Research

Converting irradiance into electrical power along a physical path proceeds through a model chain. Separating global irradiance into its components, transposing it onto the module plane, then accounting for reflection losses, module temperature, the electrical behaviour of the module, shading and inverter behaviour follow one another, and each step offers several published models. The number of possible combinations therefore runs into the thousands, and it long remained unclear how much weight each choice carries. An early study of ours worked through this systematically, and the result became one of the most cited reference points in the field.

The alternative approach is machine learning, which learns the relationship between weather variables and power production from historical data instead of describing the physical relationships explicitly. In a systematic comparison we evaluated twenty-four machine learning models on identical data under identical verification conditions. We have since examined the effect of training data length, and compared deep learning against classical machine learning models within a unified framework. The two approaches are not, however, alternatives to one another. We showed that the best accuracy comes from hybridisation, in which intermediate results of the physical model become predictors of the learning model: the physical description does what it does reliably, and the learning model corrects what physics does not cover.

This direction also includes questions that seem secondary at first yet measurably affect the outcome: module tilt and row spacing, inverter sizing, shading losses, and how accurately the technical parameters of the plant are known in the first place. We have examined each of these in separate studies. In international collaboration we also set out the modelling toolkit in a review paper, from regression approaches through model chains to hybridisation and probabilistic extensions.

A plant operator places bids on the market for the following day's generation. If the forecast is a single value, there is no way of knowing whether it describes a calm, clear day, when the estimate will hold to within a few percent, or a shifting weather front, when the error may be many times larger. In the two cases a different bidding strategy, reserve sizing or battery schedule may be optimal. Probabilistic forecasting addresses this: alongside the expected generation, it also gives its distribution.

Probabilistic forecasts build on ensemble weather prediction, in which the meteorological model is run not once but dozens of times from slightly different initial conditions, the spread of the resulting forecasts indicating the uncertainty. We extended this principle to photovoltaic modelling: we passed the same weather forecast through many different model chains, then handled the two sources of uncertainty within a single framework. This model chain ensemble is an approach originating from the group.

Raw ensembles, however, are typically overconfident: actual errors are more widely spread than the divergence between members suggests, so statistical post-processing is required. To identify the most suitable model, we compared distributional and quantile-based calibration methods on photovoltaic ensemble forecasts, and we separately examined which input variables genuinely improve the outcome of post-processing. We have also looked at how the information content of an ensemble can be exploited when the end result has to be a single deterministic forecast. We assess these methods not only for average accuracy but also for reliability and sharpness, which gives a fuller picture of forecast quality.

The quality of a forecast is usually measured by its average deviation. This is convenient: it yields a single number and makes any two methods comparable. The user, however, is not interested in average deviation but in the cost of balancing energy, the market revenue forgone, or the losses caused by a poorly scheduled battery. Our results show that the two do not coincide: the forecast with the smallest error is not always the most useful one.

Part of the question is methodological. We have shown that interpreting error metrics is not self-evident either, and that different metrics rank different forecasts as the best. We also demonstrated that where post-processing is placed in the computation chain, that is, whether it is applied to irradiance or already to power, materially changes the outcome, and that calibration rearranges the conclusions of verification itself.

The other part is economic. Using real market prices we computed the actual cost of operational photovoltaic forecasts on the day-ahead market, linking accuracy-based and economic evaluation, and we separately compared the cost of forecast errors across forecasts produced in different ways. These analyses show that costs are not evenly distributed through the year: a substantial share of balancing cost arises in a few periods when the aggregate errors are large at system level as well and reserves are scarce. The real usefulness of a forecast therefore depends largely on how accurate it is in those periods.

Numerical weather prediction models perform well from a few hours to two weeks ahead, but not for the hours immediately ahead: several hours pass before a forecast can be produced from the latest observations. Yet it is precisely this horizon of a few hours on which intraday markets operate and on which a battery's schedule has to be decided. Satellite imagery can fill this gap, because images of the cloud field, taken at regular intervals, can be fed into a forecast with little delay.

Our developments are currently proceeding as doctoral research, in three directions. The first is estimating future cloud images from earlier frames with a U-Net-based deep learning network, which predicts cloud movement more accurately than conventional displacement-vector methods. The second is estimating the power production of photovoltaic plants from satellite data. The third is determining household-scale photovoltaic generation aggregated to district level, which makes visible a substantial share of generation that is not individually metered yet matters for system operation. These results will be presented at conferences in the near future.

The work continues towards combining forecasts from different sources, since the accuracy of satellite-based, model-based and measurement-based estimates changes differently with the forecast horizon. In comparing numerical models we have also examined when a high-resolution regional model outperforms a global one. Another important direction is the use of satellite-based estimates in downstream applications, such as machine-learning-based estimation of grid imbalance.

This question has occupied us for a long time. In earlier work we developed an optimisation framework for household-scale hybrid systems that sizes photovoltaics, a wind turbine, a solar collector, a battery, a thermal storage tank and the thickness of insulation simultaneously, and takes life-cycle environmental impact as an objective alongside investment cost. The results show that economic and environmental optima generally imply different system compositions, and that the compromise between them can be quantified.

More recent work addresses a question that has received surprisingly little attention in the literature: how much the temporal profile of demand matters. We worked with characteristic Hungarian household profiles derived from measurements, differing in both their daily and their annual patterns. The same annual consumption requires substantially different renewable capacities depending on when it occurs. Quantifying that difference also makes it possible to derive the economic value of demand-side measures. We carried out the optimisation not only for full renewable coverage but for a range of renewable shares, so that the results describe not just the end state but the path towards it.

At national scale we have also examined how a future power system with a high renewable share behaves, using a probabilistic model built with machine learning. In ongoing work we are investigating the balance between green hydrogen production and electricity supply within hybrid renewable systems. Our longer-term aim is to extend our system model step by step with further technologies and with energy demand beyond the electricity sector.

Lithium-ion batteries are today almost synonymous with energy storage, yet at large scale other technologies are competitive as well. Sodium-sulphur batteries are built from abundant raw materials but only operate above three hundred degrees, because their electrodes must be molten. Vanadium redox flow batteries allow power and capacity to be sized independently, which is advantageous for longer storage durations. Both have properties that cannot be described by a constant efficiency, which is nevertheless what system-level studies usually assume.

We have built detailed system models for both technologies. For the vanadium redox flow battery we examined how the system behaves under different geographical and climatic conditions, while for the sodium-sulphur battery the emphasis was on the coupled modelling of thermal and electrical behaviour. Building on these, we analysed how such batteries behave when operating under optimised schedules, that is, under conditions close to real application. This step matters because detailed cell models are usually examined on arbitrarily chosen load profiles, so their results do not always carry over into practical applications.

The other strand of our work is the optimisation of operation, in which linear programming lets us optimise the charging and discharging of the storage unit simultaneously for every hour of a year. We have also shown that at household scale, storage control is most effective when it relies on forecasts of both generation and consumption, which connects our storage work with our forecasting research. Alongside electrochemical storage we also work on hydrogen-based storage, primarily in its system-level context.

One of our early research directions was the optimisation of plant design. Using genetic algorithms we determined the economic optimum of ground-mounted photovoltaic plants, then extended the analysis to environmental criteria: in our ecodesign work, joint multi-objective optimisation of investment and life-cycle environmental burden showed that the two criteria lead to different optimal layouts. We also examined how the temporal resolution of the meteorological data used affects design outcomes, showing that simulations based on hourly average irradiance data can easily lead to overestimating the return on investment.

Life-cycle assessment has since been a standing element of our system-level work. If a renewable system can only deliver continuous supply through substantial oversizing and large storage capacity, the environmental benefit may be smaller than expected, since manufacturing each additional unit carries a burden of its own. Our system models therefore quantify environmental impacts alongside costs.

This direction opens the next question we are working on. In a renewable-based system, the cost and environmental burden of supply are not the same at different times of the year: covering demand on a summer morning is essentially free, whereas a still January evening can only be prepared for through substantial additional investment. Quantifying this difference reliably could help direct energy efficiency measures and subsidies to where they add the most value.