Estimation of Joint Distribution of Demand and Available Renewables for Generation Adequacy Assessment

In recent years there has been a resurgence of interest in generation adequacy risk assessment, due to the need to include variable generation renewables within such calculations. This paper will describe new statistical approaches to estimating the joint distribution of demand and available VG capacity; this is required for the LOLE calculations used in many statutory adequacy studies, for example those of GB and PJM. The most popular estimation technique in the VG-integration literature is ‘hind- cast’, in which the historic joint distribution of demand and available VG is used as a predictive distribution. Through the use of bootstrap statistical analysis, this paper will show that due to extreme sparsity of data on times of high demand and low VG, hindcast results can suffer from sampling uncertainty to the extent that they have little practical meaning. An alternative estimation approach, in which a marginal distribution of available VG is rescaled according to demand level, is thus proposed. This reduces sampling uncertainty at the expense of the additional model structure assumption, and further provides a means of assessing the sensitivity of model out- puts to the VG-demand relationship by varying the function of demand by which the marginal VG distribution is rescaled

Further Results on the Probability Theory of Capacity Value of Additional Generation

New theoretical results regarding the capacity value of additional generation are presented, the motivation being explanation of results from applied renewables integration studies. Of particular note are the dependence of calculated values on underlying risk level for any capacity of additional generation, the upper limit on capacity value where there is a given probability of near-zero available capacity, and a closed form result for the case where the distribution of available existing capacity may be approximated as an exponential function. Examples of how these main results may be applied are presented

Quasiparticle lifetimes in the charged Bose gas and the cuprates

The scattering cross-section of a Coulomb potential screened by a charged Bose gas is calculated both above and below the Bose-Einstein condensation temperature, using the variable-phase method. In contrast with the case for the Bardeen-Cooper-Schrieffer superconductor, the screened scattering potential and quasiparticle lifetime are found to be very different in the superconducting and normal states. We apply the result to explain the appearance of a sharp peak in the angle-resolved photoemission spectra in some cuprates below the superconducting transition

On the capture width of wave energy converters

This paper extends the theory on capture width, a commonly used performance indicator for a wave energy converter (WEC). The capture width of a linear WEC is shown to depend on two properties: the spectral power fraction (a property introduced in this paper), which depends entirely on the sea state, and the monochromatic capture width, which is determined by the geometry of the WEC and the chosen power take off (PTO) coefficients. Each of these properties is examined in detail. Capture width is shown to be a measure of how well these two properties coincide. A study of the effects of PTO control on the capture width suggests that geometry control, a form of control that has not been the focus of much academic research, despite its use in the wave energy industry, deserves more attention. The distinction between geometry control and PTO control is outlined. While capture width is a valuable design tool, its limitations must be recognised. The assumptions made in the formulation of capture width are listed, and its limitations as a tool for estimating annual power capture of a WEC are discussed

Capacity Value of Large Tidal Barrages

This paper presents the first detailed capacity value calculation for tidal barrage generation, based on modeling of operational modes for the proposed 8-GW Severn Barrage scheme in Great Britain. The key finding is that the effective load carrying capability is very low as a percentage of installed capacity (less than 10% for the example presented here). This is because of the high probability of having zero available output at time of peak demand, if peak demand occurs on the wrong part of the tidal cycle; this result may be explained transparently using a simple two-state model of the barrage. The prospects for building a probabilistic model of tidal barrage availability are also discussed

Opportunity Cost Bidding by Wind Generators in Forward Markets: Analytical Results

Wind generation must trade in forward electricity markets based on imperfect forecasts of its output and real-time prices. When the real-time price differs for generators that are short and long, the optimal forward strategy must be based on the opportunity costs of charges and payments in real-time rather than a central estimate of wind output. We present analytical results for wind's optimal forward strategy. In the risk-neutral case, the optimal strategy is determined by the distribution of real-time available wind capacity, and the expected real-time prices conditioned on the forward price and wind out-turn; our approach is simpler and more computationally efficient than formulations requiring specification of full joint distributions or a large set of scenarios. Informative closed-form examples are derived for particular specifications of the wind-price dependence structure. In the usual case of uncertain forward prices, the optimal bidding strategy generally consists of a bid curve for wind power, rather than a fixed quantity bid. A discussion of the risk-averse problem is also provided. An analytical result is available for aversion to production volume risk; however, we doubt whether wind owners should be risk-averse with respect to the income from a single settlement period, given the large number of such periods in a year

Impact of high wind penetration on variability of unserved energy in power system adequacy

This paper presents results on variability of out-turn shortfalls about the expected value indices which are usually presented in resource adequacy studies, for a range of Loss of Load Expectation (LOLE) levels and installed wind capacities in a test system generally representative of future Great Britain system scenarios. While the details of results will clearly vary between systems, one very general conclusion is possible. In the results presented, for a given LOLE level, the probability of very severe out-turn in a future peak season is much greater at high installed wind capacity. Thus for this system, as the installed wind capacity increases, a constant level of LOLE cannot be taken as an indicator of an unchanging overall risk profile of the system. This further demonstrates that in any system, LOLE cannot be assumed to be a good summary statistic of risk profile as the installed variable generation (VG) capacity increases, and that it might be necessary to reconsider the near-universal use of expected value risk indices as the main headline indices in utility adequacy studies

Capacity Value of Solar Power: Report of the IEEE PES Task Force on Capacity Value of Solar Power

This paper reviews methods used for adequacy risk assessment considering solar power, and for assessment of the capacity value of solar power. The properties of solar power are described as seen from the perspective of the balancing authority, comparing differences in energy availability and capacity factors with those of wind. Methodology for risk calculations considering variable generation (VG) are then surveyed, including the probability background, statistical estimation approaches, and capacity value metrics. Issues in incorporating VG in capacity markets are described, followed by a review of applied studies considering solar power. Finally, recommendations for further research will be presented

Capacity Value of Wind Power

Power systems are planned such that they have adequate generation capacity to meet the load, according to a defined reliability target. The increase in the penetration of wind generation in recent years has led to a number of challenges for the planning and operation of power systems. A key metric for generation system adequacy is the capacity value of generation. The capacity value of a generator is the contribution that a given generator makes to generation system adequacy. The variable and stochastic nature of wind sets it apart from conventional energy sources. As a result, the modeling of wind generation in the same manner as conventional generation for capacity value calculations is inappropriate. In this paper a preferred method for calculation of the capacity value of wind is described and a discussion of the pertinent issues surrounding it is given. Approximate methods for the calculation are also described with their limitations highlighted. The outcome of recent wind capacity value analyses in Europe and North America, along with some new analysis, are highlighted with a discussion of relevant issues also given

Fundamental constants and tests of general relativity - Theoretical and cosmological considerations

The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between varying constants and extensions of general relativity. To finish, we discuss the link with cosmology, and more particularly with the acceleration of the Universe. We take the opportunity to summarize various possibilities to test general relativity (but also the Copernican principle) on cosmological scales.Comment: Proceedings of the workshop ``The nature of gravity, confronting theory and experiment in space'', ISSI, Bern, october 200