A parametric-programming-based framework was previously proposed to coordinate the market operations of the independent system operator (ISO) and the distribution system operator (DSO). This paper extends this framewo...
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(纸本)9780998133171
A parametric-programming-based framework was previously proposed to coordinate the market operations of the independent system operator (ISO) and the distribution system operator (DSO). This paper extends this framework by investigating optimal DSO pricing in addition to the ISO-DSO coordinated dispatch. In our DSO pricing problem, after ISO clears the wholesale market, the locational marginal price (LMP) of the ISO-DSO coupling substation is determined, the DSO utilizes this price to solve the DSO pricing problem. The DSO pricing problem determines the distribution LMP (D-LMP) in the distribution system and calculate the payment to each aggregator. Proofs are provided to 1) demonstrate the D-LMP at the ISO-DSO coupling substation from this DSO pricing problem always aligns with the wholesale LMP from the ISO;and 2) demonstrate the relationship between the DSO pricing and dispatch models. Case studies on a small illustrative example verify the performance of the proposed pricing model.
Some new concepts in regards to alpha-feasibility and alpha-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where a is a vector of distinct satisfaction degrees. Based ...
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Some new concepts in regards to alpha-feasibility and alpha-efficiency of solutions in fuzzy mathematical programming problems are introduced in this paper, where a is a vector of distinct satisfaction degrees. Based on the defined concepts, a new method is suggested to solve fuzzy mathematical programming problems. In this sense, the proposed approach enables decision makers to take into account more flexible solutions by allowing desired distinct satisfactions in constraints. In the case of linear problems with fuzzy constraints, multi-parametric programming is employed to obtain the optimal solution as an affine function of distinct satisfaction degrees. In particular, it proves that the obtained solution is convex and continuous. Therefore, the different optimal solutions can be obtained by a simple substituting the new values of satisfaction parameters into the parametric profiles without any further optimization calculations, which is desirable for online optimization and sensitivity analysis of the profit to satisfaction parameters.
In this paper model predictive control problems are reformulated as multi-parametric programs. The optimal value of control variables is obtained as an explicit function of the state variables. This reduces on-line op...
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A novel framework for flexibility assessment in the context of system design is proposed. We deal with the case when the design space is bounded by a set of affine bounds defining a convex-hull. For this class of prob...
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A novel framework for flexibility assessment in the context of system design is proposed. We deal with the case when the design space is bounded by a set of affine bounds defining a convex-hull. For this class of problems several flexibility metrics can be calculated, which are related to the minimum/maximum distances between any point in the design space and the less/most distant points at its bounds, respectively. In the first case, the distance functions are obtained via projection to individual bounds, and in the second case, the distance functions are defined via the Euclidean distance to the corners of convex hulls. These two sets of functions can then be used separately to calculate the minimum/maximum of the complete set of minimum/maximum distance functions over the full design space. This approach effectively enables the definition of four multi-parametric programming problems, and deliver four flexibility maps from their solutions. Flexibility maps based on the average of the two sets of distance functions are also delivered. This offers a plethora of complementary metrics for flexibility assessment, which extend beyond the classic approach based on the definition of feasible boxes. From the full set of solutions enabled by this framework, the minimum–minimum and maximum–maximum distance-based flexibility maps stand out as the extreme and most useful cases for flexibility assessment; the initial experimentation with these maps suggest that the average-minimum and particularly the average-maximum distance cases also provide useful information as an overall score on flexibility for any points within the design space.
Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertai...
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Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a multi-Objective Optimisation (MO2) problem. Even though, some methods have been proposed for MO2 problems under uncertainty, two separate optimisation techniques are employed;one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2 under uncertainty problem ((MOU2)-U-2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles. (C) 2016 The Authors. Published by Elsevier Ltd.
This paper presents an optimization framework for a wireless sensor network whereby, in a given route, the optimal relay selection and power allocation are performed subject to signal-to-noise ratio constraints. The p...
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This paper presents an optimization framework for a wireless sensor network whereby, in a given route, the optimal relay selection and power allocation are performed subject to signal-to-noise ratio constraints. The proposed approach determines whether a direct transmission is preferred for a given configuration of nodes, or a cooperative transmission. In the latter case, for each node, data transmission to the destination node is performed in two consecutive phases: broadcasting and relaying. The proposed strategy provides the best set of relays, the optimal broadcasting power and the optimal power values for the cooperative transmission phase. Once the minimum-energy transmission policy is obtained, the optimal routes from every node to a sink node are built-up using cooperative transmission blocks. We also present a low-complexity implementation approach of the proposed framework and provide an explicit solution to the optimization problem at hand by invoking the theory of multi-parametric programming. This technique provides the optimal solution as a function of measurable parameters in an off-line manner, and hence the on-line computational tasks are reduced to finding the parameters and evaluating simple functions. The proposed efficient approach has many potential applications in real-world problems and, to the best of the authors' knowledge, it has not been applied to communication problems before. Simulations are presented to demonstrate the efficacy of the approach.
Facing uncertainties related to large-scale renewable energy generation, power systems are confronted with immense challenges in the security operation. To capture the capability of renewable energy integration more a...
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Facing uncertainties related to large-scale renewable energy generation, power systems are confronted with immense challenges in the security operation. To capture the capability of renewable energy integration more accurately on a short timescale, this paper proposes a security region evaluation method obtaining every feasible point rather than the only maximum output point of renewable generators. This evaluation method is based on multi-parametric programming considering network operational constraints, including N-1 security constraints and variable limits. In the obtained security region, each feasible point can map the values of the objective function and optimal variables of the OPF model, which is beneficial for the real-time dispatch. Furthermore, the flexible spaces including the deep peak regulation of generators and the emergency transmission rates of lines are considered to extend the security region of renewable energy integration. The security regions of renewable generator outputs and the transmission power of tie lines, which reflect the range of renewable energy self-accommodation and outside-accommodation, are quantified considering these flexible spaces. The proposed method is tested on the IEEE 39-bus and IEEE 118-bus systems. (C) 2019 Elsevier Ltd. All rights reserved.
A coordinated economic dispatch method for multi-area power systems is proposed. Choosing boundary phase angles as coupling variables, the proposed method exploits the structure of critical regions in local problems d...
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A coordinated economic dispatch method for multi-area power systems is proposed. Choosing boundary phase angles as coupling variables, the proposed method exploits the structure of critical regions in local problems defined by active and inactive constraints. For a fixed boundary state given by the coordinator, local operators compute the coefficients of critical regions containing the boundary state and the optimal value functions then communicate them to the coordinator who in turn optimizes the boundary state to minimize the overall cost. By iterating between local operators and the coordinator, the proposed algorithm converges to the global optimal solution in finite steps, and it requires limited information sharing.
In this manuscript we present B-POP, a MATLAB toolbox for bi-level optimization through multiparametricprogramming. It features i) bi-level programming solvers for linear and quadratic programming problems, and their...
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In this manuscript we present B-POP, a MATLAB toolbox for bi-level optimization through multiparametricprogramming. It features i) bi-level programming solvers for linear and quadratic programming problems, and their mixed-integer counter-parts, ii) a versatile problem generator capable of creating random bi-level problems of arbitrary size, and iii) a library of bi-level programming test problems. The features of B-POP are demonstrated through detailed computational studies showing the capabilities and the scalability of the embedded algorithms. Moreover, two applications, i) a supply chain planning problem, and ii) a hierarchical model predictive control of a reactor system are chosen to show the applicability of bi-level programming and B-POP. (C) 2018 Elsevier Ltd. All rights reserved.
On-line model predictive control approaches require the online solution of an optimization problem. In contrast, the explicit model predictive control moves major part of computation offline. Therefore, eMPC enables o...
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On-line model predictive control approaches require the online solution of an optimization problem. In contrast, the explicit model predictive control moves major part of computation offline. Therefore, eMPC enables one to implement a MPC in real time for wide range of fast systems. The eMPC approach requires the exact system model and results a piecewise affine control law defined on a polyhedral partition in the state space. As an important limitation, disturbances may reduce performance of the explicit model predictive control. This paper presents efficient approach for handling the problem of using eMPC for constrained systems with disturbances. It proposes an approach to improve performance of the closed loop system by designing a suitable state and disturbance estimator. Conditions for observability of the disturbances are considered and it is depicted that applying the disturbance's estimation leads to rejection of the response error. It is also shown that the proposed approach prevents the reduction of feasible space. Simulation results illustrate the advantages of this approach.
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