Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow

The demand for electricity is increasing rapidly, a consequence of this is the threat to the stability of the electrical system, one of which is the stability of the voltage. Voltage instability causes the system voltage to collapse, which causes the system voltage to decrease. System voltage which decreases during maximum loading will cause blackouts. One way to overcome the voltage instability can be by using the power flow method (PF) and the Sustainable Power Flow Method (CPF). Performing PF and CPF methods will provide a clear picture of the existing power system network structure. In experiments conducted using the Java-Bali 500 kV electrical system showed that total active power generation was valued at 12,144 p.u. and total reactive power generation valued at 5,268 p.u. While the total active power load is worth 12,058 p.u. and the total reactive power load is 4.65 p.u. And get the four most critical buses or the most vulnerable to voltage instability on the Tasik Malaya, Mandarincan, Ungaran, and Pedan buses. On the Pedan bus, the most critical bus ride compared to other buses can be related to the length between buses to and to the Pedan bus which is very long which can increase profit and loss on the transmission line. These losses can replace the power supply at the load past the set critical point. And can also produce reactive power generated on the pedan bus is very small while the required amount is very large.

Because of uncertainties of renewable generation resources and load, efficient tools are required for load flow analysis in power systems. Many of the existing papers assume a set of given probability density functions (PDFs) to model uncertainties and develop parametric probabilistic load flow tools. However, the uncertainties might not fall in any standard class of PDFs. Thus, nonparametric tools are needed. This paper presents a method for nonparametric probabilistic load flow analysis to determine PDFs of the load flow outputs. The proposed method is based on the mean value first order saddle point approximation. For a system with $\boldsymbol {n}$ random variables, $\boldsymbol {(n+1)}$ load flow calculations are utilized to establish first order Taylor series expansion and then saddle point approximation is adopted to determine the probabilistic characteristic of desired output variables. The proposed nonparametric estimator provides accurate results while needing a reasonable computational effort. The estimator needs only a limited available data set of random variables without requiring information whether the data set belongs to a certain class of parametric distribution functions. Furthermore, both probability and cumulative distribution functions of load flow outputs are directly established without using integral or differential operators. The proposed method is tested on the IEEE 14-bus and the IEEE 118-bus test systems and promising results are obtained.

Advanced Probabilistic Load Flow Technique in Consideration of Non-Gaussianity and Nodal Correlation of Input Variables

The paper extends the methods of evaluating the continuity in supplying electric power systems using comparative methods of the probabilistic load flow and the stochastic load flow. In the first case a binomial distribution for the units generators and a normal one for the loads are accepted. Branch outages are simulated by fictitious power injections at the corresponding nodes. The loss of load probability and expected energy not supplied are estimated with Gauss Laplace integral functions. The results are compared with the ones obtained through a reliability simulation with DigSILENT Power Factory application.

Guide for author

It is an important part for the power system operation risk control to identify the critical lines. Fluctuation of wind power and fluctuation of load will have a great influence on power transmission and distribution, which will lead to the change of critical lines. Based on probabilistic load flow (PLF) analysis, the risk theory is introduced to put forward, and probabilistic flow betweenness considering uncertainty of wind power and load is presented for critical line identification, which reflects the influence of power grid structure characteristics, change of system running state and uncertain factors on power transmission. It can identify critical lines more accurately. Simulation calculation on CEPRI-36 bus system integrated with wind farms and IEEE-39 bus system with wind farms verify effectiveness of this method. It is able to search for the critical lines according to system running state in actual application, so as to adopt security control measures for the system.

The multiple solution analysis of probabilistic load flow

Design of new materials is quite a difficult task owing to various time and length scales and affiliated uncertainties. The major challenge is to include all these in a conventional model. Hyperparameter models in machine learning can be used to overcome these issues. In this paper, an artificial neural network (ANN) model is developed to estimate the effective elastic parameters of unidirectional fiber reinforced composites using representative volume elements (RVE) considering uncertainty in the fiber diameter. The diameter probability distribution is constructed from the acquired gray images by employing image processing operations. The generalized Polynomial Chaos (gPC) expansion is then used to represent the distribution as a random input parameter for finite element analysis, from where the effective parameters are realized. Similarly, the outputs of the FE model, i.e., elastic parameters, are approximated by gPC expansions having unknown deterministic coefficients and random orthogonal Hermite polynomials. A set of collocation points are generated from roots of the random polynomials; from there, the unknown coefficients are estimated. The realization samples are utilized to train an ANN algorithm based on supervised deep learning. The developed ANN model is later tested and validated for a new sample set of data. It is shown that the ANN model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters.

Uncertainties in dynamic response of buildings with non-linear base-isolators

Flexible alternatives to decoupled load flows at minimal computational costs

Chapter 10 - Harmonic load flow applications for industrial power systems design

An asymptotic-preserving stochastic Galerkin method for the radiative heat transfer equations with random inputs and diffusive scalings

In allusion to the uncertainty and correlation of distributed generation (DG) output in the active distribution network, a new method of probabilistic load flow (PLF) analysis was proposed based on improved sequence operation method. This method utilised the non‐parametric kernel density estimation method and established a probabilistic model of DG daily output considering the timing characteristics. Then this method proposed the multivariate joint distribution probabilistic sequence based on the present sequence operation theory to describe the sequence transformation of the probabilistic model. Finally, an improved dependent probabilistic sequence method was proposed and combined with the traditional linear power flow calculation to achieve the probability distribution information of system power flow. Simulation tests were carried out on the modified 33‐bus distribution system. Test results indicated that the proposed method can achieve more accurate results of PLF calculation and has higher computational efficiency.

Normal-transformation-based probabilistic load flow with correlated wind and load forecast errors

Adaptive stochastic Galerkin FEM