Examining random number generators used in stochastic iteration algorithms

This paper investigates random number generators in stochastic iteration algorithms that require infinite uniform sequences. We take a simple model of the general transport equation and solve it with the application of a linear congruential generator, the Mersenne twister, the mother-of-all generators, and a true random number generator based on quantum effects. With this simple model we show that for reasonably contractive operators the theoretically not infinite-uniform sequences perform also well. Finally, we demonstrate the power of stochastic iteration for the solution of the light transport problem.

A note on an integration by parts formula for the generators of uniform translations on configuration space

An integration by parts formula is derived for the first order differential operator corresponding to the action of translations on the space of locally finite simple configurations of infinitely many points on Rd. As reference measures, tempered grand canonical Gibbs measures are considered corresponding to a non-constant non-smooth intensity (one-body potential) and translation invariant potentials fulfilling the usual conditions. It is proven that such Gibbs measures fulfill the intuitive integration by parts formula if and only if the action of the translation is not broken for this particular measure. The latter is automatically fulfilled in the high temperature and low intensity regime.

Using standby generators in support of an electricity network: logistics and experience

Electricity load shifting is becoming a big topic in the world of ‘green’ retail. Marks & Spencer (M&S) aim to become the world’s most sustainable retailer (1) and part of that commitment means contributing to the future electricity network. While intelligent operation of fridges and Heating, Ventilation and Air Conditioning (HVAC) systems are a wide area of research, standby generators should be considered too, as they are the most widely adopted form of distributed generation. In this paper, the experience of using standby generators in Northern Ireland to support the grid is shared and the logistics of future projects are discussed. Interactions with maintenance schedules, electricity costs, grid code, staffing and store opening times are discussed as well as the financial implications associated with running generators for grid support.

Financial implications for companies running standby generators in support of a smart grid

Integrating renewable energy into built environments requires additional attention to the balancing of supply and demand due to their intermittent nature. Demand Side Response (DSR) has the potential to make money for organisations as well as support the System Operator as the generation mix changes. There is an opportunity to increase the use of existing technologies in order to manage demand. Company-owned standby generators are a rarely used resource; their maintenance schedule often accounts for a majority of their running hours. DSR encompasses a range of technologies and organisations; Sustainability First (2012) suggest that the System Operator (SO), energy supply companies, Distribution Network Operators (DNOs), Aggregators and Customers all stand to benefit from DSR. It is therefore important to consider impact of DSR measures to each of these stakeholders. This paper assesses the financial implications of organisations using existing standby generation equipment for DSR in order to avoid peak electricity charges. It concludes that under the current GB electricity pricing structure, there are several regions where running diesel generators at peak times is financially beneficial to organisations. Issues such as fuel costs, Carbon Reduction Commitment (CRC) charges, maintenance costs and electricity prices are discussed.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Entry and externality : hydroelectric generators in Brazil

This work analyzes the entry problem in the hydroelectric generation industry. The operation of a generator upstream regularizes the river flow for generators located downstream on the same river, increasing the production capacity of the latter. This positive externality increases the attractiveness of the locations downstream whenever a generator decides to enter upstream. Therefore, the entry decision of a generator in a given location may affect all entry decisions in potential locations for plants downstream. I first model the problem of generators located in cascade on the same river to show the positive effect of the externality. Next, I develop a method to estimate an entry model specific to the hydro generation industry which takes into account the externality of the entry decisions. Finally, I use a data set on investment decisions of Brazilian hydro-generators to estimate the model. The results show a positive incentive to locate downstream from existing plants and from locations where entry is likely to occur. An interesting by-product of the analysis is that the year effects’ estimates show an increase one year before the energy crisis of 2001, providing evidence that the market anticipated the crisis. It contradicts the governmental version that the crisis was due to an unexpected drought.

Observing the performance of distribution systems with embedded generators

In this paper, a multi-objective approach for observing the performance of distribution systems with embedded generators in the steady state, based on heuristic and power system analysis, is proposed. The proposed hybrid performance index describes the quality of the operating state in each considered distribution network configuration. In order to represent the system state, the loss allocation in the distribution systems, based on the Z-bus loss allocation method and compensation-based power flow algorithm, is determined. Also, an investigation of the impact of the integration of embedded generators on the overall performance of the distribution systems in the steady state, is performed. Results obtained from several case studies are presented and discussed. Copyright (C) 2004 John Wiley Sons, Ltd.

Comparison of Reactive Power Support in Distribution Networks Provided by Capacitor Banks and Distributed Generators

This paper presents a comparison of reactive power support in distribution networks provided by switched Capacitor Banks (CBs) and Distributed Generators (DGs). Regarding switched CBs, a Tabu Search metaheuristic algorithm is developed to determine their optimal operation with the objective of reducing the power losses in the lines on the system, while meeting network constraints. on the other hand, the optimal operation of DGs is analyzed through an evolutionary Multi-Objective (MO) programming approach. The objectives of such approach are the minimization of power losses and operation cost of the DGs. The comparison of the reactive power support provided by switched CBs and DGs is carried out using a modified IEEE 34 bus distribution test system.

Integration of the dispersed generators in the distribution management system

Since the 80s huge efforts have been made to utilize renewable energy sources to generate electric power. An important issue about using renewable energy sources is a Distribution Management System (DMS) in presence of dispersed generators. This paper reports some aspects of integration of the dispersed generators in the DMS. Besides, an investigation of impact of the dispersed generators on the overall performances of the distribution systems in steady state is performed. In order to observe losses in the distribution networks with dispersed generators, several loss allocation methods are applied. Results obtained from case study using IEEE test network, are presented and discussed. © 2003 IEEE.

Investigation into the impact of embedded generators on distribution system performance using theorem of superposition

Since the 1980s, huge efforts have been made to utilise renewable energy sources to generate electric power. One of the interesting issues about embedded generators is the question of optimal placement and sizing of the embedded generators. This paper reports an investigation of impact of the integration of embedded generators on the overall performances of the distribution networks in the steady state, using theorem of superposition. Set of distribution system indices is proposed to observe performances of the distribution networks with embedded generators. Results obtained from the case study using IEEE test network are presented and discussed.

Contribution of distributed generators to the harmonic distortion in low voltage power network

In the last 20 years immense efforts have been made to utilize renewable energy sources for electric power generation. This paper investigates some aspects of integration of the distributed generators into the low voltage distribution network. An assessment of impact of the distributed generators on the voltage and current harmonic distortion in the low voltage network is performed. Results obtained from a case study, using real-life low voltage network, are presented and discussed.

Reactive power support pricing of distributed generators with primary energy source uncertainty

In this paper, a novel methodology to price the reactive power support ancillary service of Distributed Generators (DGs) with primary energy source uncertainty is shown. The proposed methodology provides the service pricing based on the Loss of Opportunity Costs (LOC) calculation. An algorithm is proposed to reduce the uncertainty present in these generators using Multiobjective Power Flows (MOPFs) implemented in multiple probabilistic scenarios through Monte Carlo Simulations (MCS), and modeling the time series associated with the generation of active power from DGs through Markov Chains (MC). © 2011 IEEE.

Optimal allocation of distributed generators providing reactive power support ancillary service

Problems as voltage increase at the end of a feeder, demand supply unbalance in a fault condition, power quality decline, increase of power losses, and reduction of reliability levels may occur if Distributed Generators (DGs) are not properly allocated. For this reason, researchers have been employed several solution techniques to solve the problem of optimal allocation of DGs. This work is focused on the ancillary service of reactive power support provided by DGs. The main objective is to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). The LOC will be determined for different allocation alternatives of DGs as a result of a multi-objective optimization process, aiming the minimization of losses in the lines of the system and costs of active power generation from DGs, and the maximization of the static voltage stability margin of the system. The effectiveness of the proposed methodology in improving the goals outlined was demonstrated using the IEEE 34 bus distribution test feeder with two DGs cosidered to be allocated. © 2011 IEEE.

Pricing of reactive power support provided by distributed generators in transmission systems

Distributed Generation, microgrid technologies, two-way communication systems, and demand response programs are issues that are being studied in recent years within the concept of smart grids. At some level of enough penetration, the Distributed Generators (DGs) can provide benefits for sub-transmission and transmission systems through the so-called ancillary services. This work is focused on the ancillary service of reactive power support provided by DGs, specifically Wind Turbine Generators (WTGs), with high level of impact on transmission systems. The main objective of this work is to propose an optimization methodology to price this service by determining the costs in which a DG incurs when it loses sales opportunity of active power, i.e, by determining the Loss of Opportunity Costs (LOC). LOC occur when more reactive power is required than available, and the active power generation has to be reduced in order to increase the reactive power capacity. In the optimization process, three objectives are considered: active power generation costs of DGs, voltage stability margin of the system, and losses in the lines of the network. Uncertainties of WTGs are reduced solving multi-objective optimal power flows in multiple probabilistic scenarios constructed by Monte Carlo simulations, and modeling the time series associated with the active power generation of each WTG via Fuzzy Logic and Markov Chains. The proposed methodology was tested using the IEEE 14 bus test system with two WTGs installed. © 2011 IEEE.