On the solution of robust transmission expansion planning using duality theorem under polyhedral uncertainty set

El-Meligy, Mohammed A.; El-Sherbeeny, Ahmed M.; Soliman, Ahmed T.; Elgawad, Abd Elatty E. Abd; Naser, Emad A.

doi:10.1016/j.epsr.2022.107785

Cited by 12 publications

(5 citation statements)

References 30 publications

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“…[26] constructs a distributionally robust planning model considering load and wind stochastic behavior, while modeling demand response and solar power plants. A solution method to address the robust transmission planning is suggested in [27], where neither binary variables nor bilinear terms are used. Some spatial and temporal simplifications is applied to the planning problem of the generation and transmission in [28].…”

Section: B Literature Reviewmentioning

confidence: 99%

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

et al. 2023

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To have an effective transmission network and support free trading, the open and nondiscriminatory access to transmission services for all market participants under all conditions is of significant concern. To this end, a sufficient value of available transfer capability (ATC) is required, which can significantly affect the electricity market efficiency. This paper constructs a methodology for reinforcing an existing transmission network considering wind power investment to enhance ATC. In this regard, a bi-level structure is adopted whose upper level is the joint transmission expansion planning (TEP) and wind power investment subject to the technical power grid limitations. After solving the upper level, a security-constrained economic dispatch (SC-ED) is formulated to acquire the optimal generation scheduling. Then, the lower level is designed to calculate the ATC. To solve this problem, the SC-ED is first replaced by its primal and dual feasibility constraints and strong duality equality. Then, these constraints are added to the upper level. The lower level is also replaced by its corresponding constraints. Consequently, a bilinear single-level optimization problem is extracted, which is further solved by employing Konno's cutting plane algorithm. The experimental results on the IEEE 24-bus RTS show the proposed method's effectiveness. It is indicated that the ATC can be improved by 27.2 % using the formulated model at the expense of more investment cost resulting in less load shedding and less wind 𝜆 A variable indicating the growth in load or generation. 𝑃 Electric demand in the ATC evaluation problem. 𝑃 , 𝑃 , 𝑃 Power output of thermal units in the main problem, ATC evaluation problem and SC-ED problem. 𝑃 , 𝑃 , 𝑃 Power output of a wind farm in the main problem, ATC evaluation problem and SC-ED problem. 𝑃 Capacity of a wind farm. 𝑢 Binary variable indicating the installation status of a transmission line. 𝛿 ,𝛿 , 𝛿 Voltage angle in the main problem, ATC evaluation problem and SC-ED problem. 𝛿 , Voltage angle at the reference bus.

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Section: B Literature Reviewmentioning

confidence: 99%

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

et al. 2023

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“…[21] proposes a scenario-driven probabilistic framework to assess the impact of intermittent wind power on the TEP problem. Authors in [22] develop a solution algorithm to cope with the robust transmission line investment planning where the lower level is replaced by its dual. The authors claim that neither binary variables nor bilinear terms are introduced in this approach.…”

Section: Generation Schedulingmentioning

confidence: 99%

A Joint Optimization Model for Transmission Capacity and Wind Power Investment Considering System Security

et al. 2023

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Due to continuous growth in electric demand and increasing connection of renewable energy, the power systems are being operated with smaller stability margins. Therefore, a sufficient loading margin is essential to maintain the system secure and ensure voltage stability. To this end, this paper studies the joint optimization of transmission capacity and wind power investment problem, the unique feature of which is incorporating voltage stability margin (VSM) in the planning model. A bi-level model has been formulated whose upper level minimizes the total investment and operation cost minus the weighted VSM. The lower level evaluates the VSM given the optimal expansion plan from the upper level. In addition, the stochastic nature of wind power and load can impact voltage stability. Thus, uncertainties related to intermittent wind generation and demand must be modeled. We use an approximated linear representation to model the AC power system at both levels of the problem. The duality theory (primal-dual formulation) is utilized to transform bi-level programming into single-level mathematical programming. The validity of the constructed methodology is demonstrated on the IEEE 24-bus RTS, which indicates the efficacy and feasibility of the presented model. INDEX TERMSBi-level programming, Primal-dual formulation, Transmission and wind investment, Voltage stability. NOMENCLATURE A. Indices and sets: Ω Set of buses indexed by 𝑖, 𝑗. Ω Set of scenarios indexed by s. B. Parameters: 𝑔 , 𝑏 Conductance and susceptance of a transmission line. 𝐴 , 𝐵 , 𝐶 Constant parameters used to approximate a circle by a regular polygon. 𝑎 , 𝑏 , 𝑐 Production cost coefficients of a thermal unit. 𝐼 ,𝐼 Annualized investment cost of a wind farm and a transmission line. 𝑀 , 𝑀 , 𝑀 , 𝑀 Big-M parameters. 𝑃 Active power demand. 𝑄 , 𝑄 , 𝑄 Reactive power generation of thermal units in the main problem, VSM assessment problem and OPF problem. 𝑃 , 𝑃 , 𝑃 Active power generation of wind farms in the main problem, VSM assessment problem and OPF problem. 𝑄 , 𝑄 𝑄 Reactive power generation of wind farms in the main problem, VSM assessment problem and OPF problem. 𝑃 Capacity of a wind farm. 𝑢 Binary variable indicating the installation status of a transmission line. ∆𝑣 , ∆𝑣 , ∆𝑣 Voltage deviation in the main problem, VSM assessment problem and OPF problem. 𝛿 ,𝛿 𝛿 Voltage angle in the main problem, VSM assessment problem and OPF problem. 𝛿 , Voltage angle at the reference bus.

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“…A dynamic risk-based GTEP has been formulated in [40], where penalties have been included to reduce load curtailment after contingencies. A novel technique has been introduced in [41] to find a solution for a robust TEP problem. In the proposed approach, the described bi-level model was converted to a single level approach, in which all the uncertainties were integrated into the objective function.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In addition, refs. [40][41][42][43] have worked on the stochastic TEP/GTEP formulation without considering the integration of RESs. It is worth mentioning that refs.…”

Section: Literature Reviewmentioning

confidence: 99%

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Stochastic expansion planning of transmission system and energy hubs in the presence of correlated uncertain variables

Allahvirdizadeh

Shayanfar

Moghaddam

2022

IET Generation Trans & Dist

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Energy hubs (EHs), with interconnecting different energy carriers, technologies, and sectors, improve energy efficiency and enhance the flexibility of energy management. EHs can be an alternative to the upgradation of the transmission system infrastructures. Then, it is necessary to evaluate accurately the impact of integrating EHs across the power system on the expansion planning of the transmission system. This paper proposes an expansion planning of the transmission system and integrated EHs across the power system in deterministic and stochastic environments. In addition, the correlation among the uncertain variables may affect the expansion planning and scheduling decisions as well as the resulting costs. Therefore, the stochastic modelling of the proposed planning approach is developed considering the correlation among the uncertain variables. The uncertainties related to the generation of the renewable energy sources (RESs), energy demands, and electrical/thermal/cooling/gas price are addressed with a stochastic scenario-based scheme. For this purpose, numerous scenarios are generated by implementing the well-known Monte Carlo simulation (MCS) technique. Then the Cholesky decomposition technique combined with Nataf transformation is used to make the samples correlated. Next, the k-means method as an efficient scheme of data clustering is used to reduce the initial scenarios to some limited ones.

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On the solution of robust transmission expansion planning using duality theorem under polyhedral uncertainty set

Cited by 12 publications

References 30 publications

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

Transmission Expansion Planning Considering a High Share of Wind Power to Maximize Available Transfer Capability

A Joint Optimization Model for Transmission Capacity and Wind Power Investment Considering System Security

Stochastic expansion planning of transmission system and energy hubs in the presence of correlated uncertain variables

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