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Article

Calculating Operational Patterns for Electric Vehicle Charging on a Real Distribution Network Based on Renewables’ Production

Department of Electrical and Electronic Engineering Educators, School of Pedagogical & Technological Education (ASPETE), Heraklion Attikis, 141 21 Athens, Greece
*
Author to whom correspondence should be addressed.
Energies 2018, 11(9), 2400; https://doi.org/10.3390/en11092400
Received: 30 July 2018 / Revised: 16 August 2018 / Accepted: 7 September 2018 / Published: 11 September 2018

Abstract

:
The connection of electric vehicles to distribution networks has been an emerging issue of paramount importance for power systems. On one hand, it provides new opportunities for climate change mitigation, if electric energy used for charging is produced from zero emission sources. On the other hand, it stresses networks that are now required to accommodate, in addition to the loads and production from distributed generation they are initially designed for, loads from electric vehicles charging. In order to achieve maximum use of the grid without substantially affecting its performance, these issues have to be addressed in a coordinated manner, which requires adequate knowledge of the system under consideration. It is advantageous that electric vehicle charging can be controlled to a certain degree. This research provides better understanding of real distribution networks’ operation, proposing specific operational points through minimizing electric vehicle charging effects. The probabilistic Monte Carlo method on high performance computers is used for the calculations.

1. Introduction

A plethora of studies have been conducted to enhance understanding of electric vehicle connection to the grid [1], and to define expectations for electricity grid performance when distributed generation also plays its own important role [2,3]. These two, relatively new components require wise consideration [4] in order to enhance grids’ productivity; this has to be done in a manner which is interconnected [5]. One approach could be electric vehicles that are aggregated to a virtual power plant [6]; in conjunction to renewables generation, the degree to which they are able to increase grid capacity factors is investigated. Moreover, aggregation offers operational benefits to the system operator [7], who is then able to take faster and safer operational decisions. Electric vehicles batteries can present energy storage opportunities for the grid if customer comfort is lightly compromised. Under these conditions, it can provide short-term reserves and offer additional grid flexibility [8].
The increase of available computational power has also transferred to power system applications, thereby advancing the capability of researchers and operators to improve grid performance. This is a one-way path, due to the existing and increasing complexity of the addition of smart devices to the grid. Electric transportation is considered an important factor in this field [9]. Special attention is given to high performance computing (HPC) applications that use probabilistic methods, which are demanding in terms of calculations, but necessary to understand specific phenomena with adequate accuracy. Electric vehicle connections to the grid and the Monte Carlo method is an example [10]. However, stochastic methods, and especially Monte Carlo [11], is computationally demanding even for today’s standards; hence, specific operational points are developed in this study for a specific network [12].
Electric vehicles charging would also require a grid expansion design factor [13]. Current research on electric vehicles, as far as the distribution network is concerned, gives emphasis to probabilistic methods in order to predict charging patterns, and predict the expected charging behavior. This also affects the connection points for distributed generations, that could be optimally different if connected points are based on probabilistic methods, taking into consideration their intermittency [14]. As far as electric vehicles are concerned, the first step is to characterize their charging demand [15]. In some cases, the system is simulated as a whole, and the operational benefits are optimized based on electric charging owners’ behavior [16]. Alternatively, they are connected in a way that relieves distribution system constraints [17]. Active distribution network management could be done by aggregating electric vehicle behavior in a probabilistic manner [12]. Probabilistic studies have also shown good correlation between electric vehicles and renewables [18]. In this research, electric vehicle and load aggregation is performed on the level of a secondary distribution system, at the point of medium voltage (MV)/low voltage (LV) connection, and it is fully controlled.
Having mentioned the above, several studies have researched the emerging phenomenon of electric vehicles. All of them are consumer oriented, giving emphasis to electric vehicles per se, and showing minimal consideration for the electricity grid. On the other hand, the research presented in the current paper is electric grid oriented. It is focused in the procedure of creating optimal electric grid operation points for electric vehicle charging for a real distribution network [19], i.e., as it operates today, based on objective equations, solved with Monte Carlo using high performance computing.

2. Line under Investigation

This method is applied to a real representative distribution network [19]. Details of the network are available at the online dataset (http://dx.doi.org/10.7910/DVN/1I6MKU). Source code and data sets are open sourced to all users. This network spans fifty-five kilometers (55 km), a typical size for distribution rural lines, and its total installed load capacity is twelve mega-volt-amperes (12MVA). It is radially organized, and all conductors are optimized based on the expectation that higher currents appear near the feeder at the high to medium voltage substation.
It has forty-five (45) medium-to-low voltage transformers that are used to supply low voltage loads. These are the expected points for the aggregated connection of electric vehicles. The electric vehicles are connected to the secondary distribution network at low voltage levels, i.e., after the medium to low voltage transformers. It is assumed that the maximum load, including electric vehicles’, does not exceed the maximum observed active and reactive power of the existing installations. In this manner, the maximum utilization of the network is achieved.
Given that distribution network is limited, solar irradiation does not change significantly across the line. According to this assumption, production from photovoltaic plants could be safely assumed to be similar. Hence, the plants connected to the line under investigation would operate at the same percentage of installed capacity. There are also twenty-four (24) photovoltaic plants with an installed capacity totaling to 6929 ΜW. This network is not connected to any other type of distributed generation. The network in detail is available at [19].

3. Monte Carlo and Power Flow Methods

The Monte Carlo method is applied to numerically stochastic processes, and is used to simulate probabilistic physical phenomena. For this research, it is assumed that each of the forty-five (45) loading nodes of the line under consideration in this analysis can independently receive an active load Sn of up to 1 pu of its capacity:
0 S 1 S 45 1   pu
To achieve this input, a one-dimension table with 45 rows is defined that is assigned continuous random variables with values from 0 to 1. According to the following definition, a continuous random variable x has the properties of the function:
f ( x ) d x = F ( ) = 1
In other words, probability is uniform across all applicable values. However, in the reality of modern computing, absolute random numbers cannot be produced. Pseudorandom numbers are used, with satisfactory results. Pseudorandom number also demonstrate additional research related benefits. The same procedure has always been used to produce them, i.e., they are always the same for a given application. Therefore, results are replicable, hence better benchmarked and controlled.
AC power flow is the typical procedure for solving problems of power systems steady state analysis, which is also applied to this research [20]; it is a widely used and well-known procedure [21]. A typical element has the following admittance Yij:
Y i j = | Y i j | < Θ i j = | Y i j | c o s Θ i j + j | Y i j | s i n Θ i j = G i j + j B i j
and the voltage of a given bus is given as:
V i = | V i | < δ i = | V i | c o s δ i + j | V i | s i n δ i
the current of this bus is given from:
I i = Y i 1 V 1 + Y i 2 V 2 + + Y i n V n = n = 1 N Y i n V n
and its active and reactive power:
P i + j Q j = V i * n = 1 N Y i n V n
which makes:
P i + j Q j = n = 1 N | Y i n V n V i | < ( Θ i n + δ n δ i )
P i = n = 1 N | Y i n V n V i | c o s ( Θ i n + δ n δ i )
Q i = n = 1 N | Y i n V n V i | s i n ( Θ i n + δ n δ i )
at every time the scheduled power needs to be similar to the calculated:
Δ P i = P i , s c h P i , c a l c = ( P g i P d i ) P i , c a l c
Δ Q i = Q i , s c h Q i , c a l c = ( Q g i Q d i ) Q i , c a l c
and consequently
g i = P i P i , s c h = P i ( P g i P d i ) = 0
g i = Q i Q i , s c h = Q i ( Q g i Q d i ) = 0
the total active power loss is calculated by subtracting from the total generation the total load
P L = i = 1 N P i = i = 1 N P g i i = 1 N P d i
and similarly, for the reactive power
i = 1 N Q i = i = 1 N Q g i i = 1 N Q d i
Newton-Raphson is the numerical method used to solve the above-mentioned equations. A short description is provided below. If two equations are considered:
g 1 ( x 1 , x 2 , u ) = h 1 ( x 1 , x 2 , u ) b 1 = 0
g 2 ( x 1 , x 2 , u ) = h 2 ( x 1 , x 2 , u ) b 2 = 0
then, the solutions x 1 * and x 2 * can be yielded from:
g 1 ( x 1 * , x 2 * , u ) = g 1 ( x 1 ( 0 ) + Δ x 1 ( 0 ) , x 2 ( 0 ) + Δ x 2 ( 0 ) , u ) = 0
g 2 ( x 1 * , x 2 * , u ) = g 2 ( x 1 ( 0 ) + Δ x 1 ( 0 ) , x 2 ( 0 ) + Δ x 2 ( 0 ) , u ) = 0
And then expanding in Taylor series:
g 1 ( x 1 * , x 2 * , u ) = g 1 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) +   Δ x 1 ( 0 ) g 1 x 1 | 0 + Δ x 2 ( 0 ) g 1 x 2 | 0 + = 0
g 2 ( x 1 * , x 2 * , u ) = g 2 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) +   Δ x 1 ( 0 ) g 2 x 1 | 0 + Δ x 2 ( 0 ) g 2 x 2 | 0 + = 0
which can be rewritten as:
[ g 1 x 1 g 1 x 2 g 2 x 1 g 2 x 2 ] ( 0 ) [ Δ x 1 ( 0 ) Δ x 2 ( 0 ) ] = [ 0 g 1 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) 0 g 2 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) ]   = [ b 1 h 1 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) b 2 h 2 ( x 1 ( 0 ) , x 2 ( 0 ) , u ) ]
where the Jacobian matrix is:
J ( 0 ) = [ g 1 x 1 g 1 x 2 g 2 x 1 g 2 x 2 ] ( 0 )
this gives:
J ( 0 ) [ Δ x 1 ( 0 ) Δ x 2 ( 0 ) ] = [ Δ g 1 ( 0 ) Δ g 2 ( 0 ) ]
and the new estimates are:
x 1 ( 1 ) = x 1 ( 0 ) + Δ x 1 ( 0 )
x 2 ( 1 ) = x 2 ( 0 ) + Δ x 2 ( 0 )

4. Simulation Procedure

The source code for this publication has been simulated on Mathworks Matlab Runtime v92, 2017a [22], compiled on Unix operating system and run on Aris high performance computing [23]. High performance computing was not necessary to achieve the research goals; however, it reduces computational time and provides the capability of scaling up to larger electricity networks. Power load flow analysis is conducted on Matpower 6.0 code [24,25]. The source code and the results are provided in the supplementary materials of this manuscript, available on Harvard Dataverse [26].
Figure 1 presents the flow chart for the proposed calculation method. Initially, the algorithm inputs the distribution network data. This includes information of its load and production nodes connection, line characteristics, as well as their impedance and reactance to perform load flow calculations. Then the system creates random loading using the Monte Carlo method [11] for all applicable nodes, and performs load flow analysis.
The procedure repeats numerous times in order to cover all applicable cases, and the best result is stored for each operational point. An ARIS high performance computer was able to simulate each one of the operational points, using one processor, in 48 h [23]. Source code total calculation time can be improved if the number of Monte Carlo iterations are reduced, but this could lead to suboptimal results. This source code may also run on personal computers, but usually higher computational times are required.
The default solver uses Newton’s method [20]. This type of analysis is adequate to perform load aggregation and production analysis in a steady state.
The objective functions applied to this research take into consideration the maximum electric vehicle charging load and the minimum voltage across the network, based on the available production from distributed generation. From these two aspects, the charging load is more important to the analysis, and consequently, it receives a higher contribution factor. The final objective is achieved by minimizing the following equations:
f 1 ( x ) = min 0 x 1 ( 0.5 P E V ( x ) + 0.5 V m i n ( x ) )
f 2 ( x ) = min 0 x 1 ( 0.6 P E V ( x ) + 0.4 V m i n ( x ) )
f 3 ( x ) = min 0 x 1 ( 0.7 P E V ( x ) + 0.3 V m i n ( x ) )
f 4 ( x ) = min 0 x 1 ( 0.8 P E V ( x ) + 0.2 V m i n ( x ) )
where:
Pev stands for the total active load of the line. It is assumed that cos φ 1 .
P e v = 1 45 S n S t o t ,   where   S t o t   is   the   sum   of   all   loads   installed   capacity
and Vmin is the minimum voltage observed at any node of the line.
All the above are calculated for increasing production from the connected-to-the-network distributed generation sources, such as photovoltaic plants. Then ten optimal operational points for each optimization equation were created, increasing renewables’ production from zero to maximum. These are operational points for a given network based on the availability of energy produced from renewables that meet the above-mentioned objective functions.

5. Results and Discussion

Simulation results have shown consistency across all applications to this work’s minimization formulas. According to the conducted simulations, there are repeating loading optimization patterns, unique for each line according to the imposed constraints in terms of distributed generation production and minimization requirements.
For f 1 ( x ) there are five (5) operational points (Table 1 and Table 2) across the installed capacity of the distributed generation connected to the line. For each transformer connection node, the load percentage in conjunction to the maximum observed load has been calculated. It was observed that in some cases, this percentage is very low. This is due to the specific characteristics of the line, and hence, reinforcement is suggested near these transformers.
The exact manner in which this reinforcement shall be done is not currently clear to the researchers. A probabilistic approach can be applied, which can be part of future work. To achieve better performance, it is proposed that messed, instead of radial, topology be applied; however, issues of protection may arise.
For f 2 ( x ) , there are three (3) operational points (Table 3 and Table 4) across the installed capacity of the distributed generation connected to the line. To a certain degree, these are similar to the operational points derived from the other equations. This observation further supports the possibility of having line-specific optimal operation points across a wide range of operating conditions. This is to be further investigated.
For f 3 ( x ) , there are three (3) operational points (Table 5) across the installed capacity of the distributed generation connected to the line.
For f 4 ( x ) there are two (2) operational points (Table 6) across the installed capacity of the distributed generation connected to the line.
It must be noted that, even if the equation results show an increasing value, the optimal line operation points remain, to a certain degree, of the same value. It appears that these are unique for each line, and can be pre-calculated. System operators, being able to affect electric vehicles’ load, can adjust grid’s operation near to these points. Grid reinforcements can be constructed on the objective of optimizing the optimization points, thereby achieving even better line performance when electric vehicles are to be connected. Moreover, in an effort to validate the obtained results, a genetic algorithm is applied in order to minimize the objective functions (25)–(28). Genetic algorithms are widely applied in science and engineering for solving practical search and optimization problems. The same algorithm gives excellent results in several other optimization problems [27,28,29]. The obtained results of the two applied methodologies (Table 7 and Table 8) present adequate convergence, confirming the appropriateness of the proposed methodology.

6. Conclusions

This analysis provides specific operational points based on the production of the connected distributed generators. Based on these findings, potential charging service providers are able to optimize the charging of electric vehicles connected to the line under investigation. In this way, optimal operations could be achieved. It should be mentioned that it is possible to provide optimization formulas for minimizing line losses or maximizing transferred energy using the provided algorithm.
Loading patterns appear to be consistent across all performed calculations. It is believed that they are connected to the topology of the line, and are to a certain degree unconnected to the load. This is an important observation that requires further investigation.
It is observed that several transformer connection nodes display low percentages of optimal load. To the authors’ understanding, these are the areas of the grid that need reinforcement. The reinforcement can be done in a manner for the grid whereby the radial configuration is lost. In this case, new calculations are required.
Simulation results have shown improving performance of the grid for increasing production from distributed generators. This is an expected observation; however, the performed simulations are able to provide quantification.
Future work will include the creation of active protection systems based on pragmatic conditions operational system diagnosis, and further probabilistic analysis for possible reinforcements.

Supplementary Materials

All data and results of this work are available at S. Lazarou, V. Vita, C. Christodoulou and L. Ekonomou, “Replication Data for: Calculating operational patterns for electric vehicle charging on a real distribution network based on renewables’ production,” Available: http://dx.doi.org/10.7910/DVN/1MWESP and on Researchgate.com.

Author Contributions

All authors contributed equally to the development of this manuscript.

Funding

The authors acknowledge financial support for the open source publication of this work from the Special Account for Research of ASPETE through the funding program “Strengthening research of ASPETE faculty members” under the project “DECA”.

Acknowledgments

This work was supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility—ARIS—under project ID pa171102 [22]. The authors would like to acknowledge researchgate.com and Energies’ MDPI reviewers who supported our work providing improvements.

Conflicts of Interest

The authors declare no conflict of interest.

Nomenclature

LhBranch line length (in km)
RBranch line Ohmic resistance per km (in Ω/km)
LBranch line Reactance per km (in Ω/km)
S1First load transformer Complex-Apparent power (in kVA)
S2Second load transformer Complex-Apparent power (in kVA)
S45Last load transformer Complex-Apparent power (in kVA)
P1, maxFirst transformer maximum observed load (active power) (in kW)
P2, maxSecond transformer maximum observed load (active power) (in kW)
P45, maxLast transformer maximum observed load (active power) (in kW)
StotTotal load installed capacity (in kVA)
P1First photovoltaic plant Active production power (in kW)
P2Second photovoltaic plant Active production power (in kW)
P24Last photovoltaic plant Active production power (in kW)
Pev Total active load of the line
Vmin Minimum voltage observed at any node
f_1 (x)First objective function
f_2 (x)Second objective function
f_3 (x)Third objective function
f_4 (x)Forth objective function

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Figure 1. Calculating operational points optimization formula minimums.
Figure 1. Calculating operational points optimization formula minimums.
Energies 11 02400 g001
Table 1. Optimal loading per node according to f 1 ( x ) for increasing production up to 50% of the distributed generator’s installed capacity.
Table 1. Optimal loading per node according to f 1 ( x ) for increasing production up to 50% of the distributed generator’s installed capacity.
#Transformer f 1 ( x ) -without DG (Percentage of Maximum Observed Load) f 1 ( x ) -10% DG (Percentage of Maximum Observed Load) f 1 ( x ) -20% DG (Percentage of Maximum Observed Load) f 1 ( x ) -30% DG (Percentage of Maximum Observed Load) f 1 ( x ) -40% DG (Percentage of Maximum Observed Load) f 1 ( x ) -50% DG (Percentage of Maximum Observed Load)
280.83820.03010.83820.81770.39080.152
310.88580.90230.88580.95980.94250.885
390.90490.91120.90490.86880.98940.9194
450.97620.9250.97620.97960.92810.9924
490.34720.94780.34720.92350.92670.8259
610.68710.97020.68710.1240.83820.478
740.82760.4520.82760.75960.18540.9877
800.16460.61750.16460.32510.27750.3298
890.97330.84010.97330.87110.8440.8278
910.51420.79130.51420.25990.84620.8417
920.67640.91310.67640.89970.86840.9708
39_180.99340.91860.99340.84580.71570.9316
39_510.90750.91670.90750.82530.94410.9404
39_51_30.83750.78770.83750.37920.28890.0673
39_940.84070.54230.84070.82350.91480.957
45_16A0.89670.94740.89670.83950.3140.6439
45_1A_40.27020.61340.27020.79970.82430.7673
49_90.74560.39740.74560.42330.28740.9802
61_10_60.31270.90370.31270.60780.92380.7111
61_280.58560.57350.58560.88730.75830.1116
61_28_90.84310.8870.84310.32720.68550.9387
61_32_160.32560.82480.32560.68240.54530.0672
61_32_1620.45620.43510.45620.57590.54380.5693
61_32_310.38940.03610.38940.80390.19640.6203
61_32_31_10.14940.16450.14940.03440.30470.533
61_450.07550.64390.07550.80280.92170.0153
61_45_120.86850.44860.86850.97130.49820.8222
61_45_4A_10.19510.30190.19510.79560.22720.879
61_50.69460.95720.69460.81170.6190.9783
61_6_6A0.75010.12190.75010.51610.28910.7149
61_7_20.70860.62270.70860.55810.70630.919
61_7_2_1A_20.35830.86710.35830.75130.40760.5091
61_7_2_20.23940.40190.23940.65230.7160.4857
61_7_80.86120.99420.86120.86260.80570.9161
68_30.71480.8070.71480.64590.22320.851
74_1A_40.77450.24040.77450.85690.83630.7064
74_1A_4_60.5960.55710.5960.17760.52020.4533
87_30.24530.32630.24530.11830.91590.8033
87_3_10.5980.84870.5980.120.89480.9351
92_21_4_30.17930.60660.17930.49770.17640.912
92_21_660.78710.57320.78710.74460.74690.1158
92_21A0.30660.6760.30660.86690.7990.3738
92_30_10.2010.54760.2010.50930.0330.8454
92_400.46730.36910.46730.18720.24730.1147
92_8_10.92490.00750.92490.2470.43040.2284
Table 2. Optimal loading per node according to f 1 ( x ) , for increasing production from to 50% to full of the distributed generator’s installed capacity.
Table 2. Optimal loading per node according to f 1 ( x ) , for increasing production from to 50% to full of the distributed generator’s installed capacity.
#Transformer f 1 ( x ) -60% DG, 70% DG, 80% DG, 90% DG and Full DG Production (Percentage of Maximum Observed Load)#Transformer f 1 ( x ) -60% DG, 70% DG, 80% DG, 90% DG and Full DG Production (Percentage of Maximum Observed Load)#Transformer f 1 ( x ) -60% DG, 70% DG, 80% DG, 90% DG and Full DG Production (Percentage of Maximum Observed Load)
280.15245_16A0.643961_7_20.919
310.88545_1A_40.767361_7_2_1A_20.5091
390.919449_90.980261_7_2_20.4857
450.992461_10_60.711161_7_80.9161
490.825961_280.111668_30.851
610.47861_28_90.938774_1A_40.7064
740.987761_32_160.067274_1A_4_60.4533
800.329861_32_1620.569387_30.8033
890.827861_32_310.620387_3_10.9351
910.841761_32_31_10.53392_21_4_30.912
920.970861_450.015392_21_660.1158
39_180.931661_45_120.822292_21A0.3738
39_510.940461_45_4A_10.87992_30_10.8454
39_51_30.067361_50.978392_400.1147
39_940.95761_6_6A0.714992_8_10.2284
Table 3. Optimal loading per node according to f 2 ( x ) for increasing production up to 50% of the distributed generator’s installed capacity.
Table 3. Optimal loading per node according to f 2 ( x ) for increasing production up to 50% of the distributed generator’s installed capacity.
#Transformer f 2 ( x ) -without DG, 10% DG (Percentage of Maximum Observed Load) f 2 ( x ) -20% DG, 30% DG, 40% DG and 50% DG (Percentage of Maximum Observed Load)#Transformer f 2 ( x ) -without DG, 10% DG (Percentage of Maximum Observed Load) f 2 ( x ) -20% DG, 30% DG, 40% DG and 50% DG (Percentage of Maximum Observed Load)
280.03010.15261_32_310.03610.6203
310.90230.88561_32_31_10.16450.533
390.91120.919461_450.64390.0153
450.9250.992461_45_120.44860.8222
490.94780.825961_45_4A_10.30190.879
610.97020.47861_50.95720.9783
740.4520.987761_6_6A0.12190.7149
800.61750.329861_7_20.62270.919
890.84010.827861_7_2_1A_20.86710.5091
910.79130.841761_7_2_20.40190.4857
920.91310.970861_7_80.99420.9161
39_180.91860.931668_30.8070.851
39_510.91670.940474_1A_40.24040.7064
39_51_30.78770.067374_1A_4_60.55710.4533
39_940.54230.95787_30.32630.8033
45_16A0.94740.643987_3_10.84870.9351
45_1A_40.61340.767392_21_4_30.60660.912
49_90.39740.980292_21_660.57320.1158
61_10_60.90370.711192_21A0.6760.3738
61_280.57350.111692_30_10.54760.8454
61_28_90.8870.938792_400.36910.1147
61_32_160.82480.067292_8_10.00750.2284
61_32_1620.43510.5693
Table 4. Optimal loading per node according to f 2 ( x ) for increasing production from to 50% to full of the distributed generator’s installed capacity.
Table 4. Optimal loading per node according to f 2 ( x ) for increasing production from to 50% to full of the distributed generator’s installed capacity.
#Transformer f 2 ( x ) -60% DG, 70% DG, 80% DG and 90% DG (Percentage of Maximum Observed Load) f 2 ( x ) -full DG Production (Percentage of Maximum Observed Load)#Transformer f 2 ( x ) -60% DG, 70% DG, 80% DG and 90% DG (Percentage of Maximum Observed Load) f 2 ( x ) -Full DG Production (Percentage of Maximum Observed Load)
280.1520.531161_32_310.62030.3476
310.8850.905161_32_31_10.5330.8526
390.91940.96861_450.01530.881
450.99240.94561_45_120.82220.5916
490.82590.618461_45_4A_10.8790.7937
610.4780.617561_50.97830.5695
740.98770.050461_6_6A0.71490.5387
800.32980.916661_7_20.9190.6669
890.82780.856161_7_2_1A_20.50910.765
910.84170.935961_7_2_20.48570.8833
920.97080.899961_7_80.91610.9672
39_180.93160.91568_30.8510.537
39_510.94040.918974_1A_40.70640.3431
39_51_30.06730.22374_1A_4_60.45330.0839
39_940.9570.759787_30.80330.4673
45_16A0.64390.947487_3_10.93510.65
45_1A_40.76730.992892_21_4_30.9120.4871
49_90.98020.931792_21_660.11580.8276
61_10_60.71110.584792_21A0.37380.9753
61_280.11160.036892_30_10.84540.4514
61_28_90.93870.313392_400.11470.969
61_32_160.06720.161692_8_10.22840.7028
61_32_1620.56930.7703
Table 5. Optimal loading per node according to f 3 ( x ) for increasing production up to the distributed generator’s installed capacity.
Table 5. Optimal loading per node according to f 3 ( x ) for increasing production up to the distributed generator’s installed capacity.
#Transformer f 3 ( x ) -without DG (Percentage of Maximum Observed Load) f 3 ( x ) -10% DG, 20% DG, 30% DG and 40% DG (Percentage of Maximum Observed Load) f 3 ( x ) -50% DG, 60% DG, 70% DG, 80% DG, 90% DG and Full DG Production (Percentage of Maximum Observed Load)
280.03010.1520.5311
310.90230.8850.9051
390.91120.91940.968
450.9250.99240.945
490.94780.82590.6184
610.97020.4780.6175
740.4520.98770.0504
800.61750.32980.9166
890.84010.82780.8561
910.79130.84170.9359
920.91310.97080.8999
39_180.91860.93160.915
39_510.91670.94040.9189
39_51_30.78770.06730.223
39_940.54230.9570.7597
45_16A0.94740.64390.9474
45_1A_40.61340.76730.9928
49_90.39740.98020.9317
61_10_60.90370.71110.5847
61_280.57350.11160.0368
61_28_90.8870.93870.3133
61_32_160.82480.06720.1616
61_32_1620.43510.56930.7703
61_32_310.03610.62030.3476
61_32_31_10.16450.5330.8526
61_450.64390.01530.881
61_45_120.44860.82220.5916
61_45_4A_10.30190.8790.7937
61_50.95720.97830.5695
61_6_6A0.12190.71490.5387
61_7_20.62270.9190.6669
61_7_2_1A_20.86710.50910.765
61_7_2_20.40190.48570.8833
61_7_80.99420.91610.9672
68_30.8070.8510.537
74_1A_40.24040.70640.3431
74_1A_4_60.55710.45330.0839
87_30.32630.80330.4673
87_3_10.84870.93510.65
92_21_4_30.60660.9120.4871
92_21_660.57320.11580.8276
92_21A0.6760.37380.9753
92_30_10.54760.84540.4514
92_400.36910.11470.969
92_8_10.00750.22840.7028
Table 6. Optimal loading per node according to f 4 ( x ) for increasing production up to the distributed generator’s installed capacity.
Table 6. Optimal loading per node according to f 4 ( x ) for increasing production up to the distributed generator’s installed capacity.
#Transfomer f 4 ( x ) -without DG, 10% DG, 20% DG, 30% DG, 40% DG, 50% DG and 60% DG (Percentage of Maximum Observed Load) f 4 ( x ) -70% DG, 80% DG and 90% DG (Percentage of Maximum Observed Load) f 4 ( x ) -Full DG Production (Percentage of Maximum Observed Load)
280.53110.1520.5311
310.90510.8850.9051
390.9680.91940.968
450.9450.99240.945
490.61840.82590.6184
610.61750.4780.6175
740.05040.98770.0504
800.91660.32980.9166
890.85610.82780.8561
910.93590.84170.9359
920.89990.97080.8999
39_180.9150.93160.915
39_510.91890.94040.9189
39_51_30.2230.06730.223
39_940.75970.9570.7597
45_16A0.94740.64390.9474
45_1A_40.99280.76730.9928
49_90.93170.98020.9317
61_10_60.58470.71110.5847
61_280.03680.11160.0368
61_28_90.31330.93870.3133
61_32_160.16160.06720.1616
61_32_1620.77030.56930.7703
61_32_310.34760.62030.3476
61_32_31_10.85260.5330.8526
61_450.8810.01530.881
61_45_120.59160.82220.5916
61_45_4A_10.79370.8790.7937
61_50.56950.97830.5695
61_6_6A0.53870.71490.5387
61_7_20.66690.9190.6669
61_7_2_1A_20.7650.50910.765
61_7_2_20.88330.48570.8833
61_7_80.96720.91610.9672
68_30.5370.8510.537
74_1A_40.34310.70640.3431
74_1A_4_60.08390.45330.0839
87_30.46730.80330.4673
87_3_10.650.93510.65
92_21_4_30.48710.9120.4871
92_21_660.82760.11580.8276
92_21A0.97530.37380.9753
92_30_10.45140.84540.4514
92_400.9690.11470.969
92_8_10.70280.22840.7028
Table 7. Minimization results for f 1 ( x ) and f 2 .
Table 7. Minimization results for f 1 ( x ) and f 2 .
Monte CarloGA Monte CarloGA
f 1 ( x ) -without DG0.76830.7944 f 2 ( x ) -without DG0.75980.7865
f 1 ( x ) -10% DG0.78720.7942 f 2 ( x ) -10% DG0.77560.7857
f 1 ( x ) -20% DG0.79970.7958 f 2 ( x ) -20% DG0.78730.7926
f 1 ( x ) -30% DG0.80970.7997 f 2 ( x ) -30% DG0.79810.7918
f 1 ( x ) -40% DG0.81750.8265 f 2 ( x ) -40% DG0.80730.8117
f 1 ( x ) -50% DG0.82610.8346 f 2 ( x ) -50% DG0.81550.8316
f 1 ( x ) -60% DG0.83510.8487 f 2 ( x ) -60% DG0.82260.8500
f 1 ( x ) -70% DG0.8430.8346 f 2 ( x ) -70% DG0.8290.8328
f 1 ( x ) -80% DG0.84990.8425 f 2 ( x ) -80% DG0.83450.8329
f 1 ( x ) -90% DG0.85210.8523 f 2 ( x ) -90% DG0.83620.8439
f 1 ( x ) -full DG production0.85370.8748 f 2 ( x ) -full DG production0.83980.8728
Table 8. Minimization results for f 3 ( x ) and f 4 ( x ) .
Table 8. Minimization results for f 3 ( x ) and f 4 ( x ) .
Monte CarloGA Monte CarloGA
f 3 ( x ) -without DG0.75980.7821 f 4 ( x ) -without DG0.76940.7694
f 3 ( x ) -10% DG0.77410.7787 f 4 ( x ) -10% DG0.77860.7786
f 3 ( x ) -20% DG0.78370.7805 f 4 ( x ) -20% DG0.78580.7858
f 3 ( x ) -30% DG0.79180.7799 f 4 ( x ) -30% DG0.79180.7918
f 3 ( x ) -40% DG0.79870.8012 f 4 ( x ) -40% DG0.79690.7969
f 3 ( x ) -50% DG0.80530.8133 f 4 ( x ) -50% DG0.80140.8014
f 3 ( x ) -60% DG0.81110.8271 f 4 ( x ) -60% DG0.80520.8052
f 3 ( x ) -70% DG0.81620.8099 f 4 ( x ) -70% DG0.8290.829
f 3 ( x ) -80% DG0.82070.8123 f 4 ( x ) -80% DG0.83450.8345
f 3 ( x ) -90% DG0.82470.8245 f 4 ( x ) -90% DG0.83620.8362
f 3 ( x ) -full DG production0.82820.8505 f 4 ( x ) -full DG production0.81660.8166

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Lazarou, S.; Vita, V.; Christodoulou, C.; Ekonomou, L. Calculating Operational Patterns for Electric Vehicle Charging on a Real Distribution Network Based on Renewables’ Production. Energies 2018, 11, 2400. https://doi.org/10.3390/en11092400

AMA Style

Lazarou S, Vita V, Christodoulou C, Ekonomou L. Calculating Operational Patterns for Electric Vehicle Charging on a Real Distribution Network Based on Renewables’ Production. Energies. 2018; 11(9):2400. https://doi.org/10.3390/en11092400

Chicago/Turabian Style

Lazarou, Stavros, Vasiliki Vita, Christos Christodoulou, and Lambros Ekonomou. 2018. "Calculating Operational Patterns for Electric Vehicle Charging on a Real Distribution Network Based on Renewables’ Production" Energies 11, no. 9: 2400. https://doi.org/10.3390/en11092400

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