IEEE Power & Energy Magazine - July/August 2016 - 22
investment process but rather due
to operating conditions, which are
in turn characterized by publicly
Aleatory
Epistemic
known and agreed upon probNature of
Due to Inherent
Due to Imperfect
abilities. Thus, proactive models
Uncertainty
Variability
Knowledge
remove epistemic uncertainties
by directly modeling investment
behavior, while aleatory uncerIrreducible
tainty regarding system operation
Uncertainty
is irreducible but easily described
Innovative Research
by probabilities, i.e., inherent.
Although we stress the importance of distinguishing epistemic
Example: Generation Expansion
and aleatory uncertainties, we
Strategic Generation
Scenarios for
include this distinction in a higher
Expansion
Generation Expansion
Equilibrium Model for
level with respect to more pracIrreducible Uncertainty in
Generation Investment
Operating Conditions
tical dimensions because of its
conceptual importance and lack
of practical relevance outside innofigure 4. The fundamental nature of uncertainty ranges from aleatory to epistemic.
vative research. While we do not
A distinction becomes relevant only when innovative research enlightens the underattempt to argue in favor of scenarstanding of some uncertainty.
ios or equilibrium models to represent generation expansion in TEP,
it is clear that complex uncertainties such as generation expan- (e.g., long-term scenarios and earthquakes), thus presenting
sion are simultaneously composed of imperfect knowledge (i.e., the lowest level of the mathematical structure. For dealing
the economic equilibrium describing generation investment by with poorly structured U uncertainties, strategic scenarios
competing firms) and inherent variability (e.g., uncertainty in depicting divergent futures or possible singular events are
operating conditions and fuel prices, present even if the equi- used. Given the lesser mathematical structure of scenarios,
librium model of investment is completely specified). However, robust and flexible expansion plans are designed, as disthis distinction is irrelevant from a practical perspective until cussed in the section "Optimization Approaches to TEP
innovative research enlightens our understanding of the under- Under Uncertainty." We abstract from the close relationship
lying process that produces uncertainty. Increased research between the extremes of perfect and poor structure and the
efforts may never be able to explain many important sources of nature of uncertainty previously discussed to serve practice
uncertainty, such as public policy or earthquakes. Thus, model- rather than theory.
ing uncertainties in practice has not and should not focus on the
KuU extends the classical division between random and
nature of uncertainty.
nonrandom uncertainties found in TEP literature by providing a more practical and consistent framework for modeling.
The classical division states that random uncertainties are
Structure of Uncertainty:
observable events that repeat frequently, so statistics may be
Known,Unknown, and Unknowable
The structure of uncertainty is a practical modeling distinc- derived from historical data for random uncertainties (e.g.,
tion between Known, unknown, and Unknowable uncer- yearly demand growth). Any other uncertainty is nonrantainties (KuU, respectively, see Figure 5), a categorization dom and, some assert, to be treated by scenarios. Although
of uncertainties proposed by Diebold, Doherty, and Herring such division successfully identifies random uncertainties
in 2010. Known uncertainties are those where a probabilis- that may be modeled by probability distributions or stochastic representation is completely specified (e.g., hourly nodal tic processes, it fails to identify robust and fuzzy approaches
load and yearly demand growth), and therefore structured applied to TEP under uncertainty and also fails to acknowlmathematical tools such as stochastic programming (SP) edge subjective probabilities. Therefore, we further distinare readily available; unknown uncertainties are those guish nonrandom uncertainties between u and U, given the
for which probabilities are hard or impossible to assign to different modeling approaches applied in TEP research for
some events (e.g., investment costs, delays in starting opera- each class (e.g., robust/fuzzy for nodal load and scenarios for
tion, and new facility outages) and are often modeled by the long-term state of the market, respectively). K extends
sets bounding outcome (e.g., intervals centered on a nomi- the group of random uncertainties by considering all those
nal forecast) or other less-structured representations (e.g., described by probabilities, whether these are derived from
fuzzy sets). Unknowable uncertainties are situations where historical data, a stochastic process, or subjective beliefs.
even the events cannot be clearly identified in advance Although subjective probabilities are not commonly used in
july/august 2016
ieee power & energy magazine
23
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