IEEE Power & Energy Magazine - July/August 2016 - 35
Model
Formulation
Scenario
Development
Network
Simplification
Stochastic Transmission Planning
figure 2. The JHSMINE planning schematic.
(0.2) probabilities for each scenario, plan b is actually less
expensive by about Us$5 billion in expected present worth.
Thus, making a naïve decision (plan a) based on a single
scenario rather than the stochastic decision (plan b) that
considers system adaptability under several scenarios could
result in a cost penalty of the same order of magnitude as the
investments themselves.
JHSMINE-A Stochastic
Transmission Planning Tool
we now describe in greater detail an illustrative stochastic
analysis using the Johns hopkins stochastic multistage Integrated network expansion (JhsmIne) model, testing its
performance with the data from the weCC. figure 2 shows
a schematic of the basic steps involved in using JhsmIne
that we describe in this section.
Brainstorm Variables
Rate Importance of Variables
Choose Range of Variables
Provide Nine TAG Scenarios
Define Three Correlated Groups
Define Six Gap Scenarios
Combine Similar Scenarios
Review Relative Impacts and
Likelihood of Scenarios
Consolidation of Scenarios
Probability Assignments
Runs
Scenario Input from TAG
Scenario Input from JHU
figure 3. The scenario development procedures in the
JHU-WECC study.
36
ieee power & energy magazine
for the first step, we formulated the model to fully
address the key considerations of system-level interactions,
future uncertainties, and system adaptability by appropriate
definitions of the objective and constraints:
✔ minimize the probability-weighted present worth of
transmission and generation capital plus operating
costs subject to the following constraints:
* short-term operational constraints (energy balances,
Kirchhoff's voltage law to represent parallel flows,
capacity limits on plant generation and transmission
flow, wind- and solar-output limitations by hour,
operating-reserve requirements, and renewable portfolio standards)
* long-run expansion constraints (siting limitations on
the location and capacity of new lines and generation).
This model is structured as a multistage mixed-integer
linear program, which is solved as a single large optimization problem. The stages are the years considered (e.g., years
1-10 investments represent stage 1, years 11-20 investments
are stage 2), as shown in figure 1. operating hours within
each stage are chosen from a representative single year and
are either chronological for representative days (as in our
relaxed unit commitment implementation of JhsmIne) or
are randomly selected (as in our load duration curve implementation). The resulting model has on the order of 1-3
million variables, depending on the particular formulation,
number of scenarios, and number of operating hours.
In the second step, we need a comprehensive set of scenarios (called "study cases" by weCC). The variables that
vary among the scenarios should be important: they would
affect the relative desirability of different investments, and
there is a reasonably large range of possible values in the
future. The only thing we can be sure of is that the future
behavior of these variables will be different from the past,
so their possible ranges, distributions, and correlations must,
by necessity, rely on expert judgment. In the weCC study,
Johns hopkins University (JhU) collaborated with a group
of experts and stakeholders called the technical advisory
group (TaG), and developed 20 scenarios to be analyzed.
figure 3 outlines the procedure used to develop the scenarios, with a generic procedure shown on the right and our
specific implementation on the left.
as figure 3 suggests, a number of different types of
judgments were necessary, some of which were made by
the TaG experts and some by JhU staff. The members of
the TaG picked those variables they thought would most
impact the weCC system and then provided ranges (i.e.,
90% confidence intervals) for each variable. The variables
suggested for the weCC study included, among others, natural gas and coal prices, carbon tax, energy growth, peakload growth, renewable portfolio standards, and capital
costs of wind, solar, and geothermal plants (Table 1). Then,
the TaG experts considered the five original 2013 TeppC
scenarios and added nine more scenarios (particular combinations of the variables) they thought were plausible.
july/august 2016
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