This paper concentrates on the optimal bidding strategy of a plug-in electric vehicle aggregator (PEVA) using indirect load control in the day-ahead energy market, which is generally formulated as bilevel programming....
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This paper concentrates on the optimal bidding strategy of a plug-in electric vehicle aggregator (PEVA) using indirect load control in the day-ahead energy market, which is generally formulated as bilevel programming. However, this bilevel model is nonconvex and intractable due to the complementary constraints imposed to preclude plug-in electric vehicles (PEVs) from simultaneously charging and discharging. To handle this problem, an exact relaxation method is first proposed to remove the complementary constraints of the PEVs' charging and discharging behaviours. To further reduce the complexity of the model, a method is proposed for the exact relaxation of the complementary slackness of Karush-Kuhn-Tucker (KKT) conditions in the reformulated mathematical program with equilibrium constraints. By removing the complementary constraints, the relaxation methods can effectively reduce the complexity of the model and improve the computational performance. The results of the case study demonstrate the exactness and efficiency of the proposed relaxation methods. Specifically, in the test case with 1000 PEVs and 20 scenarios, 220,000 constraints are removed by the two exact relaxation methods. Moreover, using the second exact relaxation method, in the test case with 400 PEVs and 60 scenarios and the case with 1000 PEVs and 60 scenarios, the computational time drops by 30.3% and 23.3%, respectively.
In this paper, a mathematical programming with equilibrium constraints (MPEC) model for the optimal operation of unbalanced three-phase electrical distributed systems is presented. First, the problem is formulated as ...
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ISBN:
(纸本)9781665435970
In this paper, a mathematical programming with equilibrium constraints (MPEC) model for the optimal operation of unbalanced three-phase electrical distributed systems is presented. First, the problem is formulated as a non-linear programming (NLP) problem, considering photo-voltaic (PV) generation, dispatchable distributed generation (DG) units, and day-ahead minimization of total active power losses. Then, through a set of efficient linearization techniques, the unbalanced three-phase AC power flow is transformed into a linear programming (LP) model. Finally, through Karush-Kuhn-Tucker (KKT) conditions, the proposed MPEC model is formulated as the combination of the LP primal constraints, the LP dual constraints and complementary constraints. MPEC models are able to optimize without an explicit objective function. Thus, they could be used as inner constraints in bi-level problems, for formulating robust optimization models and in electricity market design for distribution systems. Results show that the proposed MPEC model obtains the same optimal solution of the primal LP problem, without an explicit objective function.
The submarine drifter is a novel Lagrangian-based observation platform to explore the ocean, but its precise and rapid depth control system design is still an open issue. The major challenge would be the complex hybri...
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The submarine drifter is a novel Lagrangian-based observation platform to explore the ocean, but its precise and rapid depth control system design is still an open issue. The major challenge would be the complex hybrid actuation system, which contains anisotropic characteristics and switching issues. In this paper, we proposed an modified complementary constrained model predictive control (MCC-MPC) scheme to meet the metrics. The scheme reformulates complex drifter and hybrid actuation system dynamics into a solvable system with complementary constraints. The nonlinear component inside the system is approximated by applying a sgn-sigmoid approximation function for the sake of linearization and computation. Then the customized online optimizer predicts the system dynamics with complementary constraints and computes the optimal control outputs in the finite horizon in an iterative loop. The validation results prove that the proposed controller can effectively control the submarine drifter to achieve the desired depth and the key metrics are 10x, 4x, and 2x better than conventional PID control, disturbance observer-based control, and conventional MPC methods, respectively.
Bilevel programming techniques deal with decision processes involving two decision makers with a hierarchical structure. In this paper, an augmented Lagrangian multiplier method is proposed to solve nonlinear bilevel ...
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Bilevel programming techniques deal with decision processes involving two decision makers with a hierarchical structure. In this paper, an augmented Lagrangian multiplier method is proposed to solve nonlinear bilevel programming (NBLP) problems. An NBLP problem is first transformed into a single level problem with complementary constraints by replacing the lower level problem with its Karush-Kuhn-Tucker optimality condition, which is sequentially smoothed by a Chen-Harker-Kanzow-Smale (CHKS) smoothing function. An augmented Lagrangian multiplier method is then applied to solve the smoothed nonlinear program to obtain an approximate optimal solution of the NBLP problem. The asymptotic properties of the augmented Lagrangian multiplier method are analyzed and the condition for solution optimality is derived. Numerical results showing viability of the approach are reported. (C) 2013 Elsevier B.V. All rights reserved.
In this paper, we present a smoothing sequential quadratic programming to compute a solution of a quadratic convex bilevel programming problem. We use the Karush-Kuhn-Tucker optimality conditions of the lower level pr...
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In this paper, we present a smoothing sequential quadratic programming to compute a solution of a quadratic convex bilevel programming problem. We use the Karush-Kuhn-Tucker optimality conditions of the lower level problem to obtain a nonsmooth optimization problem known to be a mathematical program with equilibrium constraints;the complementary conditions of the lower level problem are then appended to the upper level objective function with a classical penalty. These complementarity conditions are not relaxed from the constraints and they are reformulated as a system of smooth equations by mean of semismooth equations using Fisher-Burmeister functional. Then, using a quadratic sequential programming method, we solve a series of smooth, regular problems that progressively approximate the nonsmooth problem. Some preliminary computational results are reported, showing that our approach is efficient. (C) 2011 Elsevier Inc. All rights reserved.
The Hierarchical Voltage Control has recently become an important alternative to the traditional voltage control solutions. This paper deals with the computation of an optimal profile for the pilot bus voltages using ...
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ISBN:
(纸本)9781424422340
The Hierarchical Voltage Control has recently become an important alternative to the traditional voltage control solutions. This paper deals with the computation of an optimal profile for the pilot bus voltages using different optimization strategies. For this purpose, the mathematical model of the optimization problem was studied considering two issues: i) defining the constraints of the optimization problem in order to fulfill the actual operating condition of the Secondary Voltage Control system and ii) finding the proper objective function (OF). For validation, tests were made on the Italian Power grid by using the high level modeling system GAMS.
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