Price forward curves

Background

We simulate assets in the future for their whole lifetime, which can be up to 30 years. For this period in the future, we need an estimate of the prices on the grid during this time, to calculate expected financial results.

Estimating future prices this far in the future is extremely hard. Price changes may be due to macroeconomic factors (commodity prices, currency exchange rates, inflation, etc.) as well as conditions on the grid, which include policy aspects (renewable energy subsidies, nuclear power policy, etc.) and technological progress (cost of storage, new storage technologies, improved and cheaper solar cells, etc.).

To keep our model explainable, we assume that the seasonality of the prices (for example, prices are higher in the winter compared to spring, and are higher during weekdays compared to weekends) will not change in the future. Moreover, we do not make any assumption on the long-term trend of the curves: we generate baseline curves that have approximately the same average price each year. We also assume that the relation between basic weather variables (temperature and solar radiation) and prices will remain similar in the future. These baseline curves are then modified by assumptions about yearly average prices and yearly average volatility during the lifetime of the plant. Users are free to provide their own yearly average and volatility assumptions by using scenarios.

Calculation logic

The main steps for price generation are:

1. baseline curve creation based on historical data
2. scenario curve creation based on baselines and assumptions

Baseline curve creation

We create the baseline curves by training a deep learning auto-regressive model with temperature and global horizontal irradiance as predictors (as well as seasonality and auto-regressive features).

Note that these “raw” baseline curves can be negative.

Input

The model relies on weather data from 5 locations in each grid zones as prediction variables. The weather data has the same source described in the simulator weather. We use the following weather variables:

• Air temperature at 2 m (TEMP) in °C
• Global horizontal irradiance (GHI) in W/m2
• abs(22 - TEMP) (engineered feature)

We train the model on the JEPX day-ahead prices for each zone. We use prices in the period between 2021-04-01 to the 5 days preceding the training date for training. The training is performed weekly every Sunday at midnight JST.

The trained model is then used to generate the baseline price curves for the future. We generate prices until 2059-12-31. We use the same standardized weather data (based on mapping the future to the past) described in simulator weather as predictor variables.

Scenario curve creation

Once the baseline curves are created, we modify them according to the assumptions provided by users in the scenario associated with the asset. These assumptions are in the form of yearly average price and yearly average volatility (mean absolute deviation) for each year during the lifetime of the plant.

info

As of now, there are no explicit assumptions that can be made regarding the frequency of zero price slots during a certain year. Their frequency will be a result of the interaction between the baseline curves and the average and volatility assumptions. For example, setting a lower average price and higher volatility will tend to increase the frequency of zero-price events during that year.

As a first step, we take these assumptions from the scenario and we create a continuous curve by linear interpolation between the points defined, assuming that each year refers to the start of the financial year (1 April). We use the actuals to calculate the start point for the latest available financial year. Following this interpolation, the average price assumption $a_t$ and volatility assumption $v_t$ are then defined for each 30 minute slot.

We then calculate the rolling mean calculated on the trailing 12 months for the raw baseline price curve:

$$m_{t'} = \sum_{t=t'-365*48}^{t} \frac{p_t}{365*48} \quad \forall t' \in T$$

Where $T$ represent the total slots in the future and $p_t$ the baseline price at time t. Note that values for price slots before those in $T$ are still defined as the available actual prices in the past. Next, the price trend is calculated as:

$$R_t = \frac{p_t}{m_t} \cdot a_t \quad \forall t \in T$$

We calculate the rolling mean and deviation as:

$$G_{t'} = \sum_{t=t'-365*48}^{t} \frac{R_t}{365*48} \quad \forall t' \in T$$ $$d_{t} = R_{t} - G_t \quad \forall t \in T$$

And the rolling mean absolute deviation (MAD) as:

$$D_{t'} = \sum_{t=t'-365*48}^{t} \frac{|d_t|}{365*48} \quad \forall t' \in T$$

We can then calculate a measure of volatility as:

$$V_t = \frac{d_t}{D_t} \cdot v_t \quad \forall t \in T$$

The scenario price is then defined as:

$$P_t = \max(G_t + V_t, 0.01)$$

This scenario price is then used in the simulator to calculate the trading results and to optimize the battery operation over the asset life.