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Definition and Theory of Transmission Network Planning

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Transmission Network Investment in Liberalized Power Markets

Part of the book series: Lecture Notes in Energy ((LNEN,volume 79))

Abstract

With increasing interest in building large-scale solar parks and wind farms and the implementation of new environmental regulations that will result in retirement of some conventional power plants, the need for building new transmission is inevitable even in regions with low demand growth. Planning of such network expansion is therefore increasingly important, particularly because the cost of new transmission is typically higher in real terms than historical costs. This chapter contains five sections. In the first section, the impact of different factors affecting transmission expansion planning (TEP) is investigated, and different models for transmission investment financing and coordination are reviewed. The second section covers a literature review on TEP studies. Different TEP optimization formulations and available decomposition techniques are explained in the third section. Then, a general framework for solving large-scale TEP studies is reviewed, and computational challenges/potential solutions are investigated from different perspectives in section four. The chapter concludes with a section on numerical analysis, in which large-scale network models are used to demonstrate capabilities of optimization-based TEP studies.

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Abbreviations

\(N_b\) :

Set of buses; index k, n

\(N_g\) :

Set of all generators; index g

\(N_{wg}\) :

Set of all wind generators; index g

\(N_l\) :

Set of all lines (existing and candidate); index l, m

\(N_o\) :

Set of all existing lines; index l, m

\(N_n\) :

Set of all candidate lines; index l, m

\(L_k\) :

Set of lines connected to bus k

\(G_k\) :

Set of all generators connected to bus k

\(N_s^{\omega }\) :

Set of system operation states under scenario \(\omega \); index c (\(c=1\) represents the normal operation condition)

\(\upsilon \) :

Superscript/index for iteration number

\(\Omega \) :

Set of scenarios; index \({\omega }\)

\(\mathscr {I}\) :

Set of classes

\(\mathscr {I}_i\) :

Set of scenarios in class i

\(\mathscr {S}^i\) :

Set of clusters for class i

\(\mathscr {S}^i_j\) :

Set of scenarios in cluster j for class i

\(\mathscr {B}\) :

Set of bundles

\(\mathscr {B}_i\) :

Set of scenarios in bundle i

\(|\; \; |\) :

Size of a set

\(q_i\) :

Per MWh load shedding penalty at bus i

\(\gamma _g\) :

Per MWh wind curtailment penalty for wind farm g

\(Co_g\) :

Per MWh generation cost for generator g

\(\zeta _l\) :

Annual cost of line l construction

\(d_k\) :

Demand at bus k

B :

Diagonal matrix of line suseptance

\(P_g^{\max }\)/\(P_g^{\min }\):

Maximum/Minimum capacity of generator g

\(f_l^{\max }\)/\(f_l^{\min }\):

Maximum/Minimum capacity of line l

\(C^{\omega }\) :

Matrix of contingencies (operation states) that specifies the status of lines under different contingencies (1 for in service and 0 for out of service lines) for scenario \(\omega \); index c

\(\vartheta \) :

Variable freezing parameter

\(\rho _l\) :

Penalty factor for line l in PH algorithm

\(\kappa \) :

Size of each bundle

d :

Size of a TEP optimization problem

SC :

Number of structural constraints for a TEP problem

CV :

Number of continues variables for a TEP problem

BV :

Number of binary variables for a TEP problem

\(\tilde{\xi }\) :

Random variables (load and wind)

\(r_{k,c}\) :

Load curtailment at bus k under operating state c

\(CW_{g}\) :

Wind curtailment for wind farm g

\(p_{g}\) :

Output power of generator g

\(f_{l,c}\) :

Power flow in line l under operation state c

\(\theta _{i,c}\) :

Voltage angle at bus i under operating state c \(\Delta \theta _{l,c}\) is voltage angle difference across line l under operating state c. \(\Delta \theta _{l,c}\)= \(\theta _{k,c}\)-\(\theta _{n,c}\) for line l from bus k to bus n

\(x_l\) :

Binary decision variable for line l

\(\textit{\textbf{x}}^\omega \) :

Binary decision variables vector for scenario \(\omega \)

\(\textit{\textbf{x}}^{\mathscr {B}_i}\) :

Binary decision variables vector for bundle \(\mathscr {B}_i\)

\(\textit{\textbf{W}}_{\mathscr {B}_i}\) :

Multiplier vector for bundle \(\mathscr {B}_i\) in PH algorithm

\(\varvec{\mathscr {Z}}\) :

Binary variables matrix for clustering

\(\varvec{\mathscr {H}}\) :

Binary variables matrix for bundling

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    M. Majidi & R. Baldick

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Appendix

Appendix

In this appendix, input date for 13-bus system is provided (Tables 8, 9, and 10).

Table 8 Load and generation data in (MW)
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Table 9 Existing transmission network data
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Table 10 Candidate lines
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Majidi, M., Baldick, R. (2020). Definition and Theory of Transmission Network Planning. In: Hesamzadeh, M.R., Rosellón, J., Vogelsang, I. (eds) Transmission Network Investment in Liberalized Power Markets. Lecture Notes in Energy, vol 79. Springer, Cham. https://doi.org/10.1007/978-3-030-47929-9_2

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