Resilient Disaster Recovery Logistics of Electrical Distribution - - PowerPoint PPT Presentation

Resilient Disaster Recovery Logistics of Electrical Distribution Systems: Resource Dispatch and Microgrid Operation

Shunbo Lei Electrical Engineering & Computer Science, University of Michigan, Ann Arbor December 26, 2019 @ HUST

Outline

• Background & motivation
• Problem statement: “disaster recovery logistics”
• A two-stage framework
• Models, algorithms & case studies
• Conclusions
• Current & future research

Background & motivation

• Significant power outages
• Outage scale: numerous affected consumers (millions of people)
• Outage duration: prolonged electric service disruption (even for days
• r weeks [GridWise Alliance, NERC, etc.])
• For island power systems
• Coastal cities/bases threatened by typhoon, etc.

Observed Outages to the Bulk Electric System (Source: Energy Information Administration) News clipping from Macau

• n 23 Aug 2017. Five people

died, at least 153 were injured and two were still missing in Macau on Wednesday night, while the city also endured a power shutdown for several hours, after Typhoon Hato battered the former Portuguese enclave.

Background & motivation

• The concept of “resilience”
• Different definitions
• Same essence: guarantee electricity supply against low-probability but

high-impact natural disasters, extreme weather events, etc.

• Three elements of resilience [EPRI]
• Prevention: the application of engineering designs and advanced

technologies that harden the distribution system to limit damage

• Recovery: the use of tools and techniques to quickly restore service to

as many affected customers as practical

• Survivability: the use of innovative technologies to aid consumers,

communities, and institutions in continuing some level of normal function without complete access to the grid

Electric Power Research Institute of U.S., “Enhancing Distribution Resiliency: Opportunities for Applying Innovative Technologies,” 2013.

• Outage management of distribution systems
• Why distribution systems? → account for 70% power interruption
• A clarification: rapid restoration also enhances survivability
• Restoration decisions
• Switching actions: network topology, load pick-up, etc.
• Routing and scheduling of crews: repair damaged components,
• perate manual switches, etc.
• Other flexibilities: distributed generations, demand response, etc.

Problem statement: “disaster recovery logistics”

• Typical restoration process
• Especially effective for single-fault outage scenarios

Problem statement: “disaster recovery logistics”

2 3 4 5 1 6 7 8 2 3 4 5 1 6 7 8 2 3 4 5 1 6 7 8 2 3 4 5 1 6 7 8 2 3 4 5 1 6 7 8 2 3 4 5 1 6 7 8 (a) (b) (c) (d) (e) (f) Closed branch Open branch Load Breaker Closed switch Open switch

(a) fault occurrence (b) post-fault state (c)-(f) fault location fault isolation service restoration (f) post-restoration state After that: repair damaged component & return to normal state

• Response/restoration against extreme weather events
• More damages
• More resources (more repair crews, and transportable/mobile power

sources for isolated outage areas, etc.)

• More interdependent/coupled system (mobile power sources deliver

power via power grid and also transportation network; etc.)

• Other issues, e.g., more time periods, different time-scales

Problem statement: “disaster recovery logistics”

RC dispatch MPS dispatch DS restoration Co-optimization need coordination better improves improves improves interdependence interdependence Disaster recovery logistics

Route repair crews and mobile power sources in the transportation network, schedule them in the distribution system, and

• perate the distribution

system, in an efficient and coordinated manner, for electric service restoration.

• Resilience level as a function of time with respect to an event
• Survivability: R at [te, tr] (especially Rpe at [tpe, tr]) → Resourcefulness
• Recovery: R at [tr, tpir] → Optimal dynamic dispatch of resources

(including: repair crews, mobile power sources, and the power grid)

A two-stage framework

• M. Panteli, and P. Mancarella, “The Grid: Stronger, Bigger, Smarter?—Presenting a Conceptual Framework of Power System

Resilience,” IEEE Power and Energy Magazine, vol. 13, no. 3, pp. 58-66, May/Jun., 2015.

A two-stage framework

• An important strategy: microgrid formation
• Two stages: pre-positioning & dynamic dispatch of resources

Natural disaster strikes Pre-positioning Dynamic disaptch

Timeline

Weather forecasting and monitoring Distribution system and road network damage assessments

Week/days ahead Days/hours ahead Minutes/hours/days afterwards

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

PI 1 PI 2 PI 3 PI 4

To form a microgrid, it needs a power supply, and some topology control. Mobile power sources: supply power Repair crews and distribution switches: topologize the distribution network Pre-positioning of mobile power sources: enhance resourcefulness, so as to enhance survivability. Coordinated with: proactive network reconfiguration, so as to attain a state less impacted/stressed by the event. Dynamic dispatch of all resources: dynamically form microgrids, which are powered by mobile power sources, and topologized by repair actions of repair crews and switching actions of distribution network; and, at the same time, gradually return to normal state.

A two-stage framework

• Enhanced survivability and recovery
• Survivability enhancement: left shaded area
• Recovery enhancement: right shaded area

te tpe tr tpr tir tpir Time R

R0 Rpe

pr

R' Rpr

pe

R'

R1: Solely conventional restoration R2: Coordinated w/ dispatch of MPSs & RCs

t0 tpir

'

Resilience level By the way: In this work, we measure the resilience level by the weighted sum of supplied loads:

• Pre-positioning of mobile power sources

Models, algorithms & case studies

Outermost level Middle level Inner- most level

• Two-stage robust optimization

Pre-position mobile power sources Radiality constraints (proactive network reconfiguration) Maximum number of damages (uncertainty budgets) Real/reactive power balance Real/reactive power capacities of mobile power sources Load pick-up Power flow limits on branches DistFlow model Voltage limits

• Pre-positioning of mobile power sources
• Column-and-constraint generation algorithm

Models, algorithms & case studies

Compact form: Master problem (MP): Sub-problem (SP):

• Pre-positioning of mobile power sources
• Case I: IEEE 33-node test system

Models, algorithms & case studies

MESS stations: truck-mounted mobile emergency generators (MEGs) and mobile energy storage systems (MESSs) Charging stations: medium-duty electric vehicles (EVs) Connecting nodes of mobile power sources in pre-positioning, & network topology (EV fleet: two 150kW/150kWh electric buses MESS: 500kW/776kWh MEG: 800kW/600kVar) Statistics of 10,000 Monte Carlo simulations Enhanced survivability, especially when coordinated with proactive network reconfiguration.

• Pre-positioning of mobile power sources
• Case II: IEEE 123-node test system

Models, algorithms & case studies

(EV fleets: two 150kW/150kWh electric buses *2 MESSs: 500kW/776kWh *2 MEGs: 800kW/600kVar *2) Again, enhanced survivability, especially when coordinated with proactive network reconfiguration. Statistics of 10,000 Monte Carlo simulations Connecting nodes of mobile power sources in pre- positioning, & network topology

• Coordinated dynamic dispatch of available resources

(repair crews, mobile power sources & the power grid)

• Routing and scheduling of repair crews

Models, algorithms & case studies

Visit at most 1 damaged component at each time Scheduling Routing Required repair time of damaged components Remain intact once repaired A damaged component: repaired by only 1 crew Resource capacity of repair crews Travel time of repair crews between damaged components Formulation of routing behaviors: Proposed formulation V.S. Traveling salesman problem based formulation

• 1. Straightforward & simple (structurally equivalent to min up/down in UC)
• 2. Resolve coupling of transportation-power networks & their different timescales
• 3. More flexible and adaptive

• Coordinated dynamic dispatch of available resources

(repair crews, mobile power sources & the power grid)

• Routing and scheduling of mobile power sources

Models, algorithms & case studies

Routing & travel scheduling Power scheduling Real/reactive power outputs of MEGs Charging/discharging behaviors of MESSs Reactive power outputs of MESSs State-of-charge variations and limits of MESSs

• Coordinated dynamic dispatch of available resources

(repair crews, mobile power sources & the power grid)

• Dynamic network reconfiguration (microgrid formation) and load

pick-up of the distribution system

Models, algorithms & case studies

(a) Spanning tree (common distribution network reconfiguration) (b) Spanning forest (microgrid formation) Removing edges from a spanning tree leads to a spanning forest: Simpler More straightforward More adaptive Distribution system operational constraints

• Some graph-theoretic prerequisites
• Spanning Tree v.s. Spanning Forest
• A spanning forest with k components: a k-tree
• For a DS with k1 substation:
• Conventional DS reconfiguration → a k1-tree with each component

having one substation

• Resilient DS reconfiguration → a k2-tree with k2 ≥ k1 and each

component having at most one substation

Proposed radiality model

Topology issues in resilient DS reconfiguration: require the DS network to be a spanning forest.

Proposed radiality model

Remark 1 specifies that any α satisfying the above constraints is topologically feasible. The following theorem further indicates that any topologically feasible α satisfies the above constraints.

Sufficient condition Sufficient condition

• Compared with 2 other new radiality models

Proposed radiality model

• A. Arif, S. Ma, and Z. Wang, “Dynamic reconfiguration and fault isolation for a self-healing distribution

system,” in Proc. IEEE/PES Transm. and Distrib. Conf. and Expo., Denver, CO, USA, Apr. 2018, pp. 1–5.

• S. Ma, S. Li, Z. Wang, and F. Qiu, “Resilience-oriented design of distribution systems,” IEEE Trans. Power

Syst., in press (early access).

• Solving a integer programming (IP) mixed-integer

programming (MIP) problem

• Branch-and-bound, branch-and-cut methods, etc.
• Linear programming relaxations (LP relaxations)
• Tightness
• Similarity of the feasible regions of the IP/MIP and its LP relaxation

→ Gap between their optimal values (solutions)

• Tightest formulation: convex hull
• Compactness
• Number of variables

and constraints → Computation time

• f each iteration

Tightness & Compactness Issues

Tightness & Compactness Issues

• Explicit formulation of constraint (1)
• Characteristic/incidence vectors of spanning trees
• Spanning tree constraints
• Spanning tree polytope (convex hull)

Tightness & Compactness Issues

• Revisiting different types spanning tree constraints
• Loop-eliminating method (NP-hard): subtour elimination formulation
• Path-based method (NP-hard): directed cutset formulation
• Parent-child relation-based method: extensively used, but incorrect
• Primal & dual graphs-based model: has a flaw
• 2 new formulations: polynomial size to define spanning tree polytope

Tightness & Compactness Issues

• Directed multicommodity flow-based model
• Easy/straightforward extension of the most commonly-used

single-commodity flow-based model

Tightness & Compactness Issues

• Extended multicommodity flow-based model
• Compared with the previous model: eliminating variables λij
• Less binary variables, more constraints

Tightness & Compactness Issues

• Tightness and compactness of constraint (1)-(2)
• Generally follow the tightness and compactness of constraint (1)
• Cover the a wide spectrum of tightness and compactness

Application to microgrid formation

• A new microgrid formation optimization model
• Involved in almost all resilience-enhancing service restoration

and/or infrastructure recovery optimization problems Expansibility

• Compared with 2 commonly-used models
• Flexibility & Adaptivity
• Application convenience & Applicability, etc.

Application to microgrid formation

[16] C. Chen, J. Wang, F. Qiu, and D. Zhao, “Resilient distribution system by microgrids formation after natural disasters,” IEEE Trans. Smart Grid, vol. 7, no. 2, pp. 958–966, Mar. 2016. [17] T. Ding, Y. Lin, G. Li, and Z. Bie, “A new model for resilient distribution systems by microgrids formation,” IEEE Trans. Power Syst., vol. 32, no. 5, pp. 4145–4147, Sep. 2017. I II III I: Feasible region of the model in [16] II: Feasible region of the model in [17] III: Feasible region of the proposed model

• Coordinated dynamic dispatch of available resources
• The co-optimization objective
• Coupling between the distribution system & repair crews
• Coupling between the distribution system & mobile power sources

Models, algorithms & case studies

max weighted sum of restored loads min sum of travels of repair crews & mobile power sources A damaged component is operable only if it is repaired by one of the repair crews. Power outputs of distribution nodes depend on the connection of mobile power sources.

• Coordinated dynamic dispatch of available resources
• Linearization technique: McCormick envelopes
• Pre-assign a minimal set of repair tasks to repair crews
• Reduce the number of candidate nodes for connecting mobile power

sources

Models, algorithms & case studies

• Coordinated dynamic dispatch of available resources
• Case I: IEEE 33-node test system

Models, algorithms & case studies

Dynamically form microgrids (powered by mobile power sources, reconfigured by switching actions, extended by repairing actions.) Gradually return to the normal state

• Coordinated dynamic dispatch of available resources
• Case II: IEEE 123-node test system

Models, algorithms & case studies

• Conclusions
• Resources pre-positioning → Resourcefulness → Survivability
• Coordination/co-optimization of resources dispatch → Recovery
• Microgrid formation → Survivability & Recovery

Conclusions

• A more generalized/practical/applicable framework for

distribution system disaster recovery logistics (dispatch drone/crew dispatch for damage assessments by finding/constructing the Euler path, etc.)

• Hardening of the system, to enhance damage “prevention”
• Technical issues in microgrid formation (voltage/frequency

regulation, etc.)

Current & future research

Thank you!