Framework of Probabilistic Power System Planning
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CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 1, MARCH 2015 1
Framework of Probabilistic Power System Planning
Wenyuan Li, Fellow, IEEE
Abstract—This paper presents the framework of probabilistic has risks. Such risks cannot be identified by deterministic
power system planning. The basic concepts, criteria, procedure, criteria.
analysis techniques and tasks of probabilistic power system 4) Many major outage events across the world indicate that
planning are discussed. Probabilistic reliability evaluation and
probabilistic economic assessment are two key steps. It should the N-1 principle is insufficient to maintain a reasonable
also be recognized that probabilistic system planning has a wider system reliability level. On the other hand, it is impossible
coverage than these two aspects. An actual example using a utility to apply the N-2 or N-3 principle because it is too
system is given to demonstrate an application of probabilistic expensive in planning investments.
transmission development planning. 5) Renewable energy sources (such as wind, solar, ocean
Index Terms—Power system reliability, probabilistic system powers) have been greatly penetrated into power sys-
planning, risk assessment, system planning criteria. tems. These green sources are intermittent and random
in nature. It is extremely difficult to model renewable
I. I NTRODUCTION generations using a deterministic approach.
Probabilistic power system planning can overcome the
T HE task of power system planning is determination of
new equipment addition or retirement of aged equipment
and the implementation time of a decision. The fundamental
disadvantages of deterministic criteria and address the issues
mentioned above. However, it should be noted that the purpose
of introducing probabilistic methods into system planning is
objective of power system planning is to develop the system as
to add one more dimension to enhance system planning rather
economically as possible and maintain an acceptable reliability
than replacing the N-1 criterion. There is no conflict between
level. The deterministic system planning criteria have been
deterministic and probabilistic criteria since these two kinds
used in the utility industry for many years. These include
of criteria are applied at different stages in a planning process.
the N-1 principle for transmission system planning and a
The probabilistic behavior of power systems has been rec-
fixed percentage of capacity reserve in generation planning.
ognized for a long time. Probabilistic system reliability eval-
In general, the deterministic criteria have served the power
uation methods have been well developed in the past decades
industry well in the past. However, weaknesses associated
[1]–[12]. On one hand, quantified reliability assessment is a
with the deterministic criteria have been exposed in planning
core in probabilistic power system planning. On the other
practice of utilities. The disadvantages of the deterministic
hand, probabilistic planning is much beyond the probabilistic
criteria include the following:
reliability evaluation alone. It includes load forecasts, various
1) Only consequences of outages are considered but proba- system analyses, reliability evaluation, and economic assess-
bilities of outages are overlooked. An outage event, even ment, all in a probabilistic modeling manner. Dealing with
if extremely undesirable, is of little risk if it is so unlikely uncertainties of input data and system parameters is also an
that it can be ignored. On the other hand, if an outage essential task. The concepts, criteria, procedure and methods
event is not very severe but has a high probability of of probabilistic power system panning have been gradually
occurrence, it may still lead to relatively high risk. developed as probabilistic quantified reliability assessment
2) Uncertainties in power systems are related not only to techniques were applied to system planning issues [13]–[18].
component outages but also to various system parameters. This paper provides the framework of probabilistic pow-
Uncertainties in load forecast, generation patterns, equip- er system planning. The probabilistic planning criteria and
ment parameters, limit values and environment conditions procedure are presented in Sections II and III, respectively.
are all ignored in the deterministic criteria. Incorporating The basic analysis techniques in probabilistic system planning
the uncertainties of the system parameters can make a are discussed in Section IV, whereas the tasks of probabilistic
planning decision closer to reality. planning are summarized in Section V. An illustrative example
3) The deterministic criteria are based on “worst case” for probabilistic transmission system planning is demonstrated
studies. However, studied cases are selected by planners in Section VI, followed by the conclusions in Section VII.
and the worst case may be missed in the selection. Even
if a system withstands the worst case, the system still II. P ROBABILISTIC P LANNING C RITERIA
There are different probabilistic planning criteria. Four cri-
Manuscript received November 20, 2014; accepted January 7, 2015. Date
of publication March 30, 2015; date of current version March 5, 2015. This teria [1], [14] are discussed in this section. Which one is used
work was supported in part by the National 111 Project of China (B08036). depends on planning issues and utility’s business objectives.
W. Li is with the State Key Laboratory of Power Transmission Equipment &
System Security and New Technology, Chongqing University, China (Email: A. Probabilistic Cost Criteria
wenyuan.li@ieee.org).
Digital Object Identifier 10.17775/CSEEJPES.2015.00001 Reliability is one of multiple factors considered in probabi-
2096-0042 c 2015 CSEE
2 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 1, MARCH 2015
listic power system planning. System unreliability can be ex- an absolute threshold. Input data used in probabilistic power
pressed using unreliability costs so that system reliability and system planning always have uncertainties, particularly the
economic effects can be assessed on a unified monetary basis. data for reliability assessment based on historical statistics.
The probabilistic cost criteria are the most popular methods. Computational errors in both data and modeling can be offset
The best alternative in system planning should achieve the in a relative comparison.
minimum total cost:
Total cost = investment cost + operation cost + unreliability cost. D. Incremental Reliability Index
In some cases, it may be difficult to use the unreliability
The calculation of investment cost is a basic aspect of
cost for different reasons. In such situations, an incremental
economic assessment in system planning. The operation cost
reliability index (IRI) can be applied. The IRI is defined as
includes OMA (operation, maintenance and administration)
the reliability improvement due to per $M of investment:
expenditures, network losses, financial charges and other on-
going costs. The unreliability cost is obtained using the EENS IRI = (RIB − RIA )/Cost.
(expected energy not supplied, in MWh/year) multiplied by
a unit interruption cost (UIC, $/kWh), where the EENS is The “Cost” refers to the total cost of investment and
a reliability index that can be evaluated using a probabilistic operation (in $M) required for a reinforcement option. The
reliability assessment method. RIB and RIA are the reliability indices before and after the
An alternative approach is the benefit/cost analysis. The reinforcement, respectively. An appropriate reliability index
capital investment of a planning alternative is the cost, whereas (such as the EENS, probability, frequency or duration index)
the reduction in operation and unreliability costs due to the can be used. In most cases, the EENS is suggested since it
alternative is the benefit. The difference between the benefit is a combination of outage frequency, duration and severity,
and cost is the net benefit. The benefit divided by the cost is and carries more information than any other single index. The
the benefit/cost ratio. The net benefits or benefit/cost ratios for IRI can be used to rank projects or compare alternatives in
all selected alternatives are calculated and compared. In other a project. A demerit of the IRI approach is that the doing
words, the alternatives can be ranked using their net benefits nothing option cannot be included.
or benefit/cost ratios.
A project may be associated with multiple-stage investments III. P ROCEDURE OF P ROBABILISTIC S YSTEM P LANNING
and a multiple-year planning timeframe (such as 5 to 20 years) There are different ways to perform probabilistic power
is always considered. All the three cost components should be system planning. A general procedure is shown in Fig. 1 [1],
estimated annually to create their cash flows on the timeframe [15], in which the criteria mentioned in Section II are included.
and then a present value (PV) method [19] is applied to Both the N-1 and probabilistic criteria are combined in the
calculate the total cost or benefit/cost ratio. process.
The basic procedure includes the following four major steps:
B. Reliability Index Target 1) If the single contingency criterion is a mandate, select the
Many utilities have used reliability indices to measure the planning alternatives that meet the N-1 principle. If the N-
system performance and make an investment decision based 1 principle is not considered as a strict criterion, select all
on the indices. It is well known that the LOLE (loss of load feasible alternatives. In either case, the traditional system
expectation) index of one day per 10 years has been used as analysis techniques (power flow, optimal power flow,
a target index in generation planning for many years. This contingency analysis, and stability studies) are needed.
approach has become a firm criterion in generation planning 2) Conduct probabilistic reliability evaluation and unrelia-
of many utilities, particularly in the North America. For bility cost evaluation for the selected alternatives over
distribution systems, the SAIDI (system average interruption a planning timeframe (such as 5–20 years) using a
duration index) and SAIFI (system average interruption fre- reliability assessment tool.
quency index) have been widely used to represent system 3) Calculate the cash flows and present values of investment,
performance. A target SAIDI or SAIFI for a planning purpose operation and unreliability costs for the selected alterna-
can be specified according to historical statistics. tives in the planning time period.
It should be noted that it is not easy to set an appropriate 4) Select an appropriate criterion and conduct an overall
index target for the reliability of a transmission system. This probabilistic economic analysis.
approach should be used with caution for transmission system It can be seen that the probabilistic power system plan-
planning. ning process requires various technical assessments in which
probabilistic reliability evaluation and probabilistic economic
C. Relative Comparison analysis are the two key steps.
In many cases, the purpose of system planning is to conduct
a comparison between alternatives including the doing nothing IV. A NALYSIS T ECHNIQUES IN P ROBABILISTIC P LANNING
option. One major index or multiple indices (including relia- Probabilistic power system planning requires a variety of
bility and economic indices) can be used in the comparison. analysis techniques. This section addresses the major analysis
Performing a relative comparison is often better than using techniques in probabilistic power system planning [1].LI: FRAMEWORK OF PROBABILISTIC POWER SYSTEM PLANNING 3
Deterministic N-1 Planning drivers (load
Probabilistic reliability
study for existing growth, new generators,
evaluation tools
network equipment aging etc.) Technical, economical,
environmental, societal
and political
considerations
Is any Probabilistic
No Yes Identify viable
reinforcement reliability evaluation
alternatives Yes
needed to meet N-1 for existing network
criterion? to obtain indices
N-1 criterion
considered?
Probabilistic reliability
Yes Is there a target No evaluation for each
index? selected alternative to
obtain indices
Yes Meet target No
index? No All alternatives
considered?
Yes
Decision making (business
& financial needs,
No reinforcement
regulatory requirements, Select appropriate
societal expectation) probabilistic criterion
Prepare investment
Select probabilistic
justification for Probabilistic
indices appropriate to
reinforcement economic analysis
criterion
Fig. 1. Procedure of probabilistic power system planning.
A. Load Modeling C. Traditional System Analysis
The differences in load modeling between deterministic The traditional system analysis techniques include power
planning and probabilistic planning include the following: flow, optimal power flow, contingency analysis, voltage sta-
1) In general, only the peak load or a few load levels bility and transient stability. The techniques that are based on
are considered in deterministic planning, whereas a load deterministic assumptions are still of importance in probabilis-
curve is modeled in probabilistic planning. tic system planning. This is not only because these computing
2) A fixed load forecast value is used in deterministic tools are used to initially select feasible planning alternatives
planning, whereas a probability distribution of forecasted that meet the N-1 principle but also because probabilistic
load is needed in probabilistic planning. system analysis techniques are derived from them.
3) Both uncertainty and correlation of loads at substations
need to be modeled in probabilistic planning.
D. Probabilistic System Analysis
The probabilistic system analysis techniques include prob-
B. Generation Modeling
abilistic power flow, probabilistic contingency ranking, proba-
In addition to traditional considerations in deterministic bilistic optimal power flow, probabilistic reliability evaluation,
planning, the following factors need to be modeled in proba- probabilistic voltage stability study and probabilistic transient
bilistic planning: stability assessment. The details of the probabilistic system
1) uncertainties of generator types, locations, capacities and analysis techniques can be found in Reference [1].
unavailability in the future; As mentioned earlier, probabilistic reliability evaluation
2) correlations between different generation sources and is one of the two key steps in probabilistic planning. The
between loads and generations, particularly for renewable probabilistic reliability assessment of composite generation
generation sources [2]; and transmission systems can be summarized as follows [1]–
3) random behaviors of primary energy sources, particularly [3]:
renewable sources, such as wind speeds, solar insolations 1) A multiple level load model is created which eliminates
and tidal current speeds. the chronology and aggregates load states using hourly4 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 1, MARCH 2015
load records during one year. The uncertainty of load at As mentioned earlier, the unreliability cost equals to the
each level can be modeled using a probability distribu- product of an EENS index and a unit interruption cost. Obvi-
tion. Annualized reliability indices are calculated first by ously, this cost component is a random number that depends
using a single load level and expressed on the one year on various probabilistic factors in a system, particularly on
basis. All the load levels are considered successively and random outage events. The EENS is calculated using the
the resulting indices for each load level are weighted by probabilistic reliability evaluation method described in Section
its probability to obtain annual indices. Alternatively, a IV-D. The unit interruption cost (UIC) can be estimated using
chronological load curve model can be used if necessary. one of the following four techniques.
2) The system states at a particular load level are selected 1) The method based on customer damage functions (CDF)
using either Monte Carlo simulation or state enumeration [3]. The CDFs can be obtained from customer surveys. A
techniques. This includes the following: CDF provides the relationship curve between the average
a) Generally, generating unit states are modeled using unit interruption cost and duration of power outage.
multiple state random variables. 2) The method based on gross domestic product (GDP).
b) Transmission component states are modeled using The GDP is divided by total electric energy consumption
two-state (up and down) random variables. For some to create a dollar value per kWh, which represents the
special transmission components such as HVDC average economic damage cost due to one kWh of energy
lines, a multiple state random variable can be ap- loss.
plied. Weather-related transmission line forced out- 3) The method based on the relationship between capital
age frequencies and repair times can be determined investment projects and system EENS indices. With in-
using a method of recognizing regional weather vestment cost assessments and relevant system reliability
effects. Common-cause outages of transmission lines evaluations in a series of system reinforcement projects,
are simulated by separate random numbers. an average unit interruption cost can be estimated.
c) The bus load uncertainty and correlation are modeled 4) The method based on the lost revenue to a utility due
using a correlated probability distribution random to power outages. The unit interruption cost using this
vector. method could be the average electricity rate.
3) System analyses are performed for each selected sys-
tem state. In many cases, this requires power flow and F. Data Uncertainty
contingency analysis studies to identify possible system Probabilistic power system planning requires much more
problems. In some cases, voltage and transient stability data than deterministic planning. A successful planning de-
studies may also be required. cision depends on not only appropriate methods but also
4) An optimal power flow (OPF) model is used to reschedule acceptable accuracy of data. Two types of uncertainties exist
generations and other reactive sources, eliminate limit in load forecast and component outage data: randomness and
violations (line overloading and/or bus voltage violations) fuzziness [1]. A probabilistic model can be used to model
and avoid any load curtailment if possible or minimize the randomness and a fuzzy model can be used to represent
total load curtailment or interruption cost if unavoidable. fuzziness. For example, it has been recognized for many years
5) The reliability indices (such as the EENS) are calculat- that the outage frequency or unavailability of an overhead
ed using probabilities and consequences of all selected line is heavily related to weather conditions. Classification
system states. of weather conditions is fuzzy in nature because of vague
language in weather descriptions such as normal or adverse
E. Probabilistic Economic Analysis weather, light or heavy rain/snow, etc. When an outage is
assigned to a normal or adverse weather condition in statistical
There are three cost components in the economic analysis:
data collection, it depends on human being’s fuzzy judgment.
investment, operation and unreliability costs [1]–[3].
Many utilities may not have sufficient statistical records but
The investment analysis is a fundamental part of the eco-
engineers generally have a good judgment on the range of data
nomic assessment in a planning process. The cash flow of
uncertainty. In such cases, fuzzy models become a necessary
annual investment cost can be created using the capital return
complement to probabilistic models in order to cope with
factor (CRF) method [1], [2], [19] and actual capital estimates.
the both uncertainties of input data in probabilistic system
The uncertainties of the parameters in the economic analysis
planning.
(such as the useful life, discount rate and capital estimates of
a project) can be modeled using their probability distributions.
The cash flows of operation and unreliability costs are G. System State Selection Techniques
calculated through year-by-year evaluations. In addition to Random selection of system states (generation patterns,
fixed cost components, the operation cost of a transmission or network configurations and load levels) is an essential step in
distribution system is also related to the evaluation of network probabilistic system analysis. There are two kinds of selection
losses, simulation of system production costs and estimation techniques: state enumeration and Monte Carlo simulation.
of energy prices on power market. This is associated with Both have merits and demerits. In general, state enumeration
many uncertainty factors, including load forecasts, generation is preferable when the system size is relatively small and/or
patterns, maintenance schedules and power market behaviors. component outage probabilities are low, whereas Monte CarloLI: FRAMEWORK OF PROBABILISTIC POWER SYSTEM PLANNING 5
simulation is better for a large size system and/or relatively and the solid lines for 138 kV lines). This region is under-
high component outage probabilities. Monte Carlo methods are going significant economic development and requires major
more flexible to simulate complex conditions compared to state enhancements due to the rapid load growth in the area supplied
enumeration. General Monte Carlo simulation requires consid- by the three substations named as CWD, BMT and DAW. The
erable computing time. Many variance reduction techniques, existing 138 kV transmission system is constrained by voltage
which can significantly speed up the simulation process, have instability limits and transmission line thermal limits as the
been available for probabilistic power system analysis [3], load grows in this area.
[20]. A recent research found that incorporating cross-entropy
method into Monte Carlo simulation could significantly reduce FJN
computing time required to achieve the same accuracy in TAY
system analysis [21].
There are two types of Monte Carlo methods: sequential GMS
LAP
and non-sequential simulations. Sequential simulation can DAW
CWD BMT
accurately calculate unreliability frequency indices but is time-
consuming, whereas non-sequential simulation is much faster
but can only calculate approximate frequency indices. Both SNK
simulation methods can accurately estimate non-frequency-
TLR
related indices. In most cases, the EENS index is used in
probabilistic power system planning without need of any infor- Fig. 2. The existing regional system.
mation of frequency index. In such situations, non-sequential
simulation is generally desirable. Based on technical (the traditional system contingency anal-
ysis using the N-1 principle), environmental and social as-
V. TASKS IN P ROBABILISTIC S YSTEM P LANNING
sessments, the following three reinforcement alternatives were
Different tasks can be performed under the framework of worked out as initial options:
probabilistic power system planning. The main tasks are listed
1) Alternative 1: Constructing a double-circuit 230 kV trans-
as follows:
mission line (indicated by the bold dashed lines) from a
1) probabilistic reliability assessment for generation sources, new substation SLS to BMT switching station to replace
transmission systems, substation configurations, distribu- the existing 138 kV line, plus a second 138 kV line
tion systems, smart grids, micro-grids, protection and (indicated by the dashed line) between BMT and DAW,
control systems, and wide area measurement and control as shown in Fig. 3.
systems; 2) Alternative 2: Constructing a second 138 kV transmission
2) system interruption cost assessment (reliability worth line from a new substation SLS to BMT switching station
assessment); and a new 138 kV line from BMT to DAW, as shown in
3) least cost reinforcement planning (comparison between Fig. 4. This alternative also includes the installation of a
alternatives in a project or between projects); 110 MVAr static VAr compensator (SVC) at BMT.
4) probabilistic reactive source planning; 3) Alternative 3: Constructing a 138 kV transmission line
5) load or independent power producer (IPP) connection from substation TAY to substation DAW, plus the new
planning; substation SLS, as shown in Fig. 5. This alternative
6) project or alternative ranking using a probabilistic index also includes the installation of a 110 MVAr static VAr
(either reliability index, or economic index, or both); compensator (SVC) at BMT. The alternative is shown in
7) probabilistic analysis of power source location and sizing; Fig. 5.
8) ranking system equipment importance in a power system;
The upstream system reinforcement, which includes a 230
9) retirement or replacement planning of system equipment;
kV line from GMS to SNK and a 230 kV line from SNK to the
10) equipment spare planning (determination of the number
new substation (SLS), as shown by the dashed lines in Figs.
and timing of equipment spares);
3–5, is the common portion for all the three reinforcement
11) reliability centered maintenance;
alternatives considered in the study. The benefit and cost of
12) integrated planning of power system and primary and
the upstream system reinforcement is therefore excluded from
other secondary energy sources (natural gas/oil/coal/green
the benefit/cost analysis in this paper.
resources and thermal/cold energies).
VI. A N ACTUAL E XAMPLE B. Study Conditions
An actual transmission planning project in a regional system The probabilistic benefit/cost analyses were conducted for
of BC Hydro, Canada is used as an example to illustrate an the three alternatives. The study conditions are as follows.
application of probabilistic transmission planning [22].
1) The system reinforcement is assumed to be in service
A. Regional System and Reinforcement Alternatives in 2016 and the planning period of 20 years from 2016
The simplified single-line diagram of an existing regional to 2035 is considered in the study. The load forecast is
system is shown in Fig. 2 (the bold lines for 230 kV lines shown in Fig. 6. It can be seen that the load increases over6 CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 1, MARCH 2015
FJN
TAY
GMS
LAP
DAW
CWD BMT
SLS
SNK
TLR
Fig. 3. Alternative 1 for reinforcement.
Fig. 6. Load forecast in the studied area.
FJN
TABLE I
TAY
U NIT I NTERRUPTION C OST AND L OAD C OMPOSITION
Unit Interruption
GMS Customer Percentage (%)
LAP Cost ($/kWh)
DAW
CWD BMT
Industrial 15.76 65
SLS
Commercial 36.60 5
Residential 1.36 30
SNK
TLR TABLE II
T OTAL I NVESTMENT OF THE T HREE A LTERNATIVES ($M)
Fig. 4. Alternative 2 for reinforcement.
Alternative 1 Alternative 2 Alternative 3
285.613 247.962 259.884
FJN
TAY
TABLE III
P ROBABILITY D ISTRIBUTION OF D ISCOUNT R ATE
GMS
LAP
Discount Rate Probability
DAW
CWD SLS BMT 0.04 0.3
0.06 0.5
0.08 0.2
SNK
TLR
C. Probabilistic Benefit/Cost Analysis Results
Fig. 5. Alternative 3 for reinforcement.
The MECORE program for composite generation and trans-
mission system reliability evaluation [23] was used to quantify
the EENS indices for the existing system and three alterna-
the years, reaches the peak in 2027 and then decreases tives. The composite unit interruption cost was obtained from
afterword. the data in Table I and then was used to calculate the unrelia-
2) The outage data of system components, which are re- bility costs. The benefits due to reduction in the unreliability
quired in probabilistic reliability evaluation, are based on cost for the three alternatives are presented in Table IV. The
historical records in the previous 10 years. PLOSS program for network energy loss assessment [24],
3) The unit interruption costs for industrial, commercial which automatically incorporates a load curve into power flow
and residential customers of the utility and their load calculations, was used to calculate network energy losses. The
composition in the area are presented in Table I. It can energy loss costs are obtained by multiplying energy losses by
be seen that the industrial load is dominant in the load the energy rate. The benefits due to reduction in the energy
composition. loss cost for the three alternatives are presented in Table V.
4) The predicted energy rate is $120/MWh. This rate is used The expected annual investment costs for the three alter-
in calculating network energy loss costs. natives were evaluated using the capital return factor (CRF)
5) The total investment of each alternative includes the method and the data in Tables II & III. The CRF method is an
direct capital of new transmission lines and substation, equal annual investment cash flow method. The uncertainty of
overhead charge and interest during construction (IDC), the discount rate was incorporated in the evaluation. The OMA
and is given in Table II. (operation, maintenance and administration) cost including the
6) The probability distribution of the discount rate, which taxes were estimated on the yearly basis using the financial
includes both interest and inflation rates, is presented in estimation method in the utility. Both the expected annual
Table III. investments and OMA costs are presented in Table VI.LI: FRAMEWORK OF PROBABILISTIC POWER SYSTEM PLANNING 7
TABLE IV TABLE VI
B ENEFIT DUE TO R EDUCTION IN THE U NRELIABILITY C OST ($M) E XPECTED A NNUAL I NVESTMENTS AND OMA C OSTS
Year Alternative 1 Alternative 2 Alternative 3 Investment ($M) OMA Cost ($M)
Year
2016 21.558 19.783 11.187 Alter. 1 Alter. 2 Alter. 3 Alter. 1 Alter. 2 Alter. 3
2017 25.242 23.295 12.075 2016 17.718 15.383 16.122 0.979 0.255 0.318
2018 26.900 24.876 12.474 2017 17.718 15.383 16.122 0.979 0.499 0.318
2019 28.557 26.457 12.874 2018 17.718 15.383 16.122 1.158 0.499 0.358
2020 29.458 27.297 12.796 2019 17.718 15.383 16.122 1.237 0.790 0.358
2021 31.094 28.280 13.577 2020 17.718 15.383 16.122 1.277 0.790 0.497
2022 31.810 28.710 13.918 2021 17.718 15.383 16.122 1.317 0.790 0.537
2023 32.628 29.202 14.309 2022 17.718 15.383 16.122 1.317 0.790 0.750
2024 33.241 29.570 14.602 2023 17.718 15.383 16.122 1.317 0.790 0.750
2025 33.957 30.000 14.943 2024 17.718 15.383 16.122 1.317 0.790 0.750
2026 33.967 28.249 14.133 2025 17.718 15.383 16.122 1.317 0.790 0.750
2027 33.975 26.789 13.457 2026 17.718 15.383 16.122 1.317 0.790 0.750
2028 32.261 26.379 13.213 2027 17.718 15.383 16.122 1.317 0.790 0.750
2029 30.236 25.895 12.924 2028 17.718 15.383 16.122 1.317 0.790 0.750
2030 28.989 25.598 12.747 2029 17.718 15.383 16.122 1.317 0.790 0.750
2031 28.225 25.050 12.693
2030 17.718 15.383 16.122 1.317 0.790 0.750
2032 26.601 23.887 12.579
2031 17.718 15.383 16.122 1.317 0.790 0.750
2033 25.073 22.792 12.472
2032 17.718 15.383 16.122 1.317 0.790 0.750
2034 23.354 21.560 12.351
2033 17.718 15.383 16.122 1.317 0.790 0.750
2035 22.113 20.670 12.264
2034 17.718 15.383 16.122 1.317 0.790 0.750
2035 17.718 15.383 16.122 1.317 0.790 0.750
TABLE V TABLE VII
B ENEFIT DUE TO R EDUCTION IN THE E NERGY L OSS C OST ($M) E XPECTED P RESENT VALUE OF THE N ET B ENEFIT ($M)
Year Alternative 1 Alternative 2 Alternative 3 Alternative 1 Alternative 2 Alternative 3
2016 8.401 1.114 2.558 276.204 191.518 -4.801
2017 9.078 1.221 1.346
2018 10.874 3.942 2.056
2019 10.546 4.123 2.187 VII. C ONCLUSIONS
2020 11.553 5.525 2.741
2021 12.685 6.244 3.258 This paper presents an overview of probabilistic power
2022 13.181 6.558 3.484 system planning. The basic concepts, criteria, procedure,
2023 13.787 6.958 3.646 analysis techniques and tasks of probabilistic power system
2024 14.242 7.258 3.767 planning are discussed. Probabilistic reliability evaluation and
2025 14.773 7.608 3.909 probabilistic economic assessment are two key steps. However,
2026 14.845 7.753 4.151 it should be recognized that the contents of probabilistic power
2027 14.905 7.874 4.353 system planning are much beyond these two aspects.
2028 14.083 7.396 3.964 Probabilistic power system planning can overcome the de-
2029 13.112 6.831 3.504
merits of deterministic planning criteria since it covers both
2030 12.514 6.484 3.222
consequences and probabilities of outages events and provides
2031 12.056 6.263 3.081
2032 11.082 5.792 2.782
results closer to reality. It is important to appreciate that
2033 10.166 5.350 2.500 there is no conflict between the deterministic and probabilistic
2034 9.134 4.852 2.183 planning criteria. Both criteria can be combined to apply to a
2035 8.390 4.492 1.955 system planning process.
An actual example using a utility system is given to demon-
strate an application of probabilistic transmission development
planning. This is just a specific example. Many other planning
The expected present values of net benefit for the three tasks listed in Section V can be performed under the frame-
alternatives were calculated using the intermediate results work of probabilistic power system planning.
in Tables IV, V and VI, and the probability distribution of
discount rate in Table III. The results are given in Table VII. R EFERENCES
It can be seen that Alternatives 1 and 2 can make positive net [1] W. Li, Probabilistic Transmission System Planning. New York: Wiley
benefits, whereas Alternative 3 cannot be financially justifiable and IEEE Press, 2011.
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transmission reliability assessment in probabilistic planning of BC hydro at BC Hydro in Canada. He is a fellow of the
vancouver south metro system,” IEEE Transactions on Power Systems, IEEE, the Engineering Institute of Canada, and the
vol. 10, no. 2, pp. 964–970, 1995. Canadian Academy of Engineering. Dr. Li is an
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Power and Energy Magazine, vol. 5, no. 5, pp. 46–53, 2007. than 100 technical reports. He is an inventor of
[15] W. Li and F. P. P. Turner, “Development of probabilistic transmission several USA and Canadian patents. He has received
planning methodology at BC hydro,” in Proceedings of PMAPS 1997, over 10 national and international honors, including
1997, pp. 25–31. the IEEE Canada Outstanding Engineer Award in
[16] W. Li and P. Choudhury, “Probabilistic planning of transmission sys- 1996, IEEE PES Roy Billinton Power System Reliability Award in 2011,
tems: Why, how and an actual example,” in 2008 IEEE PES General International PMAPS Merit Award in 2012 and IEEE Canada Power Medal
Meeting, 2008, pp. 1–8. in 2014.You can also read
