Visual Tool for Assessing Stability of DER Configurations on Three-Phase Radial Networks

Abstract

We present a method for evaluating the placement of Distributed Energy Resources (DER) on distribution circuits in order to control voltages and power flows. Our previous work described Phasor-Based Control (PBC), a novel control framework where DERs inject real and reactive power to track voltage magnitude and phase angle targets. Here, we employ linearized power flow equations and integral controllers to develop a linear state space model for PBC acting on a threephase unbalanced network. We use this model to evaluate whether a given inverter-based DER configuration admits a stable set of controller gains, which cannot be done by analyzing controllability nor by using the Lyapunov equation. Instead, we sample over a parameter space to identify a stable set of controller gains. Our stability analysis requires only a line impedance model and does not entail simulating the system or solving an optimization problem. We incorporate this assessment into a publicly available visualization tool and demonstrate three processes for evaluating many control configurations on the IEEE 123-node test feeder (123NF).

The Impact of Three-phase Impedances on the Stability of DER systems

“…at all nodes (see our previous work [11] for the moderl derivation). The PBC closed-loop system model is…”

“…The closed-loop dynamics matrix (A−BF ) depends on the controller gain matrix F and the impedance matrix B. In previous work [11] we designed F such that the eigenvalues of (A − BF ) are stable, because a stable PBC system results in asymptotic phasor tracking and optimal DER operation. Here, we aim to understand how the impedance properties of B affect the eigenvalues of (A − BF ).…”

“…3) Phase Ratio vs. Stabilizing Controller Gains: Next we isolate the effect of phase ratio (11) on the stability of the DER system. We set R ij = 0 ∀ i, j, X := X 11 = X 22 = X 33 , and X := X 12 = X 13 = X 23 .…”

“…The state space model of PBC indicates that eigenvalue stability, which results in convergence as proven in [11], is dependent on the controller gains, the DER locations, and the network line impedances. In [11] we explored the impact of DER locations on the DER system's stability. In this work we explore the impact of impedance properties.…”

“…Furthermore they drive the system to an optimal state, which allows for optimal (economic) operation of the DERs while satisfying distribution-level constraints. Phasor-Based Control (PBC), which is based on the tracking of voltage phasors [10], has been implemented with incremental volt-var control [11].…”