Robust Short-term Operation of AC Power Network with Injection Uncertainties

With uncertain injections from Renewable Energy Sources (RESs) and loads, deterministic AC Optimal Power Flow (OPF) often fails to provide optimal setpoints of conventional generators. A computationally time-efficient, economical, and robust solution is essential for ACOPF with short-term injection uncertainties. Usually, applying Robust Optimization (RO) for conventional non-linear ACOPF results in computationally intractable Robust Counterpart (RC), which is undesirable as ACOPF is an operational problem. Hence, this paper proposes a single-stage non-integer non-recursive RC of ACOPF, using a dual transformation, for short-term injection uncertainties. The proposed RC is convex, tractable, and provides base-point active power generations and terminal voltage magnitudes (setpoints) of conventional generators that satisfy all constraints for all realizations of defined injection uncertainties. The non-linear impact of uncertainties on other variables is inherently modeled without using any affine policy. The proposed approach also includes the budget of uncertainty constraints for low conservatism of the obtained setpoints. Monte-Carlo Simulation (MCS) based participation factored AC power flows validate the robustness of the obtained setpoints on NESTA and case9241pegase systems for different injection uncertainties. Comparison with previous approaches indicates the efficacy of the proposed approach in terms of low operational cost and computation time.Comment: 16 pages, 5 figures, 5 table

Avoiding Braess' Paradox through Collective Intelligence

In an Ideal Shortest Path Algorithm (ISPA), at each moment each router in a network sends all of its traffic down the path that will incur the lowest cost to that traffic. In the limit of an infinitesimally small amount of traffic for a particular router, its routing that traffic via an ISPA is optimal, as far as cost incurred by that traffic is concerned. We demonstrate though that in many cases, due to the side-effects of one router's actions on another routers performance, having routers use ISPA's is suboptimal as far as global aggregate cost is concerned, even when only used to route infinitesimally small amounts of traffic. As a particular example of this we present an instance of Braess' paradox for ISPA's, in which adding new links to a network decreases overall throughput. We also demonstrate that load-balancing, in which the routing decisions are made to optimize the global cost incurred by all traffic currently being routed, is suboptimal as far as global cost averaged across time is concerned. This is also due to "side-effects", in this case of current routing decision on future traffic. The theory of COllective INtelligence (COIN) is concerned precisely with the issue of avoiding such deleterious side-effects. We present key concepts from that theory and use them to derive an idealized algorithm whose performance is better than that of the ISPA, even in the infinitesimal limit. We present experiments verifying this, and also showing that a machine-learning-based version of this COIN algorithm in which costs are only imprecisely estimated (a version potentially applicable in the real world) also outperforms the ISPA, despite having access to less information than does the ISPA. In particular, this COIN algorithm avoids Braess' paradox.Comment: 28 page

Transmission Pricing of Distributed Multilateral Energy Transactions to Ensure System Security and Guide Economic Dispatch

Transmission Pricing of Distributed Multilateral Energy Transactions to Ensure System Security and Guide Economic Dispatc

Offset-Assisted Factored Solution of Nonlinear Systems

This paper presents an improvement to the recently-introduced factored method for the solution of nonlinear equations. The basic idea consists of transforming the original system by adding an offset to all unknowns. When searching for real solutions, a real offset prevents the intermediate values of unknowns from becoming complex. Reciprocally, when searching for complex solutions, a complex offset is advisable to allow the iterative process to quickly abandon the real domain. Several examples are used to illustrate the performance of the proposed algorithm, when compared to Newton’s methodMinisterio de Economía y Competitividadt ENE2013-48428-C

Loosely Coupled Formulations for Automated Planning: An Integer Programming Perspective

We represent planning as a set of loosely coupled network flow problems, where each network corresponds to one of the state variables in the planning domain. The network nodes correspond to the state variable values and the network arcs correspond to the value transitions. The planning problem is to find a path (a sequence of actions) in each network such that, when merged, they constitute a feasible plan. In this paper we present a number of integer programming formulations that model these loosely coupled networks with varying degrees of flexibility. Since merging may introduce exponentially many ordering constraints we implement a so-called branch-and-cut algorithm, in which these constraints are dynamically generated and added to the formulation when needed. Our results are very promising, they improve upon previous planning as integer programming approaches and lay the foundation for integer programming approaches for cost optimal planning