TESTING THE MODELS |
After building the predictor models for power load and solar radiation at each location, we performed the first predictions using as inputs historical weather data for five days in April, 2015. We then compared the predictions of the model to the actual measurements of power load and solar radiation. For these tests, which do not depend on weather forecasts, we could test our model on as many days as were available from the weather database. Note that we did not test our models on any data points that we used for training. Figure 1 shows our test of the power load predictor on the five days in April 2015 shown on the horizontal axis by the day number (from 1 to 365). Figure 2 shows our test of the solar predictor on the same days. We processed the solar model’s output to ensure plausible predictions: any value that was negative was set to zero, and all values between 10:00 p.m. and 3:00 a.m. were set to zero.
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Error in load forecasts is most commonly characterized by the Mean Absolute Percent Error (MAPE). This is defined as the mean of the absolute difference between the actual and forecasted values at each point, divided by the actual value at that point, shown by the expression below.
Error for the solar prediction is more difficult to characterize in a way that can be easily compared across data sets. Many of the values are zero, and the percent error cannot be well determined for those cases. We characterize the error as Mean Absolute Error (MAE), defined as the mean of the absolute difference between real and forecasted values at each point, as shown below.
The load predictor had a MAPE of 3.96%, and the solar predictor had a MAE of 70.93 W/m^2 in these tests.
FORECASTING |
Next, we input forecasted weather data for April 12th to 14th to our models to create 48-hour-ahead predictions of the solar radiation in each of the five locations and the power load for the overall area. Figure 3 shows the load prediction, which has a MAPE of 4.12%. Figure 4 shows the best solar forecast, for Imbler, OR, which has a MAE of 36.52 W/m^2. Table 1 shows the MAE for each of the five locations.
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Note: The days of Figures 5 and 6, the 48-hour forecasts, and of Figures 3 and 4, the tests on historical data, overlap because the 48-hour weather forecast data was collected before the historical data tests were performed; the 48-hour forecasts used all forecasted data and represent the prediction results that could be expected up to 48 hours in advance.
IMPACT ON
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These forecasting results can be applied to predict the change in demand from conventional generation sources when power grid has a certain capacity of solar installations. In our case, the chosen locations do not have large photovoltaic plants, but we can see an effect of our results if we model plants of a certain capacity at the locations of our predictors. For this, we assume that the power output of the plant varies linearly with incident solar radiation, neglecting effects of temperature and other factors on photovoltaic cell efficiency. For example, if a 30 MW-capacity photovoltaic plant were installed in each of the five locations, the approximate total power that these five plants would produce is shown in Figure 5.
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Subtracting this generation from the predicted load for the same time period gives the predicted net load. Comparing the predicted load to the predicted net load, as in Figure 6., shows the predicted effect that the solar resource will have on the power grid. We can compare this with the actual net load, which comes from actual load minus the calculated solar output. The mean absolute percent deviation of the prediction from the calculated net load is 4.15%. It is clear that this deviation is largely from the power load; the solar resource has a small effect on this value since the modeled capacity is a small fraction of the load. The analysis could easily be done for additional locations or a larger installation to see a more dramatic impact on the grid. Ultimately, this method is to be applied for a certain installed capacity, and its impacts will be larger for larger capacities of solar generation.