integrated Gradients-Based Power System Transient Stability Preventive Control

Trajectory sensitivity (TS) is a powerful alternative to linearize strong-nonlinear transient stability patterns. However, due to its incomplete view of an intact power system operational space, it can be readily to drive preventive control to stuck in local stationary solution. To mitigate this issue, an integrated gradient (IG)-based stepwise control method is proposed. The key idea is to develop IG to enable a control sensitivity taking both merits of local and global sensitivity, further help preventive control escape from local stationary points. Particularly, deep belief network (DBN) is firstly utilized to parameterize pattern between transient stability index (TSI) and steady-state dispatches. It is then leveraged to infer IG to linearize transient stability constraints in real-time. Interior point method is employed to solve the linearized model. A stepwise control strategy is finally proposed to adaptively tune the integrated interval of the applied IG, such that the preventive control path can be ensured to follow the trend of improving transient stability. Case studies on two benchmarks show that the proposed method outperforms traditional TS method in terms of efficiency and economy, and provides a promising way to enhance engineering sensitivity methods.

Analytical Dual-Sequence Current Injections Feasible Region of Weak-Grid Connected VSC Under Asymmetric Grid Faults

For phase-locked-loop synchronization (PLL-Syn) based Weak-Grid connected Voltage Source Converter (WG-VSC) system under asymmetric grid faults, published works mainly focus on existing of equilibrium point and small signal stability, which cannot address PLL-Syn transient stability problems. For the first time, we have proposed an analytical solution to the question of “ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Whether the WG-VSC system can reach to a new available equilibrium point (EP) of fault-on state from original EP of pre-fault state without loss of PLL-Syn transient stability under asymmetric faults?</i> ”. Dual-sequence current injections feasible region (CIFR) of WG-VSCs in positive and negative sequence current injection space is defined firstly. Then, by considering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PLL-Syn transient stability constraint, Maximum available current constraint, and PCC Voltage constraint</i> , an analytical expression of CIFR has been obtained. Finally, experiments results based on detailed switching model in RT-BOX hardware-in-loop platform have been provided to verify the CIFR constructed in this paper. It should be noted that the work of this paper can not only address PLL-Syn transient stability problems of WG-VSC system under asymmetric faults, but also can pave the way for asymmetric fault ride-through control considering transient stability constraints.

Simulation and calculation of maximum transmission power for offshore wind plants accounting for the Electro-Magnetic transient process

The offshore wind power industry is witnessing a shift towards larger scale and longer offshore distances, pushing the transmission capacity and transmission distance of submarine cables to their maximum limits. Consequently, it is essential to evaluate the maximum transmission limit of offshore wind power. At the same time, the larger scale of the wind farm will make the Electro-Magnetic transient (EMT) processes have a greater impact on the system stability. To address these issues, this paper firstly established a wind generator (WG) model through a permanent magnet synchronous generator (PMSG) model with averaging parameters, as well as a cross-linked polyethylene (XLPE) submarine cable model to construct an offshore wind power system via AC transmission. Subsequently, a continuous EMT simulation method is proposed to calculate the maximum transmission capacity and transmission distance limit. Real-time transient simulations were conducted to check the transient stability constraints during the calculation process. Finally, through several case studies on different types of cables, the simulation and calculation results are presented to provide useful references for engineering applications.

Safe and Stable Secondary Voltage Control of Microgrids Based on Explicit Neural Networks

This paper proposes a novel safety-critical secondary voltage control method based on explicit neural networks (NNs) for islanded microgrids (MGs) that can guarantee any state inside the desired safety bound even during the transient. Firstly, an integrator is introduced in the feedback loop to fully eliminate the steady-state error caused by primary control. Then, considering the impact of secondary control on the stability of the whole system, a set of transient stability and safety constraints is developed. In order to achieve online implementation that requires fast computation, an explicit NN-based secondary voltage controller is designed to cast the time-consuming constrained optimization in the offline NN training phase, by leveraging the local Lipschitzness of activation functions. Specially, instead of using the NN as a black box, the explicit representation of NN is substituted into the closed-loop MG for transferring the stability and safety constraints. Finally, the NN is trained by safe imitation learning, where an optimization problem is formulated by maximizing the imitation accuracy and volume of the stable region while satisfying the stability and safety constraints. Thus, the safe and stable region is approximated that any trajectory initiates within will converge to the equilibrium while bounded by safety conditions. The effectiveness of the proposed method is verified on a prototype MG with detailed dynamics.

Security-constrained Transmission Expansion Planning with N-k Security Criterion and Transient Stability

The integration of large-scale wind power into the power system is a global trend in response to climate change, however, the intermittent nature of wind power presents new challenges for planners. Conventional transmission expansion planning (TEP) methods, which only consider N-1 static security, may not ensure the security of multiple contingencies and transient stability in a large-scale wind power integration scenario. Incorporating N-k-based static constraints and dynamic constraints, such as differential-algebraic-equations-(DAEs)-based transient stability constraints, into TEP can result in a heavy computational burden and render the TEP model intractable. This paper proposes a tractable mathematical model (S&DSTEP) for joint consideration of static and dynamic security in TEP with wind power. The uncertain wind power generation is captured through selected scenarios and the model is divided into a TEP master problem and multiple sub-problems for evaluating static security and transient stability. Static security is determined by the use of fault chain theory (FCT), avoiding the need for enumerating all N-k contingencies, thus reducing the computational burden. Transient stability is analyzed through the use of stabilizing cuts generated from the extended equal-area criteria (EEAC) rather than dynamic constraints expressed as DAEs. The proposed model is verified on the modified New England 39-bus system and IEEE 118-bus system, demonstrating its ability to consider transient stability while being more computationally efficient compared to the robust method that directly incorporates all contingency scenarios.

A novel non-iterative based framework for quick dynamic assessment of wind energy dominated multi-machine power system

Renewable Energy Sources have considerably expanded in recent years to address the widening energy deficit in modern power systems. Integrating these sources raises significant concerns for power system management, with transient stability constraints of networks being one of the growing issues for engineers and researchers. In this paper, the impact of Doubly Fed Induction Generators integration is analyzed to examine the transient stability on two test models. A Coupling Strength Index formulated from Network Structural Characteristics Theory is explored to detect the weakest transmission line. This method identifies line 7 to 8 and 5 to 6 as the weakest line with coupling strength index of 0.02739 and 0.105158 for IEEE 9 and 39 bus system, respectively. The system’s transient stability is then investigated with and without the Doubly Fed Induction Generators, considering a three-phase short-circuit fault applied at the middle of the identified line. Several characteristics associated with the system such as generator speed, rotor angle, and electric power were investigated. The simulation was carried out using DIgSILENT Power Factory and the results indicate that the systems are negatively impacted by the integration of Doubly Fed Induction Generators.

A Two-Stage Optimal Preventive Control Model Incorporating Transient Stability Constraints in the Presence of Multi-Resource Uncertainties

The volatility and uncertainty introduced by increasingly integrated renewable energy pose challenges to the reliable and stable operation of the power system. To mitigate the operation risks, a two-stage optimal preventive control model that incorporates transient stability constraints and considers uncertainties from multiple resources is proposed. First, the uncertainties of different re-sources are modeled, with which the non-sequential Monte Carlo sampling method is used to correspondingly generate the scenarios. Thereafter, a two-stage control model that balances operational safety and economy and realizes preventive control and emergency control is built. The operation schedule from the preventive control stage aims to minimize the transient stability probability and operation costs. If any faults destabilize the system, the emergency control stage will be activated immediately to help the system recover stability with minimal control costs. To expedite the solving of the two-stage model, a multi-objective particle swarm algorithm based on entropy-TOPSIS is proposed. Finally, the effectiveness of the proposed model and solving algorithm are validated with the modified IEEE118 node system.

Power system transient stability preventive control optimization method driven by Stacking Ensemble Learning

The dynamic characteristics of the power system are becoming more and more complex, and the difficulty of operation control is increasing. Preventive control is the main means of power system transient stability control. This paper proposes a stacking ensemble learning-driven power system transient stability preventive control optimization method. Firstly, a transient stability assessment model based on Stacking Ensemble Deep Belief Nets (SEDBN) network is established in this research. The performance of weak classifiers is improved by SEDBN’s multi-layer ensemble structure, and the created transient stability estimator can extract diverse features and has better robustness and generalization abilities. Secondly, the trained transient stability estimator is integrated into the Aptenodytes Forsteri Optimization (AFO) algorithm as a “transient stability constraint discriminator”. Finally, with the goal of minimizing the cost of preventive control, an optimization algorithm for the preventive control of power system transient stability driven by SEDBN is established. Simulation results on IEEE 39-bus systems show that the proposed method can achieve highly efficient control solutions.

Transient stability constrained distributed optimal dispatch for microgrids: A state‐based potential game approach

AbstractThe increasing proportion of renewable energy generation (REG) brings severe challenges to the optimal dispatch and stability control of microgrids. On the one hand, the dynamics of REG result in new stability problems. On the other hand, it is difficult to harmonize the benefits of distributed generators (DGs) since they often belong to different owners. To this end, this paper proposes a distributed optimal dispatching method using state‐based potential game theory, which considers both system stability and individual economy. First, an optimal dispatching model is constructed for microgrid containing various DGs. The transient stability constraint (TSC) of microgrid is given based on dissipation theory. Then, by treating each node as an agent, the optimization model is converted into a multi‐agent potential game with a state space. And a distributed algorithm is developed which is capable of handling coupled constraints. To implement the proposed method, updating rules are designed with respect to TSC based on Gerschgorin theorem, and the convergence of the algorithm are discussed. Simulation and experimental results show that the proposed method can maximize the benefits of each DG without the participation of control centre, while the ability of the microgrid to resist large disturbances is also guaranteed.

Stability margins monitoring system performance evaluation for various methods of transfer capacity calculations with transient stability constraints

The purpose of this work is to determine ways to increase the performance of available power transfer capacity analysis with transient stability constraints, as well as to evaluate the accuracy of the proposed methods. A number of developed methods for performance improvement of available power transfer capacity (APTC) analysis with transient stability (TS) constraints in the stability margins monitoring system (SMMS) were discussed in this article, in particular: network reduction, transient stability analysis with implicit integration method, parallel computing of contingencies, and sequential TS simulations startup. In addition, evaluations of the method’s accuracy of APTC calculations with TS constraints for various power transmissions were carried out.

A Machine Learning-Based Framework for Fast Prediction of Wide-Area Remedial Control Actions in Interconnected Power Systems

This paper presents a novel real-time machinelearning-based framework for remedial control action (RCA) prediction to prevent transient instability in interconnected power systems. Due to the fast dynamics of rotor angle oscillations and considering communication latencies, there is limited time to compute RCA, making RCA calculation impractical in events quickly evolving into transient instability. The proposed algorithm predicts RCA based on pre-fault and post-fault voltage values of generator buses. To cover credible scenarios, reduce prediction complexities, and increase accuracy, a micro model strategy is employed in which independent models are built for each transmission line of the system. The proposed framework consists of three main modules: stability prediction, coherency prediction, and RCA prediction. In the coherency prediction module, a time-varying algorithm is developed that determines the optimal number of generator groups and prevents unnecessarily overestimated RCAs. For each of the considered scenarios and obtained coherency patterns, a mixed-integer linear programming (MILP) model is utilized to extract the islanding and load shedding patterns considering transient stability constraints. The effectiveness of the proposed approach is demonstrated on the IEEE 39-bus system and the 74-bus Nordic test system, followed by a discussion of results.

Robust Transient Stability Emergency Control Considering Wind Power Uncertainties

Transient stability emergency control (TSEC) enhances power system transient stability during large disturbances but faces challenges in the high-penetration wind power grid where the wind power forecast error still cannot be ignored even with state-of-the-art forecasting methods. In this paper, the TSEC problem is modeled as robust nonlinear programming with the objective of maintaining rotor angle stability by generator tripping and load shedding while the uncertain wind power outputs are regarded as intervals. Interval programming is employed to solve the robust TSEC problem where the trajectory sensitivity analysis is applied to approximate the bounds of transient stability constraints. Numerical results on two test systems demonstrate that the proposed method improves computational efficiency and shows good performance on robustness.

Transient stability constrained optimal power flow considering fourth-order synchronous generator model and controls

This paper presents a novel mathematical programming model for the optimal power flow with transient stability constraints, considering a detailed fourth-order model for synchronous generators and their controls. Such controls are the simplified excitation system for voltage magnitude and a frequency control system formed by a governor and a turbine. Moreover, in order to manage convergence issues and to determine causes of instability, load shedding is included. The proposed model considers, in the same mathematical expression, the prefault or the initial steady stage, the fault stage, and the postfault. The differential equations that represent the rotor angle stability constraints were transformed into algebraic equations using the trapezoidal integration method. The proposed nonlinear programming model was implemented using the mathematical programming language AMPL and solved using the nonlinear solver IPOPT. The well-known WSCC 9-bus, and the IEEE 68-bus systems were used for testing accuracy and efficiency. A comparative analysis was also carried out with transient stability-constrained optimal power flow using the second-order generator model to be able to observe not only the economic differences but also to be able to compare the performance of the systems, that is, if the system configuration satisfies the requirements usually demanded by the transmission system operator. The results show the ability of the proposed model to predict the dynamic behavior of the system under contingency and to properly dispatch the generation resources to withstand these perturbations. It is concluded that a more detailed model provokes an overall improvement of the system stability, while performing economical and reliable dispatch decisions. • A new NLP mathematical programming model for the TSC-OPF problem. • The proposed model considers a detailed fourth-order model for generators. • The proposed model considers the excitation system, governor, and turbine controls. • A comparative analysis with the TSC-OPF using a second-order generator model.

Microgrid Operation Optimization Considering Transient Stability Constraints: A New Bidirectional Stochastic Adaptive Robust Approach

This article proposes a new bidirectional stochastic adaptive robust framework with transient stability constraints to optimally and securely operate microgrids (MGs). Within the proposed framework, the uncertainties of photovoltaic/wind turbine generation, load, and electricity price are modeled using adaptive robust optimization (ARO), while the uncertainty of unscheduled islanding occurrence is modeled by stochastic programming. Besides covering the uncertainties related to MG operation, the proposed approach considers transient stability uncertainties leading to a more secure MG operation scheduling framework. To the best of the authors’ knowledge, this is the first time that transient stability analysis along with stochastic adaptive robust optimization (SARO) is proposed for MG operational scheduling. In addition, a new bidirectional scenario generation method is proposed to model MG unscheduled-islanding occurrence and MG restoration to the grid-connected mode. Modeling both the grid-connected and unscheduled-islanded MG operation modes as well as their transitions further distinguishes the proposed approach from the previous ones. Furthermore, a new solution methodology is presented to solve the proposed MG scheduling problem. This methodology is capable of solving both SARO and transient stability constrained-optimal power flow problems. The proposed MG operation optimization framework and solution method are tested on the modified IEEE 33-bus network.

Parametric Transient Stability Constrained Optimal Power Flow Solved by Polynomial Approximation Based on the Stochastic Collocation Method

To better respond to the impact of power system-uncertain parameters on transient stability, a novel model named the parametric transient stability constrained optimal power flow (parametric TSCOPF) is proposed. It seeks the optimal control scheme of transient stability constrained optimal power flow (TSCOPF) expressed by the function of uncertain parameters in power systems. The key difficulty to solve this model lies in that the relationship between the parametric TSCOPF solution and uncertain parameters is implicit, which is hard to derive generally. To this end, this paper approximates the optimal solution of parametric TSCOPF by polynomial expressions of uncertain parameters based on the stochastic collocation method. First, the parametric TSCOPF model includes both uncertain parameters and transient stability constraints, in which the transient stability constraint is constructed as a set of polynomial expressions using the SCM. Then, to derive the relationship between the parametric TSCOPF solution and uncertain parameters, the SCM is applied to the parametric Karush–Kuhn–Tucker (KKT) conditions of the parametric TSCOPF model, so that the optimal solution of the parametric TSCOPF is approximated by using polynomial expressions with respect to uncertain parameters. The proposed parametric TSCOPF model has been tested on a 3-machine, 9-bus system, and the IEEE 145-bus system, which verifies the effectiveness of the proposed method.