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Abstract
This article presents a new methodology for decentralized capacity expansion planning for the transmission sector of a power system in a deregulated electricity market. The proposed model forms a bi-level optimization problem in which an upper-level problem represents a transmission company making its own strategic decisions on investment to maximize its profit while in the lower level, the market clearing problem of the independent system operator or market operator is formulated. A transmission company obtains its revenue based on flowgate marginal prices. The lower problem is replaced by its Karush–Kuhn–Tucker conditions, resulting in a mathematical program with an equilibrium constraint. Some linearization techniques have been employed to reach mixed-integer linear programming that can effectively be solved, and existing solvers guarantee to get to the global optimal solutions. The presented framework is applied to a simple 3-node power system and also to the IEEE 24-bus reliability test system. Results from these illustrative examples are reported and thoroughly discussed. These results signify the effectiveness of the proposed scheme to invest in the transmission part of a power system.
NOMENCLATURE
| = | Indices | |
| g | = | index for generators |
| i, j | = | index for buses |
| l | = | index of lines |
| T | = | index for transmission companies |
| = | Sets | |
| Ωb | = | set of all buses |
| ΩcT | = | set of all candidate lines (new capacity) belonging to transmission company T |
| ΩeT | = | set of all existing lines (capacity) belonging to transmission company T |
| Ωg | = | set of all generators (Ωg = ∪i ∈ ΩbΩgi) |
| Ωgi | = | set of all generators connecting to bus i |
| Ωlc | = | set of all candidate lines (Ωlc = ∪i ∈ ΩbΩlci) |
| Ωlci | = | set of all candidate lines connecting to bus i |
| Ωlcij | = | set of all candidate lines connecting to bus i and bus j |
| Ωle | = | set of all existing lines (Ωle = ∪i ∈ ΩbΩlei) |
| Ωlei | = | set of all existing lines connecting to bus i |
| Ωleij | = | set of all existing lines connecting to bus i and bus j (Ωleij = Ωlie∩Ωlej) |
| = | Constants | |
| Bcij, Bije | = | susceptance of candidate and existing line ij |
| bidg | = | submitted bid of generator g |
| bidcl | = | submitted bid of candidate flowgate l |
| = | unitary investment cost of line l | |
| PDi | = | active power demand at bus i |
| PGmaxg | = | maximum capacity of generator g |
| = | Variables | |
| DFGcl | = | dispatched flowgate of candidate line l |
| DPGg | = | dispatched power generation of generator g |
| FGcl | = | flowgate bidding of candidate line l |
| PLcl, PLle | = | power flow in candidate and existing line l |
| PLc +l, PLlc − | = | two positive additional variables to linearize absolute function |
| PLc, maxl | = | capacity of candidate line l |
| ucl | = | binary variables associated to a candidate line |
| zcl, ycl | = | auxiliary variables |
| = | dual variables/Lagrangian multipliers | |
| = | ||
| = | ||
| ξi, γel, γcl, | = | |
| = | ||
| ωc +l, ωlc − | = | |
| Δθij | = | difference of voltage angles at buses i and j |
| θi | = | voltage angle at bus i |
| = | Superscripts | |
| c | = | superscript of candidate (new) capacity |
| e | = | superscript of existing capacity |
Additional information
Notes on contributors
Tohid Akbari
Tohid Akbari received his B.Sc. and M.Sc. in electrical engineering from Iran University of Science and Technology (IUST) Tehran, Iran, in 2007 and University of Tehran (UT), Tehran, Iran in 2009. He is currently pursuing his Ph.D. in electrical engineering at the K.N. Toosi University of Technology (KNTU), Tehran, Iran. His research interests include power system economics and planning.
Mohammad Tavakoli Bina
Mohammad Tavakoli Bina received his B.Sc. and M.Sc. in power electronics and power system utility applications from UT and Ferdowsi, Iran, in 1988 and 1991, respectively, and his Ph.D. from University of Surrey, Guildford, UK, in 2001. From 1992 to 1997, he was a lecturer working on power systems with KNTU, Tehran. He joined the Faculty of Electrical and Computer Engineering at KNTU in 2001, where he is currently a professor of electrical engineering and is engaged in teaching and conducting research in the area of power electronics and utility applications.