Inversion Reduction Method for Real and Complex Distribution Feeder Models

Abstract

The proliferation of distributed generation on distribution feeders triggers a large number of integration and planning studies. Further, the complexity of distribution feeder models, short simulation time steps, and long simulation horizons rapidly render studies computational burdensome. To mend this issue, we propose a methodology for reducing the number of nodes, loads, generators, line, and transformers of p-phase distribution feeders with unbalanced loads and generation, nonsymmetric wire impedance, mutual coupling, shunt capacitance, and changes in voltage and phase. The methodology is derived on a constant power load assumption and employs a Gaussian elimination inversion technique to design the reduced feeder. Compared to previous work by the authors, the inversion reduction takes half the time and voltage errors after reduction are reduced by an order of magnitude. Using a snapshot simulation the reduction is tested on six additional publicly available feeders with a maximum voltage error 0.0075 p.u. regardless of feeder size or complexity, and typical errors on the order of 1×10 −4 p.u. For a day long QSTS simulation on the UCSD A feeder, errors are shown to increase with changes in loading when a large number of buses removed, but shows less variation for less than 85% of buses removed.

Aggregation of Voltage-Controlled Devices During Distribution Network Reduction

“…A. Overview of method derived in reference [7] Circuit reduction creates an equivalent smaller feeder of critical buses (CBs) by removing other (non-critical) buses. Critical buses are generally selected by the user, typically as a set of buses which are the focus of the analysis.…”

“…The inversion reduction technique described in this section was proposed and validated in [7] for real multi-phase distribution feeders. In Section III, we will improve and extend the generality of this method to consider voltage-controlled devices.…”

“…However, the methodology introduced in sections III and IV is independent of the inversion reduction technique, and can be applied generally to any network reduction technique which aggregates power injection devices. Rather, the method in [7] is chosen as it represents an ongoing effort by the authors.…”

“…Reference [7] introduced the inversion reduction technique, which improves on the methods of [4,6] in speed and accuracy and allows for the reduction of static capacitors and transformers, in addition to loads, PV systems, and distribution lines. Thus, only a minimal number of buses needs to be retained.…”

Reduced Modeling of Unbalanced Radial Distribution Grids in Load Area Framework

“…In [12], a network segment between two relevant busses is replaced by a two-port non-linear network; many busses have to be kept in the reduced model which is not the case in the current study. In [13], admittance matrix inversion is required for both the original and reduced network, and there is a choice to be made for the reduced impedance matrix as it is not unique; in the present study, there is no matrix inversion and no choice is required.…”