In monopolistic environment for energy transmission network capacities w=
ere designed with a wide safety margin, so for a long time expansion planni=
ng in electrical energy systems was concentrated on generation expansion pl=
anning (GEP) with the goal to cover cumulative demand uncertainty based on =
averaged historic demand data. These were modeled as stochastic optimizatio=
n problems with a one dimensional demand distribution represented by 2-stag=
e or multi-stage scenario trees that were generated by Monte Carlo methods.=
The models went to the limit of computational possibilities at any point i=
n time,

included binary decision variable, with a risk neutral approach =
and, then, only expected values in the objective function where considered =
in the time horizon over the scenarios. Very limited use was made of risk a=
verse measures.

In order to solve the large scale problems, decompos=
ition methods played a central role, in particular the following methodolog=
ies:

- Two-stage Benders Decomposition (BD) for linear problems [11]. See [8,3= 7,55], among many others.
- Multistage Benders Decomposition (BD) methodology for linear problems. = See [13] among others.
- Two-stage Lagrangean Decomposition (LD) heuristic methodology. Se= e [14,1718,29,28,33,41,42], among many others. See also [2, 56] for t= wo surveys on the state-of-the-art of two-stage stochastic unit commitment,= and using LD with bundle methods. See also [1,16,51] two-stage LD ap= proaches with bundle methods applied to energy problems.
- Multistage Clustering Lagrangean Decomposition (MCLD) heuristic methodo= logy. See [21,22,23,38], among some others.
- Regularization methods. See [9, 33, 39, 49, 50, 53], among others.
- Progressive Hedging algorithm (PHA) for multistage primal decomposition= . See [47,57], among others.
- Multistage Stochastic Dynamic Programming (SDP). See [4,15,25,26,30,32,= 40,44,45,48,54], among others.
- Multistage cluster primal decomposition. See [5,7,10,19,24,38,43,52,58]= , among others.
- Parallelized decomposition algorithms. See [3,4,5,6,9,12,34,39,43,48,52= ,58], among others.

Today, new power production possibilities, technological developments an=
d deregulation bring along several new sources of uncertainty with highly d=
iffering levels of variability. In addition to traditional demand these are=
foremost dependencies on wind, market prices, mobile electricity consumers=
like cars, power exchanges on international level, local energy producers =
on distribution network level and, to a lesser extent, solar radiation. Thi=
s introduces complex and volatile load and demand structures that pose a se=
vere challenge for strategic planning in production and transmission and, o=
n a shorter time scale, in distribution. Networks may now be equipped with =
new infrastructure like Phase Measurement Units (PMUs) and other informatio=
n technology in order to improve their cost efficiency. At the same time th=
ese upgraded networks should ensure high standards in reliability in their =
daily use and resilience against natural or human caused disasters. Compani=
es now have teams devoted to the task of generating suitable planning data.=

In optimization models, the emphasis has shifted to high dimensiona=
l stochastic data and to considering risk reduction measures instead of exp=
ected values. Computationally integrated models considering all relevant as=
pects are out of scope. Even for simplified models it is often difficult or=
not known how to provide stochastic data of sufficient quality [63]. Alter=
natives are then:

- robust optimization, where distributions are replaced by "easier" uncer= tainty sets [59],
- fuzzy methods, where uncertainties are replaced by a kind of interval a= rithmetic equipped with scenario dependent probabilities [60],
- information gap decision theory that aims at hedging against info= rmation errors [61,62].

Methods for solving these stochastic optimization problems with binary d=
ecision variables employ the same decomposition approaches listed above, bu=
t much more care needs to be devoted to the properties of the decomposition=
. For risk averse measures in multistage models, methods are distinguished =
regarding their "time consistency" or "time inconsistency". So far, stochas=
tic dynamic programming approaches are the most suitable ones for dealing w=
ith the time consistency property of risk measures, so that the original st=
ochastic problem may be decomposed more easily via scenario clustering and =
cluster dependent risk levels.

In power generation optimization mode=
ls for big companies the following are the issues of relevance, mainly addr=
essed in the context of market competition:

- when and where to install how much new production capacity, mainly cons= idering wind generators and thermal plants (decisions on nuclear power are = political)
- how to extend or renew hydro plants and where to install what pumping c= apacities. Today, solar power is typically handled at the level of di= stribution networks.

In contrast, competition is not an issue for transmission and distributi= on network operators. Regulations on efficiency, reliability and resilience= levels are the driving force in the following problems:

- when and where to install how much network capacity and information equ= ipment,
- reducing transmission losses,
- reducing distribution losses (technical and detecting non-technical one= s).

Challenges today and for the future comprise:

- The robust approach allows for safe optimization with uncertain data.&n= bsp; What information can be extracted from these robust solutions e.g. on = which additional data would be needed to improve the quality of the model?<= /li>
- Several risk averse measures have been proposed, each with&= nbsp; its advantages and disadvantages. How to make use of them in the best= way?
- How to deal with endogenous uncertainty, i.e., with optimizing big play= er decisions that influence the probability distributions that are optimize= d over?
- How to construct hierarchical decomposition approaches in a consistent = way?
- How to make use of high performance computing (HPC, multi-core or Distr= ibuted) in decomposition approaches?
- How to integrate chance constraints (ICC), e.g. with respect to reliabi= lity or resilience?

General goals for future models include: increasing the level of integra= tion; bringing models closer to reality by avoiding the excessive lineariza= tion of nonlinear aspects; reducing the gap between methods used in academi= a and those applied in practice; making use of new monitoring devices and c= ommunication systems; exploring the chances of cooperation between electric= and other energy commodity systems.

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Prof. Laureano Escudero, Universidad Rey = Juan Carlos

Dr Alireza Soroudi, University Colle= ge Dublin (UCD)

Prof. Christoph Helmberg, TU Chemnitz