1,560 research outputs found

    A non-convex alternating direction method of multipliers heuristic for optimal power flow

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    The optimal power flow (OPF) problem is fundamental to power system planing and operation. It is a non-convex optimization problem and the semidefinite programing (SDP) relaxation has been proposed recently. However, the SDP relaxation may give an infeasible solution to the original OPF problem. In this paper, we apply the alternating direction method of multiplier method to recover a feasible solution when the solution of the SDP relaxation is infeasible to the OPF problem. Specifically, the proposed procedure iterates between a convex optimization problem, and a non-convex optimization with the rank constraint. By exploiting the special structure of the rank constraint, we obtain a closed form solution of the non-convex optimization based on the singular value decomposition. As a result, we obtain a computationally tractable heuristic for the OPF problem. Although the convergence of the algorithm is not theoretically guaranteed, our simulations show that a feasible solution can be recovered using our method

    Distributed Online Modified Greedy Algorithm for Networked Storage Operation under Uncertainty

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    The integration of intermittent and stochastic renewable energy resources requires increased flexibility in the operation of the electric grid. Storage, broadly speaking, provides the flexibility of shifting energy over time; network, on the other hand, provides the flexibility of shifting energy over geographical locations. The optimal control of storage networks in stochastic environments is an important open problem. The key challenge is that, even in small networks, the corresponding constrained stochastic control problems on continuous spaces suffer from curses of dimensionality, and are intractable in general settings. For large networks, no efficient algorithm is known to give optimal or provably near-optimal performance for this problem. This paper provides an efficient algorithm to solve this problem with performance guarantees. We study the operation of storage networks, i.e., a storage system interconnected via a power network. An online algorithm, termed Online Modified Greedy algorithm, is developed for the corresponding constrained stochastic control problem. A sub-optimality bound for the algorithm is derived, and a semidefinite program is constructed to minimize the bound. In many cases, the bound approaches zero so that the algorithm is near-optimal. A task-based distributed implementation of the online algorithm relying only on local information and neighbor communication is then developed based on the alternating direction method of multipliers. Numerical examples verify the established theoretical performance bounds, and demonstrate the scalability of the algorithm.Comment: arXiv admin note: text overlap with arXiv:1405.778

    AC OPF in Radial Distribution Networks - Parts I,II

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    The optimal power-flow problem (OPF) has played a key role in the planning and operation of power systems. Due to the non-linear nature of the AC power-flow equations, the OPF problem is known to be non-convex, therefore hard to solve. Most proposed methods for solving the OPF rely on approximations that render the problem convex, but that may yield inexact solutions. Recently, Farivar and Low proposed a method that is claimed to be exact for radial distribution systems, despite no apparent approximations. In our work, we show that it is, in fact, not exact. On one hand, there is a misinterpretation of the physical network model related to the ampacity constraint of the lines' current flows. On the other hand, the proof of the exactness of the proposed relaxation requires unrealistic assumptions related to the unboundedness of specific control variables. We also show that the extension of this approach to account for exact line models might provide physically infeasible solutions. Recently, several contributions have proposed OPF algorithms that rely on the use of the alternating-direction method of multipliers (ADMM). However, as we show in this work, there are cases for which the ADMM-based solution of the non-relaxed OPF problem fails to converge. To overcome the aforementioned limitations, we propose an algorithm for the solution of a non-approximated, non-convex OPF problem in radial distribution systems that is based on the method of multipliers, and on a primal decomposition of the OPF. This work is divided in two parts. In Part I, we specifically discuss the limitations of BFM and ADMM to solve the OPF problem. In Part II, we provide a centralized version and a distributed asynchronous version of the proposed OPF algorithm and we evaluate its performances using both small-scale electrical networks, as well as a modified IEEE 13-node test feeder

    A Multi-Agent Control Approach for Optimization of Central Cooling Plants

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    This paper presents an application of a multi-agent control approach for supervisory control of large central cooling plants. The starting point for this work was a multi-agent control simulation framework developed by Cai (2015).  To adapt the framework to the problem at hand several tasks were accomplished: agents representing the performance of the different devices of the plant were developed and inserted in the framework and generalized heuristics were incorporated to make the approach less computationally intensive. A case study of an existing cooling plant with significant complexity was utilized to conduct an extensive evaluation of the approach in terms of optimality and computational resources. Simulations were carried out using one year of historical data to predict the performance of the plant under three different control strategies: 1) multi-agent control, 2) centralized optimization based on mathematical programming techniques and 3) a heuristic control strategy. The results showed that significant savings can be achieved through the implementation of multi-agent control. It is expected that, if each hardware component of the plant comes with an integrated agent that represents its behavior, then the proposed multi-agent framework could automatically generate the multi-agent structure and control algorithm after some relatively simple pre-configuration steps. This will reduce the site-specific engineering and will provide a more economic and easy to configure solution for central cooling systems
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