A Novel Small Disturbance Stochastic Stability Analysis Method Based on Entropy

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.

Integrating non-dispatchable renewable energy sources (RES) such as wave farms into electric power systems presents inherent challenges. Specifically, the variability of the resource and its non-dispatchable) nature introduces power imbalances and power system stability problems in the system over both short and medium terms. This issue is particularly relevant for isolated power systems, such as those found on several European islands, where interconnection with the mainland is lacking. Therefore, although wave energy has significant potential for integration into island power systems due to resource availability, determining the maximum RES penetration that such systems can sustain while maintaining stability is not straightforward. Power system stability is closely tied to frequency. A well-established solution for improving the stability of isolated systems when integrating non-dispatchable RES is to install devices capable of responding to over- or under-frequency events, such as energy storage systems (ESS). The literature extensively discusses ESS control techniques for frequency regulation, with one of the most straightforward approaches being to operate the ESS according to a droop control strategy (similar to a statism). In this method, the power dispatched or stored by the ESS increases proportionally to the deviation from the frequency reference value. This paper presents a case study analyzing the frequency stability of an island power system equipped with an energy storage system (ESS) when integrating a wave farm. Frequency stability is evaluated based on two variables: wave energy penetration and the ESS droop control parameter. The case study is based on the island of El Hierro (Canary Islands, Spain), an isolated electrical system with a very high penetration of RES. The island’s electrical generation system consists of a wind farm, a pumped-storage hydroelectric power plant, and conventional generation from a diesel power plant. The analysis is conducted through simulations in MATLAB Simulink. A wave farm is modeled to evaluate the generated power and its associated oscillations, based on the wave energy resource at various locations along El Hierro’s coast. Additionally, an aggregated inertial dynamic model of the electrical power system is employed to assess the impact of the wave energy farm's generation on the system’s frequency and the aging that the frequency excursions introduce in the elements of the system. The Spanish Grid Code is considered to ensure compliance with frequency regulation mechanisms in isolated systems. Simulations are performed across different scenarios, varying both the nominal power of the wave farm and the ESS droop control parameter, in order to evaluate the ESS capacity. The results identify the optimal droop control parameter for each wave farm size to ensure frequency remains within acceptable thresholds. Furthermore, the minimum ESS capacity required for each wave farm size is determined from the simulations. These findings provide a basis for ESS and wave farm dimensioning, which could be translated into economic terms to maximize revenue (this aspect is beyond the scope of the present work).

With the scale of wind power integration expanding continuously, the random characteristic of power system is more and more prominent due to the volatility and intermittency of wind energy. Because of the fluctuations brought by wind power integration, the traditional deterministic analysis methods and the conventional stochastic differential equations are difficult to accurately analyze wind power system. In this paper, Markov theory is utilized to establish a stochastic Markov dynamic model for wind power systems by considering various uncertainties. Then, based on the developed model, Lyapunov energy function and M matrix are combined together to present the analytical method of stochastic mean stability and stochastic mean square stability of wind power system. Compared with the conventional stochastic differential equation analysis method, the proposed method can overcome the shortcomings that the stochastic stability cannot be analyzed when the system operating conditions change. Finally, simulation results are provided to verify the validity and correctness of the proposed method.

Guest Editorial: Situational awareness of integrated energy systems

A robust, optimized power system stabilizer (PSS) is crucial for oscillation damping, and thus improving electrical network stability. Additionally, real-time testing methods are required to significantly reduce the likelihood of software failure in a real-world setting at the user location. This paper presents an Antlion-based proportional integral derivative (PID) PSS to improve power system stability during real-time constraints. The Antlion optimization (ALO) is developed with real-time testing methodology, using hardware-in-the-loop (HIL) that can communicate multiple digital control schemes with real-time signals. The dynamic power system model runs on the dSPACE DS1104, and the proposed PSS runs on the field programmable gate arrays (FPGA) (NI SbRIO-9636 board). The optimized PSS performance was compared with a modified particle swarm optimization (MPSO)-based PID-PSS, through different performance indices. The test cases include other step load perturbations and several short circuit faults at various locations. Twelve different test cases have been applied, through real-time constraints, to prove the robustness of the proposed PSS. These include 5 and 10% step changes through 3 different operating conditions and single, double, and triple lines to ground short circuits through 3 different operating conditions, and at various locations of the system transmission lines. The analysis demonstrates the effectiveness of ALO and MPSO in regaining the system’s stability under the three loading conditions. The integral square of the error (ISE), integral absolute of the error (IAE), integral time square of the error (ITSE), and integral time absolute of the error (ITAE) are used as performance indices in the analysis stage. The simulation results demonstrate the effectiveness of the proposed PSS, based on the ALO algorithm. It provides a robust performance, compared to the traditional PSS. Regarding the applied indices, the proposed PSS, based on the ALO algorithm, obtains significant improvement percentages in ISE, IAE, ITSE, and ITAE with 30.919%, 23.295%, 51.073%, and 53.624%, respectively.

This paper presents a basic introduction to some popular stochastic analysis methods from an unbiased disciplinary perspective. Examples ranging from fields as diverse as defense analysis, cognitive science, and instruction are illustrated throughout to demonstrate the variety of applications that benefit from such stochastic analysis methods and models. Two applications of longitudinal stochastic analysis methods to collaborative and cognitive training environments are discussed in detail. The first application applies a combination of latent mixed Markov modeling and multidimensional scaling for modeling, analyzing, and supporting the process of online knowledge sharing. In the second application, a combination of iterative nonlinear machine learning algorithms is applied to identify latent classes of problem-solving strategies. The examples illustrated in this paper are instances of an increasing global trend toward interdisciplinary research. As this trend continues to grow, research that takes advantage of the gaps and overlaps in analytical methodologies between disciplines will save time, effort, and research funds.

Due to the rising use of renewable energy sources and the use of contemporary power electronic equipment, power system stability has become a major challenge in current power systems. Controlling the power system characteristics can increase the stability of the power system. The traditional techniques for improving power system stability, such as the use of FACTS devices, are costly and may not be effective in handling the dynamic changes of the power system. As a result, by optimizing the power system parameters, an optimization-based multi-agent system can improve the stability of the power system. The Grey Wolf Optimizer based Multi Agent System (GWO-MAS) is proposed in this paper to improve power system stability. The control agents of Distributed Generations (DGs) are optimized using GWO algorithm based on the deviations in frequencies of DGs. Particle Swarm Optimization based Multi Agent System (PSO-MAS) and Conventional Multi Agent System performance are compared with the suggested technique's implementation on IEEE 30 bus system and testing in MATLAB/Simulink environment. The outcomes showed that the suggested approach is successfully improving the stability of an interconnected power system.

One of the technical solutions for improving the stability of power system is incorporation of Static Synchronous Compensators (STATCOM) and Static Synchronous Series Compensator (SSSC) controllers. However, the impact of hybridized STATCOM and SSSC on the generator damping stability of the power system to improve the post disturbance recovery voltages of the generator is necessary. Thus, in this study, hybridized model of STATCOM and SSSC controllers were incorporated on the Nigerian 31-bus power system to improve the system generator damping stability during disturbance. Transient stability of electrical power system with contingency was performed using swing equations technique. Line-Voltage Stability Index (L-VSI) technique was employed to determine the critical load bus for the placement of the controllers. Hybridized model of the STATCOM and SSSC was developed and incorporate into the selected load buses and its impact on stability of the generator oscillation damping was examined. Simulation was done in MATLAB R2023a. The generator damping ratio, total active power losses and total cost of controllers were determined. Results verified the effectiveness of hybridized model of STATCOM and SSSC controllers in improving the stability of power generator oscillation damping. Keywords : STATCOM, SSSC, Line-Voltage Stability Index, Contingency, Generator Oscillation Damping, Power Loss. DOI: 10.7176/NCS/15-04 Publication date: February 28 th 2025

Areas discussed are power system modeling, state estimation, structure decomposition, state forecasting, clustering and security measure development. A detailed dynamic model of a multi-machine power system has been developed. A process state estimator was developed to estimate the long-term dynamic behavior of the power system. The algorithm is identical to the extended Kalman filter but has a modified process noise driving term. A two-stage structure estimation technique was proposed for identifying the power system network configuration. Two approaches to structure decomposition were investigated. A time-scale decomposition of the system equations, based on a singular perturbation approach, was evaluated using a detailed model of a generating system. Spatial decomposition was examined by applying an optimal network decomposition technique to a 39-bus test system. Stochastic approximation based approaches to estimator simplification were examined. Explicit expressions were obtained for the evolution of the first and second moments of the system state. Research into security measures proceeded in three directions. The first area involves viewing the security assessment problem as a hyperplane crossing problem for a stochastic process. The second approach examined the stability of an unforced linear system where the system coefficients are subject to future jumps. The third area of research has led to the formulation of a security measure suitable for on-line assessment of transient stability.

A Dynamic simulation Model (DynMo-CBC) is developed and demonstrated for a power system comprised of a gas cooled reactor and three independent CBC loops. The reactor core is divided into three sectors that are hydraulically independent, but thermally and neutronically coupled. Each reactor sector is directly coupled to a CBC loop with a Brayton Rotating Unit designated UNM-BRU-1 and NaK-78 secondary loop with water heat pipes radiator panels. The results presented are for the startup transient to steady-state operation of the space power system at a UNM-BRU-1 shaft speed of 45 krpm, turbine and compressor inlet temperatures of 1149 K and 400 K, and reactor thermal power of 471 kWth. At these conditions, the electrical power and thermal efficiency of the S^4-CBC power system are 130.8 kWe and 27.8%.

Enhancing stability via coordinated control of generators, wind farms, and energy storage: Optimizing system parameters

Growth in power demand without increased network expansion necessitates that the stability of the power system with minimum of control systems is required to stay within the reference point of safe and reliable operation of the grid. In this paper, a three-machine nine-bus power system with a wind park is used for stability analysis and a H 2 /H ∞ robust power system stabilizer (PSS) is designed for damping oscillations. System performances after various disturbances are discussed by comparing the proposed PSS with conventional PSS. The results show that the robust PSS has stronger robustness and it is more reliable than conventional PSS (CPSS) under various disturbances.

In many situations of power system restoration or emergency control load flow, often dynamic load flow, results are needed at a time scale which makes regular load flow computations impractical. In this paper a low order dynamic model is introduced which retains fully detailed and precise representation of the critical components (such as strong backbone lines like EHV or weak tie lines) where the interest is focused and reduces the detail of representation of other parts of the system gradually with their distance from the spotlighted sections where details are needed. The result is a low order and hence very fast computation with not only detailed but also quite precise results for those parts of the system which are critical. This approach is very flexible, it can be used to compute tie line load and frequency swings on an interconnection of areas or static loads on the tie lines of such a system affecting third parties in a power trading situation. It can be used to compute precisely and fast the EHV system loads or any combinations of such elements. The operator is quite free to choose what should be represented in precise detail.

Cascading outages are a series of complex dynamic mechanisms, and could lead to major system disturbances and large blackouts. Some of the key mechanisms of cascading outages can only be studied with a dynamic power system model, which emphasizes the significance of dynamic cascading outage simulations. However, most test systems from related literature do not include sufficient data for dynamic simulations and none of them is thus able to capture all possible cascading mechanisms. The aim of this paper is to propose a small set of test systems with minimum required data, including dynamic information and protection elements, as a standard for dynamic cascading outage simulations. It presents the detailed information about each test system, and describes the algorithms that are used to generate the missing data if the baseline test cases are not complete. All proposed test systems are available through the web link: http://web.engr.oregonstate.edu/~cotillaj/ecs/Cases.html.

This study presents a study of bifurcation in a dynamic power system model. It becomes one of the major precautions for electricity suppliers and these systems must maintain a steady state in the neighborhood of the operating points. We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from a subcritical or supercritical Hopf bifurcation by computing the first Lyapunov coefficient. The MATCONT package of MATLAB was used for this study and detailed numerical simulations presented to illustrate the types of dynamic behavior. Results have proved the analyses for the model exhibit dynamical bifurcations, including Hopf bifurcations, Limit point bifurcations, Zero Hopf bifurcations and Bagdanov-taknes bifurcations.