A SOCP Relaxation for Cycle Constraints in the Optimal Power Flow Problem

Soofi, Arash Farokhi; Manshadi, Saeed D.; Dai, Renchang

doi:10.1109/tsg.2020.3023890

Cited by 30 publications

(9 citation statements)

References 30 publications

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“…In second‐order convex relaxation formulation, the constraint (5 h) is in conic relaxation form. An alternative approach to check the tightness of the procured relaxation form is the difference between

c_{ij}^{2} + s_{ij}^{2}

and

c_{ii} c_{jj}

as given in Reference 30. In a radial network, the difference is zero and the relaxation is exact due to the angles that can be uniquely identified by an arbitrary voltage reference.…”

Section: Solution Methodsmentioning

confidence: 99%

Decomposing convexified security‐constrained AC optimal power flow problem with automatic generation control reformulation

Waseem

Manshadi

2021

Int Trans Electr Energ Syst

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This paper presents a reformulation for the automatic generation control (AGC) in a decomposed convex relaxation algorithm. It finds an optimal solution to the AC optimal power flow (ACOPF) problem that is secure against a large set of contingencies. The original ACOPF problem which represents the system without contingency constraints, is convexified by applying the second-order cone relaxation method. The contingencies are filtered to distinguish those that will be treated with preventive actions from those that will be left for corrective actions. The selected contingencies for preventive action are included in the set of security constraints. Benders decomposition is employed to decompose the convexified Security-Constrained ACOPF problem into a master problem and several security check subproblems. Subproblems are evaluated in a parallel computing process with enhanced computational efficiency. AGC within each subproblem is modeled by a set of proposed valid constraints, so the procured solution is the physical response of each generation unit during a contingency. Benders optimality cuts are generated for the subproblems having mismatches and the cuts are passed to the master problem to encounter the security-constraints. The accuracy of the relaxation results is verified using the presented tightness measure. The effectiveness of the presented valid AGC constraints and scalability of the proposed algorithm is demonstrated in several case studies.

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c_{ij}^{2} + s_{ij}^{2}

and

c_{ii} c_{jj}

as given in Reference 30. In a radial network, the difference is zero and the relaxation is exact due to the angles that can be uniquely identified by an arbitrary voltage reference.…”

Section: Solution Methodsmentioning

confidence: 99%

Decomposing convexified security‐constrained AC optimal power flow problem with automatic generation control reformulation

Waseem

Manshadi

2021

Int Trans Electr Energ Syst

Self Cite

View full text Add to dashboard Cite

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“…The SOCP relaxed form of the power flow and nodal balance equations of the distribution networks with DERs is presented in (5). It should be noted that the SOCP relaxation method is exact for acyclic distribution networks [12], [13].…”

Section: Nodal Balance and Power Flow Constraintsmentioning

confidence: 99%

Analyzing Power Quality Implications of High Level Charging Rates of Electric Vehicle Within Distribution Networks

Soofi¹,

Bayani²,

Manshadi³

2021

Preprint

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This paper investigates the impact of the charging level of high penetration level of Electric Vehicles (EVs) on the power quality of the electricity distribution network. The EV owners tend to charge their EVs as fast as possible. The charging levels of EVs within the distribution network affect the voltage profile of buses of the network. In this paper, an exact Second-Order Cone Programming (SOCP) formulation of the full AC optimal power flow (ACOPF) problem of the distribution network is presented. The network includes solar generation units and EVs as Distributed Energy Resources (DERs). Different charging levels are considered to analyze the impact of EVs on the distribution network. The performance of the proposed model is illustrated for the modified IEEE-33 bus system for different charging levels for EVs. Besides, the impact of available solar power and battery degradation cost of EVs on the distribution network is investigated. It is illustrated that how EV charging will cause voltage deviation challenges for the distribution network.

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“…Furthermore, the optimization model in the above literatures includes power flow constraints and highly nonlinear ER operation constraints. It is essentially a nonconvex nonlinear programming (NLP) problem, and obtaining the solution with an acceptable time is a great challenge (Deng et al, 2021)- (Soofi et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Convex Approximation Algorithm for AC/DC Distribution Network With Energy Router

Zhang

Wang

et al. 2021

Front. Energy Res.

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The optimal operation model of AC/DC distribution network with energy router (ER) is essentially a nonconvex nonlinear programming (NLP) problem. In order to improve the feasibility of solving the model, a convex approximation algorithm is proposed in this work. The steady-state model of ER is developed with considering the loss characteristics and multiport coordinated control strategy. It is embedded in the optimization formulations of AC/DC network as basic operating equations. Then, using second-order cone relaxation technology, the power flow equations of AC and DC distribution networks are convexly relaxed. On this basis, the highly nonlinear operating model of ER is linearized by introducing a successive approximation approach. Therefore, the original NLP problem is transformed into the convex programming problem and the solution efficiency is improved. Meanwhile, an iterative solution algorithm is developed to ensure the accuracy of the convex approximation approach. Simulation results verify the feasibility and efficiency of the proposed algorithm.

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A SOCP Relaxation for Cycle Constraints in the Optimal Power Flow Problem

Cited by 30 publications

References 30 publications

Decomposing convexified security‐constrained AC optimal power flow problem with automatic generation control reformulation

Decomposing convexified security‐constrained AC optimal power flow problem with automatic generation control reformulation

Analyzing Power Quality Implications of High Level Charging Rates of Electric Vehicle Within Distribution Networks

Convex Approximation Algorithm for AC/DC Distribution Network With Energy Router

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