IEEE Power & Energy Magazine - July/August 2016 - 38

It appears that the transmission investments recommended
by stochastic programming are inherently robust against future
uncertainties (even if they were not explicitly modeled).

Near-Term Investments Recommended
by Stochastic Programming Are
More Cost- Effective
depending on the assumptions and the version of
JhsmIne used, our stochastic solutions based on five or
20 scenarios [figure 4(c)] perform Us$1-Us$12 billion
better (in terms of probability-weighted present worth)
than the investments recommended by a deterministic
model, using the weCC's 2013 base-case scenario [figure 4(a)]. for instance, as mentioned earlier, the base-case
solution, which yields the first-stage investments on the
upper right of figure 1, results in expected costs (over
the five weCC TeppC study cases) that are Us$5 billion
higher than a stochastic solution considering all five of
those scenarios (lower right, figure 1).

Stochastic Plans Are More Robust Than
Deterministic Plans Against Scenarios
Not Considered
The advantage of the stochastic solution grows to Us$11 billion if the base-case and five-scenario stochastic solutions are
compared considering all 20 scenarios. It turns out that, in
this case, considering just five scenarios versus using all 20
in the stochastic optimization yielded the same backbone grid
investments-so considering even a few scenarios may capture most of the economic benefit of stochastic planning. The
five-scenario solution did appreciably better than the base-case
solution in a large majority of the other 15 scenarios. Therefore, by choosing investments that give the system flexibility
to adapt to the considered five scenarios, the system also turns
out to adapt more readily to the other 15 scenarios that weren't
considered. Thus, it appears that the transmission investments
recommended by stochastic programming are inherently robust
against future uncertainties (even if they were not explicitly
modeled) compared to deterministic solutions.

Stochastic Planning Outperforms the
Heuristics Based on Identifying Lines
Common to Several Deterministic Plans
as noted earlier, the California Iso and mid-Continent
Iso have promoted heuristic planning processes that identify "robust" solutions as ones that include lines that appear
in several or all deterministic solutions. This planning
approach is represented by heuristic versions of JhsmIne
models. The best performing heuristic we tested is to build
lines now that are built in years 1-10 in a majority of the
july/august 2016

figure 6. The 300-bus network used in the JHU-WECC
study: the blue lines represent candidate lines that could be
chosen by the model; the circles represent possible renewable hubs.

20 individual deterministic models (one model for each of
the 20 scenarios). It does better than the base-case-only
solution, but over Us$1 billion worse than the stochastic
solutions that considered either five or 20 solutions. other
heuristic solutions based on choosing lines that appear in all
the deterministic solutions, or that are chosen by any of the
solutions, do much worse. Thus, although such a heuristic
sometimes (but not always) does better than planning for a
single scenario, the stochastic solution does even better.

Potential Improvements
The successful use of multiple scenarios to represent social,
economic, and environmental uncertainties in an economic optimization model for transmission, together with
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Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - July/August 2016
