- Email: [email protected]
Electric Vehicle Load Disaggregation Based on Limited Activation Matching Pursuits
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Energy Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online atatwww.sciencedirect.com Energy Procedia 00 (2018) 000–000
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www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy Procedia 158 Energy Procedia 00(2019) (2017)2611–2616 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Electric Vehicle Load Disaggregation Based on Limited Activation Electric Vehicle Disaggregation BasedHeating on Limited Activation The 15thLoad International Symposium on District and Cooling Matching Pursuits Matching Pursuits Assessing the feasibility of using the heat demand-outdoor Shuangyuan Wangaa, Ran Liaa*, Adrian Evansaa, Furong Liaa Shuangyuan Li *, Adrian Evans heat , Furong Li temperature functionWang for a, Ran long-term district demand forecast Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK a a
Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, Franceof eclectic vehicles (EVs) This paper proposes a novel limited activation&matching pursuits (LAMP) method to monitor the number c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300of Nantes, France This paper at proposes a novel limited matching pursuits (LAMP) method to monitor the number eclectic vehicles (EVs) connected a charging station andactivation their charging activities. LAMP is able to reflect the two-dimensional characteristics of the connected a charging station their chargingare activities. is able to coefficients reflect the two-dimensional characteristics the number andatcharging time of theand EVs. Constraints entered LAMP on the activation of the matching pursuits to avoidofover number and charging type time of EV. the EVs. Constraints are entered on the activation coefficients oftypical the matching pursuits to avoid matching a particular The method includes the development of the basis based on EV charging profiles andover the matching a particular type pursuits. of EV. The method includes the development of the on typical EV charging profiles andthat the improvement of matching A case study is undertaken based on real EVbasis data based collected from London. The results show Abstract improvement of matching pursuits. A case study is undertaken onduration real EVof data from London. The connected results show that 79.35% EVs can be accurately detected in charging station loadbased profile onecollected week. The number of EVs within 79.35% bebe accurately in charging loaddeviation profile duration of of one21.18%. week. The number of EVs connected within each halfEVs hourcan can identifieddetected with a relative meanstation absolute (RMAD) District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the each half hour can be identified with a relative mean absolute deviation (RMAD) of 21.18%. greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat Copyright © 2018 Elsevier Ltd. All rights reserved. sales. to the changed climate conditions heat demand in the future could decrease, © 2019 Due The Published Elsevier Ltd. and building renovation policies, Copyright ©Authors. 2018 Elsevier Ltd. by All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy prolonging theaccess investment This is an open articlereturn underperiod. the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). Peer-review underofresponsibility scientific committee of ICAE2018 The 10th International Conference on Applied The main scope this paper is of to the assess the feasibility of using the heat –demand – outdoor temperature function for heatEnergy. demand (ICAE2018). forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Keywords: visibility of power system, EV, matching pursuits, limited activation; buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: visibility of power system, EV, matching pursuits, limited activation; renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. 1.The Introduction results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation To reduce carbon thetoUK Government to ban and all new petrolscenarios and diesel cars and vans from scenarios, the its error value emission, increased up 59.5% (dependingpledged on the weather renovation combination considered). To reduce its carbon emission, the UK Government pledged to ban all new petrol and diesel cars and vans 2040[1]. The plan creates a huge market for electric vehicles (EVs). However, large-scale EVs connection will put a The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds from to the 2040[1]. The plan creates a huge market for electric vehicles (EVs). However, large-scale EVs connection will put a significant impact on the operation of the power system, especially the distribution network where EVs are directly decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and significant impact thecharging operation of power system, especially the distribution network where are directly renovation[2]. scenarios considered). Onload the the other hand, function intercept increased 7.8-12.7% per traditional decade EVs (depending on the connected The on rapid of an EV could reach 100 KW which isforhigher than 10 homes. Such connected [2]. The charging load ofcould an EV reach 100the KWfunction which parameters is higherinfrastructures than homes. Such coupled scenarios). The values suggested be could used to for 10 the traditional scenarios and high demand will rapid severely challenge the capacity ofmodify existing power system andconsidered, operational improve the accuracy ofnumber heat demand estimations. high demand challenge thehave capacity of existing power system infrastructures operational requirements. Awill largeseverely of researches investigated the impact and mitigation of EVs, such asand smart charging
requirements. A large number of researches have investigated the impact and mitigation of EVs, such as smart charging © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +44 (0) 1225386183.
address:author. [email protected] * E-mail Corresponding Tel.: +44 (0) 1225386183. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.02.011
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[3], optimal scheduling for EV charging stations [4] and virtual power plants [5]. For a more detailed review of vehicle charging architecture, readers can go through [6]. Another challenge brought about by EVs is the uncertainty in charging locations. As a large mobilising load, the number of EVs connected at a particular node is time-varying. Such information is critical for distribution network operators (DNOs) in terms of distribution network planning and demand side management. This includes the charging location, charging time and charging capacity. The naive method is to install a large number of sensors on EVs and charging stations to record the charging information. An obvious advantage is the accuracy and reliability. Disadvantages include privacy issues and the high cost. As the EVs and charging stations grows, the sensors required for monitoring the entire system will be prohibitive. This paper proposes a load disaggregation method to use limited data available, such as the charging station load profiles and typical EV profiles to deduce the number of EVs connected to a specific charging station as well as their charging status. Inspired by the matching pursuits (MP) method widely used in signal decomposition, compression and feature extraction [7], this proposed method will decompose the aggregated charging station load profiles into some combinations of typical EV charging patterns, in a redundant dictionary, requiring the least number of charging patterns to be used and the minimum reconstruction error. For a charging station, the total load is the sum of charging EVs, noise and loss superimposed with different starting times and patterns. This work aims to identify the number of EVs, individual charging period and charging amount. This will lay the groundwork to enhance the visibility of distribution networks. The rest of this paper is organized as follows. Section II introduces the matching pursuit method. Section III proposes the nonintrusive EV monitoring method to estimate the EV number and charging information. A case study is demonstrated in Section IV and conclusions are drawn in V. 2. EV Load Disaggregation 2.1. Matching Pursuit A redundant dictionary is denoted by matrix B, in which every column is a prototype signal called atom or basis. For a given signal y, it can be represented as a linear combine of these atoms: y = BW + γ,
(1)
where W indicates the activation coefficients of all atoms in the dictionary B. γ is the residual and W is a sparse matrix indicating the scalar weighting factors for the atoms. Sparse means that not every atom in B will be activated. Normally, matching pursuits select the best single atom at a time to maximally reduce the approximation error. The minimum stable error will be achieved through many times of iteration. 2.2. Development of EV Load Profiles as Atoms Real EV charging data from the Low Carbon London (LCL) project [8] are used in this study. The load profiles cover 24 hours and the charging load is given a half hour time base as shown in Fig. 1 (one EV over one week). In order to make the algorithm converge as soon as possible, the correlation between atoms should be kept as low as possible. For example, orthogonal bases are used in orthogonal matching pursuits (OMP). However, in this study it is difficult to generate an orthogonal basis without distortion on the of the EV’s real charging patterns. Therefore, historical EV charging data are kept in its original form. Atoms are selected by removing those charging data with high correlations from the dictionary. Fig. 2 shows the selected atoms from the historical charging profiles of 60 EVs over 2 years. The correlation coefficient is defined by: ρ(bi ,bj) =E[(bi - ui )(bj - uj )]/( σi σj ),
(2)
where, bi and bj are two atoms with expected values ui, and uj and standard deviations σi and σj. E is the expected value operator. Any charging profile will be removed if its correlation with an existing atom is higher than the defined threshold c. For some EVs, no charging activities are observed throughout a day. A threshold value e is defined to eliminate those atoms with low-value noise for the whole periods.
3
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Shuangyuan Wang et al. / Energy Procedia 158 (2019) 2611–2616
Fig. 1. The charging load profiles of EV from 13/10/2012 to 19/10/2012.
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Fig. 2. A selected 396 atoms dictionary in day length and weak correlation (correlation threshold c < 0.85, e > 0.05 kWh).
2.3. Limited Activation Model To apply the MP method for EVs monitoring, three novel adaptions have been made: i) matching pursuits is a greedy algorithm, which means that one basis is allowed to make up the whole signal at a particular point. However, this is not true in the real world situation. For example, a single EV cannot exceed its maximum charging power and the number of charging piles is limited in a substation. Therefore, it is necessary in this study to limit the magnitude of individual activation coefficient and the number active basis at a particular time. ii) Currently, most EVs cannot discharge back to the grid. This is reflected by constraining the activation coefficients to be non-negative. iii) It is also critical for charging stations to understand the start time of each charging activities. For the perspective of signal processing, the start point of an atom (i.e. EV charging profiles) may not match the start point of the matching signal (i.e. the charging station load profile). Traditional matching pursuits are based on the matching of fixed-length signals and does not have the property of time shift-invariance. A limited activation marching pursuits (LAMP) model is proposed to account for these constraints. Firstly, the shift-invariant method is adopted to improve the conventional matching pursuits, which reconstructs the signal using all of the atoms in all possible shifts. Then, a limited activing constraint is implied to the convolution of the signal and the dictionary. A dictionary D is denoted as the EVs load profiles: D = [d1, d2, …, dp],
where, di is a daily charging normalized profile of the ith EV, a vector with n = 48 elements in this case. The normalized energy is constrained by ||di||2 = 1 and i = {1, 2, …, p} is the number of basis in the dictionary, in this study p = 396. To reduce the end effects, the charging station load profile x is then expanded to a new vector y with interpolated zero vectors, y = [0n, xm, 0n], where 0n = [0, 0, …, 0] is a zero vector with n elements, m is the length of y. The shift convolution of dictionary D and signal y is the target matrix C ,which will be used to matching: C = conv(D, y),
(4)
where, conv is the convolution operator. C is a p*(2n+m) matrix whose maximum value of C is defined as C(imax, jmax), where, imax indicates the atom index, and jmax indicates the time index. So the activation coefficient a is expressed as: c , C(imax , jmax ) c a . C(imax , jmax ) , C(imax , jmax )c
To update the activing coefficients matrix W, we have
(5)
Shuangyuan Wang et al. / Energy Procedia 158 (2019) 2611–2616 S. Wang et al. / Energy Procedia 00 (2018) 000–000
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W(k+1)(imax, jmax) = W(k)(imax, jmax) + a. The residual of signal y
(k)
(6)
is defined as y(k+1) = y(k)-a di.
After an iteration, the convolution matrix C
(k+1)
(7)
is given by:
C(k+1) =conv(D, y(k+1)) =C(k)-a conv(D, di) =C(k)-a G(:, :, imax), (8) where, the matrix G is the convolution between the atoms in the dictionary D, imax indicates the index of activing atom in the dictionary which has the maximum activing value. As the activation only affects a particular range of C, we only need to update the activated range r in C. r could be derived by r = jmax + ceil(-n/2 : 1 : n/2), where jmax is the time index of the activation, ceil is rounded up operator. The iteration terminates when either the maximum iteration number N is reached or the residual signal is smaller than a threshold value ε. Fig. 3 shows the detailed scheme of the limited activing matching pursuits. First, the target matrix C is found by the convolution of the dictionary with the expanded signal, and the dictionary convolution matrix G. Second, the maximum point C(imax, jmax) in the target matrix C is found. According to the limited activation threshold c re-evaluate the activation coefficient W(imax, jmax). Third, the activation range r is found in the target matrix, as is the best matching atom index imax in the dictionary. Then the activing range in the target matrix C is updated using (8). Fourth, a check as to whether the termination condition is reached should be performed. If not, step two will be repeated and otherwise, iteration will be stopped and the activation coefficients matrix W will be exported.
Fig. 3. Scheme of limited activing matching pursuits.
It is noted that EV charging profiles are discrete. There are some zero periods in the atoms indicating that the EV is not connected at the time. Therefore, the number of activating EVs should be undertaken for each time period. The status of charging in an atom can be written as 1, di ( k ) z (k ) . i 0, di ( k )
(9)
Here, ε is a small value relative to the minimum charging power of EV. k is the index in the atom, k=1, 2, …,n. So the number of EVs connect to the charging station N(t) at a particular time t could be expressed as: N (t )
iA,t n 1 si t
zi (t -si 1)
,
(10)
where, si is the active time of the ith atom, A is the sets of active atoms index, n is the length of the atom. In generally, the mean absolute deviation (MAD) is used to assess the performance of the estimation method.
Shuangyuan Wang et al. / Energy Procedia 158 (2019) 2611–2616 S. Wang et al. / Energy Procedia 00 (2018) 000–000
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Between the original signal x(n) and the estimation signal y(n), the MAD is: MAD
1n y (i ) x (i ) . n i 1
(11)
However, mean absolute values are not comparable on different scales of data. In order to compare the error under different scales of EVs in the charging stations. A relative means absolute deviation (RMAD) is defined in (11). RMAD = 100%*MAD/u ,
(12)
where u is the average value of the load profile. 3. Case Study and Results 3.1. Load of a pseudo charging station To test the proposed method, 200 one-day charging load profiles of the EVs are randomly selected to simulate the load of a pseudo charging station. EV data are collected from the LCL data set [5]. The data sampling period is half hour over nine day’s interval. In order to avoid the truncation effect, the middle seven days data are selected as the testing data. The simulated load of the charging station is shown in Fig. 4 with a solid blue line. A significant volatility can be observed in the profile ranging from 12.03 kWh to 0.29 kWh.
Fig. 4. One week pseudo charging station load with 200 random EVs day load profiles and LAMP reconstruct signal.
Fig. 5. EVs load profiles active point distributions in the simulation and LMAP.
3.2. Results from LAMP The charging station load is disaggregated using the proposed LAMP method. The atoms and coefficients derived are deployed to reconstruct the load profile, which is depicted in a red dot line in Fig. 4. The reconstructed load profile follows the station load very well, indicating a small residual. The mean absolute deviation (MAD) load between the simulation and LAMP is 1.11kWh and the RMAD is 22.42%. As the overall load conforms, it is of interest to investigate whether individual charging activity can be accurately detected. The atom derived from LAMP indicates the charging type and the activation coefficient indicates the start time of an EV charging activity. Fig. 5 shows the distribution of the start time of all charging activities in the station represented by blue stars. There are 200 charging activities randomly distributed over time and charging types, i.e. type of atoms. The red circles show the charging type and start time estimated by LAMP. There are few cases that estimated start points by LAMP exactly match the real ones (blue star). The reason is that the proposed method allows atoms to shift along the time axis. This shift operation has created local similarity so that a charging activity can be represented by several different atoms. For example, two different atoms may share similar charging patterns over different time periods. The shift operation can move two windows to the same period and thus the two atoms can be temporarily replaceable.
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Shuangyuan Wang et al. / Energy Procedia 158 (2019) 2611–2616 S. Wang et al. / Energy Procedia 00 (2018) 000–000
Although the exact matching of individual EV is inaccurate, the LAMP could still estimate the total number of charging EVs within the window. The number of EVs charged at the station is shown in Fig. 6 by every half an hour. The blue bars are the real number of EVs while the red bars are the estimation by LAMP. The estimation is relatively accurate with a MAD of 1.81 EVs and a RMAD of 21.28%. Table 1. LAMP performances on charging stations with different sizes (number of EVs).
Fig. 6. The total number of EVs at charging station (blue) and estimation by LAMP (red) given the total load
RMAD (%)
Size (Maximum Number of EVs connected)
Estimated Load
Estimated number of EVs
30
42.59
76.34
50
38.31
52.23
100
28.74
30.49
150
22.36
21.18
200
22.42
21.28
300
18.52
24.24
500
13.25
31.73
It is noted the size of charging station will significantly affect the performance of LAMP. Large charging stations with an increasing number of EVs connected will significantly reduce the RMAD of LAMP. As listed in Table I, the RMAD of reconstructed load decrease from 42.59% for 30 EVs to 13.25% for 500 EVs. When estimating the number of EVs, the RMAD quickly decrease as the number of EVs increases from 30 to 150. The RMAD reaches a minimum of 21.18% when the number of EVs is 150 while further increase in the number of EVs will not improve the performance. 4. Conclusion This paper presents a novel LAMP method to disaggregate load of an EV charging station and estimate the number of EVs connected. The typical daily charging profiles of EVs are used as atoms in the dictionary. The non-negative and limited activation strategies are applied to reflect the characteristics of EVs. The results show more than 79% numbers of EVs can be detected. Further development of this method will focus on improving the ability of estimating the start time and type of individual EV charging. This requires an augmentation of the dictionary by collecting more data from the EVs. References [1] Asthana and M. Taylor, "Britain to ban sale of all diesel and petrol cars and vans from 2040," The Guardian, 2017. [2] P. Hanemann, M. Behnert, and T. Bruckner, "Effects of electric vehicle charging strategies on the German power system," Applied Energy, vol. 203, pp. 608-622, 2017. [3] R. A. Verzijlbergh, M. O. Grond, Z. Lukszo, J. G. Slootweg, and M. D. Ilic, "Network impacts and cost savings of controlled EV charging," IEEE transactions on Smart Grid, vol. 3, pp. 1203-1212, 2012. [4] Y. Song, Y. Zheng, and D. J. Hill, "Optimal Scheduling for EV charging stations in distribution networks: A convexified model," IEEE Transactions on Power Systems, vol. 32, pp. 1574-1575, 2017. [5] F. A. Raab, "Operational planning, modeling and control of virtual power plants with electric vehicles," Ph.D. dissertation, Technical University of Berlin, Berlin, Germany, 2018. [6] L. Rubino et al. “Review on plug-in electric vehicle charging architectures integrated with distributed energy sources for sustainable mobility” Applied Energy 207, 438-464, 2017; [7] S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Transactions on signal processing, vol. 41, pp. 33973415, 1993. [8] U K Power Networks Low Carbon London Project, [online] Available: http://innovation.ukpowernetworks.co.uk/innovation/en/Projects/tier2-projects/Low-Carbon-London-(LCL).
ScienceDirect ScienceDirect
Energy Procedia 00 (2018) 000–000 Available online www.sciencedirect.com Available online atatwww.sciencedirect.com Energy Procedia 00 (2018) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Energy Procedia 158 Energy Procedia 00(2019) (2017)2611–2616 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Electric Vehicle Load Disaggregation Based on Limited Activation Electric Vehicle Disaggregation BasedHeating on Limited Activation The 15thLoad International Symposium on District and Cooling Matching Pursuits Matching Pursuits Assessing the feasibility of using the heat demand-outdoor Shuangyuan Wangaa, Ran Liaa*, Adrian Evansaa, Furong Liaa Shuangyuan Li *, Adrian Evans heat , Furong Li temperature functionWang for a, Ran long-term district demand forecast Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK a a
Department of Electronic & Electrical Engineering, University of Bath, Bath BA2 7AY, UK
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, Franceof eclectic vehicles (EVs) This paper proposes a novel limited activation&matching pursuits (LAMP) method to monitor the number c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300of Nantes, France This paper at proposes a novel limited matching pursuits (LAMP) method to monitor the number eclectic vehicles (EVs) connected a charging station andactivation their charging activities. LAMP is able to reflect the two-dimensional characteristics of the connected a charging station their chargingare activities. is able to coefficients reflect the two-dimensional characteristics the number andatcharging time of theand EVs. Constraints entered LAMP on the activation of the matching pursuits to avoidofover number and charging type time of EV. the EVs. Constraints are entered on the activation coefficients oftypical the matching pursuits to avoid matching a particular The method includes the development of the basis based on EV charging profiles andover the matching a particular type pursuits. of EV. The method includes the development of the on typical EV charging profiles andthat the improvement of matching A case study is undertaken based on real EVbasis data based collected from London. The results show Abstract improvement of matching pursuits. A case study is undertaken onduration real EVof data from London. The connected results show that 79.35% EVs can be accurately detected in charging station loadbased profile onecollected week. The number of EVs within 79.35% bebe accurately in charging loaddeviation profile duration of of one21.18%. week. The number of EVs connected within each halfEVs hourcan can identifieddetected with a relative meanstation absolute (RMAD) District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the each half hour can be identified with a relative mean absolute deviation (RMAD) of 21.18%. greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat Copyright © 2018 Elsevier Ltd. All rights reserved. sales. to the changed climate conditions heat demand in the future could decrease, © 2019 Due The Published Elsevier Ltd. and building renovation policies, Copyright ©Authors. 2018 Elsevier Ltd. by All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy prolonging theaccess investment This is an open articlereturn underperiod. the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). Peer-review underofresponsibility scientific committee of ICAE2018 The 10th International Conference on Applied The main scope this paper is of to the assess the feasibility of using the heat –demand – outdoor temperature function for heatEnergy. demand (ICAE2018). forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Keywords: visibility of power system, EV, matching pursuits, limited activation; buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district Keywords: visibility of power system, EV, matching pursuits, limited activation; renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. 1.The Introduction results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1. Introduction (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation To reduce carbon thetoUK Government to ban and all new petrolscenarios and diesel cars and vans from scenarios, the its error value emission, increased up 59.5% (dependingpledged on the weather renovation combination considered). To reduce its carbon emission, the UK Government pledged to ban all new petrol and diesel cars and vans 2040[1]. The plan creates a huge market for electric vehicles (EVs). However, large-scale EVs connection will put a The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds from to the 2040[1]. The plan creates a huge market for electric vehicles (EVs). However, large-scale EVs connection will put a significant impact on the operation of the power system, especially the distribution network where EVs are directly decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and significant impact thecharging operation of power system, especially the distribution network where are directly renovation[2]. scenarios considered). Onload the the other hand, function intercept increased 7.8-12.7% per traditional decade EVs (depending on the connected The on rapid of an EV could reach 100 KW which isforhigher than 10 homes. Such connected [2]. The charging load ofcould an EV reach 100the KWfunction which parameters is higherinfrastructures than homes. Such coupled scenarios). The values suggested be could used to for 10 the traditional scenarios and high demand will rapid severely challenge the capacity ofmodify existing power system andconsidered, operational improve the accuracy ofnumber heat demand estimations. high demand challenge thehave capacity of existing power system infrastructures operational requirements. Awill largeseverely of researches investigated the impact and mitigation of EVs, such asand smart charging
requirements. A large number of researches have investigated the impact and mitigation of EVs, such as smart charging © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +44 (0) 1225386183.
address:author. [email protected] * E-mail Corresponding Tel.: +44 (0) 1225386183. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.02.011
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[3], optimal scheduling for EV charging stations [4] and virtual power plants [5]. For a more detailed review of vehicle charging architecture, readers can go through [6]. Another challenge brought about by EVs is the uncertainty in charging locations. As a large mobilising load, the number of EVs connected at a particular node is time-varying. Such information is critical for distribution network operators (DNOs) in terms of distribution network planning and demand side management. This includes the charging location, charging time and charging capacity. The naive method is to install a large number of sensors on EVs and charging stations to record the charging information. An obvious advantage is the accuracy and reliability. Disadvantages include privacy issues and the high cost. As the EVs and charging stations grows, the sensors required for monitoring the entire system will be prohibitive. This paper proposes a load disaggregation method to use limited data available, such as the charging station load profiles and typical EV profiles to deduce the number of EVs connected to a specific charging station as well as their charging status. Inspired by the matching pursuits (MP) method widely used in signal decomposition, compression and feature extraction [7], this proposed method will decompose the aggregated charging station load profiles into some combinations of typical EV charging patterns, in a redundant dictionary, requiring the least number of charging patterns to be used and the minimum reconstruction error. For a charging station, the total load is the sum of charging EVs, noise and loss superimposed with different starting times and patterns. This work aims to identify the number of EVs, individual charging period and charging amount. This will lay the groundwork to enhance the visibility of distribution networks. The rest of this paper is organized as follows. Section II introduces the matching pursuit method. Section III proposes the nonintrusive EV monitoring method to estimate the EV number and charging information. A case study is demonstrated in Section IV and conclusions are drawn in V. 2. EV Load Disaggregation 2.1. Matching Pursuit A redundant dictionary is denoted by matrix B, in which every column is a prototype signal called atom or basis. For a given signal y, it can be represented as a linear combine of these atoms: y = BW + γ,
(1)
where W indicates the activation coefficients of all atoms in the dictionary B. γ is the residual and W is a sparse matrix indicating the scalar weighting factors for the atoms. Sparse means that not every atom in B will be activated. Normally, matching pursuits select the best single atom at a time to maximally reduce the approximation error. The minimum stable error will be achieved through many times of iteration. 2.2. Development of EV Load Profiles as Atoms Real EV charging data from the Low Carbon London (LCL) project [8] are used in this study. The load profiles cover 24 hours and the charging load is given a half hour time base as shown in Fig. 1 (one EV over one week). In order to make the algorithm converge as soon as possible, the correlation between atoms should be kept as low as possible. For example, orthogonal bases are used in orthogonal matching pursuits (OMP). However, in this study it is difficult to generate an orthogonal basis without distortion on the of the EV’s real charging patterns. Therefore, historical EV charging data are kept in its original form. Atoms are selected by removing those charging data with high correlations from the dictionary. Fig. 2 shows the selected atoms from the historical charging profiles of 60 EVs over 2 years. The correlation coefficient is defined by: ρ(bi ,bj) =E[(bi - ui )(bj - uj )]/( σi σj ),
(2)
where, bi and bj are two atoms with expected values ui, and uj and standard deviations σi and σj. E is the expected value operator. Any charging profile will be removed if its correlation with an existing atom is higher than the defined threshold c. For some EVs, no charging activities are observed throughout a day. A threshold value e is defined to eliminate those atoms with low-value noise for the whole periods.
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Fig. 1. The charging load profiles of EV from 13/10/2012 to 19/10/2012.
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Fig. 2. A selected 396 atoms dictionary in day length and weak correlation (correlation threshold c < 0.85, e > 0.05 kWh).
2.3. Limited Activation Model To apply the MP method for EVs monitoring, three novel adaptions have been made: i) matching pursuits is a greedy algorithm, which means that one basis is allowed to make up the whole signal at a particular point. However, this is not true in the real world situation. For example, a single EV cannot exceed its maximum charging power and the number of charging piles is limited in a substation. Therefore, it is necessary in this study to limit the magnitude of individual activation coefficient and the number active basis at a particular time. ii) Currently, most EVs cannot discharge back to the grid. This is reflected by constraining the activation coefficients to be non-negative. iii) It is also critical for charging stations to understand the start time of each charging activities. For the perspective of signal processing, the start point of an atom (i.e. EV charging profiles) may not match the start point of the matching signal (i.e. the charging station load profile). Traditional matching pursuits are based on the matching of fixed-length signals and does not have the property of time shift-invariance. A limited activation marching pursuits (LAMP) model is proposed to account for these constraints. Firstly, the shift-invariant method is adopted to improve the conventional matching pursuits, which reconstructs the signal using all of the atoms in all possible shifts. Then, a limited activing constraint is implied to the convolution of the signal and the dictionary. A dictionary D is denoted as the EVs load profiles: D = [d1, d2, …, dp],
where, di is a daily charging normalized profile of the ith EV, a vector with n = 48 elements in this case. The normalized energy is constrained by ||di||2 = 1 and i = {1, 2, …, p} is the number of basis in the dictionary, in this study p = 396. To reduce the end effects, the charging station load profile x is then expanded to a new vector y with interpolated zero vectors, y = [0n, xm, 0n], where 0n = [0, 0, …, 0] is a zero vector with n elements, m is the length of y. The shift convolution of dictionary D and signal y is the target matrix C ,which will be used to matching: C = conv(D, y),
(4)
where, conv is the convolution operator. C is a p*(2n+m) matrix whose maximum value of C is defined as C(imax, jmax), where, imax indicates the atom index, and jmax indicates the time index. So the activation coefficient a is expressed as: c , C(imax , jmax ) c a . C(imax , jmax ) , C(imax , jmax )c
To update the activing coefficients matrix W, we have
(5)
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W(k+1)(imax, jmax) = W(k)(imax, jmax) + a. The residual of signal y
(k)
(6)
is defined as y(k+1) = y(k)-a di.
After an iteration, the convolution matrix C
(k+1)
(7)
is given by:
C(k+1) =conv(D, y(k+1)) =C(k)-a conv(D, di) =C(k)-a G(:, :, imax), (8) where, the matrix G is the convolution between the atoms in the dictionary D, imax indicates the index of activing atom in the dictionary which has the maximum activing value. As the activation only affects a particular range of C, we only need to update the activated range r in C. r could be derived by r = jmax + ceil(-n/2 : 1 : n/2), where jmax is the time index of the activation, ceil is rounded up operator. The iteration terminates when either the maximum iteration number N is reached or the residual signal is smaller than a threshold value ε. Fig. 3 shows the detailed scheme of the limited activing matching pursuits. First, the target matrix C is found by the convolution of the dictionary with the expanded signal, and the dictionary convolution matrix G. Second, the maximum point C(imax, jmax) in the target matrix C is found. According to the limited activation threshold c re-evaluate the activation coefficient W(imax, jmax). Third, the activation range r is found in the target matrix, as is the best matching atom index imax in the dictionary. Then the activing range in the target matrix C is updated using (8). Fourth, a check as to whether the termination condition is reached should be performed. If not, step two will be repeated and otherwise, iteration will be stopped and the activation coefficients matrix W will be exported.
Fig. 3. Scheme of limited activing matching pursuits.
It is noted that EV charging profiles are discrete. There are some zero periods in the atoms indicating that the EV is not connected at the time. Therefore, the number of activating EVs should be undertaken for each time period. The status of charging in an atom can be written as 1, di ( k ) z (k ) . i 0, di ( k )
(9)
Here, ε is a small value relative to the minimum charging power of EV. k is the index in the atom, k=1, 2, …,n. So the number of EVs connect to the charging station N(t) at a particular time t could be expressed as: N (t )
iA,t n 1 si t
zi (t -si 1)
,
(10)
where, si is the active time of the ith atom, A is the sets of active atoms index, n is the length of the atom. In generally, the mean absolute deviation (MAD) is used to assess the performance of the estimation method.
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Between the original signal x(n) and the estimation signal y(n), the MAD is: MAD
1n y (i ) x (i ) . n i 1
(11)
However, mean absolute values are not comparable on different scales of data. In order to compare the error under different scales of EVs in the charging stations. A relative means absolute deviation (RMAD) is defined in (11). RMAD = 100%*MAD/u ,
(12)
where u is the average value of the load profile. 3. Case Study and Results 3.1. Load of a pseudo charging station To test the proposed method, 200 one-day charging load profiles of the EVs are randomly selected to simulate the load of a pseudo charging station. EV data are collected from the LCL data set [5]. The data sampling period is half hour over nine day’s interval. In order to avoid the truncation effect, the middle seven days data are selected as the testing data. The simulated load of the charging station is shown in Fig. 4 with a solid blue line. A significant volatility can be observed in the profile ranging from 12.03 kWh to 0.29 kWh.
Fig. 4. One week pseudo charging station load with 200 random EVs day load profiles and LAMP reconstruct signal.
Fig. 5. EVs load profiles active point distributions in the simulation and LMAP.
3.2. Results from LAMP The charging station load is disaggregated using the proposed LAMP method. The atoms and coefficients derived are deployed to reconstruct the load profile, which is depicted in a red dot line in Fig. 4. The reconstructed load profile follows the station load very well, indicating a small residual. The mean absolute deviation (MAD) load between the simulation and LAMP is 1.11kWh and the RMAD is 22.42%. As the overall load conforms, it is of interest to investigate whether individual charging activity can be accurately detected. The atom derived from LAMP indicates the charging type and the activation coefficient indicates the start time of an EV charging activity. Fig. 5 shows the distribution of the start time of all charging activities in the station represented by blue stars. There are 200 charging activities randomly distributed over time and charging types, i.e. type of atoms. The red circles show the charging type and start time estimated by LAMP. There are few cases that estimated start points by LAMP exactly match the real ones (blue star). The reason is that the proposed method allows atoms to shift along the time axis. This shift operation has created local similarity so that a charging activity can be represented by several different atoms. For example, two different atoms may share similar charging patterns over different time periods. The shift operation can move two windows to the same period and thus the two atoms can be temporarily replaceable.
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Although the exact matching of individual EV is inaccurate, the LAMP could still estimate the total number of charging EVs within the window. The number of EVs charged at the station is shown in Fig. 6 by every half an hour. The blue bars are the real number of EVs while the red bars are the estimation by LAMP. The estimation is relatively accurate with a MAD of 1.81 EVs and a RMAD of 21.28%. Table 1. LAMP performances on charging stations with different sizes (number of EVs).
Fig. 6. The total number of EVs at charging station (blue) and estimation by LAMP (red) given the total load
RMAD (%)
Size (Maximum Number of EVs connected)
Estimated Load
Estimated number of EVs
30
42.59
76.34
50
38.31
52.23
100
28.74
30.49
150
22.36
21.18
200
22.42
21.28
300
18.52
24.24
500
13.25
31.73
It is noted the size of charging station will significantly affect the performance of LAMP. Large charging stations with an increasing number of EVs connected will significantly reduce the RMAD of LAMP. As listed in Table I, the RMAD of reconstructed load decrease from 42.59% for 30 EVs to 13.25% for 500 EVs. When estimating the number of EVs, the RMAD quickly decrease as the number of EVs increases from 30 to 150. The RMAD reaches a minimum of 21.18% when the number of EVs is 150 while further increase in the number of EVs will not improve the performance. 4. Conclusion This paper presents a novel LAMP method to disaggregate load of an EV charging station and estimate the number of EVs connected. The typical daily charging profiles of EVs are used as atoms in the dictionary. The non-negative and limited activation strategies are applied to reflect the characteristics of EVs. The results show more than 79% numbers of EVs can be detected. Further development of this method will focus on improving the ability of estimating the start time and type of individual EV charging. This requires an augmentation of the dictionary by collecting more data from the EVs. References [1] Asthana and M. Taylor, "Britain to ban sale of all diesel and petrol cars and vans from 2040," The Guardian, 2017. [2] P. Hanemann, M. Behnert, and T. Bruckner, "Effects of electric vehicle charging strategies on the German power system," Applied Energy, vol. 203, pp. 608-622, 2017. [3] R. A. Verzijlbergh, M. O. Grond, Z. Lukszo, J. G. Slootweg, and M. D. Ilic, "Network impacts and cost savings of controlled EV charging," IEEE transactions on Smart Grid, vol. 3, pp. 1203-1212, 2012. [4] Y. Song, Y. Zheng, and D. J. Hill, "Optimal Scheduling for EV charging stations in distribution networks: A convexified model," IEEE Transactions on Power Systems, vol. 32, pp. 1574-1575, 2017. [5] F. A. Raab, "Operational planning, modeling and control of virtual power plants with electric vehicles," Ph.D. dissertation, Technical University of Berlin, Berlin, Germany, 2018. [6] L. Rubino et al. “Review on plug-in electric vehicle charging architectures integrated with distributed energy sources for sustainable mobility” Applied Energy 207, 438-464, 2017; [7] S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Transactions on signal processing, vol. 41, pp. 33973415, 1993. [8] U K Power Networks Low Carbon London Project, [online] Available: http://innovation.ukpowernetworks.co.uk/innovation/en/Projects/tier2-projects/Low-Carbon-London-(LCL).