An Electric Power Consumption Analysis System for the Installation of Electric Vehicle Charging Stations

Abstract

With the rising demand for electric vehicles, the number of electric vehicle charging stations is increasing. Therefore, real-time monitoring of how the power consumption by charging stations affects the load on the peripheral power grid is important. However, related organizations generally do not provide actual power consumption data in real time, and only limited information, such as the charging time, is provided. Therefore, it is difficult to calculate and predict the power load in real time. In this paper, we propose a new model for estimating the electric power consumption from the supplied information, i.e., the charging time and the number of charging involved. The experimental results show that by displaying this information on a map, it is possible to visually monitor the electric power consumption of the charging stations with an accuracy rate of about 86%. Finally, the proposed system can be used to relocate and select the location of vehicle charging stations.

1. Introduction

Over the past decade, with the development of electric vehicle battery technology, the demand for electric vehicles has been rising rapidly in developed countries [1]. Therefore, it has become very important to choose optimal locations for charging stations [2], and maintain the load balance of the peripheral electric power supplies. If the stations are installed according to a certain distance, it is difficult to operate them efficiently. Therefore, an analysis system for electric power consumption is needed for cost reduction and the efficient operation of the charging stations. Moreover, the utilization rate and electric power consumption of the existing stations need to be analyzed to find underutilized and overutilized charging stations. Using this information, the existing stations need to be relocated or additional installation needs to be performed. For this purpose, we propose a novel system that can check the electric power consumption of each charging station in real time.

It is best to obtain the actual data of electric power consumption for the charging stations, but the real-time data provided by the related organizations are extremely limited. In the case of Korea power exchange (KPX) [3], the electric power organization in Korea, it is possible to check the real-time power supply and demand status for specific regions. However, it is difficult to verify detailed information, such as electric power consumption, at electric vehicle charging stations. The charger management organization does not have a system that can directly receive information about electric power consumption in real time. Therefore, it is necessary to estimate electric power consumption using the supplied data. In general, the electric power consumption of an electric vehicle depends on the initial state of charge (SOC) of the battery and the charging time [4], i.e., power consumption can be estimated using the charging time, initial SOC, and the data related to charging power. In particular, the operating states of the charging stations and location information can be obtained from real-time data. Hence, it is necessary to calculate the electric power consumption by generating an estimation model.

Carlos Gomez and Morcos [5] used ambient temperature and charge duration to determine the power load due to the battery charging of electric vehicles. This method was conducted under the assumption that all electric vehicle batteries were completely discharged, i.e., the initial SOC states were not considered. However, as charging time and the initial SOC of the battery have random values in a real environment, it is difficult to apply this method in a realistic situation. Cheng and Hui-mei [6] used Monte Carlo Simulation to randomly generate the initial SOC and charging time of an electric vehicle, and thereby calculated the electric power consumption. Here, the initial SOC is useful information to determine the maximum power consumption of the charging station that can be consumed in a single charge. This method calculates the charging power using a new SOC curve obtained by simply averaging the battery capacity and SOC curve values of the currently commercialized electric vehicle. However, the actual values of these two parameters (battery capacity and SOC curve) are important for calculating the power consumption of the charging stations. Therefore, this method is not suitable for calculating actual power consumption. Qiang et al. [7] calculated a battery’s SOC by measuring the change in the charging current. However, in this method, sensors must be attached to vehicles that are currently in operation so that relevant information can be received. As a result, it is not a cost-efficient method. Cauwer et al. [8] developed a model to estimate an electric vehicle’s power consumption using the kinematic parameters of the electric vehicle (EV) or the trip data as inputs. We cannot know the amount of power consumption of charging stations in a certain area. This is because, in general, a charging station is shared and used by more than one vehicle. In other words, it is hard to find out how much the charging stations load the peripheral electric power grid in a certain area. Sun et al. [9] developed a predictive model of charging load based on past power load data. The model predicted the power load of the stations using time series data, such as weather, week property, and temperature, as input variables.

In order to overcome the above-mentioned problems, we propose a new system for analyzing the electric power consumption of electric vehicle charging stations by using real-time data that reflect the actual electric vehicle information. This system can not only be used in a real environment, but also is efficient in terms of cost and accuracy as compared to existing methods.

The paper consists of the following sections. Section 2 describes an overview of the proposed system and a detailed description of each module. Section 3 describes the evaluation of the estimation model and experimental results for each of the 48 charging stations in Jeju island in Korea. Section 4 draws conclusions.

2. Proposed System

Figure 1 shows the block diagram of the proposed system. The system consists mainly of data preprocessing, data modeling, and data analysis units. The data preprocessing section processes the input data for creating the estimation model. The data modeling unit generates the model that can estimate electric power consumption using only the charging time and the number of charging. The database system section creates the database that estimates electric power consumption by receiving the information related to the vehicle charging stations in real time. By mapping real-time data to a map along with location information, the proposed system monitors electric power consumption for each charging station.

2.1. Data Preprocessing

The actual charging station data may be deformed due to a failure of the charger or error that may occur during data storage and transmission. These may lead to fatal problems in generating the estimation model of electric power consumption. Therefore, in this step, before the electric power consumption estimation is modeled with raw data, the preprocessing step removes the errors to make the data correct for use in the estimation model.

2.1.1. Data Filtering

Considering the battery capacity of the current commercial electric car (Korea standard), charging takes up to a maximum of 40 min to complete while using a generic fast charger, because the maximum power consumption no longer increases beyond 40 min in charging time as shown in Figure 2. Figure 3 shows that when a battery’s SOC reaches a certain level, the charging power consumption approaches zero. This indicates that there is little change in electric power consumption after a certain time (in this case, 40 min). Therefore, if the entirety of the charging time is used without the data filtering process, an incorrect power consumption estimation model would be obtained; therefore, the data beyond 40 min are excluded from the dataset.

2.1.2. Data Selection

The next step is to select data from the whole data range received from organizations related to the vehicle charging stations. The data include location information, start and end time of charging, and charging time. In other words, the data in real time is not data of the actual electric power consumption. So, data that can estimate power consumption is needed. Equation (1) is used to calculate the electric power consumption when electric vehicles are charged [10].

$$P_{consumption}={{\displaystyle \int }}_{t_0}^{t_0+T}P\left(t\right)dt=\left(1-SO{C}_{inl}\right)Q_r,$$

(1)

where $P_{consumption}$ is the electric power consumption during time T, $SO{C}_{inl}$ is the initial SOC of an EV’s battery, $Q_r$ is the rated capacity of the EV’s battery, $t_0$ is the starting time of charging, T is the charging duration, and P(t) is the charging power at time t.

According to Equation (1), the charging time is an important factor in calculating the electric power consumption of vehicle charging stations. Moreover, the battery SOC information of the electric vehicle at the beginning of charging is important for estimating the power consumption. This is because, even if the same charging duration is used, the electric power consumption can be different depending on the initial SOC of the battery. However, this is not real-time information that may be received by the related organization, and hence other related data are necessary to replace it. Therefore, the number of charging that is performed for a specific period is used.

As shown in Figure 2, the power consumption data distribution of an actual charging station shows several power consumption values despite the same charging time. This indicates the presence of different battery SOC levels at the beginning of charging, which supports our logic that using this data directly to create a data model is not appropriate. In order to solve this problem, all of the data of the charging station during a certain period are integrated. The distribution of the integrated data is shown in Figure 4. In the distribution, the variance of the electric power consumption for the same charging time is significantly reduced. This means that when the data are integrated, the influence of battery SOC is significantly reduced.

Therefore, the number of charging for a specific period is used to estimate the electric power consumption of each vehicle charging station instead of the SOC value, which is highly influenced by a user’s pattern. In short, charging time and the number of charging for a specific period are selected as the prediction variables (input variables).

2.2. Data Modeling

Figure 5 describes the detailed data modeling process. This process creates the estimation model using the preprocessed data described in Section 2.1. In short, we propose an electric vehicle (EV) charging power consumption regression model to estimate the electric power consumption of each vehicle charging station. A regression model is one of the techniques used for multifactor data analysis [11]. It is a statistical technique for modeling the relationship between variables [12]. The following section provides the detailed description.

EV Charging Power Consumption Regression Model

The EV charging power consumption regression model is a new estimation model of electric power consumption using the relationship between charging time and the number of charging. This model is an analytical method to find the most suitable model that can estimate the relationship between the predicted variables. The proposed model is described by Equation (2).

$$P\left(X_{CT},X_{NTC}\right)=w+w_{CT}{X}_{CT}+w_{NTC}{X}_{NTC}+e$$

(2)

where $P\left(X_{CT},X_{NTC}\right)$ is the charging power, $CT$ is the charging time, $NTC$ is the number of charging, $X_{CT}$ and $X_{NTC}$ are predictor variables, $w_{CT}$ and $w_{NTC}$ are weights for the predictor variables, and $e$ is the error (or residual), which is the discrepancy between the real and predicted power. It can be represented by rearranging Equation (3) as:

$$e=P\left(X_{CT},X_{NTC}\right)-w-w_{CT}{X}_{CT}-w_{NTC}{X}_{NTC}.$$

(3)

When the value of ‘e’ in Equation (3) is minimal, an optimal power estimation model that can estimate the relationship between the variables can be obtained. In order to do this, the optimal values of $w, w_{CT}, \mathrm{and} w_{NTC}$, which are the weights of preprocessed data related to the electric power consumption (charging time and the number of charging) are obtained by the least square method [13,14]. Using these values, the proposed model that minimizes the prediction error is created.

The least square method determines the weights from the condition that minimizes the sum of the square of the probability error (Equation (4)) [14], which is the difference between the actual and predicted data for the entire data. When the square of the probability error is minimized, the partial derivatives from Equations (5)–(7) are zero. The equations are summarized and expressed in the form of a matrix in Equation (8) [15].

$$S_r={\displaystyle \sum }_{i=1}^n{e}_i^2={\displaystyle \sum }_{i=1}^n{\left(P_{i, real}-P_{i,prediction}\right)}^2={\displaystyle \sum }_{i=1}^n{\left(P_{i,real}-w-w_{CT}{X}_{i,CT}-w_{NTC}{X}_{i,NTC}\right)}^2$$

(4)

$$\frac{\partial S_r}{\partial w}=-2{\displaystyle \sum }_{i=1}^n\left(P_{i,real}-w-w_{CT}{X}_{i,CT}-w_{NTC}{X}_{i,NTC}\right)$$

(5)

$$\frac{\partial S_r}{\partial w_{CT}}=-2{\displaystyle \sum }_{i=1}^n{X}_{i,CT}\left(P_{i,real}-w-W_{CT}{X}_{i,CT}-w_{NTC}{X}_{i,NTC}\right)$$

(6)

$$\frac{\partial S_r}{\partial w_{NTC}}=-2{\displaystyle \sum }_{i=1}^n{X}_{i,NTC}\left(P_{i,real}-w-w_{CT}{X}_{i,CT}-w_{NTC}{X}_{i,NTC}\right)$$

(7)

$$[\begin{array}{ccc}n& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,CT}& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,NTC}\\ {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,CT}& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,CT}^2& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,CT}{X}_{i,NTC}\\ {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,NTC}& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,CT}{X}_{i,NTC}& {\displaystyle {\displaystyle \sum }_{i=1}^n}{X}_{i,NTC}^2\end{array}]\left\{\begin{array}{c}w\\ w_{CT}\\ w_{NTC}\end{array}\right\}=\left\{\begin{array}{c}{\displaystyle \sum }{P}_{i,real}\\ {\displaystyle \sum }{X}_{i,CT}{P}_{i,real}\\ {\displaystyle \sum }{X}_{i,NTC}{P}_{i,real}\end{array}\right\}$$

(8)

where $S_r$, $P_{i,real}$, and $P_{i,prediction}$ are the squared error, real power, and predicted power, respectively.

All optimal weights ($w,w_{CT},w_{NTC}$) are determined from Equation (8). Using these weights, the final EV charging power consumption regression model is produced. An evaluation of this model will be discussed in Section 3.

2.3. Database System

Figure 6 shows the overall structure of the database system. This system uses a database for monitoring the electric power consumption of vehicle charging stations in real time. The real-time information provided by the related organizations is the operating state of the charging station (being charged, available, checking), and location. The charging time and the number of charging for a specific period are calculated from the operating state of the charging station. This is called the data handling process. The calculated data is stored in the database and used as the input data for the regression model. The predicted electric power consumption, charge time, and the number of charging obtained from the above process are stored in the database along with the location information, and are updated periodically. Using stored data in the database, it is possible to monitor the electric power consumption during a specific period for each charging station in real time.

3. Experimental Results

Experiments were conducted on Jeju island, which has the most active EV charging stations in Korea. As shown in Figure 7, a total of 48 currently operating EV fast charging stations were selected. We use integrated data on a monthly unit to create a model. The training set and the test set were divided by a 8:2 ratio from the whole dataset. The detailed characteristics of the data used in the experiment are listed in

Table 1. Period and the number of samples for the data on electric charging stations.

Period		The Number of Samples
Total	January 2015~May 2017	Total	1275
Train	January 2015~December 2016	Train	1035
Test	January 2017~May 2017	Test	240

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3.1. System Implementation

We implemented the proposed system using the Python language. There are two important algorithms (data preprocessing and data modeling) in our system. We wrote the procedure of the algorithms in pseudo code as follows.

The pseudo code in Figure 8 represents the data preprocessing part. To summarize Figure 8, first, it filters data whose charging time or power consumption is 0 or null. Then, it integrates the data into a specific interval (here, one month). Through this process, we can get integrated data such as charging time, power consumption, and the number of charging.

The pseudo code in Figure 9 represents the data modeling part. The algorithm of Figure 9 is summarized as follows. For the whole data, this method first calculates the square of the difference between the actual power consumption and the power consumption obtained by Equation (4). Then, values that minimize the sum of the data are obtained.

In Section 3.2, we evaluate the power consumption estimation model as obtained above.

3.2. Evaluation of EV Charging Power Consumption Regression Model

The accuracy of the EV charging power consumption regression model was evaluated by using two metrics: Mean Absolute Percentage Error (MAPE) [16] and Normalized Root Mean Square Error (NRMSE) [17]. Both of these metrics had features that were independent of the data scale.

3.2.1. Evaluation Metrics

MAPE is a widely used metric for comparing the prediction performance of different data by measuring the percentage error, and it can be expressed by Equation (9). The percentage error is the ratio of the real power value to the error, and it is expressed by Equation (10).

$$\mathrm{MAPE}=\mathrm{mean}\left(\left|p_i\right|\right)=\frac{1}{n}{\displaystyle \sum }_{i=1}^n\left|p_i\right|$$

(9)

$$p_i=100\times \frac{e_i}{P_{i,real}}, e_i=P_{i,real}-P_{i,predcition}$$

(10)

where $p_i$ is the percentage error, $e_i$ is the forecast error, $P_{i,prediction}$ is the ith predicted power value for the constituent being evaluated, and $P_{i,real}$ is the real power value for the constituent.

However, in the case of MAPE, if the data is close to zero, the percentage error may have an extremely skewed distribution. As a result, it is difficult to use it for zero or very small electric power consumption. In order to compensate for this problem, NRMSE is additionally used for the model’s evaluation.

NRMSE is a metric that normalizes the root mean square error. This is expressed by the percentage of how much the predicted data deviates from the line, and is expressed by Equation (11).

$$\mathrm{NRMSE}=\sqrt{\frac{1}{n}{\displaystyle \sum }_{i=1}^n{(P_{i,prediction}-P_{i,real})}^2}\times \frac{100}{M},$$

(11)

where M is the average of predicted power values.

3.2.2. Evaluation Results for EV Charging Power Consumption Regression Model

The EV charging power consumption regression model mentioned in Equation (2) was used to evaluate how well the electric power consumption of each charging station was estimated. The results are listed in

Table 2. Results from charging stations on Jeju island applying the EV charging power consumption regression model.

Charging Station	MAPE (%)	NRMSE (%)	RMSE (kWh)
1	15.451	15.599	179.676
2	13.936	15.710	114.085
3	16.519	20.603	296.552
4	10.711	12.931	342.108
5	13.410	13.471	303.040
6	8.158	8.707	451.650
7	16.241	17.632	458.939
8	12.995	13.213	584.069
9	9.157	11.326	211.098
10	11.025	11.295	234.659
11	12.490	13.368	158.834
12	6.981	8.243	158.525
13	18.238	15.828	236.848
14	12.195	12.090	159.809
15	16.389	16.546	449.744
16	20.904	22.016	498.520
17	19.034	19.229	739.039
18	18.772	19.359	481.611
19	9.510	11.430	178.609
20	15.430	15.538	542.412
21	15.762	16.100	749.939
22	15.980	16.376	1057.214
23	19.304	19.650	411.719
24	9.258	9.635	308.196
25	24.049	26.018	303.870
26	17.216	22.498	253.966
27	7.355	7.819	694.061
28	12.582	13.151	230.326
29	19.009	19.630	490.568
30	14.519	14.941	224.324
31	6.115	6.601	108.307
32	11.511	11.729	134.658
33	12.917	13.896	236.226
34	8.983	8.603	196.159
35	7.897	8.562	373.645
36	21.212	22.008	681.857
37	16.251	16.627	741.549
38	23.792	23.733	243.021
39	8.944	9.258	270.607
40	9.053	8.876	265.537
41	9.532	9.318	376.084
42	18.570	18.847	611.516
43	10.465	10.660	352.668
44	19.961	20.178	736.698
45	11.466	12.614	478.727
46	12.577	16.829	234.730
47	7.025	7.383	224.033
48	7.779	8.966	335.583
Average	13.680	14.472	377.200

MAPE: mean absolute percentage error; NRMSE: normalized root mean square error; RMSE: root mean square error.

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3.3. Electric Power Consumption for Each Charging Station

Table 3. Results of electric power consumption estimation of charging stations on Jeju island applying the EV charging power consumption regression model.

Charging Stations	Results of Electric Power Consumption Estimation (kWh)
	2017.01	2017.02	2017.03	2017.04	2017.05
1	976.213	756.464	1236.498	1120.140	784.790
2	590.121	636.526	750.246	652.398	485.237
3	552.208	1147.194	1385.400	1542.782	1248.813
4	2602.497	2053.176	3030.883	2941.596	2074.697
5	2289.288	1586.676	2197.996	1917.641	1751.961
6	5828.593	4424.450	5439.767	4637.634	3490.620
7	2251.293	2057.878	2325.053	2444.330	1777.947
8	3726.512	3241.946	4217.238	4595.777	3443.886
9	1457.333	1387.426	1946.216	2012.424	1623.353
10	2279.002	2111.795	2426.759	2683.346	1861.458
11	1044.293	1074.133	1052.114	1031.406	987.764
12	2148.312	1635.317	1751.103	2130.562	1298.092
13	1508.265	1346.459	1898.658	1611.827	1081.810
14	1514.377	1365.704	1473.905	1453.898	619.288
15	1880.134	1963.911	2576.878	2816.803	2143.480
16	1771.526	1391.978	1811.822	2352.860	1591.869
17	2777.195	3066.460	3613.071	3258.248	2838.273
18	3847.843	2726.409	2944.637	2436.668	1610.939
19	1297.924	1500.394	1572.037	1533.338	1158.665
20	3804.497	2695.792	2894.391	3115.515	2291.576
21	3875.569	3944.853	4596.247	4479.708	2724.338
22	5256.725	4693.957	6061.103	6627.436	4486.161
23	1570.406	1603.341	1812.393	2017.678	1445.833
24	2789.299	2398.530	3595.961	3232.477	2504.128
25	2269.890	1537.480	1521.861	736.894	515.643
26	1482.610	1221.346	1072.123	422.713	382.967
27	7719.318	7399.833	9131.319	9594.894	7220.854
28	1316.652	1268.179	1824.046	1759.201	1478.019
29	2033.390	1802.304	2055.538	2749.107	1473.253
30	1911.909	1205.752	1127.083	1309.974	880.165
31	2297.967	1522.224	1587.423	1438.403	858.937
32	1392.964	1049.064	1032.935	951.645	662.474
33	2233.240	1479.628	1363.139	1412.116	899.896
34	2843.258	1801.099	2111.919	2251.922	1417.426
35	3592.196	3758.920	4743.391	4668.606	4613.922
36	2428.187	2808.836	2981.458	2374.108	1593.516
37	3800.969	3951.975	4845.238	3869.376	2213.418
38	781.994	762.668	797.131	874.836	690.174
39	3411.264	2637.594	2818.147	2699.666	1741.803
40	3463.866	2702.977	2973.250	2804.619	1715.859
41	3778.732	3279.961	4656.288	4011.937	2588.722
42	2031.265	1606.661	1687.461	2061.026	1501.821
43	3411.113	2711.128	3631.257	2868.211	2211.715
44	2866.347	3115.549	2985.109	3067.861	2566.092
45	3106.693	3279.131	3504.625	4053.709	2819.666
46	1131.955	945.591	1325.275	1601.398	1066.371
47	3372.183	3030.108	2803.408	2987.297	1904.476
48	3824.377	3535.450	4156.584	3820.395	2907.192

shows the results of estimating the electric power consumption of the EV charging stations from January to May 2017 using the proposed regression model. Figure 10 is a graph showing how the result of Table 3 differs from the actual power consumption. The y-axis of the graph represents the power consumption of the charging station. The x-axis represents the name of the station (1 to 48). Figure 11 shows the electric power consumption data of May 2017 (from Table 3) on a map.

As shown in Figure 11, the map-based analysis system can check and analyze the electric power consumption of each charging station for a specific period in real time. The radius of the circle indicates the amount of electric power consumption at each charging station: the higher the electric power consumption, the larger the size of the circle. It is also possible to visually understand the power load level easily by dividing the power consumption into four levels and using different colors for them. By using this, it is also possible to monitor the load contribution by vehicle charging stations in the peripheral electric power grid in real time. This can be used to relocate the electric vehicle charging stations for a homogeneous distribution of electric power loads in specific areas.

4. Conclusions

The proposed system can measure and analyze the electric power consumption for each electric vehicle charging station during a specific period in real time. The proposed EV power consumption regression model estimated the electric power consumption using only the charging time and the number of charging. As a result of the evaluation, the model showed a high accuracy of about 86%.

The overall system consists of data processing, data modeling, and database systems. The data preprocessing section preprocesses the data to be used as the input of the EV power consumption regression model. We received data of actual charging time and power consumption for two years from the related organization. The data was integrated at a specific period unit to create integrated charge time and power data. We can also get a new variable, the number of charging, which is related to EV power consumption. In the data modeling part, we made a regression model that can obtain the amount of power consumption as output by using the input data created in the data preprocessing part. As a result of the evaluation using MAPE and NRMSE, the model showed a high accuracy of about 86%. Finally, in the database system part, the charging status information (charging, waiting, checking) received in real time is converted into charging time and the number of charging and stored in the database. If the power consumption for a specific period is requested, the power consumption can be estimated through the proposed regression model using the charging time and the number of charging during the corresponding period as input.

In addition, by displaying the estimated electric power consumption on a map, it was possible to identify the areas with high power consumption. So, it is expected that the proposed model can be used effectively for relocating and selecting the locations of electric vehicle charging stations.