Accurate and reliable power generation energy forecasting of small hydropower (SHP) is essential for hydropower management and scheduling. Due to nonperson supervision for a long time, there are not enough historical power generation records, so the forecasting model is difficult to be developed. In this paper, the support vector machine (SVM) is chosen as a method for short-term power generation energy prediction because it shows many unique advantages in solving small sample, nonlinear, and high dimensional pattern recognition. In order to identify appropriate parameters of the SVM prediction model, the genetic algorithm (GA) is performed. The GA-SVM prediction model is tested using the short-term observations of power generation energy in the Yunlong County and Maguan County in Yunnan province. Through the comparison of its performance with those of the ARMA model, it is demonstrated that GA-SVM model is a very potential candidate for the prediction of short-term power generation energy of SHP.
Small hydropower (SHP) is a kind of world recognized and concerned renewable clean energies. It widely attracts attention in the whole world as its great significance for medium and small rivers management, strengthening the rural water conservancy infrastructure construction, meets rural energy demand, improves the rural energy structure, reduces the pollution of the environment, responds to climate change, promotes the development of the local economy [
Up to the end of 2012, the installed capacity of SHP in China had exceeded 65 GW and annual generation over 200 TWh, which take about 30% of hydropower installed capacity and power generation, respectively, and both rank first in the world [
However, SHP plants are generally in the small remote river basin with shortage of hydrologic station and the management is weak due to nonperson supervision for a long time, so it is very difficult for forecasting STPGE of SHP because of lack of necessary runoff data. At present, a lot of research activities in short-term forecasting models of hydropower stations have been carried out, which focus on the forecasting of inflow in reservoirs [
This paper presents a novel short-term forecasting model (named GA-SVM) for power generation energy of SHP stations. In this study, support vector machine (SVM) was used to identify power generation energy based on structural risk minimization principle [
The paper is organized as follows. In the next section “Brief Introduction to SVM and GA,” SVM and GA algorithms are briefly introduced. Then, the proposed GA-SVM forecasting method is described in the following section. In the next section, this method is applied to Yunnan province, and the results are compared with those of conventional method. The final section concludes the paper.
The SVM, developed by Vapnik [
GA is a global optimal algorithm based on “survival of the fittest” in Darwin’s theory of evolution and provides an efficient and robust optimized searching method in complex space. This is an excellent search algorithm adapted to the global probability. GA operates iteratively on a population of structures, each of which represents a candidate solution to the problem, encoded as a string of symbols (chromosome), and uses randomized technical guidance to effectively search a coded parameter space. GA makes use of coding technology to transform the solved space of problem into chromosome space and also convert the decisive variable into a certain structure of individual chromosomes. During the iteration of the algorithm, according to the rules set by the fitness function, these groups made up of individuals generated next generation through selection, crossover, and mutation. Fitness factor which is beneficial to the population will be inherited, while factors that reduce fitness will be eliminated with the operation of mutation and crossover in iterations. After continuous evolutions, the optimal individuals survive, which can be approximate optimal solution of the problem.
Generally, the daily power generation energy is directly selected as forecasting object for STPGE of SHP. But, considering dynamically putting into operation small hydropower plant or hydrounit in some region, there is a difference of installed capacity of SHP between one day and another day. Since the power output of SHP plant is almost close to installed capacity in flood season, the power generation energy is also very different due to the increase in installed capacity of SHP. The model prediction performance will be affected if power generation energy of SHP is only used as input and output values of the model. Therefore, the installed capacity utilization hour represents power generation energy of SHP in region. That could not only accurately reflect the characteristics of small hydropower plant without regulation ability but also alleviate short-term fluctuations in power generation curve. The installed capacity utilization hour was
To apply SVM model to forecast STPGE of SHP plants in region, we need to know the three vital parameters RBF kernels:
The flow chart of optimizing SVM by GA.
In this study, the input and output variables are normalized in the range from 0 to 1 by (
After training and testing the GA-SVM model, the forecast value of power generation energy is calculated by
A lot of goodness-of-fit measurements have been applied to evaluate model performance. Appropriate evaluation criteria should be chosen when using multicriteria to validate model performance [
The root mean squared error (RMSE) is an arbitrary positive value and will indicate a good performance when it is close to zero. The mean absolute percentage error (MAPE) is a relative index of absolute model error and can express accuracy as a percentage [
There is extremely rich hydropower resource in Yunnan province, whose potential capacity ranks third in China. The hydropower resources of every region are extremely uneven and mainly distributed in the west and north, followed by the east and south. By the end of October 2012, the SHP plants in Yunnan had reached 1587, with 3417 units and 8453.05 MW of the installed capacity, which accounts for more than 27% and 12% of hydropower capacity in Yunnan province and SHP capacity in China, respectively [
Location of the study area.
Yunlong County is located in the west of Yunnan province with a total area of 4400.95 km2. And the annual average temperature and annual average rainfall are 15.9°C and 729.5 mm, respectively. By the end of 2013, there are 10 small hydropower plants with installed capacity 111.5 MW. Maguan County is located in the southeast of Yunnan province with a total area of 2676 km2. And the annual average temperature and annual average rainfall are 16.9°C and 1345 mm, respectively. By the end of 2013, there are 22 small hydropower plants with installed capacity of 213.89 MW.
The data derived from the two counties are both 915 days long with the period between May 1, 2011, and October 31, 2013, for which 854 days of the power generation energy data from May 1, 2011, to August 31, 2013, are used for calibration and the remaining 61 days from September 1, 2013, to October 31, 2013, are used for validation. The daily statistical parameters of calibration and validation and the entire data set for the two counties are shown in Table
The
County | Data set |
|
|
|
|
|
---|---|---|---|---|---|---|
Yunlong | Training | 800.8 | 392.6 | 0.6 | 200.2 | 2366.2 |
Testing | 1174.1 | 154.8 | −1.2 | 700.6 | 1369.6 | |
Entire | 825.7 | 392.4 | 0.5 | 200.2 | 2366.2 | |
|
||||||
Maguan | Training | 2440.4 | 1121.2 | 0.4 | 440.6 | 4805.1 |
Testing | 3402.1 | 709.9 | 0.4 | 2336.5 | 4766.3 | |
Entire | 2504.6 | 1124.3 | 0.3 | 440.6 | 4805.1 |
In this study, the GA is employed as parameter search scheme. In order to get better parameters of SVM, the maximum iterative time of GA is set as 50 and the population size is set to 30, 50, 80, 100, 120, and 150, respectively. And the optimal scope of three parameters (
The performance statistics of GA-SVM models for Yunlong County.
Population size | Optimal parameters |
Calibration | Validation | ||
---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | ||
(i) 30 | (4.0754, 0.1989, 0.0078) | 113.88 | 8.52 | 81.08 | 5.15 |
(ii) 50 | (5.5762, 0.2275, 0.0073) | 113.66 | 8.49 | 77.31 | 5.02 |
(iii) 80 | (18.7495, 0.105, 0.0103) | 113.98 | 8.53 | 80.42 | 5.08 |
(iv) 100 | (10.3452, 0.1464, 0.0077) | 113.87 | 8.51 | 80.86 | 5.11 |
(v) 120 | (24.4174, 0.0528, 0.0064) | 114.46 | 8.58 | 81.85 | 5.19 |
(vi) 150 | (9.4141, 0.0348, 0.0025) | 115.11 | 8.62 | 80.53 | 5.07 |
The performance statistics of GA-SVM models for Maguan County.
Population size | Optimal parameters |
Calibration | Validation | ||
---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | ||
(i) 30 | (2.3792, 0.6749, 0.0058) | 252.25 | 7.54 | 233.67 | 4.37 |
(ii) 50 | (7.3517, 0.056, 0.0197) | 254.95 | 7.92 | 234.36 | 4.38 |
(iii) 80 | (10.808, 0.0799, 0.0192) | 254.29 | 7.90 | 233.75 | 4.40 |
(iv) 100 | (8.4248, 0.0538, 0.0156) | 255.18 | 7.92 | 233.54 | 4.36 |
(v) 120 | (14.0828, 0.0758, 0.0191) | 254.28 | 7.89 | 233.92 | 4.40 |
(vi) 150 | (11.421, 0.058, 0.0063) | 255.87 | 7.83 | 233.02 | 4.32 |
The results from Table
For Maguan County, it can be seen from Table
In order to get a better comprehension of the GA-SVM model performance, the ARMA model was employed as a comparative purpose. The basic components to an ARMA model is autoregression (AR) and moving-average (MA). To obtain a suitable ARMA
For Yunlong County, the models ARMA (3, 12), (4, 8), (5, 13), (7, 12), (6, 12), and (8, 8), which have relatively smaller AIC values, are selected as the candidate models. Table
AIC value and performance indices of alternative ARMA models for Yunlong County.
( |
AIC | Calibration | Validation | ||
---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | ||
(3, 12) | 9.5266 | 114.30 | 8.70 | 82.07 | 5.58 |
(4, 8) | 9.5270 | 114.84 | 8.87 | 83.40 | 5.24 |
(5, 13) | 9.5153 | 113.17 | 8.98 | 78.49 | 5.06 |
(6, 12) | 9.5281 | 113.98 | 8.91 | 78.54 | 5.04 |
(7, 12) | 9.5276 | 113.80 | 8.90 | 77.88 | 4.99 |
(8, 8) | 9.5265 | 113.66 | 8.85 | 80.18 | 5.22 |
For Maguan County, the models ARMA (1, 2), (2, 1), (2, 2), (2, 3), (2, 4), and (3, 1), which have relatively smaller AIC values, are selected as the candidate models. Table
AIC value and performance indices of alternative ARMA models for Maguan County.
( |
AIC | Calibration | Validation | ||
---|---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE | ||
(1, 2) | 11.1782 | 261.22 | 7.94 | 234.76 | 4.46 |
(2, 1) | 11.1739 | 260.49 | 7.95 | 233.48 | 4.53 |
(2, 2) | 11.1755 | 260.37 | 7.96 | 234.82 | 4.55 |
(2, 3) | 11.1778 | 260.36 | 7.96 | 234.13 | 4.54 |
(2, 4) | 11.1779 | 260.14 | 7.95 | 232.24 | 4.47 |
(3, 3) | 11.1767 | 260.07 | 7.96 | 234.95 | 4.60 |
In this study, the same training and verification sets are used for the two models in order to have the same basis of comparison. Meanwhile, in order to evaluate the model performance for forecasting STPGE of SHP, the time series data are derived from two study sites in different region. And the two statistical measures are employed to evaluate the model performance.
For Yunlong County, the model’s RMSE and MAPE statistics of the calibration and validation period are summarized in Table
Model statistics of the calibration and validation period for Yunlong County.
Model | Calibration | Validation | ||
---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE |
|
GA-SVM | 113.66 | 8.49 | 77.31 | 5.02 |
ARMA | 113.80 | 8.90 | 77.88 | 4.99 |
Comparison of forecasted versus observed power generation energy using GA-SVM and ARMA model for Yunlong County.
For Maguan County, the model’s RMSE and MAPE statistics of the calibration and validation period are summarized in Table
Model statistics of the calibration and validation period for Maguan County.
Model | Calibration | Validation | ||
---|---|---|---|---|
RMSE | MAPE | RMSE | MAPE |
|
GA-SVM | 252.25 | 7.54 | 233.67 | 4.37 |
ARMA | 260.14 | 7.95 | 232.24 | 4.47 |
Comparison of forecasted versus observed power generation energy using GA-SVM and ARMA model for Maguan County.
In the present study, the GA-SVM prediction model comprising support vector machine with genetic algorithm has been developed for forecasting short-term power generation energy of small hydropower in region. The historical observed data derived from Yunlong County and Maguan County in Yunnan province in China were employed to investigate the modeling potentiality of GA-SVM. Data from May 1, 2011, to August 31, 2013, and from September 1, 2013, to October 31, 2013, are used for training and validation, respectively, in short-term power generation energy prediction. Due to the lack of small hydropower operation data, SVM is chosen as forecasting model because of its ability in solving small sample. The three parameters of SVM model are not known a priori and optimized by GA in order to get appropriate parameters for improving forecasting accuracy. In order to get a better comprehension of the GA-SVM model performance, the ARMA model was employed as a comparative purpose. The two models were constructed and their performances were compared crisply. The results indicated that the GA-SVM model can give slightly better prediction performance than the other model.
For the less data of small hydropower in region, the GA-SVM model proposed in this paper is an effective method for improving short-term forecasting accuracy. That is useful for fully absorbing small hydropower resources and avoiding water resource wasted and electricity dumped in flood season.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National High Technology Research and Development of China 863 Program (2012AA050205) and the Fundamental Research Funds for the Central Universities (DUT13JN05).