A Brief Perspective on Aggregated Forecast of Solar Power Generation

Abhik Kumar Das | Del2infinity Energy Consulting

The solar power generation shows a promising future in India. But due to the variability and intermittency, large scale renewable energy penetration in existing grid is a challenge and the proper policy and regulatory mechanisms, technological solutions and institutional structures are key issues in solar energy penetration.

Abhik Kumar Das | Del2infinity Energy Consulting

The ‘Forecasting and Scheduling’ (F&S) of variable renewable energy (Solar and Wind) generation is an essential requirement of the stable grid system due to the balancing challenge in load and generation. The concept of forecasting and scheduling of renewable energy generators and the commercial settlement was introduced in Indian context by CERC through Indian Electricity Grid Code (IEGC), 2010. Considering the recent development of different state regulations, the DSM charges are to be computed on a monthly basis. Hence IPPs have to submit their day-ahead power generation forecast and schedule (F&S) to SLDC to manage the grid stability. According to the regulation, the forecasting & scheduling (F&S) of power generation can be submitted to SLDC using two major options:

1. Plant specific F&S
2. Aggregated F&S

A forecast model of solar power generation can be viewed as probabilistic evolution to generate different plausible patterns considering the unscheduled fluctuations. A good forecasting system is a process which gives proper accuracy with minimum penalty due to deviation even in a small capacity of solar plants with high variability with minimum number of intraday revisions. This article concentrates on the theoretical structure of the aggregated forecast.

Measure Using Central Tendency

The major assumption in aggregated forecast is that the positive and negative error can cancel each other in the long run and hence the average error in aggregated forecast is very small or under acceptable limit.

To formulate the theoretical structure in a simplified manner let’s consider two solar plants of capacity C1 and C2. Without representing the detail algebraic construction of the error distribution, the aggregated forecast error at i-th time-block can be represented as 

Where  and  are the scaling factor such that

Hence, in the average case (or the expected value in error according to statistical theory) we can consider

Where  and  are the average error in aggregated forecast, forecast of plant 1 and forecast of plant 2 respectively. Since  and  are in the ratio of their plant capacity, the existent de-pooling mechanism considers to divide the penalty due to deviation of two plants according to their plant capacity or depending on the ratio of the energy generation at a particular time-block in which the penalty exists. This assumption in aggregated forecast is correct in some cases, but not sufficient, as it does not consider the variability analysis of the power generation and only plays with the measure of central tendency of the error distribution. This incomplete theory in the agrregated forecast is an issue and hence no valid logical framework is available in calculating the ‘de-pooling’ mechanism in calculating the penalty payable for each plant in case of aggregated forecast.

Measure of Dispersion

The generation of solar power is best described using the Wold’s representation theorem according of which solar generation can be represented as the summation of deterministic and stochastic time series. The error in forecasting comes from the stochastic time series in Wold’s decomposition while the maximum portion of the solar power generation is deterministic. Hence,

1. Solar power generation is not random. Moreover the ramping occurrences have specific distribution depending on plant characteristics according to Wold’s theorem.
2. The power generation characteristics (or statistical distribution) is not same for each PV panel or each plant of the group of aggregation

Considering the variation in error forecasting the variance of the aggregated error can be represented as, 

Where  and  are the variance in the error distribution for aggregated forecast, forecast of plant 1 and forecast of plant 2 respectively. Here ρ is the correlation coefficient. Considering the two plants are almost in the same location, this value tends to 1, i.e.  with some simple algebraic manipulation, it can be shown that, if  which is a natural phenomena unless the characteristics and power generation patterns in both plants are same, 

Hence, in the long run, the variance of the error distribution lies between the variance of each plant. Without much loss of generality, we can consider the error distribution in forecasting of solar follows a Gaussian distribution with mean 0 but with different standard deviations as shown in the figure.

For the error distribution, the area under the curve in -15% – +15% can represent the accuracy of the forecast as this represents the probability that the plant does not have to give any deviation penalty as the deviation error is under +/- 15%.

As shown in the figure, since the standard deviations are different for two plants, the accuracy of plant 1 is reduced due to the aggregated forecast. Hence, in the long run, the plant 1 is actually paying the penalty due to deviation of plant 2 due to aggregated forecast.

Hence, considering the multiple plants we can state that, with aggregation, the occurrence of high variability in the generation of one plant affects the error of other plants having stable generation even in the long run. Interestingly, plant specific forecasting does not have this type of anomaly as it solely depends on its own performance not affected by the performance of other plants. Moreover the commercial settlement in penalty due to deviation is comparatively simple in case of plant specific forecast.