arXiv subjects

David Kraljic

Publications and source records attributed to David Kraljic.

10 recordsLinked to original sources

arXiv2022

Inertia constants for individual power plants

Keeping the power system stable is becoming more challenging with the growing share of renewable energy sources of low or negligible inertia. Inertia constants for individual power plants are generally not known and are roughly estimated by considering the type of power generation technology and the nameplate capacity of plants. More accurate knowledge of inertia constants of individual power plants would give greater transparency to decisions of the transmission system operator (TSO) and to auctions for the procurement of inertia services. Additionally, a more accurate forecast or estimation of system inertia would improve the price signals to the power market well in advance of balancing actions taken by the TSO. We develop methods based on a combination of mathematical optimisation and machine learning that reverse-engineer the inertia constants of individual power plants from the historical values of their power production and from aggregate values of inertia in a power system. We demonstrate the methods for the power system of Great Britain (GB), where historical values for aggregate inertia are published by the TSO. We show that the recovered inertia data is crucial in understanding certain individual balancing decisions by the TSO. We use the reverse-engineered inertia constants to predict system inertia which gives valuable information to the power market.

eess.SY↗

arXiv2022

Towards realistic statistical models of the grid frequency

Increased share of renewable sources of energy in a power grid leads to larger deviations in grid frequency from the nominal value resulting in more challenging control and its modelling. In this paper we focus on the grid frequency for the power system of Great Britain because the large share of renewables makes it a template for other power grids in the future and because it exhibits peculiar statistical properties, such as long-term correlations in fluctuations, periodicity, bi-modality,and heavy tails in the distribution of the grid frequency. By modifications of the swing equation and the underlying noise statistics, which we justify qualitatively and quantitatively, we reproduce these peculiar statistical properties. We apply our model to realistic frequency response services and show our predictions outperform a standard swing equation model.

physics.soc-ph↗

arXiv2020

Centre of pressure estimation during walking using only inertial-measurement units and end-to-end statistical modelling

Estimation of the centre of pressure (COP) is an important part of the gait analysis, for example, when evaluating the functional capacity of individuals affected by motor impairment. Inertial measurement units (IMUs) and force sensors are commonly used to measure gait characteristic of healthy and impaired subjects. We present a methodology for estimating the COP solely from raw gyroscope, accelerometer, and magnetometer data from IMUs using statistical modelling. We demonstrate the viability of the method using an example of two models: a linear model and a non-linear Long-Short-Term Memory (LSTM) neural network model. Models were trained on the COP ground truth data measured using an instrumented treadmill and achieved the average intra-subject root mean square (RMS) error between estimated and ground truth COP of 12.3mm and the average inter-subject RMS error of 23.7mm which is comparable or better than similar studies so far. We show that the calibration procedure in the instrumented treadmill can be as short as a couple of minutes without the decrease in our model performance. We also show that the magnetic component of the recorded IMU signal, which is most sensitive to environmental changes, can be safely dropped without a significant decrease in model performance. Finally, we show that the number of IMUs can be reduced to five without deterioration in the model performance.

eess.SP↗

arXiv2020

Solution space of optimal heat pump schedules

We study the space of optimal schedules for a heat pump with thermal energy storage used in heating a residential building. We model the heating system as a Mixed Integer Linear Program with the objective to minimise the cost of heating. We generate a large number of realistic daily heat demands and calculate the optimal schedule for the heat pump. In addition to cost savings stemming from optimal running, we find that the space of optimal schedules is large in practice, even for the simplest model of the heating system we use, and that the optimal schedules are difficult to reproduce with statistical models. These findings strengthen the case for the use of mathematical optimisation in real-life applications.

eess.SY↗

arXiv2019

Extracting physical power plant parameters from historical behaviour

The information needed for fundamental modelling of the power markets -- the efficiency, start-up, fixed, and variable operating costs of each power plant -- is not publicly available. These parameters are usually estimated by considering the type of technology and the age of a power plant. We present a method to extract these parameters for thermal power plants on the British electricity market using only the publicly available data. For each power plant, we solve a bilevel optimisation problem, where the inner level solves the Unit Commitment (UC) problem and outputs the optimal schedule given the prices of fuel, emissions, electricity, and the unknown plant parameters. The outer level then optimises over the plant parameters matching the historical production of each plant as closely as possible.

eess.SY↗

arXiv2016

Frames of most uniform Hubble flow

It has been observed that the locally measured Hubble parameter converges quickest to the background value and the dipole structure of the velocity field is smallest in the reference frame of the Local Group of galaxies. We study the statistical properties of Lorentz boosts with respect to the Cosmic Microwave Background frame which make the Hubble flow look most uniform around a particular observer. We use a very large N-Body simulation to extract the dependence of the boost velocities on the local environment such as underdensities, overdensities, and bulk flows. We find that the observation is not unexpected if we are located in an underdensity, which is indeed the case for our position in the universe. The amplitude of the measured boost velocity for our location is consistent with the expectation in the standard cosmology.

astro-ph.CO↗

arXiv2016

Inflationary Potentials from the Exact Renormalisation Group

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. We assume that the theory contains a scalar mode with suppressed coupling to other UV fields, and that higher derivative couplings are suppressed. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the $ϕ^4$ theory.

hep-th↗

arXiv2015

Characterising cosmic inhomogeneity with anomalous diffusion

Dark matter (DM) clustering at the present epoch is investigated from a fractal viewpoint in order to determine the scale where the self-similar scaling property of the DM halo distribution transits to homogeneity. Methods based on well-established `counts-in-cells' as well as new methods based on anomalous diffusion and random walks are investigated. Both are applied to DM halos of the biggest N-Body simulation in the `Dark Sky Simulations' (DS) catalogue and an equivalent randomly distributed catalogue. Results based on the smaller `Millennium Run' (MR) simulation are revisited and improved. It is found that the MR simulation volume is too small and prone to bias to reliably identify the onset of homogeneity. Transition to homogeneity is defined when the fractal dimension of the clustered and random distributions cannot be distinguished within the associated uncertainties. The `counts-in-cells' method applied to the DS simulation then yields a homogeneity scale roughly consistent with previous work ($\sim 150$$h^{-1}$Mpc). The characteristic length-scale for anomalous diffusion to behave homogeneously is found to be at about 250$h^{-1}$Mpc. The behaviour of the fractal dimensions for a halo catalogue with the same two-point function as the original but with shuffled Fourier phases is investigated. The methods based on anomalous diffusion are shown to be sensitive to the phase information, whereas the `counts-in-cells' methods are not.

astro-ph.CO↗

arXiv2015

How rare is the Bullet Cluster (in a $Λ$CDM universe)?

The Bullet Cluster (1E0657-56) is well-known as providing visual evidence of dark matter but it is potentially incompatible with the standard $Λ$CDM cosmology due to the high relative velocity of the two colliding clusters. Previous studies have focussed on the probability of such a high relative velocity amongst selected candidate systems. This notion of `probability' is however difficult to interpret and can lead to paradoxical results. Instead, we consider the expected number of Bullet-like systems on the sky up to a specified redshift, which allows for direct comparison with observations. Using a Hubble volume N-body simulation with high resolution we investigate how the number of such systems depends on the masses of the halo pairs, their separation, and collisional angle. This enables us to extract an approximate formula for the expected number of halo-halo collisions given specific collisional parameters. We use extreme value statistics to analyse the tail of the pairwise velocity distribution and demonstrate that it is fatter than the previously assumed Gaussian form. We estimate that the number of dark matter halo pairs as or more extreme than 1E0657-56 in mass, separation and relative velocity is $1.3^{+2.0}_{-0.6}$ up to redshift $z=0.3$. However requiring the halos to have collided and passed through each other as is observed decreases this number to only 0.1. The discovery of more such systems would thus indeed present a challenge to the standard cosmology.

astro-ph.CO↗

arXiv2014

ALP Conversion and the Soft X-ray Excess in the Outskirts of the Coma Cluster

It was recently found that the soft X-ray excess in the center of the Coma cluster can be fitted by conversion of axion-like-particles (ALPs) of a cosmic axion background (CAB) to photons. We extend this analysis to the outskirts of Coma, including regions up to 5 Mpc from the center of the cluster. We extract the excess soft X-ray flux from ROSAT All-Sky Survey data and compare it to the expected flux from ALP to photon conversion of a CAB. The soft X-ray excess both in the center and the outskirts of Coma can be simultaneously fitted by ALP to photon conversion of a CAB. Given the uncertainties of the cluster magnetic field in the outskirts we constrain the parameter space of the CAB. In particular, an upper limit on the CAB mean energy and a range of allowed ALP-photon couplings are derived.

hep-ph↗