The objectives of electric power **Generation Expansion Planning (GEP) and Network Expansion Planning (NEP)=
problems are to determine the "optimal" selection of gen=
eration and network technologies (in a broad sense) and the right time<=
/em> and right place to construct (and/or dismiss) them, =
while ensuring an 1) economic, 2) reliable, and 3) environmentally acceptab=
le supply according to the predicted demand. Needless to say these problems=
involve amount of money of the order of magnitude of the tens of billions =
=E2=82=AC for large countries.**

A typical GEP optimization model has 1) a planning horizon, 2) an economic =
(multi)-objective including the present value of the total cost and other c=
omponents, 3) a long set of constraints including: capacity limitations, en=
vironment regulations, fuel costs, customers demands, fuel availability (fo=
r instance gas pipelines for CCGT) and mix diversification requirements, an=
d 4) a set of the decision variables representing the operating and expansi=
on options (that depends on the perspective of the actor). To make the matt=
er even more complicate, in the predominant market based models, the GEP an=
d NEP problems must also take into account present, and future, market rule=
s and incentives.

Some author define the GEP and NEP
*co-optimization problems* accordingly with the following definition=
:=20
*co-optimization is the simultaneous identification of two or more class=
es of investment decisions within one optimization strategy*. If co-opt=
imization is used by a monopolist integrated utility, then its main result =
is the identification of joint GEP-NEP that are lower in cost than would be=
if GEP and NEP were developed separately. However, co-optimization can als=
o be used within countries that are market based and where NEP is performed=
by one entity (TSO) while GEP is performed by others (GenCos). Co-optimiza=
tion can be naturally be compared to the =E2=80=9C
*one optimization strategy*=E2=80=9D that may consist of a formulati=
on to solve a single optimization problem (e.g., for a GenCo in the GEP per=
spective, maximize expected profit subject to budget constraints) or it may=
consist of a formulation to solve an iterative series of optimization prob=
lems (i.e., sequential yet possibly coordinated generation and transmission=
planning).

As an example of goals of a GEP-NEP co-optimization we list the following:

- savings of transmission and generation investment and operating costs
- more efficient decisions concerning generation dismissals and repowerin= g
- more appropriate treatment of intermittent resources
- efficient integration of non-traditional resources such as demand respo= nse, customer-owned generation, other distributed resources, and energy sto= rage systems
- fuel mix diversification benefits
- improved assessment of the ramifications of environmental regulation an= d compliance planning
- reduced risk and attendant effects on resource adequacy and costs.

Historically the practice was to attack the GEP problems first, and then=
the NEP ones. This approach was motivated because of 1) the complexity of =
the coupled problem(s), 2) because of the controllability of the traditiona=
l power plants with their different technologies (Nuclear, Coal, Steam Turb=
ine, CCGT, Gas Turbine, Hydro Basin), 3) because interregional power exchan=
ges were limited. However assessing both simultaneously to provide an integ=
rated plan is capable of identifying attractive solutions that may not othe=
rwise be considered. Doing so is becoming more important, due to 1) the inc=
reasing penetration of non programmable renewable resources, energy storage=
systems, distributed generation and demand response and 2) the need for in=
terregional energy transfers to take advantage of diverse and remote source=
s of power. For instance we argue that the newly launched Price Coupling of=
Regions (PCR) in EU does not only enable to clear at European level the Da=
y Ahead Markets in the short term, but also gives the opportunity to consid=
er at regional level the GEP-NEP problems in the longer terms. Thus, NEP ar=
e *not* necessarily the least-cost means of meeting those needs (con=
sidering both economic and environmental costs). Second, siting of new gene=
ration, including renewable sources, is influenced by the availability of t=
ransmission, so that different transmission expansion plans will ultimately=
result in different patterns and even mixes of generation investments.

In what follows we will consider the GEP and NEP as a single unified pro= blem, and discuss recent approaches for it.

First of all, we note that co-optimized GEP and NEP problems posed signi= ficant computational challenges. Computer resources available to planners b= efore, say, ten years ago were incapable of supporting the solutions of co-= optimization models. Fortunately, recent advances in computation methods ha= ve provided satisfactory solutions to co-optimized GEP and NEP problems wit= h reasonable computation times, so now realizing savings by using co-optimi= zation is a real possibility. Also we observe that in GEP-NEP optimization = problems uncertainty is, of course, ubiquitous.

There are several challenging issues in the co-optimization of GEP and N= EP. First, conflicting objectives: GEP can be driven by prices but the same= principle may not apply to the NEP (eg. 1). Second, power system constrain= ts such as network flow limits, load demands, and reliability requirements = link the two planning problems, which introduce an additional dimension of = difficulty in finding feasible and practical planning solutions. Third, one= of the main obligations of expansion planners is to facilitate a fair and = competitive market. The planner also has to take into account uncertainties= associated with renewable energy, non-traditional generation resources suc= h as microgrids, fuel costs, component outages (such as transmission lines,= plants, and transformers), and customer behavior including demand response= . The co-optimization of GEP and TEP becomes much more challenging when con= templating the full range of uncertainties relevant to expansion planning. = Earlier attempts uses Benders decomposition-based approach developed to sep= arate and coordinate the investment problem and operating subproblems (e.g.= [2]). Reliability issues were assessed in terms of customer interruption f= unctions in co-optimization models [3], allowing tradeoffs between outage, = investment, and operating costs. However, these earlier models were oversim= plified and thus deemed impractical for market-based generation and transmi= ssion expansion planning.

In general, co-optimization is viewed as a bi or tri-level optimization = problem for generation and transmission and iterative schemes have been use= d to coordinate the two planning problems. As an example, Baringo and Conej= o [4] presented a bi-level stochastic co-optimization model and transformed= it into a single-level mathematical programming with equilibrium constrain= ts.The author show - as expected - that transmission expansion decisions si= gnificantly affect wind power capacity expansion even though investment cos= t in transmission expansion is much lower than that in wind power capacity.= A recent study in [5] presented a co-optimization model that incorporated = transmission congestion costs. It was shown that distributed generation cou= ld mitigate congestion and defer transmission investments. A follow-up stud= y in [6] proposed a co-optimization model which accounted for incentives of= fered to independent power producers (IPP).

As for data uncertainty, stochastic programming was applied in [7] to si= mulate random outages of system components. It was shown that even simple c= o-optimization models could result in significant savings when optimizing t= ransmission and generation assets. Also stochastic programming was the main= ingredients in [7] in order to consider alternative scenarios of future ec= onomic, regulatory, and technology developments.

GEP and NEP co-optimization models include both transmission expansion p= lanning and generation planning for multiple years/decades and multiple loc= ations/regions. This leads to computational challenges due to the fact that= the details of power systems can greatly increase the size of the problem.= In addition, nonlinearity and integer variables and uncertainties can add = additional complications. As discussed in the Operational-Network = section, modeling of transmission flows by itself can be a very difficult n= on-linear program (the OPF with full AC representation). After adding inves= tment expansion decisions, the problem becomes an even harder mixed-integer= nonlinear program.

Several simplifications are therefore applied, such as:

Simplification approaches include:

- Aggregation of input data and model variables (e.g., [9])
- Simplification of dynamics and uncertainties (e.g., [9])

Approaches to modeling aggregation include:

- Location aggregation (e.g., aggregated region(s) instead of exact locat= ions)
- Time period aggregation (e.g., multiple year instead of daily data) (e.= g., [10])

However even if model aggregations and simplifications are effective for= reducing computational complexity, models then lose fidelity and accuracy = to some extent. Thus, it is desirable to solve large-scale and complicated = problems. At the present time we have probably two approaches, 1) try to li= nearize everything by means of the many possible approaches eventually reso= rting to piecewise linear modeling, or 2) using decomposition approaches su= ch as those well known in the optimization community, say:

- Benders Decomposition
- Column Generatiom
- Branch-and-Price

NEP is one ofthe main strategic decisions in power systems a= nd has a deep, long-lasting impact on the operation of the system. Relative= ly recent developments in power systems, such as renewable integration or r= egional planning, have increased considerably the complexity and relevance = of this problem. This is particularly true in the case of the European Unio= n.

The design of large-scale network expansions poses considerable ch= allenges that have been addressed in a vast array of both projects and acad= emic literature. Existing thorough academic reviews on this topic can be fo= und in references [11, 12, 13]. These papers are a very good starting point= to understand the state of the art of the network expansion planning chall= enges and current approaches.

Among the current challenges to be addressed for the network expan= sion planning we can mention the following ones:

- Its coordination with GEP, as discussed previously. On the one ha= nd, GEP is a deregulated business activity while NEP is mostly regulated. O= n the other hand, generation investments can take around three years, while= network expansion need to be anticipated longer periods.
- Renewable integration is one of the major drivers for investing i= n new transmission lines. Onshore and offshore wind power, and solar genera= tion are renewable technologies currently being developed at large scale to= meet the low-carbon electricity generation targets. A large part of this g= eneration is located in remote areas far from the load centers requiring tr= ansmission reinforcements or new connections. Besides, the intermittent nat= ure of these renewables introduces operational challenges and, from the net= work planning point of view, many varied operation situations should be con= sidered.
- Market integration is the current paradigm to achieve a competiti= ve, sustainable and reliable electric system and the network is a facilitat= or in this process. The creation of an European internal market with strong= enough interconnection capacity among the member states increases the scop= e of the planning process, from a national activity to a European scale.

Different mathematical optimization techniques are used for solvin= g the network expansion planning. They can be classified as: classical and = non-classical (metaheuristic) methods see references [12, 13].=

- Classical methods include linear, nonlinear and mixed integer pro=
gramming methods. Linear optimization ignores the discrete nature of the in=
vestment decisions but still it can be useful is system is too large to be =
solved with discrete variables or a relaxed solution is good enough. A tran=
sportation or a direct-current (DC) load flow fit in this linear formulatio=
n. Nonlinear, in particular quadratic, models appear as a way =
to represent transmission losses. Finally, mixed integer optimization allow=
s considering the integer nature of the decisions. If stochasticity in some=
parameters is included then models become stochastic and, therefore, decom=
position techniques should be used for large-scale systems. Among them, Ben=
ders decomposition, Lagrangean relaxation or column generation are frequent=
ly used.
- Non-classical metaheuristic methods include Greedy Randomized Ada=
ptive Search Procedure (GRASP), tabu search, genetic algorithms, simulated =
annealing, swarm intelligence, ant colony optimization, differential evolut=
ion, ordinal optimization, etc.

Network expansion planning is per se a multicriteria decision prob= lem although in many times a single objective function is used by combining= and monetizing the multiple criteria under a single one with the weighted-= sum method. The main criteria are usually: costs, environmental impact, mar= ket integration and other exogenous factors. Costs are measured by the attr= ibutes such as investment and operation costs of the transmission decisions= but also operation costs of the system. In the cost criterion, it can also= be introduced the reliability impact. Environmental impact is determined b= y attributes as amount of renewable integration or curtailment avoided at s= ystem level and impact of the line construction. Market integration is acco= unted as number of hours of market splitting. Social acceptance is an= exogenous criterion and, nowadays, is a major concern of the curren= t planning process and being the cause of many delays.

[1] J. H. Roh, M. Shahidehpour, and Y. Fu, =E2=80=9CMarket-based coordin= ation of transmission and generation capacity planning,=E2=80=9D IEEE Trans= actions on Power Systems, Vol. 22(4), 1406=E2=80=931419, Nov. 2007

[2] M. Pereira, L. Pinto, S. Cunha, and G. Oliveira, =E2=80=9CA decompos= ition approach to automated generation/transmission expansion planning,=E2= =80=9D IEEE Transactions on Power Apparatus and Systems, Vol. 104(11), 3074= =E2=80=933083, 1985

[3] W. Li. and R. Billinton, =E2=80=9CA minimum cost assessment method f= or composite generation and transmission system expansion planning,=E2=80= =9D IEEE Transactions on Power Systems, Vol. 8(2): 628=E2=80=93635, 1993

[4] L. Baringo and A. J. Conejo, =E2=80=9CTransmission and Wind Power In= vestment,=E2=80=9D IEEE Transactions on Power Systems, Vol. 27 (2): 885-893= , 2012

[5] M. Shahidehpour, =E2=80=9CInvesting in expansion: The many issues th= at cloud electricity planning,=E2=80=9D IEEE Power and Energy Magazine, 14-= 18, Jan 2004

[6] M. Shahidehpour, =E2=80=9CGlobal broadcast - transmission planning i= n restructured systems,=E2=80=9D IEEE Power and Energy Magazine., Vol. 5(5)= , 18-20, Sep./Oct. 2007

[7] J. A. L=C3=B3pez, K. Ponnambalam, and V. H. Quintana, =E2=80=9CGener= ation and transmission expansion under risk using stochastic programming,= =E2=80=9D IEEE Transactions on Power Systems, Vol. 22(3), 1369=E2=80=931378= , Aug. 2007

[8] A. H. van der Weijde and B. F. Hobbs, =E2=80=9CThe economics of plan= ning electricity transmission to accommodate renewables: Using two-stage op= timisation to evaluate flexibility and the cost of disregarding uncertainty= ,=E2=80=9D Energy Economics, Vol. 34(5), 2089-2101, Sept. 2012

[9] Y. Scholz, Renewable Energy Based Electricity Supply At Low Costs = =E2=80=93 Development Of The Remix Model And Application For Europe, PhD Di= ssertation, German Aerospace Center (DLR), Institute of Technical Thermodyn= amics, 2012

[10] M. Shahidehpour, W. Tinney, and Y. Fu, =E2=80=9CImpact of security = on power system operation,=E2=80=9D IEEE Proceedings, Vol. 93(11), 2013 =E2= =80=93 2025, Nov. 2005

[11] G. Latorre, R. D. Cruz, J. M. Areiza and A. Villegas, "Classificati=
on of publications and models on transmission expansion planning," *IEEE=
Transactions on Power Systems, *vol. 18, pp. 938-946, 2003.

[12] R. Hemmati, R. Hooshmand, A. Khodabakhshian, "Comprehensive review = of gen-eration and transmission expansion planning", IET Generation Transmi= ssion Distribution 7(2013) 955=E2=80=93964.

[13] S. Lumbreras, A. Ramos "The new challenges to transmission expansio= n planning. Survey of recent practice and literature review," Electric Powe= r Systems Research 134: 19-29, May 2016 10.1016/j.ep= sr.2015.10.013

**Contributor**

Prof Laureano Escudero, Universidad Rey Juan Carlos

Dr Fabrizio Lacalandra, QuanTek