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

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

Distributed Load Balancing with Nonconvex Constraints: A Randomized Algorithm with Application to Electric Vehicle Charging Scheduling

With substantial potential to reduce green house gas emission and reliance on fossil fuel, electric vehicles (EVs) have lead to a booming industry, whose growth is expected to continue for the next few decades. However, EVs present themselves as large loads to the power grid. If not coordinated wisely, the charging of EVs will overload power distribution circuits and dramatically increase power supply cost. To address this challenge, significant amount of effort has been devoted in the literature to schedule the charging of EVs in a power grid friendly way. Nonetheless, the majority of the literature assumes that EVs can be charged intermittently at any power level below certain rating, while in practice, it is preferable to charge an EV consecutively at a pre-determined power to prolong the battery lifespan. This practical EV charging constraint is nonconvex and complicates scheduling. To schedule a large number of EVs with the presence of practical nonconvex charging constraints, a distributed and randomized algorithm is proposed in this paper. The algorithm assumes the availability of a coordinator which can communicate with all EVs. In each iteration of the algorithm, the coordinator receives tentative charging profiles from the EVs and computes a broadcast control signal. After receiving this broadcast control signal, each EV generates a probability distribution over its admissible charging profiles, and samples from the distribution to update its tentative charging profile. We prove that the algorithm converges almost surely to a charging profile in finite iterations. The final charging profile (that the algorithm converges to) is random, i.e., it depends on the realization. We characterize the final charging profile—a charging profile can be a realization of the final charging profile if and only if it is a Nash equilibrium of the game in which each EV seeks to minimize the inner product of its own charging profile and the aggregate electricity demand. Furthermore, we provide a uniform suboptimality upper bound, that scales O(1=n) in the number n of EVs, for all realizations of the final charging profile

Reliability and Validity Studies of Externality of Happiness Scale Among Turkish Adults

Externality of happiness is a psychological construct that refers to the degree to which individuals perceive their level of happiness as beyond their control and mostly dependent to external factors. The aim of this study was to examine the reliability and validity of the Externality of Happiness scale (EOH) among a Turkish adult sample. A total of 230 participants (152 males and 78 females; mean age = 37.8 years, SD = 9.1) completed self-report measures of externality of happiness, life satisfaction, flouring, self-esteem, and fear of happiness. Exploratory and confirmatory factor analysis supported a one-factor structure for the EOH. The EOH was found to be negatively correlated with life satisfaction, flourishing, and self-esteem and positively correlated with fear of happiness. The scale also showed incremental value over self-esteem in predicting life satisfaction. Furthermore, the scale was found to be discriminated from fear of happiness. Moreover, evidence was provided for internal-consistency reliability. Overall, the findings suggested that Turkish version of EOH had adequate reliability and validity scores and that it can be used as a useful measurement tool to assess externality of happiness beliefs in future clinical practice and research

Exact Convex Relaxation of Optimal Power Flow in Radial Networks

The optimal power flow (OPF) problem determines a network operating point that minimizes a certain objective such as generation cost or power loss. It is nonconvex. We prove that a global optimum of OPF can be obtained by solving a second-order cone program, under a mild condition after shrinking the OPF feasible set slightly, for radial power networks. The condition can be checked a priori, and holds for the IEEE 13, 34, 37, 123-bus networks and two real-world networks

Load-shedding probabilities with hybrid renewable power generation and energy storage

The integration of renewable energy resources, such as solar and wind power, into the electric grid presents challengs partly due to the intermittency in the power output. These difficulties can be alleviated by effectively utilizing energy storage. We consider, as a case study, the integration of renewable resources into the electric power generation portfolio of an island off the coast of Southern California, Santa Catalina Island, and investigate the feasibility of replacing diesel generation entirely with solar photovoltaics (PV) and wind turbines, supplemented with energy storage. We use a simple storage model alongside a combination of renewables and varying load-shedding characterizations to determine the appropriate area of PV cells, number of wind turbines, and energy storage capacity needed to stay below a certain threshold probability for load-shedding over a pre-specified period of time and long-term expected fraction of time at load-shedding

Unusual Combination of Reversible Splenial Lesion and Meningitis-Retention Syndrome in Aseptic Meningomyelitis

[No abstract available