Short-term load forecast using support vector regression and feature learning
In a support vector regression approach to forecasting power load in an electrical grid, a feature learning scheme weights each feature in the input data with its correlation with the predicted load, increasing the prediction accuracy. The kernel matrix for the input training data is computed such that features that align better with the target variable are given greater weight. The resulting load forecast may be used to compute commands sent to demand response modules.
1. A method for forecasting short term power system load in a power supply system, comprising:
by a processor, for a plurality of input features, computing a plurality of respective correlation scores using training data, each correlation score representing a strength of correlation between an input feature and the power system load;
by a processor, computing, using the training data, a kernel matrix defining mappings of the plurality of input features for use in a non-linear support vector regression framework, the kernel matrix including a weighting of each of the plurality of input features using the respective correlation scores; and
by a processor, computing a short term power system load forecast from a set of input data, using the non-linear support vector regression framework.
2. A method as in claim 1 , wherein the kernel matrix comprises a Gaussian radial basis function.
3. A method as in claim 2 , wherein, for input training data XεR n×d having an i th feature denoted by X :,i and for a target variable denoted by YεR n×1 , a correlation score for the i th feature is computed as f i =| X :, i ,Y |, and for a pair of the training samples x i , x j εR D×1 the kernel matrix is computed as
K
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=
exp
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d
2
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x
i
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where h is an averaged pairwise distance between samples.
4. A method as in claim 1 , wherein the plurality of input features includes ambient outside temperature.
5. A method as in claim 1 , wherein the plurality of input features includes recent load history.
6. A method as in claim 5 , further comprising:
embedding the load history in a three-dimensional state space.
7. A method as in claim 5 , further comprising:
preprocessing the load history to compute daily load sums.
8. A method as in claim 1 , wherein the plurality of input features include at least one feature selected from the group consisting of humidity, wind speed, dew point and air pressure.
9. A method for reducing peak system power load using a demand response module, comprising:
by a processor, for a plurality of input features, computing a plurality of respective correlation scores using training data, each correlation score representing a strength of correlation between an input feature and the power system load;
by a processor, computing, using the training data, a kernel matrix defining mappings of the plurality of input features for use in a non-linear support vector regression framework, the kernel matrix including a weighting of each of the plurality of input features using the respective correlation scores;
by a processor, computing a short term power system load forecast from a set of input data, using the non-linear support vector regression framework; and
transmitting to the demand response module instructions for reducing peak system power load in accordance with the short term power system load forecast.
10. A method as in claim 9 , wherein the kernel matrix comprises a Gaussian radial basis function.
11. A method as in claim 10 , wherein, for input training data XεR n×d having an i th feature denoted by X :,i and for a target variable denoted by YεR n×1 , a correlation score for the i th feature is computed as f i =| :,i ,Y |, and for a pair of the training samples x i ,x j εR D×1 the kernel matrix is computed as
K
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j
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=
exp
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where h is an averaged pairwise distance between samples.
12. A method as in claim 9 , wherein the plurality of input features includes ambient outside temperature.
13. A method as in claim 9 , wherein the plurality of input features includes recent load history.
14. A non-transitory computer-readable medium having stored thereon computer readable instructions for forecasting short term power system load in a power supply system, wherein execution of the computer readable instructions by a processor causes the processor to perform operations comprising:
for a plurality of input features, computing a plurality of respective correlation scores using training data, each correlation score representing a strength of correlation between an input feature and the power system load;
computing, using the training data, a kernel matrix defining mappings of the plurality of input features for use in a non-linear support vector regression framework, the kernel matrix including a weighting of each of the plurality of input features using the respective correlation scores; and
computing a short term power system load forecast from a set of input data, using the non-linear support vector regression framework.
15. A non-transitory computer-readable medium as in claim 14 , wherein the kernel matrix comprises a Gaussian radial basis function.
16. A non-transitory computer-readable medium as in claim 15 , wherein, for input training data XεR n×d having an i th feature denoted by X :,i and for a target variable denoted by YεR n×1 , a correlation score for the i th feature is computed as f t =| X :,i ,Y |, and for a pair of the training samples x i , x j εR D×1 the kernel matrix is computed as
K
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x
i
,
x
j
)
=
exp
(
-
∑
d
=
1
D
f
d
2
(
x
i
(
d
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-
x
j
(
d
)
)
2
2
h
2
)
where h is an averaged pairwise distance between samples.
17. A non-transitory computer-readable medium as in claim 14 , wherein the plurality of input features includes ambient outside temperature.
18. A non-transitory computer-readable medium as in claim 14 , wherein the plurality of input features includes recent load history.
19. A non-transitory computer-readable medium as in claim 18 , the operations further comprising:
embedding the load history in a three-dimensional state space.
20. A non-transitory computer-readable medium as in claim 18 , the operations further comprising:
preprocessing the load history to compute daily load sums.