In this paper, we introduce a new primal-dual prediction-correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in Cai et al. (J Glob Optim 57:14...
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In this paper, we introduce a new primal-dual prediction-correction algorithm for solving a saddle point optimization problem, which serves as a bridge between the algorithms proposed in Cai et al. (J Glob Optim 57:1419-1428, 2013) and He and Yuan (SIAM J Imaging Sci 5:119-149, 2012). An interesting byproduct of the proposed method is that we obtain an easily implementable projection-based primal-dual algorithm, when the primal and dual variables belong to simple convex sets. Moreover, we establish the worst-case convergence rate result in an ergodic sense, where t represents the number of iterations.
Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy reso...
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Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy resource (DER) integrations. However, existing online algorithms have the following limitations: 1) correction only algorithms ignore the time-varying characteristics of the optimization problem;2) prediction-correction algorithms cannot handle nonlinear OPF problems;3) Most algorithms only consider the application of single-phase cases. This paper addresses the above limitations by proposing a novel measurement-based predictioncorrection online distributed OPF algorithm for multi-phase ADNs. This algorithm is based on an improved multiphase linearized alternating current (AC) power flow model that takes advantage of the voltage measurements to improve the approximation accuracy. In each sampling period, the proposed algorithm first performs a limited number of correction steps, iterating the incremental variable based on the current outputs of DERs and the voltage measurements to track the optimal solution. The DERs then execute the resultant incremental output powers. After forecasting the time-varying parameters, the proposed algorithm performs a few prediction steps to seek a better starting point for the correction steps before the next sampling. Numerical test results of the modified IEEE 37-bus and 123-bus distribution systems demonstrated that the proposed algorithm can track the optimal solution of the time-varying nonlinear OPF problem more accurately than existing online algorithms, even in extra-high penetration scenarios (>= 200%).
In [J. Venel, Numer. Math., 118 (2011), pp. 367-400], an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e., specific first order differential inclusions). The convergence...
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In [J. Venel, Numer. Math., 118 (2011), pp. 367-400], an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e., specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to compactness arguments. Here we establish that this algorithm is of order 1/2. The considered sweeping process involves a set-valued map given by a finite number of inequality constraints. The proof rests on a metric qualification condition between the sets associated to each constraint.
This paper proposes a new collaborative pricing scheme for a power-transportation coupled network based on the variational inequality (VI) approach. In the proposed scheme, nodal electricity prices and congestion toll...
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This paper proposes a new collaborative pricing scheme for a power-transportation coupled network based on the variational inequality (VI) approach. In the proposed scheme, nodal electricity prices and congestion tolls on roads and at charging stations are considered to coordinate the coupled networks in order to minimize the operational cost of the whole system. The prices are determined by a second-order cone-based AC power flow model and a mixed user equilibrium model, respectively. A collaborative pricing model (CPM) is then built based on the two models and the interactions between them. In order to avoid the intractability of the developed non-convex model, the CPM is transformed into the VI formulation. With proven existence and uniqueness of solutions of the VI formulation, a new prediction-correction algorithm is proposed to accelerate the solution of the CPM problem, which is guaranteed to converge to the optimal solution. The proposed models and algorithm are verified using case studies on a real-world test system. The results show that the proposed pricing scheme can reduce the operational cost and the proposed algorithm shows improved convergence and higher computation efficiency compared with the existing algorithms.
The automatic guidance of an unmanned submersible using an acoustic navigation system requires a state estimator that can predict the vehicle position during the navigation sample period, filter the random measurement...
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The automatic guidance of an unmanned submersible using an acoustic navigation system requires a state estimator that can predict the vehicle position during the navigation sample period, filter the random measurement disturbance and estimate the mean disturbance due to sea current. The hydrodynamic parameters of the vehicle are nonlinear and can vary with the magnitude and direction of the relative fluid velocity within the duration of the period of the navigation sample. A prediction-correction algorithm is described that incorporates real-time gain adaption to minimise the filter-error variance and a correction to offset the bias of the model and sea current disturbances.
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