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Need an Eval? Feature Development NetLoad Inc continuously develops new features and new products. DGM 1, 3 forecasting model parameters can be estimated by following matrix operations:. Significant connected load variation can happen in every year due to the addition of new loads.
Similarly, the installed capacity of wind and solar generation is also rapidly increasing around the world. This also restricts the selection of more than two previous year net load data [ 3 ]. Therefore, selecting more than two previous year net load data cannot help to improve the forecasting accuracy. Net load forecasts obtained from the above models should be compared with actual net load values for forecasting performance evaluation. Mean value of absolute errors over an interval can be given as,.
Backpropagation based ANN model is implemented for comparison [ 24 ]. Optimal performance of proposed model can be ensured by evaluating correlation residues such as ACF. Low correlation and zero mean residues show that no information remains in input net load data, which could be used for improving the forecasting accuracy. Therefore, residual correlation evaluation can be done for proposed models to ensure optimal performance.
Load and wind power generation data is directly taken from BPA and solar power generation is modelled using solar radiation data. Large number of wind plants are available in BPA balancing area, having an aggregated installed capacity of MW. Aggregated capacity of MW solar power generation is modelled using solar radiation data, to account globally increasing solar PV generation.
Selected system has MW installed capacity of renewable generation and total renewable generation never reaches to total load, which has an average value of MW. This results in a positive NLTS data for all time steps.
Load, wind generation, solar generation and estimated net load of one morning hour in winter season is shown in Fig. Figure 2 shows that net load is positive for all time steps as renewable generation is too low as compared to system load.
Load is slightly increasing for the shown hour as industrial and commercial loads start to build in morning hours. Solar generation also increases due to increasing radiation in morning, while wind generation does not show any trend. Proposed models obtain point net load forecasts. DGM 1, 1 model is trained using data and tested on data. Proposed Grey index models use AGO as data pre-processing technique. AGO transform actual net load time series into monotonically increasing data. Model parameters are evaluated from those monotonically escalating data.
Therefore, model adequacy test is conducted on net load AGO data. Model adequacy is evaluated by ACF. Figure 4 shows that net load AGO data has moving characteristics and strong auto correlation with previous time steps.
So, Grey index models are suitable for net load AGO data forecasting as those can transfer momentum present in previous time steps data. Proposed model accuracy can also increase by adding previous years similar day net load data as they show almost similar climatic conditions.
Similar days are selected based on date, weekday or weekend or holiday information. For obtaining forecasts of weekdays, same date day in the previous year is selected, if it is weekday and nearest date day is selected, if it is weekend.
For obtaining forecasts of weekend days, same date day in the previous year is selected, if it is weekend day and nearest date weekend day is selected, if it is weekday. For obtaining forecasts of holidays, same holidays are selected from previous years. Proposed Grey index based direct NLF models are implemented for different seasons such as winter, transition and summer. Net load forecasts are obtained for morning, noon, evening and night hours of winter season to show the performance throughout the day.
Performance plot of one morning hour is shown in Fig. Figure 5 shows that forecasts obtained from Grey index models have same pattern, because previous time step values are common in all Grey index models. Previous years similar day data addition in DGM 1, 2 and DGM 1, 3 models helps to improve the accuracy and it can be observed that forecasts obtained from DGM 1, 3 model are closer to actual values, than any other model.
Absolute errors of proposed Grey index models and reference ANN model in complete winter season are shown in Fig. Red lines in Fig. However, long upper whisker shows that some extreme absolute errors are present in DGM 1, 3 model. Absolute error distributions can be summarized in terms of forecasting performance parameters. Table 1 shows that night hours have least MAE values for all models, because net load is the function of only two uncertain variables load and wind power generation during night intervals.
Night hours also show higher MAPE, because aggregated load is lowest during night hours. Aggregated load in night hours is low due to the absence of industrial and commercial loads, even though heating load is higher. Morning and evening hours show higher MAE and lower MAPE than noon hours, because net load magnitude in noon hours is low due to higher solar power generation and lower heating load.
DGM 1, 2 model shows 7. DGM 1, 3 model shows Also, Therefore, it is clear that proposed DGM 1, 3 model outperforms other models in winter season.
Morning, noon, evening and night hours of transition season are also selected to show the performance throughout the day. Similar to winter season, performance plot of one morning hour is shown in Fig. Transition season performance plot also follows the pattern of winter season. Net load magnitude of transition season is lower compared to winter season due to higher solar power generation and absence of heating load.
Lower net load magnitude results in higher MAPE even for lower absolute errors. Absolute error distribution of various models in transition season is shown in Fig.
Error distribution of different models can be summarized in terms of forecasting performance parameters. Similar to Tables 1 and 2 also shows that night hours have least MAE as night time net load is the function of only two uncertain variables load and wind power generation.
Night hours show higher MAPE, because aggregated load is lowest during night hours due to the absence of industrial and commercial loads. MAE is highest in noon, because contribution of all three uncertain variables load, wind and solar power generation is quite high in net load. MAE magnitudes of morning and evening hours are comparable in transition seasons. However, transition season evening hours show highest MAPE as net load magnitude is low due to high wind power generation.
DGM 1, 2 model shows 2. Also, 1. Therefore, its clear that proposed DGM 1, 3 model outperforms other models in transition season, similar to winter season. Net load forecasts are obtained for morning, noon, evening and night hours of summer season to show the performance throughout the day.
Forecasts obtained by Grey index models show similar pattern, because inputs of all three models contain previous time step net load data. Similar to winter and transition season, use of previous years similar day data as input in DGM 1, 2 and DGM 1, 3 models helped to improve the accuracy. It can be observed that forecasts obtained from DGM 1, 3 model are very close to actual values than other models. Absolute errors of proposed Grey index models and reference ANN model in complete summer season are shown in Fig.
Similar to other seasons, box plot of absolute error shows that forecasting accuracy is improved from DGM 1, 1 model to DGM 1, 3 model. DGM 1, 3 model has lowest median and also absolute errors are distributed closer to zero than other models. In contrast with other two seasons, DGM 1, 3 model shows shortest whisker in summer season.
Therefore, there is no extreme forecasting errors for DGM 1, 3 model in summer season. In contrast to winter and transition seasons, summer season night hours show highest MAE and lower MAPE values as night time wind power generation and load are comparatively high. Load is higher due to cooling loads. High wind power generation results in high net load forecasting errors, which leads to higher MAE values. High aggregated load results in higher net load magnitudes and results in lower MAPE values, as actual net load values are present in the denominator of percentage error estimation.
This can be observed in Table 3. DGM 1, 2 model shows However, there is small reduction of 0. Therefore, its clear that proposed DGM 1, 3 model outperforms other models in summer season, similar to winter and transition seasons.
However, net load forecast trajectory shows slight variation from net load trajectory minute dynamic variations , because proposed models use momentum of last twelve data points to produce next time step forecast. Forecast may vary if next time step data shows extreme trend variation as compared to recent data. Annual performance is evaluated by compiling seasonal analysis. Forecasts obtained in winter, transition and summer seasons are used for annual analysis.
There is 6. Also, DGM 1, 3 model shows 5. Therefore, it is clear that annually DGM 1, 3 model outperforms other models. Reference ANN model use backpropagation-based weight adjustment to minimize error. Proposed models use momentum of last twelve data points to produce next time step forecast and a rolling approach by regularly data updating. Proposed models use momentum of last 12 data points to produce next time step forecast and a rolling approach by regularly data updating.
Same can be observed from Figs. Proposed model forecasts follow increasing and decreasing trend of actual data; however, momentum transfer is leads to overestimated point forecasts. Also, overestimation tendency is less as compared to reference ANN model.
Proposed models can produce accurate forecasts even with renewable generation changes, as historical renewable generation variations are included in net load time series and model parameters are estimated using such data.
However, high uncertainty in renewable generation may enhance net load forecasting error. Positively correlated uncertain changes among load and renewable generation, and negatively correlated wind and solar generation reduces the effect of uncertainty. Negatively correlated uncertain changes among load and renewable generation, and positively correlated wind and solar generation increases the effect of uncertainty. ACF plots show that residues have low correlation; apart from one outlier, all residual correlations are with in 0.
Also, mean value of residuals is closer to zero and ACF plot does not show any kind of correlation pattern. Therefore, no information remains in input net load data to improve forecasting model performance. High renewable penetrated power systems necessitate accurate net load forecasts for optimal system operations such as generator scheduling and generation ramping requirement estimation.
Also, increasing renewable penetration in power systems continuously forces to reduce dispatching times frames from day ahead to fives minutes in markets like MISO and CAISO. This necessitates fast and accurate net load forecasts in such very short time frames.
Such fast, accurate and very short time frame net load forecasts can be obtained by direct NLF. Forecasting performance analysis show that proposed models are suitable to obtain accurate net load forecasts in all seasons. Addition of previous years similar day data along with previous time step data as forecasting inputs helped to improve forecasting accuracy from DGM 1, 1 to DGM 1, 3 model.
Therefore, accurate net-load forecasts obtained from proposed DGM 1, 3 model can be used for different power system operations such as generation scheduling. Seasonal analysis shows that summer season shows least error compared to other seasons due to the less uncertain weather. Direct net load forecasting accuracy can be further improved by avoiding input data outliers using digital signal processing-based data filtering techniques.
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