Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret

Chen, Bokan; Wang, Jianhui; Wang, Lizhi; He, Yanyi; Wang, Zhaoyu

doi:10.1109/tpwrs.2014.2313841

“…In the context of expansion planning models for power systems, approaches based on the minimization of the maximum regret have been proposed in the nineties [23] for generation expansion planning and recently for transmission expansion planning [2], [24]. In addition, in industry, the min-max regret has also been already accepted as the most appropriate metric for transmission expansion planning by the major player of the power sector in the UK, namely National Grid [25], [26].…”

Section: Introductionmentioning

confidence: 99%

A Five-Level MILP Model for Flexible Transmission Network Planning Under Uncertainty: A Min–Max Regret Approach

Moreira

¹

,

Štrbac

²

,

Moreno

³

et al. 2018

IEEE Trans. Power Syst.

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Abstract-The benefits of new transmission investment significantly depend on deployment patterns of renewable electricity generation that are characterized by severe uncertainty. In this context, this paper presents a novel methodology to solve the transmission expansion planning (TEP) problem under generation expansion uncertainty in a min-max regret fashion, when considering flexible network options and n − 1 security criterion. To do so, we propose a five-level mixed integer linear programming (MILP) based model that comprises: (i) the optimal network investment plan (including phase shifters), (ii) the realization of generation expansion, (iii) the co-optimization of energy and reserves given transmission and generation expansions, (iv) the realization of system outages, and (v) the decision on optimal post-contingency corrective control. In order to solve the fivelevel model, we present a cutting plane algorithm that ultimately identifies the optimal min-max regret flexible transmission plan in a finite number of steps. The numerical studies carried out demonstrate: (a) the significant benefits associated with flexible network investment options to hedge transmission expansion plans against generation expansion uncertainty and system outages, (b) strategic planning-under-uncertainty uncovers the full benefit of flexible options which may remain undetected under deterministic, perfect information, methods and (c) the computational scalability of the proposed approach.Index Terms-transmission expansion planing under uncertainty, multi-level optimization, network security, power systems economics.

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“…Reference [18] presented a Markov demand model that considers a constant continuous deviation, with zero mean, around a predictable trend and the possibility of a sudden load increase because of an industrial plant moving in; the parameters of the Markov model can be estimated from past experience and economic prediction. An example in [18] shows the prediction of the minimum and maximum bus load values, based on which scenarios can be constructed; reference [19], which discusses a recent long-term expansion planning study, quotes minimum and maximum bus load values that reflect conservative and highly uncertain demand estimates.…”

Section: Introductionmentioning

confidence: 99%

“…ROSION implements a solution to a twostage robust optimization formulation using a distinct implementation of the column-and-constraint generation algorithm [14]. The need for robust optimization solutions has been recognized in several application areas [15], [19]- [23]. It is also preferred in storage investment planning over stochastic optimization, where practical applications require accurate statistical models that are not usually available [24].…”

Section: Introductionmentioning

confidence: 99%

Robust Optimization of Storage Investment on Transmission Networks

Jabr

¹

,

Džafić

²

,

Pal

³

2015

IEEE Trans. Power Syst.

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Abstract-This paper discusses the need for the integration of storage systems on transmission networks having renewable sources, and presents a tool for energy storage planning. The tool employs robust optimization to minimize the investment in storage units that guarantee a feasible system operation, without load or renewable power curtailment, for all scenarios in the convex hull of a discrete uncertainty set; it is termed ROSION-Robust Optimization of Storage Investment On Networks. The computational engine in ROSION is a specific tailored implementation of a column-and-constraint generation algorithm for two-stage robust optimization problems, where a lower and an upper bound on the optimal objective function value are successively calculated until convergence. The lower bound is computed using mixed-integer linear programming and the upper bound via linear programming applied to a sequence of similar problems. ROSION is demonstrated for storage planning on the IEEE 14-bus and 118-bus networks, and the robustness of the designs is validated via Monte Carlo simulation.Index Terms-Design optimization, energy storage, integer linear programming, optimization methods, power system planning.

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“…An example in [18] shows the prediction of the minimum and maximum bus load values, based on which scenarios can be constructed; ref. [19], which discusses a recent long-term expansion planning study, quotes minimum and maximum bus load values that reflect conservative and highly uncertain demand estimates.…”

Section: Introductionmentioning

confidence: 99%

“…ROSION implements a solution to a two-stage robust optimization formulation using a distinct implementation of the column-and-constraint generation algorithm [14]. The need for robust optimization solutions has been recognized in several application areas [15], [19]- [23]. It is also preferred in storage investment planning over stochastic optimization, where practical applications require accurate statistical models that are not usually available [24].…”

Section: Introductionmentioning

confidence: 99%

Topology Error and Bad Data Processing in Generalized State Estimation

Lourenço

¹

,

Coelho

²

,

Pal

³

2015

IEEE Trans. Power Syst.

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Abstract-This paper discusses the need for the integration of storage systems on transmission networks having renewable sources, and presents a tool for energy storage planning. The tool employs robust optimization to minimize the investment in storage units that guarantee a feasible system operation, without load or renewable power curtailment, for all scenarios in the convex hull of a discrete uncertainty set; it is termed ROSION -Robust Optimization of Storage Investment On Networks. The computational engine in ROSION is a specific tailored implementation of a column-and-constraint generation algorithm for two-stage robust optimization problems, where a lower and an upper bound on the optimal objective function value are successively calculated until convergence. The lower bound is computed using mixed-integer linear programming and the upper bound via linear programming applied to a sequence of similar problems. ROSION is demonstrated for storage planning on the IEEE 14-bus and 118-bus networks, and the robustness of the designs is validated via Monte-Carlo simulation.Index Terms-Design optimization, energy storage, integer linear programming, optimization methods, power system planning. NOMENCLATURE A. Storage Planning Problem BijLine susceptance between nodes i and j, defined as a positive number. Ei0Initial stored energy in the storage unit at node i. E ifFinal stored energy in the storage unit at node i.Maximum storage capacity of the unit at node i.Minimum storage capacity of the unit at node i. fi(.)Convex generation cost function at node i. KDPenalty coefficient for demand curtailment. KRPenalty coefficient for renewable energy curtailment. KSCapital recovery factor of storage investment.n Number of nodes in the system. NiNumber of linear segments in the cost curve of the generator at node i. PCDi (t) Demand power curtailment at node i and in period t. PCRi (t) Renewable power curtailment at node i and in period t. PDi (t) Power demand at node i and in period t. P Gik (t) Power generation at node i, over segment k, and in period t. PGi (t)Power generation at node i and in period t.

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Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret

Cited by 164 publications

References 24 publications

A Five-Level MILP Model for Flexible Transmission Network Planning Under Uncertainty: A Min–Max Regret Approach

A Five-Level MILP Model for Flexible Transmission Network Planning Under Uncertainty: A Min–Max Regret Approach

Robust Optimization of Storage Investment on Transmission Networks

Topology Error and Bad Data Processing in Generalized State Estimation

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