Improved microgrid resiliency through distributionally robust optimization under a policy-mode framework

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Improved microgrid resiliency through

distributionally robust optimization under a

policy-mode framework

Nawaf Nazir

Energy and Environment Directorate

Paciﬁc Northwest National Laboratory

Richland, USA

nawaf.nazir@pnnl.gov

Thiagarajan Ramachandaran

Energy and Environment Directorate

Paciﬁc Northwest National Laboratory

Richland, USA

thiagarajan.ramachandaran@pnnl.gov

Soumya Kundu

Energy and Environment Directorate

Paciﬁc Northwest National Laboratory

Richland, USA

soumya.kundu@pnnl.gov

Veronica Adetola

Energy and Environment Directorate

Paciﬁc Northwest National Laboratory

Richland, USA

veronica.adetola@pnnl.gov

Abstract—Critical energy infrastructure are constantly under

stress due to the ever increasing disruptions caused by wildﬁres,

hurricanes, other weather related extreme events and cyber-

attacks. Hence it becomes important to make critical infrastruc-

ture resilient to threats from such cyber-physical events. Such

events are however hard to predict and numerous in nature

and type, making it infeasible to become resilient to all possible

cyber-physical event as such an approach would make the system

operation overly conservative. Furthermore, distributions of such

events are hard to predict and historical data available on such

events is sparse. To deal with these issues, we present a policy-

mode framework that enumerates and predicts the probability

of various cyber-physical events on top of a distributionally

robust optimization (DRO) that is robust to the sparsity of the

available historical data. The proposed algorithm is illustrated on

an islanded microgrid example: a modiﬁed IEEE 123-node feeder

with distributed energy resources (DERs) and energy storage.

Index Terms—Distributionally robust optimization (DRO),

cyber-physical events, critical infrastructure, extreme events,

data-driven methods

I. INTRODUCTION

Critical energy infrastructure has undergone signiﬁcant

changes in the past decades with the increased penetration

of distributed energy resources (DERs) and other inverter-

interfaced generation. While this has helped to achieve green-

house gas emission reduction goals [1], it has also made

the energy grid more vulnerable to breakdowns due to the

uncertainty and variability in renewable energy generation [2],

[3]. Furthermore, the risk of weather related outages such as

wildﬁres, hurricanes and other natural disasters have increased

in the past years [4] and so have the risk of possible cyber-

attacks [5]. This work provides a framework for improved re-

siliency of critical infrastructure systems, with an emphasis on

microgrid resiliency. Microgrids are a group of ﬂexible energy

The authors are with the Electricity Infrastructure and Buildings Division

at PNNL, Richland, WA 99354, USA.

resources operating together locally as a single controllable

entity [6]. In our framework, we assess the risk associated

with various cyber-physical events and based on the risk

assessment operate the system under a particular policy-mode.

This allows us to be resilient against the risks without being

overly conservative. Then in order to deal with the sparsity

of data available on such cyber-physical events, we develop a

distributionally robust optimization (DRO) formulation that is

robust to a range of disturbance distributions.

Literature review/related work: Chance constraints con-

stitute a means to provide certain guarantees on constraint

satisfaction under uncertainty [7] and have found applications

in several domains including in power system optimization

under uncertainty. However, a major drawback of chance con-

straint formulations is that they only consider the probability of

constraint violation and not the impact. In many critical infras-

tructure systems, minimizing the impact of uncertainties is far

more signiﬁcant. Conditional value at risk (CVaR) approaches

do account for the risk in constraint violation [8], however,

many of these methods require assumptions on the probability

distribution of the uncertainty and convex reformulations exist

only for a very small set of such distributions (e.g., Gaussian),

which may not hold in practice.

Distributionally robust chance constraint problems have

been well studied in the literature [9]. Even though, these

methods consider the risk in constraint violations, they can

often be overly conservative and furthermore still require

assumptions on the underlying distribution (e.g., moments)

to be accurate. In case the uncertainty distribution is not

known beforehand, sample based approaches have been used

in literature [10]. However, in case of rare events sampling

based approaches cannot be applied directly, since they would

require an impractical number of samples to yield reasonable

solutions [11], something which may not be available in

arXiv:2210.12586v2 [math.OC] 11 Mar 2024

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Improvedmicrogridresiliencythroughdistributionallyrobustoptimizationunderapolicy-modeframeworkNawafNazirEnergyandEnvironmentDirectoratePacificNorthwestNationalLaboratoryRichland,USAnawaf.nazir@pnnl.govThiagarajanRamachandaranEnergyandEnvironmentDirectoratePacificNorthwestNationalLaboratoryRichland,U...

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Improved microgrid resiliency through distributionally robust optimization under a policy-mode framework

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