Probabilistic Power Flow Analysis With Generation Dispatch Including Photovoltaic Resources

In this paper, an efficient approach is presented for probabilistic power flow analysis of complex structures with parameter uncertainties. A component-based technique is used to generate Reduced-Order Models (ROMs) of low- to mid-frequency vibration and power flow. Using this framework, two techniques are employed for probabilistic vibration power flow analysis: (1) a Locally Linear Interpolation (LLI) method, which is a new response surface construction method that has been specifically developed for probabilistic vibration analysis and (2) the Advanced Mean Value (AMV) method, which is a more general technique from the reliability literature. The advantages and limitations of the LLI method are examined and compared to those of the AMV method with respect to probabilistic power flow analysis. Numerical results are shown for a simple example system, an L-shaped plate, and for an important engineering application, a ground vehicle structure.

Based on Monte Carlo and interior point method, this paper presents a probabilistic optimal power flow analysis method for the virtual power plant (VPP) containing photovoltaic (PV) generation, which can take into account both the randomness and correlation of PV generators' power outputs and loads at different locations. An optimal power flow model of VPP is firstly given to minimize the operation cost of VPP. The inverse transformation method and Cholesky decomposition technique are used to simulate the correlations between PV power outputs and loads, which obey Beta and Normal distributions respectively. Finally, the modified IEEE 30-bus test system is used to demonstrate the effectiveness and application of the presented method in the probabilistic optimal power flow analysis of VPP.

This study presents the design of wide‐area fractional order damping controller for low frequency inter‐area oscillations in Western Electricity Coordinating Council (WECC) system. The developed wide‐area damping control scheme is implemented in a decentralised manner by examining the entire system through decentralised identification at the level of each generator bus and FACTS devices in large‐scale system. The decentralised identification is done by applying n4sid (Subspace State Space System Identification) algorithm to the time‐domain simulated response of WECC system. The main features of the proposed approach are: (a) measurement‐based control which does not require complete model of WECC; (b) minimise the communicating signals required for damping controller and incorporate practical method of time‐delay compensator (TDC) design to reduce the effect of time‐varying delay. The performance of wide‐area control (WAC) scheme is tested on the practical WECC system and verified by non‐linear time‐domain simulation. The proposed decentralised WAC scheme is compared with local and centralised control scheme, which enhances the damping of inter‐area oscillation effectively compared to local control scheme and more reliable compared to centralised control scheme and its robustness is verified over a wide‐range of operating conditions.

Achieving clean energy goals will require significant advances in regard to addressing the computational needs for next-generation renewable-dominated power grids. One critical obstacle that lies in the way of transitioning today’s power grid to a renewable-dominated power grid is the lack of a faster-than-real-time stability assessment technology for operating a fast-changing power grid. This paper proposes an artificial intelligence (AI) -based method that predicts the system’s stability margin information (e.g., the frequency nadir in the frequency stability assessment and the critical clearing time (CCT) value in the transient stability assessment) directly from the system operating conditions without performing the conventional time-consuming time-domain simulations over detailed dynamic models. Since the AI method shifts the majority of the computational burden to offline training, the online evaluation is extremely fast. This paper has tested the AI-based stability assessment method using multiple dispatch cases that are converted and tuned from actual dispatch cases of the Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. The results show that the AI-based method could accurately predict the stability margin of such a large power system in less than 0.2 milliseconds using the offline-trained AI agent. Therefore, the proposed method has great potential to achieve faster-than-real-time stability assessment for practical large power systems while preserving sufficient accuracy.

Wind farms commonly cluster in regions rich in wind resources. Thus, correlation of wind speeds from different wind farms should not be ignored when modeling a power system with large wind energy penetration. This paper proposes a probabilistic optimal power flow (POPF) technique based on the quasi-Monte Carlo simulation (QMCS) considering the correlation of wind speeds using copula functions. In this paper, a copula function is used to model the dependent structure of random wind speeds and their forecast errors. QMCS is employed in the sampling procedure to reduce computation burden. The proposed method is applied in probabilistic power flow (PPF). Furthermore, the PPF is used in the POPF problem that aims at minimizing the expectation and downside risk of fuel cost simultaneously. Simulation studies are conducted on a modified IEEE 118-bus power system with wind farms integrated in two areas, and the results show that the accuracy and efficiency are improved by the proposed method.

Recent large penetrations of solar photovoltaic (PV) generation and the inertial characteristics of inverter-based generation technologies have caught the attention of those in the electric power industry in the United States. This paper presents a systematic approach to develop test cases of high penetrations of PV for the Western Interconnection. First, to examine the accuracy of the base case model, the Western Electricity Coordinating Council (WECC) model is validated by using measurement data from synchronized phasor measurement units. Based on the 2022 Light Spring case, we developed four high PV penetration cases for the WECC system that are of interest to the industry: 5% PV+15 % wind, 25% PV+15% wind, 45% PV+15% wind, 65% PV+15% wind). Additionally, a method to project PV is proposed that is based on collected, realistic PV distribution information, including the current and future PV power plant locations and penetrations in the WECC system. Both the utility-scale PV plant and residential rooftop PV are included in this study.

With the increasing number of distributed power sources connected to the active distribution network, it brings greater uncertainty to the operation of the distribution network, which is intertwined with the uncertainty of the load, and brings challenges to the power flow calculation of the distribution network. To solve this problem, a probabilistic power flow calculation algorithm for active distribution network is proposed. The power flow equation of the active distribution system is linearized by Taylor series. In order to improve the efficiency of power flow calculation, the semi-invariant method and Gram-Charlier expansion are used to deal with random variables in the power flow model. The proposed method is verified on the IEEE-33 system, and the results show that the proposed method can significantly reduce the calculation time while ensuring the calculation accuracy.

A probabilistic resilience assessment method for distribution system operation with probabilistic optimal power flow

In recent years with the distributed generation (DG) technology like photovoltaic system generation (PVS) widely applied, some system problems such as voltage exceeding is gradually remarkable. The PVS access node and capacity will influence the voltage exceeding probability. In order to make full use of PVS and make sure the voltage exceeding probability limit within a certain range to ensure the power quality, the suitable PVS access node and capacity is needed. Base on this, the objective function and its constraint conditions of the suitable PVS access node and capacity are established. This problem becomes a nonlinear combinatorial optimization problem. This paper use improved genetic algorithm to solve this problem. And the solution of voltage exceeding probability uses the combined Cumulants and the Gram-Charlier expansion method.

The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multi-slack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy. The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

Simulation of the transient stability problem of a power system, which is the assessment of the short term angular and voltage stability of the system following a disturbance, is of vital importance. It is widely known in the industry that different transient stability packages can give substantially different results for the same (or at least similar) system models. Due to the usual lack of real-world data in the transient stability domain, in this paper we “validate” the software packages against each other. This is done by simulating the Western Electricity Coordinating Council (WECC) system models in three different widely-used software packages. Two specific approaches utilized to perform this validation are discussed. Also, the sources of discrepancies seen in the results from the different packages are investigated. This enables us to identify the differences in implementation of dynamic models in these different transient stability softwares, and also facilitates some improvements in these packages. In this process, we present certain example transient stability analyses of the WECC system models for different contingencies.

Frequency control from photovoltaic (PV) power plants has great potential to address the frequency response challenge of the power system with high penetrations of renewable generation. Using model-based approaches to determine the optimal PV headroom reserve, however, requires significant online computation and is intractable for an interconnection level system. This paper proposes a machine learning based strategy, that is suitable for real-time operation, to determine the optimal PV reserve for frequency control. The proposed machine learning algorithm is trained and tested on 1,987 offline simulations of a 60% renewable penetration Western Electricity Coordinating Council (WECC) system. Furthermore, the proposed reserve determination strategy is applied on a realistic 1-day operation profile of the WECC system and demonstrates a savings of more than 40% PV headroom compared to a conservative approach. It is evident that the proposed strategy can efficiently and effectively determine the optimal PV frequency control reserve for realistic interconnection systems.

A new thermal turbine-governor modeling approach based on the improved simulation of base-loaded units and load-controlled units, has been developed in the Western Electricity Coordinating Council (WECC). The development of this model went through an extensive study process, which included validation to staged WECC system tests and verification with respect to numerous large system disturbances. The new modeling approach is being currently used in all operation and planning studies in the WECC. Although the model discussed in this article was concerned with the governing of the WECC, specifically, the Western Interconnection in North America, the general principles of the new thermal governor modeling approach clearly apply to all interconnections, large and small.

This paper introduces two extenstions to the cumulant method (CM) for probabilistic optimal power flow (P-OPF) studies; the first is an enhancement to provide improved handling of limits within the P-OPF problems and the second is a way to include correlated variables. The first enhancement is termed the Limit corrected cumulant method (LCCM) which specifically addresses errors in the existing CM when limits, away from the mean solution, are encountered while solving a P-OPF problem. The LCCM approach relies on the CM to produce multiple probability density functions (PDFs) and then combines these PDFs together to generate final PDFs. The second enhancement for incorporating correlated variables into P-OPF problems is based on the composition of correlated variables from several independent ones. The proposed approaches are verified against Monte Carlo simulations (MCS) consisting of 10 000 samples and demonstrate significant improvements when compared with traditional CM results.

The large-scale integration of renewable energy has reduced power system flexibility and exacerbated supply–demand imbalances. In industrial parks, the combined variability of high energy-consuming industrial loads and photovoltaic (PV) generation further complicates the energy management challenge. Aiming to enhance the operational flexibility of industrial parks and mitigate supply–demand imbalances, this paper proposes a multi-time-scale stochastic energy management strategy that accounts for the uncertainty associated with PV generation. First, a conditional generative adversarial network (CGAN) is employed to generate the representative PV generation scenarios, thereby enabling the modeling of PV generation uncertainty within the optimal dispatch model. Considering the coupling mechanisms and control characteristics of various regulation resources within the industrial park, a multi-time-scale dispatch model is developed. In the day-ahead dispatch phase, the operational costs are minimized by optimizing the production plans of industrial loads. In contrast, in the intraday phase, the more flexible measures, such as adjusting the tap positions of arc furnaces and controlling the charge/discharge of energy storage systems, are employed to smooth power fluctuations within the park. A case study validated the effectiveness of the proposed approach, demonstrating a 7.56% reduction in power fluctuations and a 4.34% decrease in daily operating costs. These results highlight the significance of leveraging industrial loads in park-level systems to enhance cost efficiency and renewable energy integration.