Enhancing Power Distribution Grid Resilience Against Massive Wildfires by Fei Teng B.S. in Automation, June 2018, North China Electric Power University A Thesis submitted to The Faculty of The School of Engineering and Applied Science of The George Washington University in partial satisfaction of the requirements for the degree of Master of Science August 31, 2020 Thesis directed by Payman Dehghanian Assistant Professor of Electrical and Computer Engineering
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Enhancing Power Distribution Grid Resilience Against Massive Wildfires
by Fei Teng
B.S. in Automation, June 2018, North China Electric Power University
A Thesis submitted to
The Faculty ofThe School of Engineering and Applied Science
of The George Washington Universityin partial satisfaction of the requirements
for the degree of Master of Science
August 31, 2020
Thesis directed by
Payman DehghanianAssistant Professor of Electrical and Computer Engineering
Shiyuan Wang, and Bo Wang, for making my time at the George Washington University a
wonderful experience.
Most of all, I am fully indebted to my parents for their support, without whom, the
pursuit of this advanced degree would never have been started and accomplished.
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Abstract
Enhancing Power Distribution Grid Resilience Against Massive Wildfires
In the past decades, wildfire hazards occurred more and more frequently. During summer
seasons in regions with high temperature, power distribution systems especially those located
near the forests are prone to wildfires. The temperature of conductor lines exposed to the fire
increases rapidly, the shape and strength of which are, therefore, permanently reduced. The
conventional reliability view is insufficient to cope with these challenges in modern power
systems since such hazards cause prolonged and extensive outages, much more severe than
those previously accounted for in system reliability assessments. Improving the resilience of
the power grid, hence, becomes increasingly important and urgent. To enhance the resilience
of the system against wildfires, the characteristics of wildfires need to be first studied so that
effective mitigation strategies, e.g., dynamic line rating of the overhead power lines, can be
proposed taking into account the impact of fires and the existence of uncertainties.
This thesis mainly focuses on designing an optimal operation strategy to minimize load
shedding when distribution lines are affected by wildfires. Taking the uncertainties related
to solar and wind – that influence the spread of wildfire and the renewable generators – into
account, a stochastic mixed-integer nonlinear programming model is proposed and applied
to a modified 33-bus power distribution system. The formulation aims to minimize the social
cost which associates with the status of each wind turbine and the energy storage systems.
By this means, the most effective operation strategy against wildfires is found, thereby
enhancing the grid resilience and reducing the load outages during and following wildfire
event. A sensitivity analysis is conducted on the overhead lines affected and the number of
active components in the system to further investigate the best mitigation approach in the
power distribution system when exposed to massive wildfires.
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List of Figures
1.1 Elements of Resilience by Electric Power Research Institute (EPRI) . . . . . 71.2 The conceptual resilience curve related to a HILP event . . . . . . . . . . . . 8
2.1 Wildfire causes from 2013 to 2017 . . . . . . . . . . . . . . . . . . . . . . . 112.2 Number of arcs burned by wildfires in the world during 1871–2020 . . . . . 122.3 Flow of events, causes, and preventive solutions . . . . . . . . . . . . . . . . 17
3.1 Linear relationship for convection heat loss in case of non-zero wind speed(T a=273k) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Piece-wise linearization of the radiation heat loss (T a=273k) . . . . . . . . 273.3 Weibull distribution of the wind speed . . . . . . . . . . . . . . . . . . . . . 283.4 Wind speed mean value and stochastic values . . . . . . . . . . . . . . . . . 283.5 Wind direction mean value during a 24-hour period . . . . . . . . . . . . . . 293.6 Solar radiation mean value and stochastic values . . . . . . . . . . . . . . . 293.7 Distance between the power line conductor and fire in different scenarios . . 303.8 Conductor heat gain rate from the fire in different scenarios . . . . . . . . . 31
4.1 Single-line diagram of the modified 33-node power distribution system . . . 334.2 Relationship between the output power of a wind turbine and the wind speed 354.3 Relationship between the output power of a PV and the solar radiation . . . . 364.4 Expected Load Shedding for 10, 50 and 100 Generated Scenarios . . . . . . 414.5 Expected energy exchange with the upstream system . . . . . . . . . . . . . 424.6 Power exchange price with the upstream system . . . . . . . . . . . . . . . . 434.7 Expected generated power and status of MTs . . . . . . . . . . . . . . . . . 434.8 Expected discharging power and SOC of ESS . . . . . . . . . . . . . . . . . 44
5.1 Objective function value: sensitivity analysis on every single line affected bywildfire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Expected load shedding when line 25 effected . . . . . . . . . . . . . . . . . 475.4 Objective function value when 2 lines are affected by wildfire . . . . . . . . 475.5 Expected load shedding when 2 lines are affected by wildfire . . . . . . . . . 485.6 Expected power exchange when 2 lines are affected by wildfire . . . . . . . 485.7 Objective function value when 3 lines are affected by wildfire . . . . . . . . 495.8 Expected load shedding when 3 lines are affected by wildfire . . . . . . . . . 505.9 Expected power exchange when 3 lines are affected by wildfire . . . . . . . 505.10 Objective function value when adding one distributed resource . . . . . . . . 515.11 Expected load shedding when adding one distributed resource . . . . . . . . 525.12 Expected power exchange when adding one distributed resource . . . . . . . 52
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List of Tables
1.1 Statistics of Outage Events in the U.S. Between 1984-2006 . . . . . . . . . . 21.2 The Conceptual Contrast Between Reliability and Resilience . . . . . . . . . 3
4.1 Location And Capacity of Distribution System Components . . . . . . . . . 344.2 Location and Capacity of Distribution System Components . . . . . . . . . 384.3 Simulation Results Concerning Different Number of scenarios . . . . . . . . 424.4 Revenues and costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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Nomenclature
A. Sets and Indices
i, j ∈ NB Indices/set of nodes.
i j Indices/set of distribution lines between nodes i and j.
t ∈ NT Indices/set of time periods.
(i, j) ∈ L Indices/set of branches.
NB,NT,NL Number of all nodes, time periods, and branches.
ω Indices/set of scenarios.
MT ∈M Set of all Micro Turbines (MTs).
ESS ∈M Set of all energy storage systems (ESSs).
S ∈M Set of all photo-voltaic panels (PV).
B. Parameters and Constants
B.1. Fire Model
T f Flame zone temperature (k).
L f Fire front length (m).
α f Fire tilt angle (rad).
ρb The bulk density of the fuel (kg/m3).
ε f Flame zone emissivity
B.2. Environmental Conditions
τ Dimensionless atmospheric transmissivity.
B Stefan-Boltzman constant (W/m2K4)
V wind Wind speed (m/s).
σwind Angle between the fire and power line conductors (rad).
T a Ambient temperature (k).
ka Thermal conductivity of air (W/mK).
µα Dynamic viscosity of air (kg/ms).
viii
ρα Density of air (kg/m3).
kindex Shape index of the Weibull distribution.
C Scale index of the Weibull distribution.
B.3. Conductor Specifications
mCp Total heat capacity of conductor (J/mK).
D Conductor diameter (m).
K Solar absorptivity.
φ sun Solar radiation rate (W/m2).
Ri j,a Ambient line resistance.
T max Conductor maximum temperature permitted (k).
B.4. Price and Costs
VoLL Value of lost load ($/MWh).
cD Price for selling electricity ($/MWh).
cMT Price for micro turbine generation ($/MW).
csu/sd Micro turbine switching cost ($).
B.5. Power Distribution System Components
Pdemandi,ω,t Real power demand at node i at time t (MW).
Qdemandi,ω,t Reactive power demand at node i at time t (MVar).
nST Conversion efficiency of energy storage systems.
EST Energy capacity of energy storage systems.
C. Functions and Variables
C.1. Fire Model
θf
i j,t View angle between fire and conductor line i j at time t (rad).
d fi j,t Distance between wildfire and the conductor line i j at time t (m).
V ft Fire spread rate (m/s) at time t.
Ti j,t Conductor temperature of overhead line i j at time t (k).
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φf
t Radiative heat flux at time t (W/m2).
C.2. Heat Gain and Loss
qlinei j,t Resistance heat gain rate of line i j at time t (W/m).
qsuni j,t Solar heat gain rate of line i j at time t (W/m).
q f irei j,t Fire heat gain rate of line i j at time t (W/m).
qconi j,t Convection heat loss rate of line i j at time t (W/m).
qradi j,t ) Radiation heat loss rate of line i j at time t (W/m).
C.3. Power System Model
pDi,t ,qDi,t Real and reactive demand supplied at node i at time t (MW, MVar).
Pp fi j,t ,Q
p fi j,t Real and reactive power flow on branch (i, j) at time t (MW, MVar).
SOCSTi,t SOC of ESS at time t.
pChi,ω,t , pDC
i,ω,t Charging and discharging power of ESS at node i at time t (MW).
pMTi,t ,qMT
i,t Real and reactive power output of MT at node i (MW, MVar).
PWTi,t ,PS
i,t Real power output of WT and PV at node i at time t (MW).
V sqri,t Squared voltage magnitude at node i at time t (kV2).
pshedi,t ,qshed
i,t Real and reactive load shedding at node i at time t (MW, MVar).
pUPt Active power exchange with the upstream system at time t (MW).
D. Binary Variables
αi j,t Connection status of branch (i, j) at time t
1 (1 if the branch is connected, 0 otherwise).
usoci,t Charging and discharging status of ESS at node i at time t
1 (1 if charging, 0 otherwise).
ui,t Status of MT at node i at time t
1 (1 if the MT is generating, 0 otherwise).
ϕUPt Buying or selling energy to the up stream network at time t
1 (1 if buying, 0 otherwise).
x
Chapter 1: Introduction
1.1 Problem Statement
Power grids, as the most complex man-made cyber-physical system to date, have been
traditionally designed and planned to operate reliably under normal operating conditions and
withstand potential credible outages. In the last decade, it has become more apparent that
further considerations beyond the traditional system reliability view are needed for keeping
the lights on at all times [1]. Table 1.1 shows the statistics of 933 power outage events,
reported by the North American Electric Reliability Corporation (NERC), between 1984
to 2006 [2]. Extreme weather events and natural disasters have relatively low frequencies,
but a greater impact on the electric power supply and a larger size of affected electricity
customers, among these outage cause categories. According to the statistics provided in [3],
a total of 178 weather disasters occurred from 1980’s to 2014 in the US alone with the
overall damages exceeding the US $1 trillion.
Due to the growing demand to ensure higher quality electricity to end customers and
particularly critical services, and intensified public focus and regulatory oversights, safe-
guarding the nation’s electric power grid resilience and ensuring a continuous, reliable, and
affordable supply of energy in the face of the high-impact low-probability (HILP) events
are among the top priorities for the electric power industry and has become more and more
critical to people’s well-being and every aspect of our increasingly-electrified economy. The
HILP events include two categories: (i) natural hazards, such as hurricanes, earthquakes
tornadoes, windstorms, wildfires, ice storms, etc.; (ii) man-made disasters, such as cyber or
physical attacks on the power system infrastructure. Here in this thesis, the focus will be on
the power grid resilience to wildfires [4].
Wildfire, similar to other natural disasters, is the one for which everyone pauses to listen
each time it appears on the news. Sadly, for some families wildfires represent the loss of
1
% of events Mean size in MW Mean size in customers
10 scenarios seem to be the best choice since the computation time is the least while
the results are similar to other cases. In the following sections, we will consider only 10
scenarios.
The expected energy exchange with the upstream network is presented in Figure 4.5.
Figure 4.5: Expected energy exchange with the upstream system
It is observed that until time 16, the power is only bought from the upstream system.
Considering the power exchange price in Figure 4.6, the reason is that the price of MT
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Figure 4.6: Power exchange price with the upstream system
generation (80$/MWh) is greater than the buying price from the upstream network before
time 16, and the system cannot balance with only renewable generators and ESSs. After
16 hours, the power exchange has a higher price; accordingly, to make most revenue the
power is generated by MTs and sold to the main grid as in Figure 4.7. At time 20, the energy
exchange cost is still higher than the cost of MTs, but the power is bought from the upstream
network to charge the ESSs to prepare for the outage of line 1-2.
Figure 4.7: Expected generated power and status of MTs
As shown in Figure 4.8, at the beginning of the day, ESSs are charging until time 16 to
maximize the revenue from selling energy to the customers and the upstream network. After
time 18, the discharging power is lower to save for later use when line 1-2 is in outage due
43
to the progressive wildfire.
Figure 4.8: Expected discharging power and SOC of ESS
Table 4.4 presents the load shedding cost, the revenue from selling energy to customers,
the cost of DGs and the cost of exchanging power with the upstream network.
Table 4.4: revenues and costs
Load shedding cost Revenue from customers Generation cost Power exchange cost
3.56 69.16 8.04 4.302.547 67.505 8.099 4.54
4.4 Conclusion
In this chapter, a stochastic mixed-integer linear programming model is developed consider-
ing the wildfire model with different series of scenarios. The proposed model is applied to
an IEEE 33-bus system and the social cost was set as the objective function. The results
show that the 10 scenario model is the proper one for further analysis considering the com-
putational complexity.The proposed optimization model provides the mitigation strategies of
a resilient operation of the power distribution system when facing an approaching wildfire.
44
Chapter 5: Sensitivity Analysis
5.1 Introduction
In this chapter, the proposed model and analysis data in Chapter 4 will be further studied to
investigate the sensitivity of the solutions to changes in each element in the system. Four
cases are studied to get a better understanding of the impact of wildfires on the system
operation and how to minimize the wildfire consequences considering possible uncertainties
in the system elements and how the fire progresses.
5.2 Case Study: Wildfire Affecting Different Overhead Power Lines
5.2.1 Case 1: Wildfire Affecting Different Single Lines
In Chapter 4, we assume that only line 1 (from node 1 to node 2) was threatened by the
approaching fire. In order to show how a wildfire affects different power line and to quantify
the impacts accordingly, in this section all 32 lines are set as possible targets affected
separately by a wildfire. The objective function value and the load shedding cost are shown
below in Figure 5.1. The results demonstrate that when power line 25 (connecting node 6 to
node 26) is out of service, the consequence load shedding is the maximum. This is because
the branch isolated from the system comprises only one ESS and one WT, the capacity of
which can not satisfy the total demand in the system.
This observation can be further supported by the detailed load shedding chart at each
node when line 25 is affected by wildfire in Figure 5.3.
5.2.2 Case 2: Wildfire Affecting Different Double Lines
In this case, the same model in Chapter 4 is applied to cases where the wildfire is considered
to affect two lines at the same time. These two lines need to be connected lines (adjacent).
45
Figure 5.1: Objective function value: sensitivity analysis on every single line affected bywildfire
Figure 5.2: Expected load shedding cost: sensitivity analysis on every single line affectedby wildfire
46
Figure 5.3: Expected load shedding when line 25 effected
Based on the results observed in Case 1, lines 1&2, lines 8&9 and line 22&23 are chosen as
three pairs of lines being affected by a the studied wildfire.
Figure 5.4: Objective function value when 2 lines are affected by wildfire
The objective function values of the base case 1 and case 2 are shown in Figure 5.4.
When the wildfire affect line 1&2, the social cost is the maximum value; this is mostly due
to the load shedding cost depicted in Figure 5.5. When lines 1&2 are affected, the branch
from node 2 to node 22 is separated from the system, and the only ESS left cannot meet
47
the demand, while in other cases, only the node between these two lines is effected. When
Figure 5.5: Expected load shedding when 2 lines are affected by wildfire
line 1 and line 2 are affected simultaneously by the fire, since line 1 is the line connecting
the system to the main grid, there is no energy exchange when it is out of service. In other
situations, the generators and storage systems connected with the separated (isolated) parts
cannot meet their demand, so the energy is always imported from the main grid as can be
seen in Figure 5.6.
Figure 5.6: Expected power exchange when 2 lines are affected by wildfire
48
5.2.3 Case 3: Wildfire affecting different three lines
Case 3 focuses on the situation when 3 lines are disconnected when wildfire approaches
the system. As discussed in case 2, these 3 lines are also connected (adjacent) lines. Line
1&2&3 and line 4&6&25 are the two scenarios selected here for analysis. Figure 5.7 depicts
the social cost in each situation.
Figure 5.7: Objective function value when 3 lines are affected by wildfire
In the first case, node 2 is isolated, while the rest of the DS is divided into two parts: the
individual distribution system, and a single branch from node 19 to node 22 supplied by the
ESS connected to node 19. Since the main grid is unavailable for the system, DGs and ESSs
are critical for maintaining the demand-supply balance. At node 11, only a PV is connected,
and the its capacity is not large enough compared with the demand; also, the ESS in the
isolated branch is not able to satisfy the demand. So the load has to be shed in nodes 2, 11,
19, 21, 27, and 30 (see in Figure 5.8). In the second case, node 6 is isolated, while the rest
part is separated into 3 parts: the upper part of node 5 which connects with the upstream
system, a microgrid system consisting of six generators from node 7 to node 18, 3 and a
branch from node 26 to node 33. The first 2 parts are able to supply the load demand while
49
the third part has only one ESS and one MT, so the nodes of this branch had load shedding
in this situation.
Figure 5.8: Expected load shedding when 3 lines are affected by wildfire
When line 1 is effected by the wildfire, there is no energy exchange with the upstream
network since it is the only transfer line. When other lines are affected, part 1 of the divided
system which connects with the main grid buys the energy from it continuously since it
cannot supply its demand by itself.
Figure 5.9: Expected power exchange when 3 lines are affected by wildfire
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5.3 Case Study: Modified IEEE 33-Node Distribution System with Different Num-
bers of DGs and ESSs
In this section, one more distributed resource is connected to the system. The capacity of
each element is the same as that in Chapter 4. The results are shown below compared with
those in the base case condition studied earlier. Only one element is added at each time, and
they are all connected to node 30.
Figure 5.10: Objective function value when adding one distributed resource
Considering the difference in the results obtained in each case, it is observed that much
less load shedding would be recorded in the system if a MT was connected. And the
generators and storage systems can decrease the load shedding in general.
The power exchange profile in each case is also shown in Figure 5.12.
When renewable generators are added, they can supply some demand so less power is
bought from the main grid before MT start up at hour 16 and more sold afterward. When
MT is added, it is not working until time 16 when the price of selling the electricity to the
upstream network is greater than the generation cost. After 16 hours, more energy is sold
making more revenue. When ESS is added to the system, more energy is bought at the
51
Figure 5.11: Expected load shedding when adding one distributed resource
Figure 5.12: Expected power exchange when adding one distributed resource
52
beginning for charging purposes while ESS discharging to the grid happens more toward the
end of the studied time horizon.
5.4 Conclusion
In this chapter, different numbers of lines are set out of service as a result of the progressive
wildfire, and DGs are added to the network to analyze their sensitivity and performance
when facing a wildfire. It is recognized that the spatial load shedding depends on the lines
affected by wildfire as well as the position, number, and type of generators and storage
systems in the network. The analysis of this chapter will help distribution system planners
and decision makers better decide on sizing and siting of distributed energy resources across
the network aiming to achieve an enhanced grid-support and resilience against wildfires
should they happen in the future. Future research could include the analysis of the system
in response to wildfires in the presence of different energy storage technologies and grid-
support resources [140–149].
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Chapter 6: Conclusion
6.1 Conclusion
With the recent increase in the frequency and intensity of wildfires around the world, and the
projection for a higher trend in the years to come, maintaining and enhancing the ability of
the power system to be resilient against such disruptions is a challenge. When the wildfire
approaches the power system, the thermal burden and stress is added and the affected
lines could allow less current flowing through them or even become out of service. It is
significantly important to efficiently and smartly exploit the available resources to minimize
the consequences of a wildfire, e.g., load shedding in the system. Dynamic Line Rating
is considered to model the thermal impacts of wildfires on power lines and a stochastic
mixed-integer linear program (MILP) optimization model is established aiming to minimize
the social cost of the system when exposed to a wildfire.
In Chapter 3, the wildfire hazard model and the associated uncertainties were presented.
Different numbers of scenarios were generated employing the normal distribution approach
to account for the extreme event uncertainty. The non-steady state heat balance constraint
was used to model the impact of wildfires on the temperature of power line conductors. The
results were considered as inputs in the following chapters.
In Chapter 4, the optimization model aiming to mitigate the impacts of a progressive
wildfire on the power distribution system was presented and studied. To explore the ef-
fectiveness of the suggested model, a base case was considered with fire progression. It
is observed that the resilient operation of the system can be achieved with reduced load
shedding and a lower social cost.
In Chapter 5, the impact of various factors in the optimization model was studied. The
same test system with the same wildfire model was optimized with different lines being
affected and different availability of distributed energy resources across the network. The
54
results revealed that the load shedding depends on the combinations of the position (spatial
factor) of the resources and lines being affected as the wildfire progresses (temporal factor).
6.2 Future Research
Future work may include investigating the combination of the thermal and physical influ-
ences of wildfires on the shape of overhead lines since the high temperature can cause sag
to the conductors. Future research may also include the contribution of flexible loads and
the interdependent services in the resilience evaluation of the system [150] and the repair
strategies in facilitating the power system restoration during the post-disaster outage scenar-
ios. Also, the role of intelligent electronic devices (IEDs) [151–156] as well as the existing
and next-generation sensors [157–167] on detecting and preventing the wildfire-triggering
events in power systems should be studied.
55
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