Energy and Power Engineering, 2013, 5, 816-823
doi:10.4236/epe.2013.54B157 Published Online July 2013 (http://www.scirp.org/journal/epe)
An Interval Probability-based Inexact Two-stage
Stochastic Model for Regional Electricity Supply and GHG
Mitigation Management under Uncertainty*
Yulei Xie, Guohe Huang, Wei Li, Ye Tang
North China Electric Power University, Key Laboratory of Regional Energy System Optimization,
Ministry of Education, Beijing, China
Received October, 2012
ABSTRACT
In this study, an interval probability-b ased inexact two -stage stochastic (IP-ITSP) model is develop ed for env ironmental
pollutants control and greenhouse gas (GHG) emissions reduction management in regional energy system under uncer-
tainties. In the IP-ITSP model, methods of interval probability, interval-parameter programming (IPP) and two-stage
stochastic programming (TSP) are introduced into an integer programming framework; the developed model can tackle
uncertainties described in terms of interval values an d interval probability d istribution s. The dev eloped mod el is applied
to a case of planning GHG -emission mitigation in a regional electricity system, demonstrating that IP-ITSP is applica-
ble to reflecting complexities of multi-uncertain ty, and capable of addressing the problem of GHG-emission reduction.
4 scenarios corresponding to different GHG -emission mitigation levels are examined; the results indicates that the
model could help decision makers identify desired GHG mitigation policies under various economic costs and envi-
ronmental requirements.
Keywords: Interval Probability; Inexact Two-stage Stochastic Programming; Electricity Generation; GHG-Mitigation;
Energy System
1. Introduction
For many decades, the constantly increment of regional
electricity demand has forced managers to contemplate
and propose ever more comprehensive, complex and
ambitious plans for electric power systems. However,
most CO2 emissions are emitted mainly from electricity
generation processes of burning fossil fuels such as coal,
oil and natural gas [1]. A number of impact factors, such
as population growth, rapid urbanization and industriali-
zation, and global economic development, would inevi-
tably result in conflicts among economic objective, elec-
tricity demand/supply, and environmental requirement.
Moreover, such planning efforts are complicated with a
variety of uncertain parameters as well as their interac-
tions [2]. It is thus deemed necessary to develop effective
optimization methods for supporting regional electric
power systems management with GHG-emission mitiga-
tion under such complex ities.
Previously, a number of mathematical techniques have
been introduced to deal with these uncertainties [3-6].
Among these techniques, inexact two stage stochastic
programming model (ITSP) integrated with interval pa-
rameter programming (IPP) and two stage stochastic
programming (TSP) has received extensive attentions to
express uncertain parameters with random and dynamic
feature as probability distributions and discrete intervals
over the past years [7]. Generally, all of the stochastic
programming models require probabilistic specifications
for uncertain parameters. However, in many practical
situations, discrete probability distributions of future
events may be predicted using existing statistics and ex-
pert judgment. For long run decision making problems,
these probabilities are in most cases subjective and diffi-
cult to estimate. For example, in electric power manage-
ment system, it is often associated with difficulties in
acquiring the probability distribution of the random
variables/ parameters due to the insufficient available
data or the existence of multiple uncertainties. When
only limited or imprecise information is available while
the stochastic programming method is used, the detailed
probabilistic distributions need to be generated based on
unrealistic assumptions, resulting in potential errors with
the modeling inputs and outputs. Interval probability
*Supported by Major Science and Technology Program for Water
Pollution Control an d Treatment (NO. 2009Z X 07 631-03).

Y. L. XIE ET AL. 817
distribution, which was based on the interval numbers
and stochastic mathematics method, was effective for
dealing with uncertainties on probability distribution [8].
Interval probability distribution relates to the case where
over the interval of possible probab ilities some v alu es are
more possible than others. Previously, a number of inex-
act optimization methods coupled with interval probabil-
ity distribution were developed for dealing with uncer-
tainties presented as intervals and/or random variables
[8]. Nevertheless, no previous study was reported on
interval probability distribution-based two stage stochas-
tic programming for GHG-emission management in re-
gional electric power systems.
Therefore, as an extension of the pervious study, the
objective of this study is to develop an interval probabil-
ity distribution- based two stage stochastic programming
(IP-TSP) and applies it to the planning of regional elec-
tric power systems with GHG-emission mitigation. The
IP-TSP will integrate optimization techniques of interval
parameter programming, two stage stochastic program-
ming, and interval probability distribution into a general
framework to handle multiple uncertainties. In a hypo-
thetical regional electric power system, the developed
method will be used to analyze various policy scenarios
that are associated with different levels of economic
consequences when the promised electricity generation
targets are violated. The results will help managers to not
only make decisions of electricity generation schemes
but also gain insight into the tradeoffs between system
risk and economic objectives.
2. Methodology
2.1. Interval Pro ba b il i ty Di s t ri b ut i on
Traditional methods of the stochastic decision making
are based on the assumption that we know the probabili-
ties of different situations ‚In some situations, it would
be difficult generating the exact value of the p robabilities,
and more uncertainties would exit in the energy systems
to affect the probability distribution of the stochastic pa-
rameters. The interval would be able to effectively reflect
the uncertainties of the possible value of probability. In
order to make decisions under such interval probabilities,
Reference [8] developed a natural way of decision mak-
ing under interval probab ilities. For example, th ere exists
exactly one averaging operation with interval probabili-
ties, and this averaging operation has the form:
11 122 2
11 22
{([ ,],),([ ,],),...,([ ,],)}
...
nn n
nn
Cppc ppcppc
pc pcpc
 
 (1)
where
11
11 11
11
nn
jj
jj
j
jj
nn nn
jj jj
jj jj
pp
pp
pp pp


p


 
 


 


 (2)
Thus, the interval probabilities can be transferred into
deterministic probabilities.
2.2. Interval Prob ab il i ty Di st r ib ut i on - base d
Two-stage Stochastic Programming
In the two stage stochastic program, the conditional
probabilities, are supposed to have a predefined exact
value. However, in some situations these probabilities are
difficult to evaluate and only an estimation of their pos-
sible value may be available. Therefore, these probabili-
ties may be considered as interval probability distribu-
tions. Thus, an interval probability distribution- based
inexact two-stage stochastic programming (IP-TSP) can
be formulated as follow:
11
111
max nn
K
j
jkj
jjk
jk
f
cx pdy

 

 
 (3a)
subject to:
1
1
1,1, 2,...,
n
rj jr
j
axb rm
 



 (3b)
11
2
11
ˆ,1, 2,...,;
1, 2,...,
nn
ij jijjkik
jj
axeyw im
kK
 




 (3c)
,1, 2,...,
kkk
pk 
 K

 (3d)
11
11 11
11
KK
kk
kk
kk
KKKK
kk kk
kk kk
p

k


 

 
 
 


 


 (3e)
1
1
K
k
k
p


 (3f)
1
0,1, 2,...,
j
x
j
  n
K
]
(3g)
1
0,1, 2,...,;1,2,...,
jk
yj nk
 (3h)
where ,
kkk
p





 
K
are interval numbers that is the
probability of occurrence for scenario k, with 0
k
p
and 11
k
k
p


; ˆik
w

are random variables associated
with probability k. In model (1), the decision variables
are divided into two subsets. The
p
j
t
x
 represents the
first-stage variables, which have to be decided before the
random variables are disclosed;
j
kt are related to the
recourse actions against any infeasibilities after uncer-
tainties are disclosed.
y

Y. L. XIE ET AL.
818
For Model (3), if
j
x
 are considered as uncertain in-
puts, the existing methods for solving inexact linear pro-
gramming problems cannot be used directly [7]. In this
study, an optimized set of targ et values will be identified
by having
j

in Model (3) be decision variables. Ac-
cordingly, let
j
jjj
x
x   x

 , where
j
jj
x
xx



and jt [0,1]


;
j

are decision variables that are used
for identifying an optimized set of target values (
j
x

) in
order to support the related policy analyses [7]. Accord-
ing to Reference [9], the IP-ITSP model can be trans-
formed into two deterministic submodels that correspond
to the lower and upper bounds of the objective function
value, respectively.
3. Application to Ghg-Emission Mitigation in
a Regional Electric Power System
Consider a typical regional-scale electric power system
wherein a manager is responsible for allocating energy
resources/services from multiple facilities to multiple
end-users through multiple technologies within a plan-
ning horizon. The decision maker can formulate the
problem as minimizing the expected cost of various en-
ergy activities in the region over the planning horizon.
Moreover, decision makers always seek to control the
emissions of environmental pollutants (e.g., sulfur diox-
ide (SO2), nitrogen oxides (NOx), particulate matter (PM))
and greenhouse gas (GHG) in order to meet the regional
environmental requirement [10]. In the energy conver-
sion sector, every conversion technology has an electric-
ity generation target. If the target is not exceeded, a
regular cost will be brought to the system; otherwise, the
system will be subject to penalties resulted from the extra
labor, management, operation and maintenance costs, or
capacity expansion and higher costs for imported energy.
The future electricity demand during the planning hori-
zon is often modeled as an uncertain parameter associ-
ated with an interval probability distribution. Most of the
other parameters (such as technological efficiency, eco-
nomic parameters and utilization factors) are expressed
as intervals. Therefore, The FP-ITSP approach is consid-
ered appropriate for addressing this planning problem.
Table 1 presents the available electricity demands under
different interval probability distributions. Electricity
generation target, environmental pollutants control and
the related economic data are shown in Table 2. Besides,
coal-fired power has a residual capacity of 1.0 GW,
natural gas-fired power has a residual capacity of 0.28
GW, hydropower has a residual capacity of 0.26 GW.
The representative costs and technical data are investi-
gated based on governmental reports and other related
literature [4-6,10].
Based on a detailed analysis of the study system, four
major sets of objectives were considered when modeling
this system to achieve the following aims: (a) the lowest
cost of purchasing coal, nature gas, crude oil, diesel and
gasoline, (b) the lowest operation cost for coal-fired
power, gas-fired power, hydropower, wind power, solar
power, and nuclear power, (c) the lowest capacity expan-
sion cost, and (d) the lowest air pollutant mitigation cost.
In detail, the objective functions and constraints were
formulated as follows
Table 1. The available electricity demands under different
interval probability distributions.
Demand levels
Activity Low Medium High
The amount
of available
electricity [105.00, 125.00][120.00, 145.00] [140.00, 168.00]
Probability [0.15, 0.35] [0.45, 0.60] [0.05, 0.15]
Table 2. Electricity generation target and the related economic data.
Electricity generation target and the related economic data
k = 1 k = 2 k = 3 k = 4 k = 5 k = 6
Generation target of each power conversion technology (103GWh)
[15, 100] [0, 55] [0, 35] [0, 25] [0, 15] [0, 10]
Regular costs for power generation by each power conversion technology ($106/103GWh)
[4.00, 6.00] [5.00, 7.00] [5.50, 7.50] [2.50, 3.50] [2.00, 3.00] [10.00, 14.00]
Surplus costs for power generation by each power conversion technology ($106/103GWh)
[2.00, 3.00] [2.50, 4.50] [3.50, 5.50] [1.50, 2.50] [1.00, 2.00] [6.00, 9.00]
Cost of removal SO2 in each power conversion process ($/tonnes)
[38.50, 45.50] [32.50, 40.50] 0 0 0 0
Cost of removal NOx in each power conversion process ($/tonnes)
[55.50, 75.00] [42.50, 65.50] 0 0 0 0
Cost of removal PM2.5 in each pow er conversion process ($/tonnes)
[120.50, 135.50] 0 0 0 0 0

Y. L. XIE ET AL. 819
(1) (2) (3) (4)Minmizef  (4a)
1
(1) i
I
i
i
PESZ


 (4b)
111
()(2) kk
KKH
kh
kkh
WPVPPPV p



 kkh
Q

k


h
,h
h
)h
h
h
H
(4c)
111
(3) km km
KMH
hkmh
kmh
YECICp

  (4d)
11
11
11
(4) ()
()
()
KH
khkhk k
kh
KH
khkh k
kh
KH
khkh kk
kh
WpQSOTCTS
WpQNOTCTN
WpQPMTCTM








 



(4e)
subject to:
(),
ikk kh
WZFEQ  
(4f)
[Mass balance for coal]
1
1()
K
kh
kkh
WQ ZDTE

 

 (4g)
max 0, , kkkh
WWQ k

  (4h)
1,,(
M
kkhk kmhkm
m
k
WQ STRCYECk



  (4i)
[Mass balance for electricity generation]
1
0
integer
,,
kmh
Ykmh









(4j)
1
,1,
v
mkmh khY 

 (4k)
[Capacity expansion]
1()(1),
K
kkh kS
k
WQSOTES h 
 


 (4l)
1()(1),
K
kkh kN
k
WQNOT EN 
 

 
 (4m)
1()(1),
K
kkh k O
k
WQPMT EPM 
 

 
 (4n)

1,
kkh
K
k
kWQ COTEMh


 
 (4o)
[Environmental constraints]
,1,2,...,
hhh
ph 

 (4p)
11
11 11
11
HH
hh
hh
hh
HH HH
hh hh
hh hh
p

h


 



 
 


 


 (4q)
11
H
h
h
p


 (4r)
where
f

is the expected system cost (million dollar);
is the electricity conversion technology, k = 1 for
coal-fired power, 2 for natural gas fired power, 3 for hy-
dropower, 4 for wind-power, 5 for solar power and 6 for
nuclear power; is the capacity expansion option, m
=1, 2, 3…, v; is the level of power load, h = 1, 2, 3…,
H; i
k
m
h
Z

is the energy sources supply (PJ), i = 1 for im-
port electricity, i = 2 for coal supply, i = 3 for natural-gas
supply, i = 4 hydropower supply, i = 5 for solar power
supply, i = 6 for wind power supply, i = 7 for nuclear
power supply; i
PES

is energy sources supply cost
($million/PJ); k
PV

is the variable cost for converting
technologies k; k
PP

is penalty cost of converting tech-
nologies k for excess electricity generation ($million/
GWh); kh
Q

is the excess power generation by technol-
ogy k in scenario h; h is the probability of electricity
demand; kmh
p
Y

is the binary variable for technology k
with expansion option m; k is the allowable power
generation by technology k in load level h; km is the
capacity expansion size option m for electricity genera-
tion technology k (GW); km is the capital cost for
electricity generation technology k expansion size m
($Million/GW); k
W
IC
EC
COT

is the CO2 emission intensity of
power generation technology k (kiloton/GWh); k
SOT

is the SO2 emission intensity of power generation tech-
nology k (kiloton/GWh); k is the NOx emission
intensity of power generation technology k (kiloton/
GWh); t
NOT
PMT

is the PM10 emission intensity of power
generation technology k (kiloton/GWh); k
CTS

is the
SO2 removal cost of power generation technology k (dol-
lar/kiloton); k CTN

is the NO2 removal cost of power
generation technology k (dollar/kiloton); t CTM

is the
PM10 removal cost of power generation technology k
(dollar/kiloton); k
F
E

is the conversion efficiency(TJ/
GWh); h
DTE

is the electricity demand in load level h
(GWh); k is the residual capacity of electricity gen-
eration technology k (GW); S
RC

 is the SO2 removal effi-
ciency of power generation technology k;
N


is the
NOx removal efficiency of power generation technology
k; O


is the PM10 removal efficiency of power genera-
tion technology k; EM

is the total allowable CO2
emissions (kiloton); ES

is the total allowable SO2
emissions (kiloton); EN

is the total allowable NO2
emissions (kiloton); EPM

is the total allowable PM10
emissions in period t (kiloton).

Y. L. XIE ET AL.
820
4. Results Analysis
Table 3 presents the electricity generation targets under
different GHG reduction scenarios. As a part of interme-
diate energy conversion, the electricity generation tech-
nologies in clude coal-fired power, n atural gas-fired pow-
er, hydropower, wind power, solar power, and nuclear
power. Due to the higher cost during the power genera-
tion process, the pre-regulated electricity generated by
natural gas-fired power, solar power, and nuclear power
conversion technologies would always zero under dif-
ferent GHG reduction emission scenarios, and the major
power generation technologies include coal-fired power,
hydropower, an d wind power. The pre- regulated electric-
ity generated by coal- fired power would decrease as the
level of GHG-reduction increasing. For example, it
would decrease from 42.11× 103 GWh (without GHG-
reduction) to 16.85× 103 GWh (60% GHG-reduction).
Under the four scenarios, the amount of pre-regulated
electricity generated by hydropower would be 13.45 ×
103GWh, 17.66 × 103 GWh, 23.74 × 103 GWh, and
32.16 × 103 GWh under the scenarios of 0%, 20%, 40%
and 60% GHG-reduction emission levels, respectively.
The pre-regulated electricity generated by wind power
would always 25.00× 103 GWh under different GHG
reduction emission scenarios.
If the electricity targets cannot meet the random de-
mand, during different excess GHG reduction emission
scenarios, electricity has to be produced under different
demand levels. The excess generation quantities of each
power conversion technology would be different from
under different demand levels and different GHG-reduc-
tion levels as shown in Table 4. In case of insufficient
electricity supply, wind power would be firstly as the
recourse activities to compensate the deficits of electric-
ity shortages, the coal-fired power and hydropower
would only be supplements. Moreover, as the electricity
demand level increasing, excess electricity generated by
the three power technologies would increase. For exam-
ple, under 0% GHG-reduction level, the excess electric-
ity generated by wind power technologies would be 0, [0,
1.95] × 103 GWh, and [0, 11.5] × 103 GWh during the
low, medium, and high level of electricity demand, re-
spectively. In addition, as the GHG-reduction level in-
creasing, the excess power generation would also in-
crease, for example, under the high level of electricity
demand, the excess electricity generated by hydropower
technologies would be 13.45 × 103 GWh, 17.66 × 103
GWh, 20.00 × 103 GWh, an d [20.00, 21.81] × 103 GWh
during 0%, 20%, 40% and 60% of GHG-reduction emis-
sion levels, respectively.
Table 3. Solutions of electricity generation targets under GHG reduction scenarios.
Electricity generation targets (103 GWh)
GHG-emission
reduction level Coal-fired power
(k = 1) Natural gas-fired power (k = 2) Hydropower (k = 3) Wind-power (k = 4) Solar power (k = 5) Nuclear power (k = 6)
0% 42.11 0 13.45 25.00 0 0
20% 33.68 0 17.66 25.00 0 0
40% 25.26 0 23.74 25.00 0 0
60% 16.85 0 32.16 25.00 0 0
Table 4. Solutions of th e excess power generation of each con versation technology.
Excess power generation of each conversation technology(103 GWh)
Level CO2 emission reduction level k = 1 k = 2 k = 3 k = 4 k = 5 k = 6
0% 0 0 0 [3.45, 6.95] 0 0
20% 0 0 0 [7.66, 11.16] 0 0
40% 0 0 0 [10.00, 13.50] 0 0
L
60% 0 0 0 [10.00, 13.50] 0 0
0% [0, 1.95] 0 0 [18.45, 25.00] 0 0
20% [0, 6.16] 0 0 [22.66, 25.00] 0 0
40% [0, 8.50] 0 0 25.00 0 0
M
60% [0, 8.50] 0 0 25.00 0 0
0% [0, 11.50] 0 13.45 25.00 0 0
20% [0, 11.50] 0 17.66 25.00 0 0
40% [0, 11.50] 0 20.00 25.00 0 0
H
60% [0, 9.69] 0 [20.00, 21.81]25.00 0 0
C opyright © 2013 SciRes. EPE

Y. L. XIE ET AL. 821
As shown in Figure 1, compared the six power gen-
eration technologies’ contribution to the different levels
of electricity demand, it indicates that different power
conversion technologies have varied generation quanti-
ties under changed GHG-emission reduction scenarios.
As the previous section analysis, natural gas -fire d p owe r,
0
10
20
30
40
50
60
h=1h=2h=3h=1h=2h=3h=1h=2h=3h=1h=2h=3h=1 h=2 h=3 h=1 h=2 h=3
k=1k=2k=3k=4k=5 k=6
Power ge neration (10
3
GWh)
(a) 0% GHG -r educti on emis si onL ower bound
Upper bound
0
10
20
30
40
50
60
h=1h=2h=3 h=1h=2h=3 h=1h=2h=3h=1 h=2 h=3 h=1h=2 h=3h=1h=2h=3
k=1k=2k=3k=4 k=5 k=6
Power generation (10
3
GWh)
(b ) 20% GHG-re duction emissionL ower bound
Upper bound
0
10
20
30
40
50
60
h=1h=2h=3h=1h=2h=3h=1h=2h=3 h=1 h=2 h=3 h=1 h=2 h=3 h=1h=2h=3
k=1k=2 k=3 k=4 k=5k=6
Power generation (103GWh)
(c) 40% GHG-reduc tion emissionL ower bou nd
Up pe r bound
0
10
20
30
40
50
60
h=1h=2h=3 h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2h=3 h=1 h=2 h=3 h=1 h=2 h=3
k=1k=2k=3k=4k=5 k=6
Power generation (10
3
GWh)
(d) 60% GHG-re duc t ion emis sionL ower bound
Up pe r bound
Figure 1. Amount of power generation with 0%, 20%, 40% and 60% GHG reduction.
C opyright © 2013 SciRes. EPE

Y. L. XIE ET AL.
822
solar power and nuclear power would be zero under dif-
ferent levels of GHG-reduction emission. This is because
nuclear power would enhance the diversity of power
generation, and thus increase the stability and security of
the study system, solar power would be limited by space
and resource during the study area, and the related cost of
gas-fired power conversion technology is slightly higher
than coal-fired power. Under 0% of GHG-reduction
emission, coal-fired power would be the most important
electricity supply source, wind power would be the most
important electricity generation technologies under 20%,
40%, and 60% GHG-emission reduction. As the GHG-
emission reduction level increasing, the total amount of
coal-fired power would decrease, especially, under the
scenario of 60% GHG-emission reduction, the hydro-
power generation would be bigger than coal-fired power.
For example, under 60% GHG-emission reduction, the
total power generation of coal-fired power technologies
would be 16.84× 103 GWh, [16.84, 25.34] × 103 GWh,
and [16.84, 26.53] × 103 GWh in the scenarios of low,
medium, and high demand level, respectively; the hy-
dropower would be 32.16× 103 GWh, 32.16× 103 GWh,
and [52.16, 53.97] × 103 GWh under the three demand
levels; the amount of wind power generation would
[35.00, 38.50] × 103 GWh, 50.00× 103 GWh, 50.00×
103 GWh under the low, medium, and h igh level of elec-
tricity demand, respectively. It indicates that although
coal-fired power conversion technology has relatively
low operating and penalty costs and comparatively low
capital cost for capacity expansion, it has a higher GHG-
emission during the electricity generation process; more
and more environment-friendly power conversion tech-
nologies would be chosen for electricity generation to
satisfy the ever-increasing electricity demands and en-
hancing GHG-emission reduction requirements.
Moreover, imported power would be purchased to fill
the power shortage by the energy system decision makers.
In this study, in order to enhance the regional power sys-
tem reliability, it assumes that [20,30] % of the total
electricity demand would be the maximum amount of
imported power. Under different scenarios, because of the
due to lower cost, the imported electricity would reach to
the maximum limitation, being [21.00, 37.50] × 103GWh.
As shown in Figure 2, the system cost would rise up
along with increasing GHG-emission reduction. The
system cost would be $ [491.84, 727.52] × 106, $
[500.57, 744.41] × 106, $ [510.91, 759.24] × 106, and $
[523.26, 772.37] × 106 under 0%, 20%, 40%, and 60%
GHG-reduction, respectively. The cost of GHG mitiga-
tion (per kiloton) would increase, being $[1.09, 1.30] ×
106, $[1.19, 1.38] × 106, and $[1.15, 1.31] × 106, under
20%, 40%, and 60% GHG-emission reduction, respec-
tively. It indicates that under the scenarios of GHG-re-
duction, the coal-fired power generation technologies
with lower cost in electricity generation process would
be replaced by hydropower, wind power which has a
higher operation cost, besides, the increasing electricity
demand leads to various power generating facilities to be
0
0.5
1
1.5
2
0
400
800
1200
0%20% 40% 60%
C o s t o f p e r GHG m it igat io n (10
6
dollar/tonnes)
Total cost of the system(10
6
doll ar)
Low er bound of the system cost
Upper bound of the system cost
L ower bound of t he per unit GH G-re duc t ion cost
Upper bound of the pe r unit GHG-reduct ion cost
Figure 2. Costs under different GHG red uction scenarios.
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Y. L. XIE ET AL. 823
expanded, bringing about a high capital cost.
5. Conclusion
An interval probability-based inexact two-stage stochas-
tic (IP-ITSP) model is developed for regional electricity
system and greenhouse gas (GHG) emissions reduction
management under uncertainties. The method is based on
interval probability, interval-parameter programming
(IPP) and two-stage stochastic programming (TSP). Un-
certainties in the energy system could present as both
interval probability distributions and interval values to be
incorporated within a general optimization framework.
The developed model is applied to a case of planning
GHG-emission mitigation in a regional electricity system,
demonstrating that IP-ITSP is applicable to reflecting
complexities of multi-uncertainty, and capable of ad-
dressing the problem of GHG-emission reduction. 4 sce-
narios corresponding to different GHG -emission mitiga-
tion levels are examined; Solutions provide an effective
linkage between the predefined environmental policies
and the associated economic implications (e.g., losses
and penalties caused by improper policies). The solutions
contain a combination of deterministic, interval and dis-
tributional information, and can thus facilitate the reflec-
tion for different forms of uncertainties. The results indi-
cate that the model can help managers obtain multiple
decision alternatives, as well as provide bases for further
analyses of tradeoffs between energy management cost
and GHG-emission reduction.
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