In vertically integrated systems the strategic electrical network manage= ment is performed in an integrated fashion by the monopolist, whereas in th= ose market based, this problem is responsibility of another entity usu= ally called the Transmission System Operator (TSO). The transmission networ= k is the nervous system of any EES and the strategic network management pos= es very challenging issues. Basically in the long term perspective, the mai= n goal are:

- Reinforce the networks itself by constructing new branches and possibly=
dismissing old ones. Additionally the decision of installing network techn=
ologies, together with their siting, can be considered in the grid reinforc=
ement process. These technologies could enhance the operation/controllabili=
ty of the grid and include: Phasor Measurement Units (
*PMUs*), Wide-= Area Measurement Systems (*WAMS*), and*notably*Flexible Alt= ernating Current Transmission Systems (*FACTS*). It is in fact known that power flowing on individu= al lines cannot be controlled, though these devices are improving the abili= ty of system operators to do so (possibly in conjunction with OTS = related operations). - Energy Storage System siting and sizing, say deciding where locate and = the size of an ESS (e.g. 2).
- Smart grids design. The actual design of a smart grid in a certain loca= l area is another universe of related (optimization) problems, and surely i= ncludes also previous two class of problems.

In order to approach the three above-mentioned classes of problems, many= tools described in the short term management are obsviously used.= Their usage is somehow differently oriented however:

**Load Flow**: LF is actually*not*an optimization= problem, it is (just) a calculation of the power flowing along an electric= al network where we have fixed the generation schedule and the load in the = several nodes of the grid. While being not an optimization problem, it give= s evidence on the networks operating points under different conditions. Und= er strategic perspective LF can be used integrated in a what if analysis to= ol.**Optimal Power Flow**: The OPF problem deals with the opt= imization of the generating cost, and possibly hydro resources, considering= the electricity grid. In considering the grid OPF takes into account the n= on linear Kirchhoff laws and the restrictions on power flow on each branch = (transmission line) and voltage angles. Typically the generation cost optim= ization is performed considering all the units status (on or off)*fixed to a feasible status otherwise found. As for the LF, also OPF u= nder strategic perspective can be used integrated in a what if analysis too= l.To date there are many formulations of OPF from the first one appeared in= the sixties, they basically fall into two broad classes:**The Direct Current (DC) model*: here the network structure is t= aken into account, including the capacity of the transmission links, but a = simplified version of Kirchhoff laws is used so that the corresponding cons= traints are still linear.*The Alternative Current (AC) model:*here the full version o= f Kirchhoff laws is used, leading to highly nonlinear and nonconvex constra= ints. To cope with these difficulties a recent interesting avenue of resear= ch concerns the fact that the non-convex AC constraints can be written as q= uadratic relations. In particular quadratic relaxation approach have been p= roposed which builds upon the narrow bounds observed on decision vari= ables (e.g. phase angle differences, voltage magnitudes) involved in power = systems providing a formulation of the AC power flows equations that can be= better incorporated into UC models with discrete variables. Again in the l= ong term, the level of details of the OPF models can be adjusted depending = on the goals.

**Security Constrained UC (SCUC):**SCUC is an integrat= ed problem, say an integration of OPF and UC. So from one side one wants to= consider a detailed set of constraints from power plants and from the othe= r the physics of the grid itself as in an OPF. The inclusion of the status = variables as in an ordinary UC further complicates the problem.

=**N-k OPF/SCUC/security:**This problem is an example o= f how things are decoupled in power systems. The issue here is to find a le= ast cost schedule of production and flows that is also resistant to unpredi= ctable fault of one of the component (power plant, network branch etc.). Th= e n-1 security problem refers to a single fault. From a methodological= standpoint one could consider n-k SCUC as an integrated problem, and some = modeling proposal in this direction have been presented. In practice TSO te= nd to decouple OPF or SCUC from n-k, solving this latter problem by adding = security requirements to an already*quasi-*fixed solution from SCUC= (e.g. 1)

Differently from the short term management, in the strategic vi=
ew, these problems are solved in models equipped with an upper lever set of=
decision variables, that indicate the virtual presence (or dismission) or =
a certain set of new branches, special devices and some representation of t=
heir costs. Additionally in recent times, due to the increasing capability =
of storage mainly at the distribution level, also the size, types and sitin=
g of such storage equipment contributes to the set of the decision variable=
s. From a methodological standpoint, very often these prescriptive problems=
are tackled in a what if analysis fashion, or with approaches that fall in=
the broad definition of *optimization with costly function*. In oth=
er words the upper level decision variables are seen as a set on which the =
decision maker does sensitivity or in a more sophisticated approaches as a =
set of variables whose change on cascade produces another optimization prob=
lem with other - more operating - variables. However especially in the scie=
ntific literature there are attempts to model the whole problem with all va=
riables at the same level.

Indeed, it is very important to consider the operation and scheduling of= generation and storage units already at design phase to determine the most= convenient combination (i.e. minimum objective function) of technology sel= ection and size. This is especially true when dealing with selection, sizin= g and unit commitment of long-term, or seasonal, energy storage. Long-term = storage systems have recently caught much attention due to their ability to= compensate the seasonal intermittency of renewable energy sources. However= , compensating renewable fluctuations at the seasonal scale is particularly= challenging: on the one hand, a few systems, such as hydro storage, hydrog= en storage and large thermal storage can be used to this purpose; on the ot= her hand, the optimization problem is complicated due to the different peri= odicities of the involved operation cycles, i.e. from daily to yearly. This= implies long time horizons with fine resolution which, in its turn, transl= ates into very large optimization problems. Furthermore, such systems often= require the integration of different energy carriers, e.g. electricity, he= at and hydrogen. Exploiting the interaction between different energy infras= tructure, in the so-called multi-energy systems (MES), allows to improve th= e technical, economic and environmental performance of the overall system [= 3].

In this framework, including the unit commitment problem already at desi= gn phase implies taking into account the expected profiles of electricity a= nd gas prices, weather conditions, and electricity and thermal demands alon= g entire years. Moreover, the technical features of conversion and storage = units should be accurately described. The resulting optimization problem ca= n be described through a mixed integer nonlinear program (MINLP), which is = often simplified in a mixed integer linear problem (MILP) due to the global= optimality guarantees and the effectiveness of the available commercial so= lvers (e.g. CPLEX, Gurobi, Mosek, etc.). In this context, integer variables= are generally implemented to describe the number of installed units for a = given unit, whereas binary variables are typically used to describe the on/= off status of a certain technology. Furthermore, decomposition approaches r= elying on meta-heuristic algorithms for unit selection and sizing have been= proposed. A comprehensive review of MINLP, MILP and decomposition approach= es for the design of MES including storage technologies has been carried ou= t by [4]. However, independently of the implemented approach, significant m= odel simplifications are required to maintain the tractability of the probl= em. Such simplifications include limiting the number of considered technolo= gies, restricting technology installation to a subset of locations, analyzi= ng entire years based on seasonal design days or weeks, or aggregating the = hours of each day into a few periods.

[1] D. Bienstock and A. Verma. The n - k problem in power grids: New mod= els, formulations and numerical experiments. 1386 Siam J. on Optimization, = 2011.

[2] Mostafa Nick, Rachid Cherkaoui, Mario Paolon= e. Optimal siting and sizing of distributed energy storage systems v= ia alternating direction method of multipliers. International Journal of El= ectrical Power & Energy Systems. 03/2015.

[3] P. Mancarella, MES (multi-energy systems): An overview o= f concepts and evaluation models, Energy. 65 (2014) 1=E2=80=9317.

[4] C. Elsido, A. Bischi, P. Silva, E. Martelli, Two-stage M= INLP algorithm for the optimal synthesis and design of networks of CHP unit= s, Energy. 121 (2017) 403=E2=80=93426.

**Contributor**

Prof. Laureano Escudero, Universidad Rey Juan Carlos<= /span>

Dr Fabrizio Lacalandra, QuanTek

Dr Paolo Gabrielli, ETH Z=C3=BCrich