Schedulable capacity forecasting for electric vehicles based on big data analysis
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Abstract
Fast and accurate forecasting of schedulable capacity of electric vehicles (EVs) plays an important role in enabling the integration of EVs into future smart grids as distributed energy storage systems. Traditional methods are insufficient to deal with large-scale actual schedulable capacity data. This paper proposes forecasting models for schedulable capacity of EVs through the parallel gradient boosting decision tree algorithm and big data analysis for multi-time scales. The time scale of these data analysis comprises the real time of one minute, ultra-short-term of one hour and one-day-ahead scale of 24 hours. The predicted results for different time scales can be used for various ancillary services. The proposed algorithm is validated using operation data of 521 EVs in the field. The results show that compared with other machine learning methods such as the parallel random forest algorithm and parallel k-nearest neighbor algorithm, the proposed algorithm requires less training time with better forecasting accuracy and analytical processing ability in big data environment.
Keywords
Electric vehicle (EV) Schedulable capacity Machine learning Big data Multi-time scale1 Introduction
With increasing environmental concerns, electric vehicles (EVs) and renewable energy sources are receiving more and more attention all over the world [1]. According to the data from International Energy Agency [2], the number of global EV reached 3.1 million in 2017, increasing by 57% over the previous year, while the number of EV on the road is expected to reach 125 million by 2030. China will be the first country to start replacing traditional fuel vehicles with electric ones. At the same time, in 2030 renewable energy in China will account for 15% of the total energy consumption [3].
Large-scale integration of EVs and renewable energy into the grid poses great challenges in the operation of the power system due to their uncertainty and intermittent nature. Generally, large centralized energy storage systems (ESSs) can mitigate these problems, however, this would require expensive installations of large-capacity battery banks, pumped hydro and other large systems [4, 5].
Large-scale mobile and distributed ESS, composed of numerous on-board EV batteries can provide similar solutions, if their duality as ‘loads’ and ‘sources’ can be utilized and demand-side response technologies are applied [6, 7]. This allows to increase the penetration of renewable power generation or improve the resiliency and stability by forming microgrids [8, 9].
An important prerequisite for EVs to provide ancillary services to utilities or efficient operation of microgrids is to forecast the EV schedulable capacity (EVSC) in a fast and accurate way. In this way, system operators can optimize the schedule for the participation of EVs in ancillary services.
In current literature, EVSC is generally obtained using probabilistic EV models [10, 11, 12, 13, 14, 15], including plug-in time probability models based on binomial distributions [10], plug-in location probability models [11] and the aggregated queuing network model [12]. In [13, 14, 15], a Monte Carlo method is used to simulate the behavior of different types of EVs operating under realistic conditions, including start-stop time, charging rate, charging time, etc. In other nonprobability models, the state of charge (SOC) of the EV batteries is used to obtain EVSC for individual and aggregated EVs [16, 17]. Several parameter hypotheses are needed in most of these models, also due to the scarcity of historical data.
With the development of communication and Internet of Things technologies, real-time operation data of individual EVs can be acquired from their battery management system (BMS). The large amounts of actual operation data such as SOC, times of EVs access to charging infrastructure, etc., enable to develop more accurate EVSC models. Nevertheless, dealing with the processing and analysis of a very large number of data poses great challenges. For example, if we assume that half of the 100 million EVs estimated on road in China by 2030 [2] will be involved in power system scheduling operation, and the collection interval of related information is one minute, the volume of data will reach 1–2 petabyte each year. Therefore, this paper treats the forecasting of EVSC based on real-time operation data of individual EVs as an essentially big data analysis problem.
Big data analysis and management are clear trends of future smart grids. This is challenging for traditional machine learning (ML) algorithms, since they are designed for a single machine and are not suitable to deal with big data [18]. Thus, more efficient ML algorithms for parallel computing or for big data are required.
The parallel processing methods proposed in literature can be divided into three groups. Group one refers to parallel processing of traditional algorithms by using Hadoop and Spark cluster technology [19, 20, 21]. Group two is the combination of clustering or optimization algorithms and traditional ML algorithms [22, 23, 24]. Group three is a combination of group one and group two [25, 26, 27]. In group one, the parallelization of the algorithm effectively improves the computing speed and accuracy of load forecasting in parallel computing framework MapReduce and Spark. For example, [19] analyses the forecasting time and error for data sets with different sizes in different sizes of Hadoop clusters. In group two, clustering algorithms on large-scale data sets can be used to improve the performance markedly [22, 23]. For group three, [25] and [26] propose new hybrid algorithms, which combine the improved particle swarm optimization and extreme learning machine, fuzzy C clustering and support vector machines (SVM), respectively. The problems of over-fitting and long training time caused by the increase of data scale are faced by multi-distributed back propagation (BP) neural networks [27].
Different from the algorithms above, [19] and [28] propose ensemble learning algorithms of random forest (RF) and gradient boosting decision tree (GBDT), respectively. Ensemble learning algorithm integrates multiple base learners into a strong learner to improve the forecasting accuracy. It is considered as one of the important future research directions of ML [29]. Unlike traditional multi-linear regression (MLR) algorithm [30], GBDT can flexibly handle a certain number of different types of feature attributes, including continuous and discrete values [31]. Thus, it is widely used in traffic and load forecasting. However, since the output of the algorithm is the result of multiple iterations, there is a strong inter-dependence among regression trees, thus it is difficult to realize the parallelization of the GBDT algorithm.
The parallel GBDT (PGBDT) algorithm is derived from the GBDT algorithm and enables parallel computations. It requires less iteration time than GBDT by parallel processing of a large number of gradient and optimization computations without affecting the prediction accuracy of the model. Thus it is applicable to the big data scenario, although it has not been used so far for EVSC forecasting (EVSCF).
The application of big data analysis equipped with ML algorithms has been mainly found in the field of load forecasting, but rarely for EVSCF. In [15] and [32], the application of SVM, RF and decision tree (DT) algorithms are investigated for EVSCF. It is found that SVM and RF have an improved performance, when the forecasting curves of EVSCF fluctuate less, while RF is more effective than SVM, when there are large fluctuations [15]. DTs are heavily dependent on their input data, which means that even small variations in data may result in large changes in the structure of the optimal DT. In this paper, in order to address this problem, two new algorithms, suitable for big data analysis, i.e., PGBDT and parallel k-nearest neighbors (PKNN), are applied to the EVSCF problem and the results are analyzed.
With the rapid growth of EVs, un-controlled charging of a large number EVs may cause the phenomenon of “peak peaking”, i.e., increase the peak-to-valley difference of the utility and affect the stable operation of power grid. EVSCF methods provide strong data support for load peak shifting, frequency regulation, economic dispatch and intelligent EV charging/discharging strategies. These different applications require the results of EVSCF for the scheduling of renewable energy or load at different time scales [33, 34]. For example, real-time load forecasting has a time horizon of several seconds to 10 minutes and is used for frequency/voltage regulation, in order to eliminate the effect of volatility of renewable energies [35]; ultra-short-term load forecasting has a time scale of one hour or short-term load forecasting of several hours to tens of hours for economic dispatch and peak shaving and valley filling [36, 37]. Forecasting of renewable generation is usually required for ultra-short-term 15 minutes to four hours ahead and for short-term 24–72 hours ahead [38].
So far, time scaling of EVs for power system operation has not been properly discussed. References [15] and [31] deal only with real time and one-day-ahead time scales. In this paper, ultra-short-term scaling of one hour is additionally incorporated for the first time in the EVSCF models. In this way, EVs can be used for more power system services such as real-time optimization, peak shaving and valley filling, economic dispatch, etc.
Overall, the main contribution of this paper is the development of EVSCF models for multi-time scales based on the PGBDT algorithm which is used to forecast EVSC faster and more accurately.
The results of real-time EVSCF based on a large amount of real-time operation data from BMS of individual EVs are used as historical data for training the EVSCF models for ultra-short-term scale of one hour and one-day-ahead scale of 24 hours. The PGBDT algorithm is initially proposed and tested on a big data platform for multi-time scale EVSCF models to prove its feasibility and effectiveness.
The rest of this paper is organized as follows. In Section 2, the PGBDT algorithm is described. Section 3 discusses EVSCF models for multi-time scales. In Section 4, the proposed models are validated and compared with parallel random forest (PRF) and PKNN algorithms on a big data platform. This is followed by conclusions in Section 5.
2 PGBDT algorithm
- Step1: Initialize the model (3) by setting the initial and maximum number of iterations m as one and M, respectively, and the initial function \(f_{0} (\varvec{x})\) as shown in (4).where p is a constant value for minimizing the loss function; and \(f_{0} (\varvec{x})\) is a regression tree with only one node.$$f_{0} (\varvec{x}) = \mathop {\arg \hbox{min} }\limits_{p} \sum\limits_{i = 1}^{n} {L(y_{i} ,p)}$$(4)
- Step2: Obtain the negative gradient of the loss function as shown in (5), and \(f_{m-1} (\varvec{x})\) is the model after (m−1)^{th} iteration.$$r_{mi} = - \left( {\frac{{\partial L(y_{i} ,f(\varvec{x}_{i} ))}}{{\partial f(\varvec{x}_{i} )}}} \right)_{{f(\varvec{x}) = f_{m - 1} (\varvec{x})}}$$(5)The m^{th} regression tree is constructed according to all samples and their negative gradients [39], and its splitting rule is to divide it into two regions according to the value s of the k^{th} feature attribute: \(S_{left} \left( {k, s} \right) = \{ x_{i} \left| {x_{i}^{k} \le s} \right.\}\) and \(S_{right} \left( {k, s} \right) = \{ x_{i} \left| {x_{i}^{k} > s} \right.\}\). The minimization of the sum of regional variances after splitting is shown in (6):where the training sample S with size n is divided into left-dataset S_{left} and right-dataset S_{right} according to splitting s, the size of which are n_{left} and n_{right}, respectively.$$\begin{aligned} Gain(k,s) = \mathop {\hbox{min} }\limits_{k,s} \left[ {\sum\limits_{{x_{i} \in S_{left} }} {\left( {y_{i} - \frac{1}{{n_{left} }}\sum\limits_{i = 1}^{{n_{left} }} {y_{i} } } \right)^{2} } + } \right. \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\sum\limits_{{x_{i} \in S_{right} }} {\left( {y_{i} - \frac{1}{{n_{right} }}\sum\limits_{i = 1}^{{n_{right} }} {y_{i} } } \right)^{2} } } \right] \hfill \\ \end{aligned}$$(6)
Thus, its corresponding J-terminal node regions \(R_{mj} ,j = 1,\;2,\; \ldots ,\;J\) are obtained.
- Step3: Obtain the corresponding least-squares coefficient \(b_{mj}\) of the m^{th} regression tree as in (7).$$b_{mj} = \bar{r}_{mi} \varepsilon (\varvec{x}_{i} )\;\;\;\;\varvec{x}_{i} \in R_{mj}$$(7)where \(\bar{r}_{mi}\) is the average value of negative gradient of m^{th} regression tree; and \(\varepsilon ({\varvec{x}}_{i} )\) is an indicator function.$$\varepsilon \left( {\varvec{x}_{i} } \right) = \left\{ {\begin{array}{*{20}c} {1\;\;\;\;\;\;\varvec{x}_{i} \in R_{mj} } \\ {0\;\;\;\;\;\;\varvec{x}_{i} \notin R_{mj} } \\ \end{array} } \right.$$(8)
- Step4: Find the scaling factor \(c_{m}\) of the m^{th} regression tree for solving the “linear search” by (9).$$c_{m} = \mathop {\arg \hbox{min} }\limits_{c} \sum\limits_{{\varvec{x}_{i} \in R_{mj} }} {L\left( {y_{i} ,f_{m - 1} (\varvec{x}_{i} ) + c\sum\limits_{j = 1}^{J} {b_{mj} } } \right)}$$(9)
- Step 5: Update the model \(f_{m} (\varvec{x})\) as (10).$$f_{m} (\varvec{x}) = f_{m - 1} (\varvec{x}) + c_{m} \sum\limits_{j = 1}^{J} {b_{mj} }$$(10)
Step 6: If \(m < M\), let \(m = m + 1\) and repeat Step 2 to Step 5, otherwise output the final \(f_{M} (\varvec{x})\).
From (11), it can be seen that the PGBDT algorithm is a combined algorithm. It approximates the expected model by iterating a series of regression trees to improve the model accuracy and provides a strong predictive performance and generalization ability. Each regression tree can be parallelized by finding splits on each non-terminal node of the regression tree in parallel, whose splitting criteria depends on the minimization of variance after splitting. Therefore, the whole model of PGBDT can be parallelized by generating each regression tree in parallel during its generation process.
3 EVSCF models for multi-time scales
3.1 Time scales used in the proposed EVSCF models
3.2 Real-time EVSCF model
3.2.1 Classification of EVs connected to grid
The proposed real-time EVSCF model is based on real-time data of individual EVs, which are acquired from the BMS of each EV.
In order to ensure the accuracy of real-time EVSCF model, the selected time scale for the prediction model is equal to the time interval of the real-time operation data acquisition, which is one minute in this paper. Since the SOC of the EV battery changes slightly within one minute, EVSC in real time is calculated dynamically through the real-time data acquisition and big data analysis method, and can be regarded as the forecasted value of EVSC for the next minute. To build the EVSCF model in real time, it is necessary firstly to classify the individual EVs accessing the utility network according to their levels of SOC so that the aggregated charging or discharging capacity of EVs can be obtained.
- 1)
If \(t_{d,l} < t_{s}\) or \(t_{d,l} < t_{d,c}\), \(EV_{d}\) is not allowed to participate in the scheduling plan.
- 2)
If \(t_{d,l} \ge t_{s}\) and \(t_{d,l} \ge t_{d,c}\): ① if \(SOC_{d}^{t} < SOC_{d}^{\hbox{min} }\), \(EV_{d}\) is allowed to be charged; ② if \(SOC_{d}^{\hbox{max} } < SOC_{d}^{t}\), \(EV_{d}\) is allowed to be discharged; ③ if \(SOC_{d}^{\hbox{min} } < SOC_{d}^{t} < SOC_{d}^{\hbox{max} }\), \(EV_{d}\) is allowed to be charged or discharged according to the scheduling plan.
Note that \(EV_{d}\) is the d^{th} EV; \(SOC_{d}^{t}\) is the SOC of \(EV_{d}\) at current time t; and \(SOC_{d}^{\hbox{min} }\) and \(SOC_{d}^{\hbox{max} }\) are the minimum and maximum expected SOC for each \(EV_{d}\), respectively.
3.2.2 Definition of charging/discharging rate
3.2.3 Real-time EVSCF model
3.3 Ultra-short-term and one-day-ahead EVSCF models
3.3.1 Construction of training dataset and testing dataset
- 1)The average values of SCC and SDC of EVSC at the same time t of the previous month are \(\overline{SCC}_{t,mon}^{all}\) and \(\overline{SDC}_{t,mon}^{all}\), which are calculated as in (17) and (18), respectively:$$\overline{SCC}_{t,mon}^{all} { = }\frac{1}{l}\sum\limits_{k = 1}^{l} {SCC_{t,mon}^{k} }$$(17)where l is the total number of days of the previous month; SCC_{t,mon}^{k}, SDC_{t,mon}^{k} are the values of SCC and SDC of EVSC at the same time t on the k^{th} day of the previous month, respectively.$$\overline{SDC}_{t,mon}^{all} { = }\frac{1}{l}\sum\limits_{k = 1}^{l} {SDC_{t,mon}^{k} }$$(18)
- 2)The average values of SCC and SDC of EVSC at the same time t last week are \(\overline{SCC}_{t,week}^{all}\) and \(\overline{SDC}_{t,week}^{all}\), which are calculated as in (19) and (20), respectively, where SCC_{t,week}^{k}, SDC_{t,week}^{k} are the values of SCC and SDC of EVSC at time t on the k^{th} day of last week:$$\overline{SCC}_{t,week}^{all} { = }\frac{1}{ 7}\sum\limits_{k = 1}^{7} {SCC_{t,week}^{k} }$$(19)$$\overline{SDC}_{t,week}^{all} { = }\frac{1}{ 7}\sum\limits_{k = 1}^{7} {SDC_{t,week}^{k} }$$(20)
- 3)
The values of SCC and SDC of EVSC at the same time t of the previous day are \(SCC_{t,day}\) and \(SDC_{t,day}\).
According to different time attributes, the following four feature attributes are selected as inputs at the training stage: current time t (a total number of 1440 time slots, represented by 0 to 1439), indication of rush hour, holiday or working time.
In summary, through the correlation analysis, the data set with length q is divided into two parts: training dataset with length p and testing dataset with length q-p. The next step is to construct EVSCF models for ultra-short-term and one-day-ahead scales, as follows.
3.3.2 Ultra-short-term and one-day-ahead EVSCF models
- 1)
Input training dataset A including the feature attributes and actual value of EVSC \(y_{t - p}\), \(A = \{ (y_{t - p} , \varvec{h}_{t - p} , \varvec{w}_{t - p} )\}_{t = 1}^{p}\) comprises 10 feature attributes of the training dataset with length p; \(\varvec{h}_{t - p} = [x_{t - p}^{1} , x_{t - p}^{2} , \ldots , x_{t - p}^{6} ]\) is a 6-dimensional vector with the historical data of EVSC; and \(\varvec{w}_{t - p} = [x_{t - p}^{7} , x_{t - p}^{8} , x_{t - p}^{9} , x_{t - p}^{10} ]\) is a 4-dimensional vector with the time attributes of EVSC.
- 2)
Set the parameters of the PGBDT algorithm including the number of iterations I and maximum depth d.
- 3)Train the model represented by (21) by the training dataset A:$$y_{t - p} = f (\varvec{h}_{t - p} , \varvec{w}_{t - p} )$$(21)
- 4)Substitute testing dataset B into the model, and obtain the predicted value of EVSCF \(y_{t}^{e}\) as (22):$$y_{t}^{e} = f (\varvec{h}_{t - p} , \varvec{w}_{t - p} )$$(22)
\(B = \{ (y_{t} , \varvec{h}_{t} , \varvec{w}_{t} )\}_{t = p + 1}^{q}\) has 10 feature attributes of the testing dataset with length q–p.
3.3.3 Evaluation indexes
3.4 Implementation of EVSCF models with PGBDT algorithm and big data analysis
3.4.1 Real-time EVSCF framework based on big data
Equations (12)–(16) form the real-time EVSCF model. Although the proposed model looks simple, it is difficult to apply, since it needs to process the large amount of related data of EVs in real time. In this paper, Hadoop is used to solve the storage problem of big data by the Hadoop distributed file system (HDFS) [40]. Moreover, Spark designed for large-scale data processing is used. The Spark streaming can process stream data with a minimum interval of 500 ms. In this paper, the real-time processing interval is 60 s, which enables parallel computation to meet real-time requirements.
3.4.2 Framework of EVSCF models based on PGBDT
The structure of EVSCF models based on PGBDT algorithm for multi-time scales is shown in Fig. 2. The real-time EVSCF model is built, as shown in Fig. 2a, and the historical data of the real-time EVSCF is combined with the time attributes to generate the training dataset and testing dataset. According to the different prediction periods, the training dataset and testing dataset are updated in order to apply rolling forecasting. Finally, one-day-ahead and ultra-short-term EVSCF models based on the PGBDT algorithm are trained, tested and evaluated, as shown in Fig. 2b.
4 Study cases
4.1 Big data platform configuration
Big data platform configuration parameters
Master/slave node | IP address | Software version |
---|---|---|
Master | 192.168.16.135 | Hadoop-2.7.0, Spark-1.6.0- bin-hadoop-2.7.0 |
Slave1 | 192.168.16.198 | |
Slave2 | 192.168.16.199 | |
Slave3 | 192.168.16.229 |
With the big data platform, the real-time data of 521 EVs are used to test the EVSCF models proposed in Section 3. These data are acquired from BMS of each EV with one-minute resolution, (17 GB in total) in the period from Nov. 1, 2015, 00:00 to Apr. 30, 2016, 23:59 [15].
4.2 Processing time analysis of different real-time EVSCF data scales
Processing time for different data size of real-time EVSCF
Data scale (GB) | T_{c}(s) | T_{s}(s) | S_{speedup} |
---|---|---|---|
0.5 | 22 | 246 | 11 |
1.0 | 37 | 643 | 17 |
5.0 | 109 | 2808 | 25 |
17.0 | 196 | 13030 | 66 |
It can be seen from Table 2 that with the increasing data size of real-time EVSCF, the speed-up factor increases from 11 to 66. The acceleration effect is obvious, reflecting the ability of the proposed method to process large-scale data.
4.3 Simulation results and discussions
4.3.1 Real-time EVSCF
In summary, EVSC for EVs is lower during the daytime, close to 0 during rush hours and higher during the night. The time characteristics of EVSC are consistent with the operation frequency of buses. The probability of access to grid at night is much higher than at daytime, which results in higher EVSC for EV buses at night. Based on this characteristic, charging of EVs can be shifted, not only reducing the peak power, but also being charged at low electricity prices. Operation regularity also provides the basis for EVSC predictability. The analysis results of big data show the characteristics of EVSC, namely, volatility, intermittent and predictability.
4.3.2 Ultra-short-term EVSCF
For ultra-short-term and one-day-ahead EVSCF models, the real-time historical EVSC data from Nov. 1, 2015, 00:00 to Apr. 23, 2016, 23:59 are used for training datasets, while the historical EVSC data from Apr. 24, 2016, 00:00 to Apr. 30, 2016, 23:59 are used for testing datasets. Therefore, ultra-short-term EVSCF is set an hour in advance to forecast the next hour, rolling to the 168^{th} hour (7 × 24 hours).
Set of parameters for different algorithms
Algorithm | Set of parameters |
---|---|
PGBDT | Number of iterations I = 4; maximum depth d= 8 |
PRF | Number of trees T= 40; number of bins B= 64; Maximum depth d = 5 |
PKNN | Number of nearest neighbors k = 100 |
Prediction errors and training time of ML algorithms for ultra-short-term EVSCF
Algorithm | Training time (s) | MAPE (%) | RMSE (%) |
---|---|---|---|
SCC-PGBDT | 6.59 | 3.79 | 4.79 |
SCC-PRF | 9.82 | 10.31 | 16.09 |
SCC-PKNN | 20.07 | 27.80 | 41.10 |
SDC-PGBDT | 6.11 | 3.37 | 3.96 |
SDC-PRF | 9.53 | 9.87 | 16.44 |
SDC-PKNN | 20.78 | 27.89 | 37.15 |
4.3.3 One-day-ahead EVSCF
Prediction errors and training time of ML algorithms for one-day-ahead EVSCF
Algorithm | Training time (s) | MAPE (%) | RMSE (%) |
---|---|---|---|
SCC-PGBDT | 8.19 | 4.11 | 4.15 |
SCC-PRF | 11.63 | 11.00 | 19.45 |
SCC-PKNN | 20.64 | 29.18 | 47.94 |
SDC-PGBDT | 8.59 | 3.97 | 3.99 |
SDC-PRF | 14.78 | 10.35 | 21.09 |
SDC-PKNN | 21.25 | 28.02 | 62.44 |
5 Conclusion
This paper investigates the EVSCF using big data analysis and ML algorithms. EVSCF models are established for multi-time scales based on actual operation data of EVs. Real-time EVSCF is achieved using the constructed big data platform, where the speed of Hadoop and Spark is 66 times faster than traditional methods. The proposed models are tested and compared with PRF and PKNN, exhibiting superior performance. The simulation results containing real operation data of EVs connected to the grid with one-minute resolution. It shows that for one-hour ultra-short-term EVSCF model, the PGBDT algorithm has the highest accuracy for SCC and SDC, with the forecasting errors in MAPE of 3.79% and 3.37%, and reduced training time by 30% and 60%, respectively, compared with those obtained by PRF and by PKNN. The performance of PGBDT-based EVSCF model for one-day-ahead 24 hours is much better than PRF and PKNN, proving its reliable forecasting performance and generalization ability. The simulation results also prove that the proposed PGBDT-based EVSCF models can take advantage of the analytical ability of ML under a big data environment and provide powerful support for EV participation in grid scheduling and ancillary services.
Notes
Acknowledgement
This work was supported by National Natural Science Foundation of China (No. 51577047) and International Collaboration Project supported by Bureau of Science and Technology, Anhui Province (No. 1604b0602015).
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