Search Results (8)

To address active power fluctuations in power grids induced by high renewable energy penetration and overcome the limitations of existing probabilistic power flow (PPF) methods that ignore generator frequency regulation constraints, this paper proposes a segmented stochastic power flow modeling method and an efficient analytical framework that incorporates the actions and capacity constraints of regulation units. Firstly, a dual dynamic piecewise linear power injection model is established based on “frequency deviation interval stratification and unit limit-reaching sequence ordering,” clarifying the hierarchical activation sequence of “loads first, followed by conventional units, and finally automatic generation control (AGC) units” along with the coupled adjustment logic upon reaching limits, thereby accurately reflecting the actual frequency regulation process. Subsequently, this model is integrated with the State-Independent Linearized Power Flow (DLPF) model to develop a segmented stochastic power flow framework. For the first time, a deep integration of unscented transformation (UT) and regulation-aware power allocation is achieved, coupled with the Nataf transformation to handle correlations among random variables, forming an analytical framework that balances accuracy and computational efficiency. Case studies on the New England 39-bus system demonstrate that the proposed method yields results highly consistent with those of Monte Carlo simulations while significantly enhancing computational efficiency. The DLPF model is validated to be applicable under scenarios where voltage remains within 0.95–1.05 p.u., and line transmission power does not exceed 85% of rated capacity, exhibiting strong robustness against parameter fluctuations and capacity variations. Furthermore, the method reveals voltage distribution patterns in wind-integrated power systems, providing reliable support for operational risk assessment in grids with high shares of renewable energy. Full article

Extreme disasters such as typhoons pose severe frequency stability challenges to modern power systems with a high penetration of new energy sources. Traditional probabilistic power flow (PPF) methods, which assume constant frequency, are insufficient for accurately capturing these risks. This paper proposes a PPF assessment method for wind-integrated power systems that considers system frequency characteristics under typhoon disasters. First, a probability model of wind power output uncertainty under typhoon disasters is constructed based on the hybrid adaptive kernel density estimation (HAKDE) method. Next, the frequency response characteristics are explicitly introduced, with the steady-state frequency deviation $\Delta f$ utilized as the state variable for the PPF solution, and an extended cumulant method PPF model is thus established. This model can concurrently determine the probability distributions and statistical characteristics of nodal voltages, branch power flows, and the steady-state frequency of the system. Case studies on a modified IEEE 39-bus system demonstrate that the proposed method effectively quantifies frequency violation probabilities that are overlooked by traditional models. Full article

Power flow analysis of low-voltage network (LVN) is one of the most crucial methods for achieving refined management of such networks. To accurately calculate the three-phase (TP) probabilistic power flow (PPF) distribution in LVN, this paper first draws on the injection-type Newton method; by leveraging TP power measurements relative to the neutral point obtained from smart meters, the injected power is expressed in terms of injected current equations, thereby establishing TP power flow models for various components within the low-voltage distribution transformer area grid. Subsequently, addressing the stochastic fluctuation models of load power and photovoltaic output, this paper employs conventional numerical methods and an improved Latin hypercube sampling technique. Utilizing linearized power flow equations and based on the improved semi-invariant method (SIM) and Gram–Charlier (GC) series fitting, a calculation method for three-phase PPF in low-voltage distribution transformer area grids using the improved semi-invariant is proposed. Finally, simulations of the proposed three-phase PPF method are conducted using the IEEE-13 node distribution system. The simulation results demonstrate that the proposed method can effectively perform three-phase PPF calculations for the distribution transformer area grid and accurately obtain probabilistic distribution information of the TP power flow within the grid. Full article

The uncertainty caused by renewable energy (RES) and diverse load demands may cause power flow fluctuations in modern power systems, where the probabilistic power flow (PPF) is a reliable method for quantifying and analyzing such power flow fluctuations. This paper proposes a higher-order Markov chain-based modeling framework to represent the stochastic behaviors of the photovoltaic (PV) output and load profiles. The proposed method effectively captures nonlinear temporal autocorrelations across multiple time intervals. In addition, by constructing joint probability distributions, the proposed method can not only handle the situation of linear correlations among distinct PV outputs and similar load types but also reveal nonlinear correlations between co-located PV generation and load variations. In addition, an inverse transformation strategy is developed to generate spatially and temporally correlated PV–load scenarios, ensuring more realistic system representations. Finally, the Mehler formula is adopted to calculate equivalent correlation coefficients under high-linearity conditions, which enhances the computational tractability of the overall approach. Numerical case studies demonstrate that our method achieves both accuracy and efficiency in PPF computations while preserving critical spatio-temporal correlation characteristics. Full article

Today, renewable energy sources (RESs) are increasingly being integrated into power systems. This means adding more sources of uncertainty to the power system. To deal with the uncertainty of input random variables (RVs) in power system calculation and analysis problems, probabilistic power flow (PPF) techniques have been introduced and proven to be effective. Currently, although there are many techniques proposed for solving the PPF problem, the Monte Carlo simulation (MCS) method is still considered as the method with the highest accuracy and its results are used as a reference for the evaluation of other methods. However, MCS often requires very high computational intensity, and this makes practical application difficult, especially with large-scale power systems. In the current paper, an advanced data clustering technique is proposed to process input RV data in order to the decrease computational burden of solving the PPF problem while upholding an acceptable level of accuracy. The proposed method can be effectively applied to solve practical problems in the operating time horizon of power systems. The developed approach is tested on the modified IEEE-300 bus system, indicating good performance in reducing computation time. Full article

With the sharp increase in fluctuant sources in power systems, the deterministic power flow (DPF) calculation has been unable to meet the demands of practical applications; thus, the probabilistic method becomes indispensable for the reliable and stable operation of power systems. This paper adopts the probabilistic power flow (PPF) method, which is a Monte Carlo simulation (MCS) based on the Latin hypercube sampling (LHS) method, to analyze the uncertainties of power systems. Specifically, the available load supply capability (ALSC) based on the branch loading rate is used to analyze the safety margin of the whole system, while the improved power flow entropy is introduced to quantify the equilibrium of power flow distribution. The repeated power flow (RPF) calculation is combined with the PPF method, and, hence, the probabilistic repeated power flow (PRPF) method is proposed to calculate the power flow entropy at the initial state and the probabilistic ALSC. To flexibly control the power flow, the unified power flow controller (UPFC) is added to the AC power system. The different control coefficients of UPFC are set to reveal the relationship between power flow entropy and available load supply capability under the stochastic scenarios. Finally, the modified IEEE14 test system is used to study the adjustment abilities of UPFC. With consideration of uncertainties in the test case, the positive effect of UPFC on the power flow entropy and the probabilistic ALSC under stochastic scenarios is deeply studied. Full article

Because the penetration level of renewable energy sources has increased rapidly in recent years, uncertainty in power system operation is gradually increasing. As an efficient tool for power system analysis under uncertainty, probabilistic power flow (PPF) is becoming increasingly important. The point-estimate method (PEM) is a well-known PPF algorithm. However, two significant defects limit the practical use of this method. One is that the PEM struggles to estimate high-order moments accurately; this defect makes it difficult for the PEM to describe the distribution of non-Gaussian output random variables (ORVs). The other is that the calculation burden is strongly related to the scale of input random variables (IRVs), which makes the PEM difficult to use in large-scale power systems. A novel approach based on principal component analysis (PCA) and high-dimensional model representation (HDMR) is proposed here to overcome the defects of the traditional PEM. PCA is applied to decrease the dimension scale of IRVs and eliminate correlations. HDMR is applied to estimate the moments of ORVs. Because HDMR considers the cooperative effects of IRVs, it has a significantly smaller estimation error for high-order moments in particular. Case studies show that the proposed method can achieve a better performance in terms of accuracy and efficiency than traditional PEM. Full article

This paper proposes a probabilistic power flow (PPF) method considering continuous and discrete variables (continuous and discrete power flow, CDPF) for power systems. The proposed method—based on the cumulant method (CM) and multiple deterministic power flow (MDPF) calculations—can deal with continuous variables such as wind power generation (WPG) and loads, and discrete variables such as fuel cell generation (FCG). In this paper, continuous variables follow a normal distribution (loads) or a non-normal distribution (WPG), and discrete variables follow a binomial distribution (FCG). Through testing on IEEE 14-bus and IEEE 118-bus power systems, the proposed method (CDPF) has better accuracy compared with the CM, and higher efficiency compared with the Monte Carlo simulation method (MCSM). Full article