The Private and Social Value of Blackout Risk Reduction
Anand Govindarajan, Pennsylvania State University, Phone +1 814 865 3437, E-mail: axg5179@psu.edu
Seth Blumsack, Pennsylvania State University, Phone +1 814 863 7597, E-mail: sethb@psu.edu
Abstract
Combined heat and power (CHP) systems provide a mechanism for individual electricity
customers to generate energy locally rather than drawing from the power grid. During periods of
normal operation this provides an energy savings benefit to CHP-enabled electricity customers,
which has been well-discussed in the existing literature. We focus on another important source of
benefits, namely those related to decreasing or avoiding the costs associated with power
blackouts. These system benefits have both a “private” component that accrues to the CHP
owner/operator and a “social” component that accrues to all other grid-connected customers.
When blackouts do occur, CHP-enabled customers will be able to continue to receive electric
service from local generation, provided that fuel supplies are not interrupted. This is the private
benefit accruing to the CHP owner/operator. If CHP units are deployed at scale and operated in
such a way as to decrease stress on power grids during times of peak demand, these CHP units
provide a risk-reduction service to the grid as a whole (the “social” benefit) by reducing the
probability of blackouts occurring. Using the Mid-Atlantic power grid as a case study, we use
historical blackout data to estimate season-specific blackout risk as a function of total demand
for grid-provided power and estimate the risk reduction associated with a modest deployment of
CHP throughout the Mid-Atlantic region. Our analysis suggests that deployment of 1,000
building-integrated CHP units in the Mid-Atlantic would confer benefits of $2 million to $2.5
million per year to CHP owners. We estimate social benefits, in the form of blackout risk
reduction, amount to $14 million to $40 million per year. The magnitude of these benefits is
most sensitive to how building-integrated CHP units are operated.
1
1. Introduction
Distributed generation (DG), including Combined heat and power (CHP), is being looked
up as an alternative to the current structure of power grids with increased use of local generation
near demand centers. Recent electrical blackouts caused by extreme weather events (such as
Hurricane Sandy in 2013) and by the continued overloading of an aging electrical grid (the
August 2003 blackout affecting much of the U.S. Midwest and Northeast) have reinforced the
role that distributed power generation (DG) can play in “energy surety” or “survivability” – the
ability of energy systems to continue delivery services in the face of extreme events.
CHP is the onsite generation of electricity from generators (primarily fueled by natural
gas) where the coproduced heat is captured and used for site specific purposes like room heating,
water heating etc. CHP systems are highly efficient compared to the conventional method of
delivering power through the grid1. Typical CHP systems power single-user buildings or a group
of buildings in case of a shared micro-grid. Since the same fuel source is used to generate heat
and power, CHP can be beneficial economically and environmentally.
The onsite generators can also act as a back-up source of power during blackouts and
provide continuous supply of power and heat/cooling to the site. Facilities which had installed
CHP systems were able to continue normal operations during the August 14, 2003 blackout (Oak
Ridge National Lab 2012) and power outages caused by Hurricane Sandy (ICF International
2013). Most of these facilities had invested on black start (and other services) to operate CHP
independent of the grid. Both of these studies concluded that CHP was effective in providing
1
CHP Basics, U.S Department of Energy http://www1.eere.energy.gov/manufacturing/distributedenergy/chp_basics.html
2
continuous supply of power to the sites during blackouts. An interesting finding (as stated by
CHP owners) was that the reliability benefit was more significant than the operational costs
reduction from CHP.
Several studies have examined and quantified the peak shaving benefits, savings from
reduced operational costs and emission reduction benefits of CHP (King and Morgan 2007; P. J.
Mago, Fumo, and Chamra 2009; P.J. Mago and Chamra 2009; Pedro J. Mago and Smith 2012;
Maidment, Zhao, and Riffat 2001; Siler-Evans, Morgan, and Azevedo 2012; Strachan and Farrell
2006; Ziher and Poredos 2006). Our work has focused on quantifying the reliability benefit
associated with increased CHP deployment. There are two such benefits. First, the owners of
installed CHP units benefit because the CHP unit can act as a source of backup power during a
blackout. We refer to this as the “private” reliability benefit since it accrues only to the CHP
owner (or owners, in the case of a shared or district system). Second, with sufficiently large
deployment levels CHP investments themselves may reduce the likelihood of a blackout
occurring. Blackouts are more likely to be instigated during times when the electrical grid is
under stress, and removing demand from the grid (onto local CHP systems) can reduce this
stress. We refer to this as the “social” benefit of CHP since it accrues to others besides the CHP
owner (i.e., anyone on the grid that would benefit from avoiding a blackout), and the CHP owner
is not compensated by those who benefit. In other words, there is a “positive network
externality” associated with blackout risk reduction via CHP installation decisions.
Our approach integrates four separate modelling components: An econometric model of
blackout risk in the Mid-Atlantic region (the PJM transmission grid); an econometric model of
locational electricity prices within PJM; a simulation model of building-integrated CHP
operation; and building energy models that generate electricity demands for commercial
3
buildings with and without integrated CHP. Each of these modelling elements is described
briefly below:
(1)
Our econometric model for blackout risk is estimated using a rare-events logit
approach, using data on reported blackouts within the PJM region reported to the U.S.
Department of Energy (excluding those related to extreme weather) and data from PJM on
historical hourly system loads. We estimate a rare-events logit model that estimates the
likelihood of a blackout being initiated in each hour as a function of electric loads in PJM and
temporal characteristics such as seasons and time of day. (We compare our results from the rareevents logit model with those of a conventional logit model and find few differences in estimated
blackout probabilities.) We also estimate an econometric model for blackout duration as a
function of blackout size (customers affected) and temporal variables.
(2)
Locational electricity prices within PJM are estimated using the econometric
approach developed in Sahraei-Ardakani and Blumsack (2014), which estimates locational
supply curves within regional power grids that accounts for spatial differences in fuels utilization
and congestion on the electric transmission grid. This model utilizes hourly demand and pricing
data from PJM, as well as fuel prices from the U.S. Energy Information Administration.
(3)
CHP usage profiles are developed for specific commercial building types using
the BCHP tool available from the U.S. Department of Energy.
(4)
Building energy profiles with and without CHP are developed using the BCHP
tool and a building-integrated CHP assessment approach from the Berkeley National Laboratory.
4
Our overall modelling approach is to estimate baseline hourly blackout risk and
locational electricity price profiles for the PJM region. We then simulate hourly energy profiles
for up to 1,000 commercial buildings in PJM with and without integrated CHP systems. As more
buildings add CHP systems, these customers save on electricity costs and the building energy
loads removed from the grid will lower wholesale power prices. These two effects together
constitute the private benefit of CHP adoption by commercial buildings. Removing loads from
the grid and placing them on CHP also reduces the risk of blackouts, which amounts to the social
value in our study. This social value of blackout risk reduction is monetized using an approach
suggested by Sullivan, et al. (2010).
We find that a modest level of CHP deployment, relative to the overall size of the PJM
market as a whole, can yield blackout risk reduction benefits to the PJM system as a whole
amounting to between $14,000 and $40,000 annually for each CHP unit. This social reliability
benefit is roughly an order of magnitude larger than the private reliability benefit that we
estimate. Moreover, the estimated private reliability benefit (based on blackout costs from the
existing literature) is several times smaller than the benefit associated with avoided energy
purchases. These findings suggest that potential CHP adopters should not be influenced by their
private reliability benefits but that a side payment or subsidy based on the social blackout risk
reduction would be appropriate.
2. Modeling the likelihood and expected duration of blackouts in PJM
The U.S electricity grid operates at high reliability and power outage events are relatively
infrequent. But, the complex structure of power grids makes it vulnerable to failures. Historical
data suggests that occurrence of blackouts have increased over time (Hines, Apt, and Talukdar
5
2009; Simonoff, Restrepo, and Zimmerman 2007). Blackout events are instigated when there is a
disturbance in the power system because of hurricanes or storms, equipment failures, targeted
attack on the infrastructure or other external causes. The power grid is also vulnerable to
cascading failures when disturbances initiated in a region propagate to other parts through
subsequent components failure. The likelihood of a smaller outage events growing into a big
cascading failure sharply increases when the grid is already under stress (Dobson et al. 2007).
Concurrently, historical data suggests that the odds of a blackout increases significantly during
mid-afternoon hours when the grid is under stress due to peak demand (Hines, Apt, and Talukdar
2009).
The North American Electric Reliability Corporation (NERC) requires electric utilities to
report power outage events and this data is available with the Disturbance Analysis Working
Group. Hines et al. (2009) compiled and filtered this data for regions within the PJM electricity
market.2 We use this data in our statistical blackout model. Descriptive statistics for various
primary causes triggering the blackouts in PJM between 1984 and 2006 are shown in Table 1.
Weather is the primary cause of power outages in PJM, triggering more than one-third of events,
followed by natural disasters (e.g. hurricanes and ice storms). Table 2 shows the mean duration
and the frequency of blackouts initiated during various seasons and times of day in PJM. About
half of the blackouts in our data set occurred during summer months with a mean duration of
about 18 hours. Blackouts are more likely to be triggered during afternoon hours (12 -5 pm) and
blackouts triggered during evening and night-time hours tend to have longer restoration times.
2
Hines et al. (2009) have shared the raw data used for their study at http://www.uvm.edu/~phines/publications/2009/blackouts.html. (Last accessed 10/9/2014).
6
Table 1. Descriptive statistics for different primary causes of blackouts in PJM between
1984 -2006
Primary Causes
Natural disaster
Weather
Fire
Intentional attack3
Supply shortage
Other external causes
Equipment Failure
Operator Error
Voltage reduction/Volunteer
reduction
% of
events
Mean
duration
(hours)
Mean
size
in MW
lost
Mean size in
Customers
affected
10
36.15
1.54
1.54
3.85
5.38
20
5.38
31.00
26.05
4.12
50.94
8.75
1.54
3.55
1.98
423.46
295.82
100
0
151.6
102.57
142.76
333.57
299250
171477
33764
0
465013
3500
16203
73925
16.15
23.77
224.04
10666
Table 2. Mean duration of blackouts initiated at different seasons and time of day
Time
Variable
Season
Summer
Winter
Fall/Spring
Mean
Duration
(hours)
% events
18.82
17.15
15.93
50.74
22.06
27.21
9.75
11.43
28.28
25.19
22.79
34.56
24.26
18.38
Time of day
Morning
Noon
Evening
Night
For this study, voltage reduction/volunteer reduction events (which do not affect
electricity service) and events with no recorded sizes (MW and number of customer affected) are
3
There were no recorded size (MW or number of customers affected) for these events.
7
excluded. Also, the data may be incomplete as the utilities are not required to report small power
outage events as pointed out by Hines et al (2009).
Power outage costs depend on both the likelihood and the duration of a blackout. The aim
is to develop a model for hourly blackout likelihood and the expected duration given a blackout
in PJM. Existing analyses have developed models using historical data on recorded power outage
events. For example, Zerriffi et al (2007) uses historical data on blackout events in North
America to construct statistical models and predict expected outcomes (the size, duration etc.) of
an attack on the power grid. Holmgren and Molin (2006) examine the vulnerability of power
systems using disturbance data in Swedish power transmission and distribution systems.
A logit regression model is used to model the hourly blackout likelihood in PJM. The
dependent variable is dichotomous i.e. the response is coded as 1 if a blackout is initiated in an
hour or 0 otherwise. Blackouts are relatively infrequent events, which poses some challenges for
the application of the logit model. When events are rare (a large number of zeros relative to ones
in the dependent variable), the conventional logit probability estimates can be downward biased
(King and Zeng, 2001). The origin of this problem is small sampling bias in maximum likelihood
estimation of the logit model. While there is no strict definition for what constitutes ‘rare events,’
King and Zheng (2001) rare events data as “binary dependent variables with dozens to thousands
of times fewer ones than zeros”. Our blackout data set meets this definition of rare events. We
thus employ the “rare events logit regression” methodology proposed in King and Zeng, (2001)
to address this bias4. This method implements the corrections for small sample bias generating
approximately unbiased and lower variance estimates of logit coefficients.
The logit regression model for hourly blackout likelihood is specified as,
4
This method is available as a software package, ‘relogit’ executable in STATA.
8
𝑌𝑖,𝑡 = 𝑒𝑥𝑝(𝑋𝑖,𝑡 𝛽 + 𝜀𝑖,𝑡 )
Where,
𝑋𝑖,𝑡 𝛽 = 𝛽0 + 𝛽1 ∗ 𝑆𝑒𝑎𝑠𝑜𝑛𝑖,𝑡 + 𝛽2 ∗ 𝑇𝑖𝑚𝑒𝑜𝑓𝑑𝑎𝑦𝑖,𝑡 + 𝛽3 ∗ 𝑊𝑒𝑒𝑘𝑑𝑎𝑦𝑖,𝑡 + 𝛽4 ∗ 𝐷𝑒𝑚𝑎𝑛𝑑𝑖,𝑡 + 𝛽5 ∗ 𝐼𝑛𝑡𝑖,𝑡
(1)
The dependent variable ‘Y’ is coded 1 if there is a blackout triggered in hour t or 0
otherwise. Season and Timeofday are categorical variables which explains seasonal and time of
day trends in blackout likelihood. The variable Season is a vector consisting of summer, winter
(reference variable) and fall/spring. The variable Timeofday is a vector consisting of morning,
noon, evening and night (reference variable). Weekday is a dummy variable which is coded 1 if
the blackout is triggered during a weekday or 0 otherwise. Demand is the hourly total system
demand in PJM. Data for total system demand in PJM was available starting from 1993, hence
blackout events occurring before 1993 were excluded for this analysis.
There is also an
interaction variable Int capturing interaction between Timeofday and Demand.
We use a similar approach as Zerriffi et al (2007) to model the expected duration of a
blackout. Linear regression is used to model the natural logarithms of duration of a blackout. The
OLS regression model is specified as,
𝑌𝑖,𝑡 = 𝛽0 + 𝛽1 ∗ 𝑆𝑒𝑎𝑠𝑜𝑛𝑖,𝑡 + 𝛽2 ∗ 𝑇𝑖𝑚𝑒𝑜𝑓𝑑𝑎𝑦𝑖,𝑡 + 𝛽3 ∗ 𝑃𝑟𝑖𝑚𝑎𝑟𝑦𝑐𝑎𝑢𝑠𝑒𝑖,𝑡 + 𝛽4 ∗ 𝐶𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠𝑖,𝑡 + ℇ𝑖,𝑡
(2)
The dependent variable ‘Y’ is the natural logarithm of duration of a blackout, Season and
Timeofday are categorical vector variables which explains seasonal and time of day trends in
9
blackout duration. Primarycause is a categorical variable for various primary causes triggering
blackout. Customers is the natural logarithms of the number of customers affected.
3. Modeling Private and Social Reliability Benefits
CHP provides locally generated power and sustains operations in a facility during a
blackout as was seen during Hurricane Sandy. Our work has focused on quantifying the
reliability benefit associated with increased CHP deployment. There are two such benefits.
Firstly, the owners of installed CHP units benefit because the CHP unit can act as a source of
backup power during a blackout. We refer to this as the “private” reliability benefit since it
accrues only to the CHP owner (or owners, in the case of a shared or district system). The private
benefits to CHP owners will be the avoided electricity purchase costs and the avoided customer
interruption costs by operating CHP during a blackout. The gross savings from a single CHP unit
will be,
G𝑟𝑜𝑠𝑠 𝑆𝑎𝑣𝑖𝑛𝑔𝑠, 𝑆𝑖,𝑡 = {𝑃𝐵,𝑡 × 𝑄𝐵,𝑡 − 𝑃′ 𝑖,𝑡 × 𝑄 ′ 𝑖,𝑡 } + {𝐶𝑖 (𝑐, 𝑏) × 𝑓𝑡 }
(3)
The subscript i denotes the number of CHP units and t represents the hour. 𝑄𝑏 and 𝑃𝑏 are
the baseline demand and electricity price in every hour without any CHP unit respectively , 𝑄 ′ is
the reduced demand with a portion of electric demand met by CHP and 𝑃′ is the new electricity
price. In this case, the demand satisfied by a single CHP unit is small relative to the zonal
demand, and will not reduce demand sufficiently to change the zonal electricity price or the
blackout probability. So the baseline price (𝑃𝑏 ) and new electricity price (𝑃′ ) will be the same.
𝐶 is the power outage cost incurred by the customer (without CHP) given the customer
characteristics (c) and blackout characteristics (b). It is assumed that CHP system has the
10
capability to be operated throughout the duration of blackout. 𝑓 is the average blackout
probability for a given hour.
A substantial number of CHP installations will, collectively, reduce the demand for
electricity provided by the grid, thus reducing wholesale electricity prices. Equation 3 can be
rewritten as,
G𝑟𝑜𝑠𝑠 𝑆𝑎𝑣𝑖𝑛𝑔𝑠, 𝑆𝑖,𝑡 = {𝑃𝐵,𝑡 × 𝑄𝐵,𝑡 − 𝑃′ 𝑖,𝑡 (𝑛) × 𝑄 ′ 𝑖,𝑡 } + { 𝐶𝑖 (𝑐, 𝑏) × 𝑓𝑡 (𝑛)}
(4)
where n represents the number of CHP units already deployed. When n is sufficiently
large, the new electricity price (𝑃′ ) will be lower than the baseline price(𝑃𝑏 ) depending on the
level of CHP deployment. The average blackout probability for a given season also depends on
number of CHP unis already installed. With incremental CHP adoption, the average blackout
probability decreases.
Secondly, as discussed above, sufficiently large deployment of CHP investments may
reduce the likelihood of a blackout from occurring. Blackouts are more likely to be instigated
when the electrical grid is under stress and removing demand from the grid (onto local CHP
systems) can reduce this stress. The benefits to non-CHP owners or the societal benefits will be
the reduced power outage costs resulting because of the reduced risk.
𝑆𝑜𝑐𝑖𝑒𝑡𝑎𝑙 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠, 𝑆𝐵𝑡 = ∆𝑓𝑖,𝑡 (𝑛) ∗ 𝐶𝑖 (𝑐, 𝑏)
(5)
𝛥𝑓 is the blackout probability reduction corresponding to the demand reduction from n number
of CHP units deployed, C is the sum of power outage costs experienced by non-CHP owners.
11
The reduction in the blackout risk corresponding to the level of CHP deployment is estimated by
the logit model discussed in section 2 (equation1).
The capital cost for CHP is the upfront cost of the power generating unit and the cost of
black start services to operate CHP independent of the grid. The variable cost includes fuel
(natural gas) cost for CHP system operation, the maintenance cost and additional fuel cost to
operate CHP during a blackout.
𝐶𝑎𝑝𝑡𝑎𝑖𝑙 𝐶𝑜𝑠𝑡𝑠, 𝐶𝑖 = 𝐶𝑖,𝑝𝑔𝑢 + 𝐶𝑖,𝑏
(6)
𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡𝑠, 𝑉𝐶𝑖 = 𝐶𝑖,𝑓 + 𝐶𝑖,𝑜&𝑚 + 𝐶𝑖,𝑎𝑓
(7)
𝐶𝑖,𝑝𝑔𝑢 is the cost of the power generating unit, 𝐶𝑖,𝑏 is the cost of black start services, 𝐶𝑖,𝑓
is the cost of fuel to run the CHP unit and 𝐶𝑖,𝑜&𝑚 is the operating and maintenance costs, 𝐶𝑖,𝑎𝑓 is
the additional fuel cost to operate CHP during a blackout.
4. Building a CHP Adoption Case Study
4.1 CHP adoption in commercial buildings
This study focuses on the deployment of CHP among various types of commercial
buildings in Philadelphia. We draw upon the approach illustrated in Govindarajan (2012) to
simulate a large-scale adoption of CHP in commercial buildings. The approach uses building
stock data and simulated energy load profiles for commercial buildings (with and without CHP)
to estimate hourly CHP usage in a year. Table 3 shows the commercial buildings stock used in
Govindarajan (2012). The ranking represents the most advantageous site for CHP deployment
(hospital) followed by less advantageous sites. The energy load profiles were simulated using the
BCHP screening tool. Simulations were done for three scenarios for each building type –
12
baseline without CHP, CHP system following thermal loads (FTL) and CHP system following
electrical load (FEL).
Table 3. Commercial buildings stock in Philadelphia
Rank
Building Type Number of buildings
1
Hospital
50
2
Hotel
74
3
Restaurant
29
4
Office
284
5
Supermarket
51
6
School
63
7
Motel
22
8
Warehouse
439
We simulate deployment of CHP units according to the priority rankings developed by
the Lawrence Berkley National Laboratory (Lawrence Berkeley National Lab 1991). Our
analysis assumes that CHP units will be installed at the most advantageous sites first (according
to the LBNL rankings) followed by deployment at progressively less advantageous sites. We
thus assume that CHP units will be installed first in all the hospitals (which are ranked the most
advantageous single-use cases for CHP) followed by hotels and so on, as shown in Table 3. All
CHP units are operated during peak demand periods in the grid and there is no operation during
weekends. Reflecting a limitation in the building stock data, we assume that building types have
homogeneous thermal and electric load profiles within type and those demand profiles are wellrepresented by the BCHP tool. For each CHP operation strategy (FEL/FTL), the difference
between the building load with and without CHP represents the hourly demand reduction in the
13
grid. Following this, hourly demand in PJM electricity markets is reduced (using demand in 2006
as the baseline) with every CHP unit deployed. The hourly blackout probability reduction is
estimated (using equation 1) with the reduction in hourly demand for each CHP operation
strategy.
4.2 Power outage costs estimation
We draw upon an approach illustrated by (Sullivan et al. 2010) to estimate power outage
costs for different commercial buildings. Sullivan et al. (2010) uses a two-part econometric
model that estimates the probability that an outage cost is greater than zero and the size of outage
costs using survey data from electric utilities. The model uses expected outage conditions
(duration, time of occurrence etc.) and customer characteristics (building type, annual MWh etc.)
as inputs to estimate the level of outage costs. Table 4 summarizes the regression coefficients of
the variables used in the econometric model developed by Sullivan et al (2010) and the source of
inputs for our analysis.
In order to calculate power outage costs, we use the expected blackout duration (from the
OLS model, equation 2) and allow this duration to vary by season. We construct a weighted
average of expected duration across all types of blackout instigators using the frequency of
blackouts (for every primary cause) as weights for different seasons. The expected outage
conditions reflect the blackout frequency from the historical data described in section 2. For
example, since about 23 percent of the blackouts have occurred in the morning, the weight
placed on the variable ‘Morning’ will be 0.23 (see table 2). The annual electricity consumption
(in MWh) for different commercial buildings is obtained from the simulated load profiles (from
BCHP tool). The industry mix listed (in table 6) excludes industry types like construction,
14
manufacturing and mining etc. since our focus is on commercial buildings. Restaurants and
supermarkets were classified as ‘wholesale and retail trade’ and other buildings types (table 3)
were classified ‘industry unknown’. To estimate outage costs for a supermarket, for example, the
input for ‘wholesale and retail’ will be assigned 1 (and rest 0).
Table 4. Regression coefficients of econometric model by Sullivan et al (2010)
Variable
Outage Characteristics
Duration(in minutes)
Regression coefficients from
Sullivan et al (2010)
Probit
GLM
Variable inputs
used in this study
Expected duration
from OLS model
(equation 2)
0.007
0.0091
0
0
Morning
Noon
Evening
Summer
Weekday
0.2002
0.3805
-0.0197
0.4608
0.1511
0.0185
0.28
0.3058
-0.0773
0.2522
Blackout frequency
summarized in
table 2
Advanced Warning
0.0762
-0.0883
No advanced
warning
0.0852
0.4509
-0.0002
-0.0002
0
0
0.455
0.1642
0.1502
0.2727
0.5216
1.0763
0.0267
0.0804
0.2657
0.127
-1.7
4.5241
Duration Squared
Customer Characteristics
Natural log of Annual
MWh
Duration * ln MWh
Duration squared *ln
MWh
Industry mix
Wholesale and retail
Services
Industry unknown
backup generation or
power conditioning
backup generation and
power conditioning
constant
Annual
consumption data
from BCHP tool
Building type
classification
Average values
from Sullivan et al,
(2010)
15
5. Results
5.1 Blackout likelihood and expected duration
The results of our logit model for blackout probability (equation 1) are shown in table 5.
The results suggest statistically significant seasonal and time of day trends associated with
blackout likelihood. Blackouts are more likely during summer months as compared to winter
months. Also, blackouts are more likely to be triggered during morning and afternoon hours as
compared to night time. There is a positive and significant relationship between blackout
likelihood and demand for electricity in PJM. A unit percent increase in demand will increase
odds of a blackout by 0.0022 % holding other variables constant. In other words, demand
reduction will lead to reduced blackout likelihood and this effect will be greater during summer
months.
Table 5. Logit regression model results: Hourly blackout likelihood in PJM
Variables
Season
Summer
Fall/Spring
Time of day
Morning
Afternoon
Evening
PJM Demand
Logit Model
Rare Events Logit
Model
Logit Model
(2nd order demand)
0.541*
(0.304)
0.316
(0.321)
0.529*
(0.303)
0.319
(0.322)
0.532*
(0.305)
0.303
(0.321)
2.091**
(0.903)
2.004***
(0.685)
0.441
(0.797)
2.20E-05 **
(1.08E-05)
1.854***
(0.692)
1.944***
(0.622)
0.471
(0.789)
2.4E-05**
(1.06E-05)
1.138**
(0.514)
1.558***
(0.423)
0.727
(0.512)
1.85E-10**
(9.11E-11)
Interaction between
demand and time of
day
16
Interaction 1
Interaction 2
Interaction 3
Weekday
Constant
-4.81E-05**
(2.32E-05)
-2.27E-05*
(1.41E-05)
5.49E-06
(1.06E-05)
0.307
(0.287)
-9.404
(0.612)
-0.42E-05**
(1.63E-5)
-2.2E-05*
(2.24E-05)
4.53E-06
(1.33E-05)
0.275
(0.289)
-9.345
(0.598)
Number of Observations
122,640
122,640
Log likelihood
-581.861
LR chi2(10)
36.74
Prob > chi2
0.0001
Pseudo R2
0.0306
Standard errors in parentheses, *** p<0.01, ** p<0.05, *p<0.1
-5.17E-10**
(2.72E-10)
-2.22E-10**
(1.21E-10)
3.56E-12
(1.06E-10)
0.307
(0.285)
-8.901
(0.452)
122,640
-581.723
37.02
0
0.0308
We implemented both a conventional logit model and the rare events logit model (King
and Zheng, 2001). The results of the rare events logit regression (Table 5) are similar to that of
the logit model. This suggests that the small sample bias, pointed out by King and Zeng (2001),
was not severe in the blackout data used in this study5. As a robustness check, the logit model
was estimated for a second degree order of PJM demand and the results were similar (also shown
in Table 5).
Table 6. Linear regression model results: Expected duration of a blackout in PJM
Variables
Customers affected
Season
Summer
Winter
Time of day
5
Linear regression model
Coefficients
0.664***
Standard Error
0.155
0.353
1.06
0.564
0.660
Collier and Hoeffler (2004) used rare events logit and found that the small sample bias was not severe in their data
17
Morning
Afternoon
Evening
Primary cause
Natural Disaster
Weather
Fire
Equipment Failure
-1.965**
-0.92
-0.76
0.943
0.819
0.802
-0.43
0.19
2.32
-0.22
1.337
1.169
1.991
1.235
Operator Error
-0.72
1.334
constant
-3.75
2.330
Number of
57
observations
Prob > F
0.0003
R-squared
0.508
Adjusted R-squared
0.388
Root MSE
1.559
Standard errors in parentheses, *** p<0.01, ** p<0.05, *p<0.1
The results of the regression model for blackout duration (equation 2) are shown in Table
66. The number of customers affected is significant and positively related to the duration of
blackout. Adjusted predictions are used to explain seasonal and primary cause effects.
Table 7 summarizes the adjusted predictions for primary blackout causes during different
seasons. Adjusted predictions represent the estimated natural log of blackout duration at mean
value of natural log of customers affected. The expected duration (in hours) is the exponential of
the values provided in table 7. Holding other variables in the model fixed, weather and fire
related blackouts has higher duration across all seasons. Power outages resulting from operator
error has low restoration times. Natural disaster has lower restoration times than weather or
equipment failure related blackouts. This result, though not intuitive, is consistent with the
6
Observations with no recorded duration were excluded.
18
findings by Simonoff et al. (2005). Restoration times are higher for blackouts occurring at night
compared to morning and afternoon hours.
Table 7. Adjusted predictions for primary causes at different season and time of day
Primary Cause
Natural Disaster
Weather
Fire
Other External
Causes
Equipment Failure
Operator Error
Season (hours)
Time of day (hours)
Summe
r
1.47
2.08
4.22
Winte
r
1.11
1.73
3.87
Fall/Sprin
g
2.18
2.79
4.93
Mornin
g
0.66
1.27
3.41
Afternoo
n
1.70
2.32
4.46
Evenin
g
1.86
2.48
4.62
Nigh
t
2.62
3.24
5.38
1.90
1.54
2.61
1.09
2.13
2.29
3.05
1.68
1.17
1.32
0.82
2.39
1.88
0.87
0.36
1.91
1.41
2.07
1.57
2.83
2.33
Based on simulated CHP deployment in the Mid-Atlantic region amounting to 1,000
single-user units for commercial buildings, reductions in grid-provided electricity are in the
hundreds of Megawatts per hour (on average). The magnitude of loads taken off the grid depends
on whether CHP units are operated to follow on-site electrical load (FEL mode) or on-site
thermal load (FTL mode). Operating all 1,000 CHP units in FEL or FTL mode will reduce the
blackout risk by about 1.7% and 0.6 % respectively. Figure 1 shows the reduction in hourly
blackout probability (averaged across a year) with incremental CHP adoption. The blackout risk
reduction is higher when CHP is operated in FEL mode through larger reductions in zonal
demand. Figure 2 shows the hourly blackout probability (averaged across summer months) with
incremental CHP adoption. The result suggests that while the likelihood of a blackout in any
given hour is small, blackouts are more likely to occur during the summer peaks as during other
times of the year (see Figure 2). While estimates in Figures 2 and 3 appear small in magnitude,
19
they translate to more substantial numbers when translated into expected economic losses
associated with blackouts.
8.26E-04
Hourly blackout probability
8.24E-04
8.22E-04
8.20E-04
8.18E-04
8.16E-04
8.14E-04
8.12E-04
8.10E-04
8.08E-04
0
200
400
600
800
1000
Number of CHP units
FTL
FEL
Figure 1. Hourly blackout probability with incremental CHP adoption
20
Hourly blackout probability (Summer)
1.14E-03
1.13E-03
1.13E-03
1.12E-03
1.12E-03
1.11E-03
1.11E-03
0
200
400
600
800
1000
Number of CHP units
FTL
FEL
Figure 2. Hourly summer blackout probability as a function of incremental CHP
deployment
6.2 Private benefits to CHP owners
Private reliability benefits to CHP owners are the avoided power outage costs where
building sites could use the local electricity generated from CHP and sustain critical operations
during a blackout. CHP would be operated primarily following the site’s thermal /electric load
during normal days and earn benefits from avoided electricity purchases. Figure 3 shows annual
power outage costs for different commercial building types in Philadelphia. The private benefits
from avoiding blackouts may reach into the thousands of dollars per event. The power outage
costs are calculated as the product of the seasonal blackout probability (estimated from equation
1) and the seasonal power outage costs for a given building type (estimated using the approach in
section 4.2). The seasonal values are then added up to get an annual estimates of power outage
cost.
21
Annual Power Outage Costs ($)
7000
6000
5000
4000
3000
2000
1000
0
Figure 3. Power outage costs for commercial buildings in Philadelphia, based on the
blackout risk model and Sullivan (2010)
Figure 4 shows the total private benefits of up to one thousand single user CHP units for
commercial buildings (equation 4). The primary axis (on the left) shows the avoided outage costs
(i.e., reliability benefits) and the secondary axis (on the right) shows the net energy savings from
avoided electricity purchases (net savings would incorporate the cost of natural gas to fuel the
CHP unit, plus other operational or maintenance costs). The estimates (shown in figure 4)
accounts for blackout risk reduction and electricity price reduction from incremental CHP
adoption.
22
9
Reliabilty benefits FEL
Reliability benefits FTL
8
Millions
Millions
2.5
Energy savings FEL
Energy savings FTL
7
Net Energy savings($)
Annual power outage costs($)
2
6
1.5
5
4
1
3
2
0.5
1
0
0
0
200
400
600
800
1000
Number of CHP units
Figure 4. Private reliability and energy-savings benefits from CHP adoption
Our estimates of energy savings outweigh the reliability benefit from avoided power
outage costs for both CHP operation modes (FEL and FTL). The annual power outage costs are
higher in case of CHP-FTL as compared to CHP-FEL with incremental CHP adoption. Though
the difference is not large, it arises because the CHP-FEL mode involves larger reductions in
demand for grid-provided electricity thus resulting in larger blackout risk reduction.
23
The reduction in power outage costs for CHP-FTL and CHP-FEL with incremental CHP
adoption (from blackout risk reduction) is shown in Figure 5. The reduction in outage costs
associated with risk reduction (i.e., a lower likelihood of blackouts, as distinct from the ability
for CHP units to continue providing services during blackouts) is up to two orders of magnitude
smaller than energy savings during times when no blackouts occur. The savings from CHP-FEL
is higher since there will be more onsite electricity generation, hence higher avoided electricity
costs as compared to CHP-FTL. The savings curve tends to flatten as number of CHP unit
Reduction in power outage costs ($)
deployed increases indicating that the incremental savings from CHP decreases.
30000
25000
20000
15000
10000
5000
0
0
200
400
600
800
1000
Number of CHP units
FTL
FEL
Figure 5. Monetized risk reduction for CHP owners and operators under CHP-FTL and
CHP-FEL operational rules
6.3 Social benefits from large-scale CHP adoption
With sufficient deployment scale and proper operational protocols (i.e., operating CHP to
follow electrical loads during peak demand periods), CHP deployment may benefit the grid as a
24
whole by reducing stress and thus reducing blackout risk. There is a social value associated
where customers who don’t deploy CHP will be benefited from reduced risk of a blackout. We
estimate a baseline power outage cost for all commercial customers using the approach discussed
in Sullivan et al (2010). We, then calculate the reduction in the baseline cost as a results of the
reduction in blackout risk (using equation 5). Figure 6 shows the reduction in power outage costs
to commercial customers (or non-CHP owners) with incremental CHP adoption. The social
benefits amounts up to $39 million (or $39,000 per CHP unit) when CHP is operated in FEL
mode. The social benefits are lower, amounting up to $14 million (or $14,000 per CHP unit)
Billions
when CHP is operated in FTL mode.
3.65
3.645
3.64
Blackout costs
3.635
3.63
3.625
3.62
3.615
3.61
3.605
3.6
0
200
400
600
800
1000
Number of CHP units
FTL
FEL
Figure 6. Social benefits with incremental CHP adoption
25
7. Conclusion
With sufficient deployment scale and proper operational protocols (i.e., operating CHP to
follow electrical loads during peak demand periods), even modest levels of CHP deployment in
regional electric grids can yield substantial reliability-related benefits. Using historical data on
blackout frequencies, durations and scope (number of customers affected) from the Mid-Atlantic
electricity market, we have quantified blackout risk as a function of system-wide electricity
demand. Unsurprisingly, risk is highest during the winter and summer peaks, with summer
blackout risk being somewhat larger than winter blackout risk.
CHP units operated to ameliorate peak demand can benefit electricity consumers in two
ways. First, CHP-enabled customers can continue to receive electricity service even when
power-grid interruptions occur, as long as fuel supplies are not interrupted. This “private
reliability benefit” would amount to between $2 and $2.5 million per year with a deployment
level of 1,000 CHP units throughout the Mid-Atlantic region. The average private benefit would
thus amount to $2,000 to $2,500 per year. The reliability benefit is larger when CHP units are
operated in a mode that follows electrical load versus following thermal load. The private
reliability benefit, however, is smaller than the energy-savings benefit by a factor of 1.5 to 4. The
energy-savings benefit is generally larger than the private reliability benefit, suggesting that
building-integrated CHP units have little private incentive to operate in a way that maximizes
blackout risk reduction for the grid as a whole.
The second mode of reliability benefit from CHP deployment accrues to the grid as a
whole through the reduction of stress and thus blackout risk. There is a social value associated
where customers who don’t deploy CHP will be benefited from reduced risk of a blackout. We
estimate that the social benefits of blackout risk reduction amount to $39 million annually (or
26
$39,000 per CHP unit) when CHP is operated in a way to follow electrical load during peak
periods. Our estimated social benefits are lower - $14 million annually for deployment of 1,000
CHP units ($14,000 per unit) when CHP is operated to follow thermal load.
Our work suggests that payments to CHP owners/operators for these reliability benefits
would be economically justified, but our analysis does have some drawbacks. First, our blackout
risk model is relevant only to blackouts that are related to equipment overloads, and not extreme
events such as hurricanes or ice storms. CHP could provide a social reliability benefit in these
circumstances in a type of micro-grid configuration, but our model is not able to capture this type
of benefit. Second, the logit model can be used to estimate the impacts of relatively small
changes in risk, but not large changes. In the scope of the PJM electricity market, with
generating capacity of nearly 200 GW and peak demands of around 180 GW, we believe that
simulating the removal of less than 0.5% of that demand is appropriate for the logit model.
Removal of larger levels of demand, perhaps 10%, would be less appropriate. Our model thus
has some limitations in terms of its ability to estimate blackout risk reduction with very large
CHP deployments.
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