This paper presents a three-phase power-flow algorithm, in the sequence-component frame, for the microgrid (μgrid) and active distribution system (ADS) applications. The developed algorithm accommodates single-phase laterals, unbalanced loads and lines, and three/four-wire distribution lines. This paper also presents steady-state sequence-component frame models of distributed energy resource (DER) units for the developed power-flow approach under balanced/unbalanced conditions. The DER models represent the synchronous-generator based and the electronically-coupled DER units. Both constant power (PQ) and regulated-voltage (PV) modes of operation of DER units are considered. The application of the developed power-flow method for two study systems is presented. The study results are validated based on comparison with the detailed solution of the system differential equations in time domain, using the PSCAD/EMTDC software tool.

https://www.engr.colostate.edu/academic/ece/graduate_exams/grad_exams/Panwar.pdf

Unbalanced Model and Power-Flow Analysis of Microgrids and Active Distribution Systems

In power transmission systems, the false data injection (FDI) attacks against state estimation (SE) have been well studied. However, due to the unique features of power distribution systems including: the low x/r ratio, existence of one-and/or two-phase branches, unbalanced load distributions, and unsymmetrical line parameters; the research on FDI attacks against distribution system SE (DSSE) is still open. In this paper, we investigate the vulnerability of DSSE to FDI attacks. In particular, we first propose a local state-based linear DSSE for multiphase and unbalanced smart distribution systems, which can facilitate the construction of FDI attacks numerically with the least information of system states. Then, the construction of three-phase coupled FDI attacks is introduced. The consideration of the coupling among phases by the three-phase coupled FDI attacks may require the modification of a large number of measurements by the attackers. To reduce the number of required measurements, the perfect three-phase decoupled FDI attacks, which consider the weak couplings among phases, is investigated. The probabilities of successful three-phase decoupled FDI attacks in strongly three-phase coupled systems are also derived numerically. The performance of the proposed FDI attacks against DSSE is evaluated based on IEEE test feeders. The case study results indicate the feasibility of the FDI attacks against DSSE in practical multiphase and unbalanced smart distribution systems. Future research directions including potential countermeasures are also highlighted.

False Data Injection Attacks Against State Estimation in Multiphase and Unbalanced Smart Distribution Systems

Analysis of power systems is typically made using the method of either phase coordinates or symmetrical components depending on the type of network (un/symmetrical). The use of the symmetrical components method, a three-phase specific application of the Fortescue transformation, has been limited to pure three-phase symmetrical networks. Therefore phase coordinates has been the method used most for the analysis of distribution networks. This paper is extending the use of the symmetrical components method to distribution networks combining one-phase, two-phase, and three-phase symmetrical network parts. This paper derives a new integrated approach for the description of such networks based on Fortescue transformation. This approach is demonstrated using the forward-backward sweeping algorithm (FBS).

Three-phase power flow in distribution networks using Fortescue transformation

Power Flow solutions based on Fortescue's Method of Symmetrical Components have been so far limited only to three-phase transmission networks. Complete network solution could be reached only by applying standard methods based on phase coordinate system. This paper shows that it is possible to apply Fortescue's General Transformations for power flow solution on complete network. Special matrices for handling distribution network configurations are derived. Presented approach offers greater computational performances when solving power flow problem in distribution networks.

Fortescue Transformations for three-phase power flow analysis in distribution networks

This paper develops a generalized admittance matrix approach in Fortescue coordinate system to solve unbalanced/unsymmetrical distribution networks including different number of phases. This generalized Fortescue π equivalent is defined in this paper for solving the heterogeneous phase, and thus Fortescue, network model. The performance of the approach is demonstrated in different model networks with number of nodes ranging between 168 and 14200. It is found that the current iteration method exploiting the decoupling in admittance matrix in Fortescue coordinate is substantially faster than the typical unbalanced three-phase solution in phase domain. The method has a significant potential for application in real time active power network management.

Generalized $\pi$ Fortescue Equivalent Admittance Matrix Approach to Power Flow Solution

This paper presents a new power-flow method for analyzing unbalanced distribution networks. In this method, an unbalanced distribution network Is decomposed to: 1) main three-phase network with three-phase line segments and 2) unbalanced laterals with two-phase and single-phase line segments. The proposed method allows solving the main three-phase network based on the decoupled positive-, negative, and zero-sequence networks. The unbalanced laterals are solved using the forward/backward method In phase components. The solution process Involves three main steps. Firstly, In phase components, the backward step Is executed to calculate an equivalent current Injection for each unbalanced lateral. Secondly, the main three-phase network Is solved In sequence components. The standard Newton-Raphson and fast decoupled methods are used for solving the positive-sequence network whereas the negative- and zero-sequence networks are represented by two nodal voltage equations. Finally, In phase components, the forward step Is performed to update the voltages In the unbalanced laterals. The three-steps are repeated till convergence happen. Distribution network characteristics such as line coupling, transformer phase shifts, voltage regulators, PV nodes, capacitor banks, and spot or distributed loads with any type and connection are considered. Solution of unbalanced radial feeders shows that the proposed hybrid algorithm Is accurate.

Development of unbalanced three-phase distribution power flow analysis using sequence and phase components

In this paper, the harmonic penetration method is developed as a component-based application The direct nodal voltage harmonic solution is developed as an independent software component and then integrated with existing three-phase power-flow software components The harmonic solution reuses many facilities available in the fundamental frequency power-flow object components The nonlinear devices such as six pulse converters are modeled as entity objects and inherited from the basic object-oriented power-system device model at fundamental frequency Also, the linear solver also is reused form the power-flow component library The application of object components shows that the development of complicated algorithms becomes easy due to the high code reusability

A.-H. Abdul-Rashid

Papers

Development of unbalanced three-phase distribution power flow analysis using sequence and phase components

Reusing Three-Phase Power-Flow Object Components for Unbalanced Harmonic Analysis