A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks

This paper deals with the problem of the optimal placement and sizing of distributed generators (DGs) in alternating current (AC) distribution networks by proposing a hybrid master–slave optimization procedure. In the master stage, the discrete version of the sine–cosine algorithm (SCA) determines the optimal location of the DGs, i.e., the nodes where these must be located, by using an integer codification. In the slave stage, the problem of the optimal sizing of the DGs is solved through the implementation of the second-order cone programming (SOCP) equivalent model to obtain solutions for the resulting optimal power flow problem. As the main advantage, the proposed approach allows converting the original mixed-integer nonlinear programming formulation into a mixed-integer SOCP equivalent. That is, each combination of nodes provided by the master level SCA algorithm to locate distributed generators brings an optimal solution in terms of its sizing; since SOCP is a convex optimization model that ensures the global optimum finding. Numerical validations of the proposed hybrid SCA-SOCP to optimal placement and sizing of DGs in AC distribution networks show its capacity to find global optimal solutions. Some classical distribution networks (33 and 69 nodes) were tested, and some comparisons were made using reported results from literature. In addition, simulation cases with unity and variable power factor are made, including the possibility of locating photovoltaic sources considering daily load and generation curves. All the simulations were carried out in the MATLAB software using the CVX optimization tool

Investigation of power grid islanding based on nonlinear Koopman modes

QC 20221026</p

Investigation of power grid islanding based on nonlinear Koopman modes

QC 20221026</p

The Equivalence between Successive Approximations and Matricial Load Flow Formulations

This paper shows the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach. Both formulations allow solving the load flow problem in meshed and radial distribution grids even if these are operated with alternating current (AC) or direct current (DC) technologies. Both load flow methods are completely described in this research to make a fair comparison between them and demonstrate their equivalence. Numerical comparisons in the 33- and 69-bus test feeder with radial topology show that both methods have the same number of iterations to find the solution with a convergence error defined as 1×10−10

Genetic-Convex Model for Dynamic Reactive Power Compensation in Distribution Networks Using D-STATCOMs

This paper proposes a new hybrid master–slave optimization approach to address the problem of the optimal placement and sizing of distribution static compensators (D-STATCOMs) in electrical distribution grids. The optimal location of the D-STATCOMs is identified by implementing the classical and well-known Chu and Beasley genetic algorithm, which employs an integer codification to select the nodes where these will be installed. To determine the optimal sizes of the D-STATCOMs, a second-order cone programming reformulation of the optimal power flow problem is employed with the aim of minimizing the total costs of the daily energy losses. The objective function considered in this study is the minimization of the annual operative costs associated with energy losses and installation investments in D-STATCOMs. This objective function is subject to classical power balance constraints and device capabilities, which generates a mixed-integer nonlinear programming model that is solved with the proposed genetic-convex strategy. Numerical validations in the 33-node test feeder with radial configuration show the proposed genetic-convex model’s effectiveness to minimize the annual operative costs of the grid when compared with the optimization solvers available in GAMS software

Data-Driven Trajectory Prediction of Grid Power Frequency Based on Neural Models

Frequency in power systems is a real-time information that shows the balance between generation and demand. Good system frequency observation is vital for system security and protection. This paper analyses the system frequency response following disturbances and proposes a data-driven approach for predicting it by using machine learning techniques like Nonlinear Auto-regressive (NAR) Neural Networks (NN) and Long Short Term Memory (LSTM) networks from simulated and measured Phasor Measurement Unit (PMU) data. The proposed method uses a horizon-window that reconstructs the frequency input time-series data in order to predict the frequency features such as Nadir. Simulated scenarios are based on the gradual inertia reduction by including non-synchronous generation into the Nordic 32 test system, whereas the PMU collected data is taken from different locations in the Nordic Power System (NPS). Several horizon-windows are experimented in order to observe an adequate margin of prediction. Scenarios considering noisy signals are also evaluated in order to provide a robustness index of predictability. Results show the proper performance of the method and the adequate level of prediction based on the Root Mean Squared Error (RMSE) index