Swing Dynamics as Primal-Dual Algorithm for Optimal Load Control

Frequency regulation and generation-load balancing are key issues in power transmission networks. Complementary to generation control, loads provide flexible and fast responsive sources for frequency regulation, and local frequency measurement capability of loads offers the opportunity of decentralized control. In this paper, we propose an optimal load control problem, which balances the load reduction (or increase) with the generation shortfall (or surplus), resynchronizes the bus frequencies, and minimizes a measure of aggregate disutility of participation in such a load control. We find that, a frequency-based load control coupled with the dynamics of swing equations and branch power flows serve as a distributed primal-dual algorithm to solve the optimal load control problem and its dual. Simulation shows that the proposed mechanism can restore frequency, balance load with generation and achieve the optimum of the load control problem within several seconds after a disturbance in generation. Through simulation, we also compare the performance of optimal load control with automatic generation control (AGC), and discuss the effect of their incorporation

Fast Load Control with Stochastic Frequency Measurement

Matching demand with supply and regulating frequency are key issues in power system operations. Flexibility and local frequency measurement capability of loads offer new regulation mechanisms through load control. We present a frequency-based fast load control scheme which aims to match total demand with supply while minimizing the global end-use disutility. Local frequency measurement enables loads to make decentralized decisions on their power from the estimates of total demand-supply mismatch. To resolve the errors in such estimates caused by stochastic frequency measurement errors, loads communicate via a neighborhood area network. Case studies show that the proposed load control can balance demand with supply and restore the frequency at the timescale faster than AGC, even when the loads use a highly simplified system model in their algorithms. Moreover, we discuss the tradeoff between communication and performance, and show with experiments that a moderate amount of communication significantly improves the performance

On the spectral characterization of pineapple graphs

The pineapple graph $K_p^q$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ($q\geq 1,\ p\geq 3$). Zhang and Zhang ["Some graphs determined by their spectra", Linear Algebra and its Applications, 431 (2009) 1443-1454] claim that the pineapple graphs are determined by their adjacency spectrum. We show that their claim is false by constructing graphs which are cospectral and non-isomorphic with $K_p^q$ for every $p\geq 4$ and various values of $q$. In addition we prove that the claim is true if $q=2$, and refer to the literature for $q=1$, $p=3$, and $(p,q)=(4,3)$

Exact Convex Relaxation of Optimal Power Flow in Tree Networks

The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution networks, which are tree networks, due to the emergence of distributed generation and controllable loads. In this paper, we study the OPF problem in tree networks. The OPF problem is nonconvex. We prove that after a "small" modification to the OPF problem, its global optimum can be recovered via a second-order cone programming (SOCP) relaxation, under a "mild" condition that can be checked apriori. Empirical studies justify that the modification to OPF is "small" and that the "mild" condition holds for the IEEE 13-bus distribution network and two real-world networks with high penetration of distributed generation.Comment: 22 pages, 7 figure

Exact Convex Relaxation of Optimal Power Flow in Radial Networks

The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly, the global optimum of OPF can be recovered via a second-order cone programming (SOCP) relaxation under a condition that can be checked a priori. The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two real-world networks, and has a physical interpretation.Comment: 32 pages, 10 figures, submitted to IEEE Transaction on Automatic Control. arXiv admin note: text overlap with arXiv:1208.407

The technical and economic efficiency analyses of performance of brown trout (Salmo trutta fario l., 1758) fed by the commercial diets enriched with different levels of linolenic acid (lna; 18:3 n-3)

This study was designed to determine the technical and economic efficiency levels of the commercial basal feeds enriched with 10%, 5% and 0% rates of LNA (LNA10, LNA5 and LNA0) on the growth performance of brown trout by analyzing the marginal factor cost (MFC) and the marginal revenue of physical product (MRPP). A total of 300 brown trout with an initial individual weight of 4±0.05 g were randomly divided in 12 cages (25 fingerlings in each cage), and kept under 24L:0D (light/dark) photoperiod condition for 9 weeks treated by LNA10, LNA5 and LNA0. The results of the study showed that LNA0 and LNA10 of the effective feed sources, respectively on the growth performance of brown trout were more suitable to produce as the homogeneous products for the consumers and differentiated those for the drug industry in view of the economic and technical efficiencies

Cospectrality results for signed graphs with two eigenvalues unequal to ±1\pm 1

Recently the collection $\cal G$ of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ has been determined. Here we investigate $\cal G$ for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in $\cal G$ determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the Friendship graph $F_\ell$, and show that there is no connected signed graph cospectral but not switching equivalent with $F_\ell$

On Signed Graphs With at Most Two Eigenvalues Unequal to ±1\pm 1

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to 1 or -1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching

Cospectrality Results for Signed Graphs with Two Eigenvalues Unequal to ±1\pm 1

Recently the collection $\cal G$ of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ has been determined. Here we investigate $\cal G$ for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in $\cal G$ determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the Friendship graph $F_\ell$, and show that there is no connected signed graph cospectral but not switching equivalent with $F_\ell$

Cospectrality Results for Signed Graphs with Two Eigenvalues Unequal to ±1\pm 1

Recently the collection $\cal G$ of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to $\pm 1$ has been determined. Here we investigate $\cal G$ for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in $\cal G$ determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the Friendship graph $F_\ell$, and show that there is no connected signed graph cospectral but not switching equivalent with $F_\ell$