Chapter 18 - Power System Stability

With widespread application of voltage source converter (VSC) as a key energy-conversion power electronic device by using the phase-locked loop (PLL) technique for synchronization, the system dynamics has become much complicated. In this paper, the nonlinear dynamics and transient stability of the PLL-based VSC system are investigated, within a unified framework of the (normalized) generalized swing equation. It is found that there are three different types of bifurcation, including the generalized saddle-node, Hopf, and homoclinic bifurcations. Within the coexistence parameter region, the basin boundary of the stable equilibrium point shows either a closed-loop or a fish-like pattern. With the help of the equal area criterion (EAC), the transient stabilities under different transient disturbances including short circuit, voltage dip, and power rise are analyzed. Because the equivalent damping of the VSC is state-dependent, the theoretical results based on the EAC are examined. Furthermore, based on the analytical results from the generalized swing equation, the principle for all major transient stability enhancement methods is uncovered. All these findings are well verified by extensive electromagnetic transient simulations. Therefore, the generalized swing equation provides a deeper physical insight and plays a crucial role in transient stability problems in power-electronic-dominated power systems, similar to the swing equation in traditional power systems.

Fast electric vehicle(EV) charging stations have become one of the fastest-growing penetrated power electronics (PE) interfaced loads to the electric power system. The lack of accurate model of the fast EV charger in transient stability (TS) simulation tools limits the effectiveness of power system dynamic performance evaluation and stability analysis. In this paper, The electromechanical model of a fast EV charging unit is proposed, which is suitable for large-scale power system dynamic analysis in TS simulators. The EV charger model is simplified to guarantee a balance between model accuracy and simplicity. The validity of the proposed model has been demonstrated by a comparative study with the benchmark model created in PSCAD/EMTDC.

Braking resistor is a very powerful tool to improve transient stability in a power system. Usually, a fixed value of the braking resistor is considered for the transient stability analysis. However, when the braking resistor is in operation, temperature of the resistor material rises above ambient temperature which ultimately causes the resistance value to increase. This paper analyzes the effect of the temperature rise of the fuzzy logic-controlled braking resistor on the transient stability in a multimachine power system. The performance of the braking resistor scheme with fuzzy controller is compared to that of with conventional proportional-integral-derivative (PID) controller. Simulation results of both balanced and unbalanced faults at different points in the system indicate that the temperature rise of the fuzzy logic-controlled braking resistors has little or almost no effect on the transient stability of the multimachine power system. Moreover, it is found that the performance of fuzzy logic controller is better than that of conventional PID controller. Thus, the proposed fuzzy control strategy provides a simple and effective method of transient stability enhancement.

The power transient stability analysis is one of the basis for determining the control strategy of power system security and stability. Considering the influence of power grid topology on the transient stability of power system, the transient stability evaluation model is constructed based on the graph attention neural network. The electrical components and their transient operation data are mapped to the graph data with the spatial topology characteristics of power system for model training, so as to improve the topological generalization performance of the model. The marginal contribution of input characteristics to the output of transient power angle stability evaluation model is quantitatively calculated based on Shapley additive explanation (SHAP), so as to improve the interpretability of data-driven method for transient power angle stability evaluation. The effectiveness of the proposed method is verified by the IEEE 39-bus system.

The renewable energy system and power grid are usually connected through a grid-connected converter (GCC), whose transient performance is significantly essential during the grid faults. In actual operation, reactive power compensation devices are often connected to the common coupling point (PCC) to improve voltage stability. However, there is a lack of analysis when considering the influence of reactive power compensation devices on GCC's transient stability. In this paper, the mathematical model of GCC when static var generator (SVG) is adopted for reactive power compensation is established. The AC-side equivalent circuit of the system, the state equation and the output power characteristic curve of GCC are obtained. On this basis, the equal-area criterion (EAC) for GCC is proposed to analyze its transient stability. Finally, the simulation of remote voltage sag under different short circuit ratio (SCR) is carried out to verify the correctness of the theoretical analysis.

With the development of science and technology, the cost of offshore wind power development and transmission has gradually decreased, making offshore wind power technology a research hotspot. The installed capacity has been increasing year by year. China has abundant offshore wind energy resources, which are much richer than those on land and are available for exploitation. Offshore wind speeds are stable and do not produce harmful substances. Therefore, studying the transient voltage stability of offshore wind power grid-connected systems to improve the utilization efficiency of offshore wind power and protect the ecological environment is critical. After large-scale wind power is connected to the grid, ensuring the stability of the system's transient voltage becomes crucial. This paper aims to deeply study the transient voltage stability of offshore wind farm grid-connected systems, providing theoretical support for the subsequent design and operation of offshore wind farms. A simulation model of a typical power system integrated with offshore wind farms was established using PSAT. Relevant transient voltage stability indices were calculated, and the impact of varying wind speeds on the transient voltage stability of the grid-connected system was investigated. Static Var Compensators (SVC) and Static Synchronous Compensators (STATCOM) were installed for comparative analysis. The results demonstrate that excessively low wind speeds degrade the system's transient stability, and the installation of SVC provides superior improvement in transient voltage stability compared to STATCOM.

The integration of uncertain photovoltaics (PVs) and flexible loads leads to uncertainties in the power system dynamic simulation results. Furthermore, geographically close PV farms are correlated and may exhibit nonlinear correlations. This article proposes a copula-based sparse polynomial chaos expansion (PCE) framework for quantifying the impacts of uncertain dynamic PVs and loads on power system dynamic simulations and stability. The dynamics include both PV and load stochasticity and those governed by differential and algebraic equations. The copula statistics are utilized to accurately characterize the dependence structure of PVs and further used to develop the copula-PCE for quantifying the impacts of uncertain PVs and loads. A probabilistic TSI is also developed to assess the uncertainties from PVs and loads on the system stability. To address the cases, where both stable and unstable conditions coexist, a preprocessing step via sample classification is proposed. The effects of different dependence structures of PVs and different numbers of uncertain sources are investigated. Comparison results with other methods on the modified IEEE 39- and 118-bus systems, including the Monte Carlo method, Latin hypercube sampling, and traditional PCE without consideration of uncertain input correlations show that the proposed method is able to accurately quantify the uncertain dynamic simulations and transient system stability while being computationally efficient.

This paper presents a study of FACTS devices applications, in particularly choice of adequate shunt compensators (type of FACTS devices, location) in order to improve voltage and transient angle stability. The study is carried out for the 500kV Southern Vietnam power system in 2020 with a high load scenario. The load flow calculation, P-V curve analysis and transient stability study are examined by using the PSS/E-33 software. The obtained results show that with the application of FACTS devices, voltage stability and transient angle stability of this power system are considerably improved.

In present scenario power grid networks are intricately interconnected, and by the opening of the electrical power market, power networks have become more complex. Now the various aspects of safety, security, controllability, power quality, and stability are equally important. In this paper, our main focus will be on improving stability; transient stability. While improving transient stability conventional lead-lag Power System Stabilizer (PSS) provide low frequency oscillations. Main use of Static VAr Compensator (SVC) is to improve transient stability through voltage control. For simulation, 4 generator-6 bus multi machine power network is taken for the analysis of the proposed scheme and the results of two types of controllers, i.e. PSS and SVC are compared.

To address the challenges of transient voltage stability in modern power systems with high renewables penetration, this paper proposes a multiple stability margin indexes-oriented online risk evaluation and adjustment framework based on a digital twin platform. The System Voltage Deviation Index (SVDI) is first introduced as a quantitative metric to assess transient voltage stability from time-domain simulation results, capturing the system’s dynamic response under large disturbances. An arbitrary Polynomial Chaos (aPC) expansion combined with Sobol sensitivity analysis is then employed to model the nonlinear relationship between SVDI and uncertain inputs such as wind power, photovoltaic output, and dynamic load variations, enabling accurate identification of key nodes influencing stability. Furthermore, an emergency control optimization model is developed that jointly considers voltage, frequency, and rotor angle stability margins, as well as the economic costs of load shedding, with a trajectory sensitivity-based local linearization technique applied to enhance computational efficiency. The proposed method is validated on a hybrid AC/DC test system (CSEE-VS), and results show that, compared with a traditional control strategy, the optimized approach reduces total load shedding from 322.59 MW to 191.40 MW, decreases economic cost from 229.18 to 178.11, and improves the transient rotor angle stability index from 0.31 to 0.34 and the transient frequency stability index from 0.3162 to 1.511, while maintaining acceptable voltage stability performance. These findings demonstrate that the proposed framework can accurately assess online operational risks, pinpoint vulnerable nodes, and generate cost-effective, stability-guaranteeing control strategies, showing strong potential for practical deployment in renewable-integrated power grids.

In order to maintain the stable operation of power systems, quick and accurate transient stability assessment (TSA) after the fault clearance is important. Machine learning methods have been widely used in the transient stability analysis of power systems. However, how to make good use of time series data of PMUs and effectively balance the contradiction between rapidity and accuracy brings new challenges to TSA. To address this problem, we propose an anti-jitter dynamic evaluation method based on long-short term memory (LSTM) network. In this model, the trajectory cluster characteristics of generators power angles after fault clearance are taken as inputs, and an improved LSTM is used to learn the nonlinear mapping relationship between the input characteristics and the transient stability. Meanwhile, by the use of sliding time windows and anti-jitter mechanism, a hierarchical real-time prediction framework is constructed to effectively utilize the time series data of PMUs. The case studies on two systems indicate that the proposed method has superior evaluation accuracy and general performance. In addition, the proposed method can effectively evaluate the stability margin or instability degree of samples, which provides reliable reference information for emergency control.

With large wind energy integration into power systems, wind farms begin to influence power systems in a much more significant manner. As wind energy systems utilize different generator technologies from the one utilized in the conventional power plants, the steady-state, transient and small-signal dynamics, as well as, power system stability will thus be significantly affected. The impact of wind energy systems on the power system dynamics and stability is thus of practical importance. As there is a significant increase in installation of wind turbines equipped with doubly-fed induction generator (DFIG) in recent years, a dynamic model of the DFIG wind turbine is firstly developed in this thesis. The model is validated against field measurement data, and the validation gives confidence about the accuracy and applicability of the developed model. DFIG wind farms consist of tens to hundreds of identical DFIG wind turbines increasing the complexity of the wind farm model and simulation time. A novel aggregation technique is developed in this thesis that incorporates a multiplication factor, namely mechanical torque compensation factor (MTCF), to the mechanical torque of the full aggregated wind farm model. The MTCF is initially constructed to approximate a Gaussian function by using fuzzy logic method. By optimizing the MTCF on a trial and error basis, less than 10 percent discrepancy is then achieved between the proposed aggregated model and the complete model. The proposed aggregation technique is then applied to a 120 MVA offshore wind farm comprising of 72 DFIG wind turbines and shows higher accuracy in approximating the wind farm dynamics as it appears at the point of common coupling (PCC) as compared to the full aggregated model. The proposed aggregated model computes faster than the complete wind farm model by 90.3 percent during normal operations and 87 percent during grid disturbances. To overcome the adverse effects due to the fluctuating nature of wind, two wind power smoothing methods are proposed using a fuzzy logic pitch angle controller for a smooth performance with a minimum drop in output power. One method performs partial smoothing with only 4.74 percent drop in the output power while the other method offers complete smoothing with a 8.28 percent drop in output power. The impact of wind energy integration on power system transient stability (PSTS) is studied quantitatively with the transient energy margin (TEM), which is calculated through the evaluation of the transient energy function (TEF). This study is carried out in two ways in the thesis. One is to analyse the impact of transient fault on the DFIG wind turbine as compared to SGs for different factors, like the fault clearing time, the grid coupling, the inertia constant and the voltage sag. The study reveals that transient stability of the DFIG wind turbine is hardly affected by the grid coupling, the inertia constant and the generator terminal voltage sag variations indicating its consistent transient performance within a wide range of these factors. The fault clearing time should be almost 11 percent faster for the system with the DFIG than the synchronous generator (SG). The other is to investigate the impact of the DFIG wind farm on the PSTS with the variation of different factors, which are the voltage sag, the fault clearing time, the load and the wind power penetration level. The study reveals that power systems integrated with DFIG wind farms are sensitive to transient events with high voltage sag, high fault clearing time, low load operation and high wind power penetration level. Machines at different locations individually possess distinct fault response and suffer from a large-scale power imbalance. As a result, reliable operation of DFIG wind farm integrated power systems demands upgraded equipment, such as advanced switchgear, fast breakers/isolators, efficient power reserve systems and advanced reactive power compensating device, etc.

An optimized algorithm for optimal power flow based on deep learning

Renewable energy generation equipment exhibits rapid control characteristics at millisecond or even microsecond timescales, which significantly differs from the electromechanical transient characteristics of traditional synchronous generators. When these two types of sources interact in a power system, they can substantially alter the system's dynamic response, posing serious challenges to power system stability. This paper focuses on transient stability analysis in power systems. Based on the equal-area criterion, the influence mechanism of high-penetration renewable energy integration on power system transient stability is investigated by analyzing the impact of renewable energy penetration levels and spatial distribution on system power characteristics. Finally, simulation tests on the New England 10-machine 39-bus system are conducted to validate the theoretical analysis.

Transient stability, which is an important aspect in maintaining power system operation, was the focus of this research. Critical clearing time calculation, popular for assesing the transient stability by observing the generator rotor angle performance, was utilized as the assesment method. Wind turbine effect in transient stability is added as the specific problem representing the current condition in Indonesian power system. Three study cases were observed, namely observing the effect of wind farm integration, observing the effect of thermal generator loading, and observing the effect of wind farm penetration level on transient stability. The research is conducted in modified IEEE 9 Bus system with wind turbine modeled as doubly fed induction generator using DIgSILENT 15.1 environment. The result showed that the effect o wind farm integration and the greater the loading of a thermal generator in the system worsen the transient stability performance. Increasing the penetration level of the wind farm in the system also worsen the system transient stability even if the energy cost is zero.