Local Energy Communities in Spain: Economic Implications of the New Tariff and Variable Coefficients

The European Union advocates for legislative support to local energy communities. Measures include the promotion of dynamic energy allocation and discriminatory electricity tariffs such as the recent Spanish framework. However, the impact of these normative changes is not yet evaluated. This paper inquires into the impact of dynamic allocation coefficient and different electricity tariffs on the profitability of local energy communities. To do so, a linear optimisation model is developed and applied to real consumer data in Spain around a variable capacity photovoltaic generation plant. Comparing the economic performance of the static or variable power allocation under the effect of changing electricity tariffs. While both measures are beneficial, the new electricity tariffs result in larger profitability increases than the planned variable coefficients. The combination of measures allows for profitability improvements of up to 25% being complementary measures. However, installations that maximise the potential for electricity generation are still not as profitable due to the low purchase price of surplus energy. While discriminatory electricity price tariffs and variable allocation coefficients are positive measures, further measures are needed for these communities to install generation plants as large as the potential that each case allows.

On the Maximum Number of Integer Colourings with Forbidden Monochromatic Sums

Let $f(n,r)$ denote the maximum number of colourings of $A \subseteq \lbrace 1,\ldots,n\rbrace$ with $r$ colours such that each colour class is sum-free. Here, a sum is a subset $\lbrace x,y,z\rbrace$ such that $x+y=z$. We show that $f(n,2) = 2^{\lceil n/2\rceil}$, and describe the extremal subsets. Further, using linear optimisation, we asymptotically determine the logarithm of $f(n,r)$ for $r \leqslant 5$. Similar results were obtained by Hán and Jiménez in the setting of finite abelian groups.

A non-linear optimisation method to extract summary statistics from Kaplan-Meier survival plots using the published P value

Background Meta-analyses of studies evaluating survival (time-to-event) outcomes are a powerful technique to assess the strength of evidence for a given disease or treatment. However, these studies rely on the adequate reporting of summary statistics in the source articles to facilitate further analysis. Unfortunately, many studies, especially within the field of prognostic research do not report such statistics, making secondary analyses challenging. Consequently, methods have been developed to infer missing statistics from the commonly published Kaplan-Meier (KM) plots but are liable to error especially when the published number at risk is not included. Methods We therefore developed a method using non-linear optimisation (nlopt) that only requires the KM plot and the commonly published P value to better estimate the underlying censoring pattern. We use this information to then calculate the natural logarithm of the hazard ratio (ln (HR)) and its variance (var) ln (HR), statistics important for meta-analyses. Results We compared this method to the Parmar method which also does not require the number at risk to be published. In a validation set consisting of 13 KM studies, a statistically significant improvement in calculating ln (HR) when using an exact P value was obtained (mean absolute error 0.014 vs 0.077, P = 0.003). Thus, when the true HR has a value of 1.5, inference of the HR using the proposed method would set limits between 1.49/1.52, an improvement of the 1.39/1.62 limits obtained using the Parmar method. We also used Monte Carlo simulations to establish recommendations for the number and positioning of points required for the method. Conclusion The proposed non-linear optimisation method is an improvement on the existing method when only a KM plot and P value are included and as such will enhance the accuracy of meta-analyses performed for studies analysing time-to-event outcomes. The nlopt source code is available, as is a simple-to-use web implementation of the method.

Dynamic model of photovoltaic module temperature as a function of atmospheric conditions

The temperature of photovoltaic modules is modelled as a dynamic function of ambient temperature, shortwave and longwave irradiance and wind speed, in order to allow for a more accurate characterisation of their efficiency. A simple dynamic thermal model is developed by extending an existing parametric steady-state model using an exponential smoothing kernel to include the effect of the heat capacity of the system. The four parameters of the model are fitted to measured data from three photovoltaic systems in the Allgäu region in Germany using non-linear optimisation. The dynamic model reduces the root-mean-square error between measured and modelled module temperature to 1.58 K on average, compared to 3.03 K for the steady-state model, whereas the maximum instantaneous error is reduced from 20.02 to 6.58 K.

Numerical Linear Programming under Non-Probabilistic Uncertainty Models — Interval and Fuzzy Sets

This paper considers a linear optimisation problem under uncertainty with at least one element modelled as a non-probabilistic uncertainty. The uncertainty is expressed in the coefficient matrices of constraints and/or coefficients of goal function. Previous work converts such problems to classical (linear) optimisation problems and eliminates uncertainty by converting the linear programming under uncertainty problem to a decision problem using imprecise probability and imprecise decision theory. Our aim here is to generalise this approach numerically and present three methods to calculate the solution. We investigate what numerical results can be obtained for interval and fuzzy types of uncertainty models and compare them to classical probabilistic cases — for two different optimality criteria: maximinity and maximality. We also provide an efficient method to calculate the maximal solutions in the fuzzy set model. A numerical example is considered for illustration of the results.

Impact of Long-Term Water Inflow Uncertainty on Wholesale Electricity Prices in Markets with High Shares of Renewable Energies and Storages

Renewable energy shares in electricity markets are increasing and therefore also require an increase in flexibility options. Conventional electricity price modelling with optimisation models in thermally dominated markets is not appropriate in markets with high shares of renewable energies and storages because price structures are not adequately represented. Previous research has already identified the impact of uncertainty in renewable energy feed-in on investment and dispatch decisions. However, we are not aware of any work that investigates the influence of uncertainties on price structures by means of optimisation models. Appropriate modelling of electricity price structures is important for investment and policy decisions. We have investigated the influence of uncertainty concerning water inflow by applying a second stage stochastic dual dynamic programming approach in a linear optimisation model using Norway as an example. We found that the influence of uncertainty concerning water inflow combined with high shares of storages has a strong impact on the electricity price structures. The identified structures are highly influenced by seasonal water inflow, electricity demand, wind, and export profiles. Additionally, they are reinforced by seasonal primary energy source prices and import prices. Incorporating uncertainties in linear optimisation models improves the price modelling and provides, to a large extent, an explanation for the seasonal patterns of Norwegian electricity market prices. The paper explains the basic pricing mechanisms in markets with high shares of storages and renewable energies which are subject to uncertainty. To identify these fundamental mechanisms, we focused on uncertainty regarding water inflow, but the basic results hold true for uncertainties regarding other renewable energies as well.

3D Localisation of Target using Elevation Angle Algorithm with the use of Ground Radars

A new novel method based on elevation angle algorithm (EAA) is proposed in this paper, to obtain 3D position of target using range and azimuth measurements of two ground 2D radars. The EAA estimates optimal target elevation angle wrt contributing radar by solving a non-linear optimisation problem using Levenberg-Marquardt method in geo-centric frame such as earth-centred-earth-fixed. The target position in geodetic frame (WGS84) is then obtained using slant range, azimuth and estimated elevation angle. The proposed method is evaluated using simulated but realistic radar data and accuracy of estimated position is found to be comparable with true position (error within acceptable limit). The method is also evaluated with real data from actual ground 2D radars and estimated target position is found to be comparable with reference navigation data (GPS) on-board of target. For each radar, corresponding Extended Kalman filter (EKF) is used to handle noisy, asynchronous measurements and to provide estimated range and azimuth at common reference time for altitude estimation using proposed EAA method. In case of real data, the estimated altitude is found to be comparable GPS altitude with error less than 5 % of true altitude. From the study, it is found that EAA is suitable to estimate target position using measurements from only two contributing asynchronous 2D radars in real-time as compared to some other techniques such triangulation and Trilateration where at-least three radars are required to get the position of target. This method can be useful to utilise network of vintage long range 2D radars to determine target position and to fill the gap wherever/whenever target is out of detection range of 3D radars. In addition, EAA method is compared with commonly used methodology such range only localisation and results are presented.

Geo.KW - Coupling hydrothermal and infrastructure modeling at urban scale for an efficient use of shallow geothermal energy

<p>To reduce anthropogenic climate change, the energy demand from all energy sectors has to be met by renewable energies, wherever possible.<br>Shallow geothermal energy usage, powered by green electricity, provides heating/cooling at a high level of efficiency, which is difficult to achieve with renewable energy alone.<br>We have created a coupling approach, which combines hydrothermal and infrastructure modeling at an urban scale to efficiently position shallow geothermal systems between existing power plants and conflicting groundwater usage, optimised by economical and ecological contraints.<br>We are using Pflotran, a finite volume Darcy-Richards model for our hydrothermal model.<br>The implementation of the energy infrastructure is done with urbs, a linear optimisation model for distributed energy systems.<br>We utilize preCICE, a coupling library for multi-physics simulations, for fully parallel peer-to-peer data exchange between these modeling domains.<br>Iterative optimization is meant to ensure the convergence of the fully coupled model.</p>