Scalable Assessment and Optimization of Power Distribution Automation Networks

Abstract

In this chapter, we present a novel state space exploration method for distribution automation power grids built on top of an analytical survivability model. Our survivability model-based approach enables efficient state space exploration in a principled way using random-greedy heuristic strategies. The proposed heuristic strategies aim to maximize survivability under budget constraints, accounting for cable undergrounding and tree trimming costs, with load constraints per feeder line. The heuristics are inspired by the analytical results of optimal strategies for simpler versions of the allocation problem. Finally, we parameterize our models using historical data of recent large storms. We have looked into the named storms that occurred during the 2012 Atlantic hurricane season as provided by the U.S. Government National Hurricane Center and numerically evaluated the proposed heuristics with data derived from our abstraction of the Con Edison overhead distribution power grid in Westchester county.

Appendices

Appendices

Appendix A: Survivability Model

We describe the survivability model already presented in [2], which is one of the building blocks of the proposed power distribution optimization approach. Figure 4 illustrates the model.

Fig. 4

Phased-recovery model characterizes recovery after failure in a set of sections of a line

Table 2 Table of parameters

As shown in Fig. 4, after a failure, the system transitions to one of three states depending on the availability of backup power, distributed generation, and communication. If communication is available, the system transitions to state 1 if backup power from a backup substation is available and to state 3 if distributed generation (e.g., from solar panels) will be tried. These transitions occur with rates $\hat{p} \hat{q}/\varepsilon$ and $\hat{p} (1-\hat{q})/\varepsilon$, respectively. From state 1, the system is amenable to automatic restoration, which produces a transition to state 5. In state 5, manual repair is required in order to finalize the repair procedure. Manual repair occurs with rate $\delta$. From state 3, distributed generation is activated with rate $\beta \hat{r}$. In case of success, the system transitions to state 2. In state 2, automatic repair occurs at rate $\alpha '$. Note that in case communication is not available after the failure, it is restored with rate $\gamma$, and the system transitions to states 1 if a secondary backup path is available and to state 3 otherwise. In any other state, the system is also amenable to manual repair, which occurs at rate $\delta$.

We use the model in Fig. 4 to compute the survivability metric of interest, namely average energy not supplied (AENS). To this end, we parametrize the model using the constants presented in Table 2. The default values of the parameters are set based on expert knowledge. Note that $\hat{q}$ and $\hat{r}$ are additional parameters of the model, which are derived from the probabilities of section failure as explained in [2, Sect. 4.4]. In order to compute the expected energy not supplied, to each state prior to repair in the model we associate reward rates, which are the expected energy not supplied per time unit at that state. These reward rates are derived from the probabilities of section failure and the section loads as explained in [2, Sect. 4.4]. Thus, the inputs to the survivability model for use in this chapter are the probability of failure in each section and the average load in each section.

Appendix B: Algorithm Pseudocode

Algorithm 1 shows the pseudocode of the optimization solution discussed in Sect. 4.2.