Post-disruption performance recovery to enhance resilience of interconnected network systems

ABSTRACT

Mitigating the effect of disruptive events at the operating phase of complex systems therefore improving the systems’ resilience is an important yet challenging task. To improve the resilience, one way is to enhance the failure restoration capability with appropriate performance recovery strategies. However, considering different characteristics of disruptive events, the challenge is to develop a generally applicable framework to optimally coordinate different recovery strategies within a given budget. In order to tackle the challenge, this paper presents a post-disruption recovery framework for networked systems to optimize the performance. In this study, coordination of different recovery agents is achieved by using mathematical programming technique, while the assignment of the required resource for restoration is found by a heuristic algorithm. Case studies based on IEEE test feeders are used to demonstrate the feasibility of the developed framework, as well as the effects of optimal resource allocation nested in the restoration framework.

KEYWORDS:

• Resilience
• networked system
• disruption management

Nomenclature

Indices and Sets

$i,j$	=	Nodes index
$\mathbf{N}$	=	Set of nodes
${\mathbf{N}}_{\mathbf{G}}$	=	Set of candidate nodes that DER can connect to
$\mathbf{L}$	=	Set of edges (i, j)
${\mathbf{L}}_{\mathbf{t}}^{\mathbf{d}\mathbf{a}\mathbf{m}\mathbf{a}\mathbf{g}\mathbf{e}}$	=	Set of damaged edges at time t
$\mathbf{G}$	=	Set of DER g
$\mathbf{R}$	=	Set of RC r

Variables

${\alpha }_{i,t}^g$	=	Binary connection status of the DER
$a_{ij,t}^r$	=	Binary working status of the RC
${\eta }_{ij,t}^r$	=	Binary repairing status of the edge ij
${{\beta }_i}_{j,t}$	=	Binary ON/OFF status of the edge ij
${\mu }_{ij,t}$	=	Binary operable status of the edge ij
${\epsilon }_{ij,t}$	=	Binary ON/OFF status for fictitious edges
$f_{ij,t}$	=	Fictitious flow from i to j at time t
$o_{i,t}$	=	Binary load pick-up condition for node i
$G_{i,t}$	=	Power generation from the substation node
$P{g}_t{}^g$/$Q{g}_t{}^g$	=	Resource/reactive power outputting from DER g at time t
${P_i}_{j,t}$/${Q_i}_{j,t}$	=	Resource flow/reactive power flow from i to j
$P{g}_{i,t}$/$Q{g}_{i,t}$	=	Dispatched resource/reactive power generation at node i
$V_{i,t}$	=	Voltage at node i at time t
${\delta }_{i,t}$	=	Relaxation variable for DistFlow model

Parameters

$t{r}_{ij}{}^g$	=	Traveling time for DER g from node i to j
$t{r}_{l_1,l_2}^r$	=	Traveling time for RC r from edge 1 to 2
$trepai{r}_{ij}$	=	Repair time for the damaged edge ij
$N$	=	Number of nodes
${\overline{RC}}_r$	=	Assigned Capacity of the RC r
${\overline{Pg}}_g$/${\overline{Qg}}_g$	=	Assigned Capacity of the DER g
${\overline{flow}}_{ij}$	=	Capacity of the edge ij
${\bar{G}}_{i,t}$	=	Maximum generation from the substation node
${\bar{p}}_{i,t}$/${\bar{q}}_{i,t}$	=	Resource/reactive power load requirement at node i at time t
$r_i$/$x_i$	=	Resistance/reactance at node i
$w_i$	=	Priority weight of the load at node i
$\tau$	=	Scaling factor for the resource cost of DERs and RCs

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is partially supported by the National Science Foundation through the Faculty Early Career Development (CAREER) award (CMMI-1813111), and the Institute of Sustainability, Energy and Environment (iSEE) at The University of Illinois at Urbana-Champaign.

Notes on contributors

Jiaxin Wu

Jiaxin Wu is currently a Ph.D. candidate in the Department of Industrial and Enterprise Systems Engineering at University of Illinois at Urbana-Champaign. His research has been focused on developing novel design and operation strategies to improve the reliability and failure resilience of complex engineered systems, with applications in power systems.

Pingfeng Wang

Pingfeng Wang is currently an associate professor in the Department of Industrial and Enterprise Systems Engineering at University of Illinois at Urbana-Champaign. His research interests include engineering design for reliability and failure resilience, failure diagnostics, prognostics and health management. He is the recipient of the National Science Foundation CAREER award in 2014, the Young Researcher Award from International Society of Green Manufacturing and Applications in 2012, and the Young Investigator Award from ASME design automation committee in 2016. Dr. Wang is currently serving as the associate editor for ASME journal of mechanical design (JMD), and the review editor for the Springer journal of structural and multidisciplinary optimization (SAMO).