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Utilization of electric vehicles and renewable energy sources used as distributed generators for improving characteristics of electric power distribution systems
Energy xxx (2015) 1e11
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Energy journal homepage: www.elsevier.com/locate/energy
Utilization of electric vehicles and renewable energy sources used as distributed generators for improving characteristics of electric power distribution systems Hassan Fathabadi* Engineering Department, Kharazmi University, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 March 2015 Received in revised form 12 June 2015 Accepted 17 June 2015 Available online xxx
In this study, different effects of EVs (electric vehicles)/PHEVs (plug-in hybrid electric vehicles) with V2G (vehicle-to-grid) connection capability and renewable energy sources used as DGs (distributed generators) on a power distribution network are analyzed. A power distribution network including CPGs (conventional power generators) located in powerhouses, different types of renewable energy sources consisting of PV (photovoltaic), WT (wind turbine) and FC (fuel cell) systems used as DGs, and EVs with V2G connection capability is considered. Limitations of the power distribution network and an objective function including the power production cost, power loss, and voltage profile that are the most significant parameters of a power grid are defined. The objective function is minimized in the four cases that are the grid with CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs. For the first time, theoretical results together with simulation verifications performed in ETAP/MATLAB environments explicitly verify that the lowest electric power production cost and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and charging/discharging EVs, while the lowest power loss is obtained by utilizing CPGs and DGs in a grid. © 2015 Elsevier Ltd. All rights reserved.
Keywords: EVs (electric vehicles) PHEVs (plug-in hybrid electric vehicles) V2G (vehicle to grid) Renewable energy sources DGs (distributed generators)
1. Introduction The usage of EVs (electric vehicles) and PHEVs (plug-in hybrid electric vehicles) has many benefits due to the issues such as air pollution, energy saving, reduction in fossil fuels consumption, etc [1e3]. It is worthwhile to note that there are also some differences between EVs and PHEVs [4]. Similarly, renewable energy sources such as wind and solar energies have been widely used to provide energy in many countries [5e8]. Renewable energy sources are generally utilized as distributed generations in traditional power distribution networks and new smart grids because they usually produce small-scale power on the sites that are close to the users. Thus, the main electric power generators are the CPGs (conventional power generators) located in powerhouses [9e15]. Improving the characteristics of renewable energy sources connected to a power grid such as grid-connected fuel cells, wind generators and photovoltaic systems has been the subject of much research [16e18]. For example, harmonic reduction of doubly fed
* Tel./fax: þ98 97145323. E-mail addresses: [email protected], [email protected].
induction wind generator connected to a distorted and unbalanced grid was reported in Ref. [19]. In a grid, a reduction in power loss can be obtained by suitably utilizing DGs in the grid that have been reported in some researches [20e22]. To reach this goal, the DGs locations in the power distribution network are very important [23e25]. It is important to note that other benefits of utilizing DGs such as probable reduction in the cost of electric power production should be studied case by case because in some cases such as utilizing diesel generators as DGs, the power production cost may even increases. On the other hand, EVs/PHEVs with vehicle to grid (V2G) connection capability have been introduced in the literature [26,27]. Analysis of different impacts of EVs/PHEVs with V2G connection capability on electric power distribution systems is an important issue. Although Li-ion batteries are practically the main storage systems used in EVs/PHEVs [28e30] but other types of electrochemical energy buffers can be also used as storage systems in EVs/PHEVs [31]. Regardless of the storage system types used in EVs/PHEVs, they play the role of distributed energy storage systems in a grid that should be involved in demand response analysis when EVs/PHEVs are connected to the grid. Research about EVs effects on power systems in Northern Europe showed that how a large-scale
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Nomenclature CDG(k,h) price of electric power produced by kth DG at t ¼ h (hour) (V/kWh) CCPG(k,h) price of electric power produced by kth CPG at t ¼ h (hour) (V/kWh) CCharge(k,h) price of electric power consumed by charging kth EV at t ¼ h (hour) (V/kWh) CDischarge(k,h) price of electric power produced by discharging kth EV at t ¼ h (hour) (V/kWh) Ctotal total cost of the electric energy produced in the grid during 24 h (V) FDG cost of the electric power produced by DGs during 24 h (V) FEV cost of the electric power produced by EVs during 24 h (V) FCPG cost of the electric power produced by CPGs during 24 h (V) NB buses number of the grid NCPG number of CPGs in the grid NDG number of DGs in the grid NEV number of EVs in the grid PDG(k,h) electric power produced by kth DG at t ¼ h (hour) (kW) PCPG(k,h) electric power produced by kth CPG at t ¼ h (hour) (kW) PDischarge(k,h) electric power produced by discharging kth EV at t ¼ h (hour) (kW) PCharge(k,h) electric power consumed by charging kth EV at t ¼ h (hour) (kW) PDGMax(k,h) maximum electric power produced by kth DG at t ¼ h (hour) (kW)
implementation of EVs/PHEVs towards 2030 would influence the power systems of five Northern European countries, Denmark, Finland, Germany, Norway, and Sweden. The provided results validated that EVs/PHEVs can significantly facilitate wind power investments. Furthermore, due to V2G connection capability, EVs/ PHEVs can reduce the need for new coal/natural gas power capacities [32]. Other research carried out in Brazil showed that a fleet of PHEVs with V2G connection capability can be used to regularize energy imbalances of the electric power distribution system in northeastern Brazil [33]. The results showed that the surplus power generated by wind farms during the day can be given back to the grid by recharging the PHEVs into the grid overnight. Impact of EVs on power system reliability was analyzed in Refs. [34], the research concludes that EVs can provide an extent for a power distribution system using a suitable charging/discharging strategy. Considering the mentioned researches, this study concerns with the analysis of different effects of EVs/PHEVs with V2G connection capability and renewable energy sources used as DGs on a electric power distribution network. A practical power distribution network including CPGs, different types of renewable energy sources used as DGs, and 60 EVs with V2G capability is considered. Limitations of a real power grid and an objective function including the electric power production cost, power loss, and voltage profile are defined and presented. Then, the objective function is minimized in the four cases that are the grid with only CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs. The main contributions of this work is that
PCPGMax(k,h) maximum electric power produced by kth CPG at t ¼ h (hour) (kW) PStore(k,h) electric power stored by kth EV at t ¼ h (hour) (kW) PUsed(k,h) electric power used by kth EV at t ¼ h (hour) (kW) PBatCapacity(k) battery capacity of kth EV (kWh) PDischargeMax(k) maximum electric power that can be discharged by kth EV (kW) PChargeMax(k) maximum electric power consumed by charging kth EV (kW) PLoad(k,h) electric power consumed by kth load at t ¼ h (hour) (kW) PLoss(h) instant active power loss in the grid at t ¼ h (hour) (kW) rkm ohmic resistance between kth bus and mth bus (U) rkk ohmic resistance of kth bus (U) Sk set of all the buses that have been directly connected to kth bus VB(k,h) voltage of kth bus at t ¼ h (hour) (V) VBp.u.(k,h) voltage of kth bus at t ¼ h (hour) (p.u.) VBp.u.Max maximum voltage bus (p.u.) VBp.u.Min minimum voltage bus (p.u.) w1 weight coefficient of the total cost in the objective function w2 weight coefficient of the active power loss in the objective function w3 weight coefficient of the t voltage profile deviation in the objective function xkk reactance of kth bus (U) xkm reactance between kth bus and mth bus (U) zkm impedance between kth bus and mth bus (U) zkk impedance of kth bus (U)
theoretical results together with simulation verifications performed in ETAP/MATLAB environments explicitly verify that the lowest electric power production cost and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and charging/discharging EVs, while the lowest power loss is obtained by utilizing CPGs and DGs in a grid. The secondary benefits of simultaneously utilizing the three mentioned power sources are energy saving and reduction in fuel consumption. The rest of the paper is organized as follows. The objective function and limitations are presented in Section 2. Section 3 deals with minimizing the objective function in the four cases and analyzing simulated results. Section 4 concludes the paper.
2. Formulizing objective function and limitations In this study, the electric energy consumed in a power distribution system is provided by the three energy sources as following: A) DGs generally consisting of renewable energy sources such as wind energy, solar energy, etc. B) Discharge of EVs into the grid using V2G connection capability. C) CPGs generally located in powerhouses. Thus, the total cost of the electric energy production in the grid during 24 h (one day) can be expressed as:
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H. Fathabadi / Energy xxx (2015) 1e11
Ctotal ¼ FDG þ FEV þ FCPG
(1)
where FDG, FEV and FCPG are the costs of the electric powers generated by the DGs, EVs and CPGs, respectively. For one day (24 h), FDG is obtained as:
3
NB X rkk jVB ðk; hÞj2 k¼1
jzkk j2
þ PLoss ðhÞ ¼
NDG X
PDG ðk; hÞ þ
k¼1
þ
NEV X
N CPG X
PCPG ðk; hÞ
k¼1
PDischarge ðk; hÞ
k¼1
FDG ¼
NDG X 24 X
PDG ðk; hÞ CDG ðk; hÞ 1 hour
(2)
k¼1 h¼1
NEV X
NB X
PLoad ðk; hÞ
k¼1
PCharge ðk; hÞ
k¼1
(9)
Similarly, FCPG is found as:
FCPG ¼
N 24 CPG X X
PCPG ðk; hÞ CCPG ðk; hÞ 1 hour
(3)
k¼1 h¼1
During charging process of EVs, they buy electric energy from the grid, so the gird has an income, but EVs sell electric energy to the grid during discharging process, so it has a cost for the grid. Thus, FEV consists of two terms, the first term which is related to EVs charging is negative while the second term associated with EVs discharging is positive. Thus, FEV is expressed as:
FEV
PCharge ðk; hÞ CCharge ðk; hÞ 1 hour
i
NB X X
PLoss ðhÞ ¼
0:5 rkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
m2Sk k¼1
(10)
Thus, the active power loss during one day (24 h) is obtained as:
PLoss24h ¼
NEV X 24 h X PDischarge ðk; hÞ CDischarge ðk; hÞ 1 hour ¼ k¼1 h¼1
where PLoss(h) is the instant active power loss in the grid at t ¼ h (hour), and is found as:
24 X
PLoss ðhÞ
h¼1
¼
(4)
NB 24 X X X
0:5rkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
h¼1 m2Sk k¼1
(11)
Similarly, the instant reactive powers distributed in the grid should satisfy the following equation at t ¼ h (hour):
2.1. Limitations There are several limitations in a grid consisting of DGs, EVs and CPGs that should be satisfied during normal operation of the grid. For DGs, the following limitation should be considered:
PDG ðk; hÞ PDGMax ðk; hÞ
(5)
where k ¼ 1, 2,..., NDG and h ¼ 1, 2,..., 24. Similar limitation should be considered for CPGs as following:
PCPG ðk; hÞ PCPGMax ðk; hÞ
(6)
where k ¼ 1, 2,..., NCPG and h ¼ 1, 2,..., 24. The rechargeable battery of each EV (electric vehicle) should satisfy the following balance equation:
PStore ðk; hÞ ¼ PStore ðk; h 1Þ þ PCharge ðk; hÞ PUsed ðk; hÞ PDischarge ðk; hÞ
NB X xkk jVB ðk; hÞj2 k¼1
¼
jzkk j NDG X k¼1
2
NB X X
þ
0:5xkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
m2Sk k¼1
QDG ðk; hÞ þ
N CPG X k¼1
QCPG ðk; hÞ
NB X
QLoad ðk; hÞ
It is worthwhile to note that EVs charging and discharging both only consist of active power transmission, so they do not produce any positive or negative reactive power. On the other hand, all the bus voltages should be more than an acceptable minimum voltage, and also less than an acceptable maximum voltage at any time as below:
VBp:u:Min VBp:u: ðk; hÞ VBp:u:Max (7)
(12)
k¼1
(13)
where k ¼ 1, 2,..., NB and h ¼ 1, 2,..., 24.
where k ¼ 1, 2,..., NEV and h ¼ 1, 2,..., 24. The following limitations should be considered when Eq. (7) is numerically solved:
8 24 > P > > PStore ðk; hÞ 1 hour PBatCapacity ðkÞ < h¼1
> PDischarge ðk; hÞ PDischargeMax ðkÞ :X > > :P ðk; hÞ P ðkÞ :Y Charge
2.2. Objective function
(8)
ChargeMax
where X and Y are binary variables (X, Y 2{0,1}), so that X. Y ¼ 0 because battery charging and discharging can not be simultaneously performed. Eq. (7) presents the systematic power balance for the rechargeable battery of each EV during daily activities consisting of the battery charging, discharging, electric power consumption, and the electric energy previously stored in the battery. Eq. (8) similarly gives the related limitations. Thus, Eqs. (7), (8) do not depend on the battery model type, and are valid for all the rechargeable battery models [35]. The instant active powers distributed in the grid should satisfy the following equation at any time such as t ¼ h (hour):
In this study, the main objectives are as below: Minimizing the total cost of the electric energy produced in the grid during 24 h (Ctotal) Minimizing the active power loss in the grid during 24 h (PLoss24h) Minimizing the deviation of all the bus voltages (voltage profile) in per unit (p.u.) from 1 p.u. Thus, there are three objectives that should be considered to form the objective function. In the objective function, each objective has a weight coefficient the value of which shows the relative importance of that objective compared to the other two objectives. Considering the three mentioned objectives, and using Eqs. (1) and (11), the objective function is defined as:
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H. Fathabadi / Energy xxx (2015) 1e11
NB X 2 2 F Ctotal ; PLoss24h ; VBp:u: ðk; hÞ ¼ w1 Ctotal þ w2 PLoss24h þ w3 k¼1 24 X VBp:u: ðk; hÞ 12
It can be summarized that to configure an optimal power grid, the objective function F(Ctotal, PLoss24h, VBp.u.(k,h)) presented with Eq. (16) should be minimized while the limitations expressed with Eqs. (5)e(10) and Eqs. (12) and (13) should be simultaneously satisfied.
h¼1
(14) where w1, w2 and w3 are the weight coefficients related to the total cost of the electric energy production, active power loss, and voltage profile deviation, respectively. They should also satisfy the following criteria:
w1 þ w2 þ w3 ¼ 1
(15)
The value of each weight coefficient should be chosen by the user based on the relative importance of its related objective that should be minimized. For example, choosing w1 ¼ 0.60, w2 ¼ 0.25, w3 ¼ 0.15 means that minimizing the electric energy production cost the weight coefficient of which is w1 has more importance compared to minimizing the active power loss and voltage profile deviation that their related weight coefficients are w2 and w3, respectively, and also minimizing the active power loss has more importance compared to minimizing the voltage profile deviation. In this research, the value of the three weight coefficients have been chosen as w1 ¼ 0.60, w2 ¼ 0.25 and w3 ¼ 0.15 by Iranian governmental Niroo Corporation which is the exclusive corporation in Iran that produces, distributes and sells electric power because the results of this research will be used by Niroo Corporation for the power distribution network of Manjil city in Iran. Thus, the objective function can be rewritten as:
2 2 F Ctotal ; PLoss24h ; VBp:u: ðk; hÞ ¼ 0:6 Ctotal þ 0:25 PLoss24h þ 0:15
NB X 24 X VBp:u: ðk; hÞ 12 k¼1 h¼1
(16)
3. Minimizing objective function, power flow and simulated results In this study, the 33-bus power distribution network shown in Fig. 1 has been considered to provide simulated results. The mentioned power distribution network is the urban power distribution network of Manjil city in Iran. The 33-bus distribution network includes 10 DGs consisting of 3 PV (photovoltaic) power generation systems, 4 WTs (wind turbines), and 3 FCs (fuel cells). The electric power produced by all the CPGs is injected into the distribution network through the bus marked with the number of 0. The specifications of the 33-bus power distribution network are summarized in Table 1. The battery charging and discharging of EVs are performed in the parking lots. The curve of the average annual load demand in the network during 24 h reported by Iranian governmental Niroo Corporation is shown in Fig. 2. In Manjil city, the load demands in winter, autumn, and spring are very similar to the average annual load demand curve shown in Fig. 2, the only important difference is in the power amounts, not in the shape and slopes of the load demand curve. Thus, the load demand optimization for the three seasons consisting of winter, autumn, and spring is similar to the load demand optimization for the average annual load demand that is performed in the rest of this section. In this research, the average annual load demand curve has been used because of extending the results of this research to the whole of the year, although a separate load demand optimization is also performed for summer season in Sub-section 3.6. The price of the electric energy delivered by the CPGs during 24 h has been summarized in Table 2. The amount and price of the electric power produced by the DGs during 24 h are also reported in Appendix 1.
Fig. 1. 33-bus power distribution network.
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H. Fathabadi / Energy xxx (2015) 1e11
produced by the CPGs and DGs as reported in Table 2 and Appendix 1. To highlight the impacts of the 10 DGs and 60 EVs, and to perform a comparative study, four cases are considered in this section. For all the cases, power flows are obtained using NRA (NewtoneRaphson algorithm) [36e38], the maximum output power of the CPGs in Eq. (6) is assumed asPCPGMax(k,h) ¼ 6 MW, and the limitations for the bus voltages are considered as0.9 V Bp.u.(k,h) 1.1, where k ¼ 1, 2,..., NB and h ¼ 1, 2,..., 24. The four cases are as below:
Table 1 Specifications of 33-bus power distribution network. Branch number
Output bus
Input bus
rij (U)
xij (U)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
0 1 1 2 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 22 23 25 26 27 28 29 30 31
1 2 18 3 22 4 5 6 25 7 8 9 10 11 12 13 14 15 16 17 19 20 21 23 24 26 27 28 29 30 31 32
0.1332 0.7122 0.2699 0.3890 0.6039 0.1911 0.7262 1.0514 1.0656 0.2007 0.3822 1.4984 0.5528 0.6033 0.7618 1.3157 0.7472 0.3280 3.0084 0.8190 1.0241 0.6518 1.2973 1.2944 0.1497 0.2901 1.0810 0.8209 0.5180 0.9946 0.3169 0.3481
0.0471 0.2517 0.0954 0.1048 0.2134 0.0515 0.1957 0.2833 0.2872 0.0541 0.1030 0.4038 0.1488 0.1626 0.2053 0.3546 0.2014 0.0884 0.8107 0.2207 0.3620 0.2304 0.4585 0.4575 0.0529 0.0782 0.2913 0.2212 0.1396 0.2680 0.0854 0.0938
5
Case 1: The 33-bus power distribution network with the CPGs. Case 2: The 33-bus power distribution network with both the CPGs and 10 DGs. Case 3: The 33-bus power distribution network with both the CPGs and 60 EVs. Case 4: The 33-bus power distribution network with the CPGs, 10 DGs and 60 EVs.
3.1. Minimizing objective function and simulated results for case 1 The produced power by the CPGs during 24 h, total cost of the electric energy production in the grid during 24 h (Ctotal), 24-h power loss (PLoss24h), and bus voltages are obtained using NRA, the load demand shown in Fig. 2, and minimizing the objective function F(Ctotal, PLoss24h, VBp.u.(k,h)) expressed with Eq. (16) while the limitations presented with Eqs. (6), (9)e(10) and Eqs. 12 and 13 are satisfied. The flow chart of the optimization process implemented for this case is shown in detail in Fig. 3. The electric power produced by the CPGs during 24 h and the voltage profile are shown in Fig. 4 and Fig. 5, respectively. The total cost of the electric energy production in the grid and power loss during 24 h are also reported in the first row of Table 4. 3.2. Minimizing objective function and simulated results for case 2 In this case, the produced power by the CPGs and 10 DGs, total cost of the electric energy production in the grid, power loss, and bus voltages are similarly obtained using NRA, the load demand shown in Fig. 2, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. (6), (9)e(10), Eqs. 12 and 13, and Eq. (5) in which PDGMax(k,h) is substituted from Appendix 1 are satisfied. The electric power produced by the CPGs and 10 DGs during 24 h, and also the voltage profile are shown in Fig. 6 and Fig. 5, respectively. The total cost of the electric energy production and power loss are also presented in the second row of Table 4. As mentioned, the DGs are three types of renewable energy sources, PV (photovoltaic), WT (wind turbine), and FC (fuel cell) that the output power of each type is shown in Fig. 7.
Fig. 2. Average annual load demand in the network during 24 h.
Sixty EVs have been considered, and all the EVs use similar rechargeable Li-ion battery the specifications of which are summarized in Table 3. It is clear that the battery charging cost of the EVs during 24 h is determined by the price of the electric energy
3.3. Minimizing objective function and simulated results for case 3 In case 3, the 33-bus power distribution network is supplied with the electric power produced by the CPGs and recharging 60
Table 2 Price of the electric power produced by the CPGs during 24 h. Hour Price (V/kWh) Hour Price (V/kWh)
1
2
3
0.07
0.06
13 0.09
14 0.09
4 0.06
15 0.1
5 0.06
16 0.1
6
7
8
9
10
11
12
0.06
0.07
0.07
0.08
0.09
0.1
0.1
0.1
17 0.12
18 0.13
19 0.15
20 0.16
21 0.16
22 0.15
23 0.13
24 0.1
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H. Fathabadi / Energy xxx (2015) 1e11
Table 3 Specifications of the Li-ion battery used in the 60 EVs. Charge rate
Discharge rate
Battery capacity (PBatCapacity)
Transportation distance
Discharge price
5.4 kW/h
2.8 kW/h
22 kWh
160 km
0.07 (V/kWh)
Fig. 3. Flow chart of the optimization process implemented for case 1.
Fig. 4. Electric power produced by CPGs during 24 h in case 1.
Fig. 5. Comparative voltage profiles in case 1 and case 2.
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7
Table 4 Simulated results for the average annual load demand optimization: Total cost of the electric energy production and power loss for each case. Case Case Case Case Case
1 2 3 4
Ctotal (V)
CPGs (V)
V2G (V)
DGs (V)
Power loss (kW)
7606.35 7453.45 7345.30 7192.45
7606.35 6997.80 7303.85 6775.25
e e 41.45 28.75
e 455.65 e 388.45
2583.62 2246.36 2446.71 2298.48
Fig. 8. Charging/discharging the batteries of the 60 EVs during 24 h in case 3.
Fig. 6. Electric power produced by CPGs and DGs during 24 h in case 2.
EVs. The electric energy consumed by each EV for daily trip is generally between 30% and 45% of the battery capacity that is enough for a daily trip with an EV between 48 km and 72 km. The EVs are charged by the grid between 1 and 6 A M., and are discharged into the grid using V2G connection capability between 6 and 12 P M.. The electric powers absorbed/delivered during charging/discharging the batteries of the 60 EVs are shown in Fig. 8. In this case, the electric energy needed for charging the batteries of the EVs should be provided by the grid, so the load demand increases as shown in Fig. 9. It is important to note that batteries charging is perform between 1 and 6 A M. when the load demand is low, and batteries discharging is performed between 6 and 12 P M. when the load demand increases. Thus,
Fig. 7. Power produced by each type of DGs during 24 h in case 2.
Fig. 9. New load demand in the grid during 24 h in case 3.
charging and discharging the batteries effectively improves the load demand curve. The produced power by the CPGs and discharging the 60 EVs, the total cost of the electric energy production in the grid, power
Fig. 10. Electric power produced by the CPGs and discharging the EVs during 24 h in case 3.
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Fig. 13. Comparative voltage profiles in case 1 and case 4.
3.5. Analysis of the simulated results Fig. 11. Comparative voltage profiles in case 1 and case 3.
loss, and bus voltages are again obtained using NRA, the new load demand shown in Fig. 9, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 6e10 and Eqs. 12 and 13 are satisfied. The electric power produced by the CPGs and discharging the 60 EVs, and also the voltage profile are shown in Fig. 10 and Fig. 11, respectively. The total cost of the electric energy production and power loss related to case 3 are reported in the third row of Table 4. 3.4. Minimizing objective function and simulated results for case 4 In this case, the electric power consumed by the 33-bus power distribution network is provided by the CPGs, 10 DGs and recharging the 60 EVs. The produced power by the CPGs, 10 DGs and discharging the 60 EVs, total cost of the electric energy production in the grid, power loss, and bus voltages are obtained using NRA, the new load demand (loads and the power needed for charging EVs) which is shown in detail in Fig. 12, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 5e10 and Eqs. 12 and 13 are satisfied. Power balance in the grid consisting of the power loss, new load demand, electric power produced by the CPGs, 10 DGs and recharging the EVs are shown in Fig. 12. The voltage profile is shown in Fig. 13, and the total cost of the electric energy production and power loss related to the case 4 are also reported in the fourth row of Table 4.
Fig. 12. Power balance in the grid in case 4.
Comparing the simulated results obtained in the four cases for the average annual load demand in the network highlights the following items: 1) Utilizing DGs in a grid (case 2) not only decreases the total cost of electric power production but also improves the voltage profile of the grid. In this case, there is a significant reduction in the power loss of the grid that is less than all the other cases. 2) Utilizing EVs with V2G connection capability (case 3) in a grid not only decreases the power production cost and power loss but also improves the voltage profile. 3) Utilizing both DGs and EVs in a grid (case 4) effectively decreases the power production cost, and significantly improve the voltage profile. In this case, there is also a reduction in the power loss of the grid compared to case 1 and case 3. Thus, it can be summarized that the lowest power production cost and the best voltage profile are obtained by utilizing CPGs, DGs and EVs in a grid while the lowest power loss is obtained by utilizing CPGs and DGs. 3.6. Minimizing objective function and simulated results for all cases in summer In Manjil city, the load demands in winter, autumn and spring are very similar to the average annual load demand curve shown in Fig. 2, the only important difference is in the power amounts, not in the shape and slopes of the load demand curve. Thus, the load demand optimization for the three seasons, winter, autumn, and spring does not add any new results to the research, and is similar to what performed in this research for the average annual load demand. But in summer, the load demand in the power distribution network of Manjil city is considerably different from the average annual load demand because the average temperature of Manjil city is 42C+ in summer, and thus, the cooling systems consume a large amount of electric power. To make clear the point, the load demand in the power distribution network of Manjil city in summer reported by Iranian governmental Niroo Corporation is shown in Fig. 14. Similar to Sub-sections 3.1e3.4, for the four mentioned cases, the load demand optimization in summer is again performed in this Sub-section. Similarly, the electric powers absorbed/delivered during charging/discharging the batteries of the 60 EVs are again same as that shown in Fig. 8. The produced power by the CPGs, 10 DGs and discharging the 60 EVs, total cost of the electric energy production in the grid, power loss, and bus voltages are
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9
Comparing the simulated results for the summer season summarized in Table 5 with the simulated results for the average annual load demand in the network reported in Table 4 again verifies the three conclusive items highlighted in Sub-section 3.5. 4. Conclusion
Fig. 14. Load demand in the power distribution network of Manjil city in summer. Table 5 Simulated results for the load demand optimization in summer: Total cost of the electric energy production and power loss for each case. Case Case Case Case Case
1 2 3 4
Ctotal (V)
CPGs (V)
V2G (V)
DGs (V)
Power loss (kW)
9617.40 9311.65 9176.95 8944.60
9617.40 8702.25 9135.50 8432.10
e e 41.45 28.75
e 609.40 e 483.75
3208.92 2803.11 3017.86 2889.33
again obtained using NRA, the new load demand in summer shown in Fig. 14, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 5e10 and Eqs. 12 and 13 are satisfied. The total cost of the electric energy production and power loss related to the four cases are reported in Table 5.
DG number
Bus
In this paper, the effects of charging/discharging EVs/PHEVs and renewable energy sources used as DGs on a power distribution network were evaluated. The urban power distribution network of Manjil city in Iran that includes CPGs, 60 EVs with V2G connection capability, and 10 DGs consisting of 3 PV power generation systems, 4 WTs and 3 FCs was considered. Four cases that are the grid with only CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs were analyzed. The load demand optimization was separately performed for both the average annual load demand and load demand in summer. The theoretical and simulated results explicitly showed that the minimum cost of power electric production and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and EVs, while the lowest power loss is obtained by utilizing CPGs and DGs. As mentioned, this research work analyzed the effects of charging/discharging EVs/PHEVs and distributed renewable energy sources on the power distribution network of Manjil city in Iran that is an urban power distribution network. As likely future work, evaluating different effects of EVs/PHEVs and DGs on a continuous power distribution network of a specific country in which different cities have different load demands can be considered. Appendix 1. Amount and price of the electric power produced by the DGs during 24 h.
Energy type
Power (p.u.) Price (V/kWh)
Hour 1
2
3
4
5
6
7
8
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
(continued on next page)
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(continued ) DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour
DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price
9
10
11
12
13
14
15
16
9
10
11
12
13
14
15
16
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.085 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour 17
18
19
20
21
22
23
24
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
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Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Utilization of electric vehicles and renewable energy sources used as distributed generators for improving characteristics of electric power distribution systems Hassan Fathabadi* Engineering Department, Kharazmi University, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 March 2015 Received in revised form 12 June 2015 Accepted 17 June 2015 Available online xxx
In this study, different effects of EVs (electric vehicles)/PHEVs (plug-in hybrid electric vehicles) with V2G (vehicle-to-grid) connection capability and renewable energy sources used as DGs (distributed generators) on a power distribution network are analyzed. A power distribution network including CPGs (conventional power generators) located in powerhouses, different types of renewable energy sources consisting of PV (photovoltaic), WT (wind turbine) and FC (fuel cell) systems used as DGs, and EVs with V2G connection capability is considered. Limitations of the power distribution network and an objective function including the power production cost, power loss, and voltage profile that are the most significant parameters of a power grid are defined. The objective function is minimized in the four cases that are the grid with CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs. For the first time, theoretical results together with simulation verifications performed in ETAP/MATLAB environments explicitly verify that the lowest electric power production cost and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and charging/discharging EVs, while the lowest power loss is obtained by utilizing CPGs and DGs in a grid. © 2015 Elsevier Ltd. All rights reserved.
Keywords: EVs (electric vehicles) PHEVs (plug-in hybrid electric vehicles) V2G (vehicle to grid) Renewable energy sources DGs (distributed generators)
1. Introduction The usage of EVs (electric vehicles) and PHEVs (plug-in hybrid electric vehicles) has many benefits due to the issues such as air pollution, energy saving, reduction in fossil fuels consumption, etc [1e3]. It is worthwhile to note that there are also some differences between EVs and PHEVs [4]. Similarly, renewable energy sources such as wind and solar energies have been widely used to provide energy in many countries [5e8]. Renewable energy sources are generally utilized as distributed generations in traditional power distribution networks and new smart grids because they usually produce small-scale power on the sites that are close to the users. Thus, the main electric power generators are the CPGs (conventional power generators) located in powerhouses [9e15]. Improving the characteristics of renewable energy sources connected to a power grid such as grid-connected fuel cells, wind generators and photovoltaic systems has been the subject of much research [16e18]. For example, harmonic reduction of doubly fed
* Tel./fax: þ98 97145323. E-mail addresses: [email protected], [email protected].
induction wind generator connected to a distorted and unbalanced grid was reported in Ref. [19]. In a grid, a reduction in power loss can be obtained by suitably utilizing DGs in the grid that have been reported in some researches [20e22]. To reach this goal, the DGs locations in the power distribution network are very important [23e25]. It is important to note that other benefits of utilizing DGs such as probable reduction in the cost of electric power production should be studied case by case because in some cases such as utilizing diesel generators as DGs, the power production cost may even increases. On the other hand, EVs/PHEVs with vehicle to grid (V2G) connection capability have been introduced in the literature [26,27]. Analysis of different impacts of EVs/PHEVs with V2G connection capability on electric power distribution systems is an important issue. Although Li-ion batteries are practically the main storage systems used in EVs/PHEVs [28e30] but other types of electrochemical energy buffers can be also used as storage systems in EVs/PHEVs [31]. Regardless of the storage system types used in EVs/PHEVs, they play the role of distributed energy storage systems in a grid that should be involved in demand response analysis when EVs/PHEVs are connected to the grid. Research about EVs effects on power systems in Northern Europe showed that how a large-scale
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2
H. Fathabadi / Energy xxx (2015) 1e11
Nomenclature CDG(k,h) price of electric power produced by kth DG at t ¼ h (hour) (V/kWh) CCPG(k,h) price of electric power produced by kth CPG at t ¼ h (hour) (V/kWh) CCharge(k,h) price of electric power consumed by charging kth EV at t ¼ h (hour) (V/kWh) CDischarge(k,h) price of electric power produced by discharging kth EV at t ¼ h (hour) (V/kWh) Ctotal total cost of the electric energy produced in the grid during 24 h (V) FDG cost of the electric power produced by DGs during 24 h (V) FEV cost of the electric power produced by EVs during 24 h (V) FCPG cost of the electric power produced by CPGs during 24 h (V) NB buses number of the grid NCPG number of CPGs in the grid NDG number of DGs in the grid NEV number of EVs in the grid PDG(k,h) electric power produced by kth DG at t ¼ h (hour) (kW) PCPG(k,h) electric power produced by kth CPG at t ¼ h (hour) (kW) PDischarge(k,h) electric power produced by discharging kth EV at t ¼ h (hour) (kW) PCharge(k,h) electric power consumed by charging kth EV at t ¼ h (hour) (kW) PDGMax(k,h) maximum electric power produced by kth DG at t ¼ h (hour) (kW)
implementation of EVs/PHEVs towards 2030 would influence the power systems of five Northern European countries, Denmark, Finland, Germany, Norway, and Sweden. The provided results validated that EVs/PHEVs can significantly facilitate wind power investments. Furthermore, due to V2G connection capability, EVs/ PHEVs can reduce the need for new coal/natural gas power capacities [32]. Other research carried out in Brazil showed that a fleet of PHEVs with V2G connection capability can be used to regularize energy imbalances of the electric power distribution system in northeastern Brazil [33]. The results showed that the surplus power generated by wind farms during the day can be given back to the grid by recharging the PHEVs into the grid overnight. Impact of EVs on power system reliability was analyzed in Refs. [34], the research concludes that EVs can provide an extent for a power distribution system using a suitable charging/discharging strategy. Considering the mentioned researches, this study concerns with the analysis of different effects of EVs/PHEVs with V2G connection capability and renewable energy sources used as DGs on a electric power distribution network. A practical power distribution network including CPGs, different types of renewable energy sources used as DGs, and 60 EVs with V2G capability is considered. Limitations of a real power grid and an objective function including the electric power production cost, power loss, and voltage profile are defined and presented. Then, the objective function is minimized in the four cases that are the grid with only CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs. The main contributions of this work is that
PCPGMax(k,h) maximum electric power produced by kth CPG at t ¼ h (hour) (kW) PStore(k,h) electric power stored by kth EV at t ¼ h (hour) (kW) PUsed(k,h) electric power used by kth EV at t ¼ h (hour) (kW) PBatCapacity(k) battery capacity of kth EV (kWh) PDischargeMax(k) maximum electric power that can be discharged by kth EV (kW) PChargeMax(k) maximum electric power consumed by charging kth EV (kW) PLoad(k,h) electric power consumed by kth load at t ¼ h (hour) (kW) PLoss(h) instant active power loss in the grid at t ¼ h (hour) (kW) rkm ohmic resistance between kth bus and mth bus (U) rkk ohmic resistance of kth bus (U) Sk set of all the buses that have been directly connected to kth bus VB(k,h) voltage of kth bus at t ¼ h (hour) (V) VBp.u.(k,h) voltage of kth bus at t ¼ h (hour) (p.u.) VBp.u.Max maximum voltage bus (p.u.) VBp.u.Min minimum voltage bus (p.u.) w1 weight coefficient of the total cost in the objective function w2 weight coefficient of the active power loss in the objective function w3 weight coefficient of the t voltage profile deviation in the objective function xkk reactance of kth bus (U) xkm reactance between kth bus and mth bus (U) zkm impedance between kth bus and mth bus (U) zkk impedance of kth bus (U)
theoretical results together with simulation verifications performed in ETAP/MATLAB environments explicitly verify that the lowest electric power production cost and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and charging/discharging EVs, while the lowest power loss is obtained by utilizing CPGs and DGs in a grid. The secondary benefits of simultaneously utilizing the three mentioned power sources are energy saving and reduction in fuel consumption. The rest of the paper is organized as follows. The objective function and limitations are presented in Section 2. Section 3 deals with minimizing the objective function in the four cases and analyzing simulated results. Section 4 concludes the paper.
2. Formulizing objective function and limitations In this study, the electric energy consumed in a power distribution system is provided by the three energy sources as following: A) DGs generally consisting of renewable energy sources such as wind energy, solar energy, etc. B) Discharge of EVs into the grid using V2G connection capability. C) CPGs generally located in powerhouses. Thus, the total cost of the electric energy production in the grid during 24 h (one day) can be expressed as:
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H. Fathabadi / Energy xxx (2015) 1e11
Ctotal ¼ FDG þ FEV þ FCPG
(1)
where FDG, FEV and FCPG are the costs of the electric powers generated by the DGs, EVs and CPGs, respectively. For one day (24 h), FDG is obtained as:
3
NB X rkk jVB ðk; hÞj2 k¼1
jzkk j2
þ PLoss ðhÞ ¼
NDG X
PDG ðk; hÞ þ
k¼1
þ
NEV X
N CPG X
PCPG ðk; hÞ
k¼1
PDischarge ðk; hÞ
k¼1
FDG ¼
NDG X 24 X
PDG ðk; hÞ CDG ðk; hÞ 1 hour
(2)
k¼1 h¼1
NEV X
NB X
PLoad ðk; hÞ
k¼1
PCharge ðk; hÞ
k¼1
(9)
Similarly, FCPG is found as:
FCPG ¼
N 24 CPG X X
PCPG ðk; hÞ CCPG ðk; hÞ 1 hour
(3)
k¼1 h¼1
During charging process of EVs, they buy electric energy from the grid, so the gird has an income, but EVs sell electric energy to the grid during discharging process, so it has a cost for the grid. Thus, FEV consists of two terms, the first term which is related to EVs charging is negative while the second term associated with EVs discharging is positive. Thus, FEV is expressed as:
FEV
PCharge ðk; hÞ CCharge ðk; hÞ 1 hour
i
NB X X
PLoss ðhÞ ¼
0:5 rkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
m2Sk k¼1
(10)
Thus, the active power loss during one day (24 h) is obtained as:
PLoss24h ¼
NEV X 24 h X PDischarge ðk; hÞ CDischarge ðk; hÞ 1 hour ¼ k¼1 h¼1
where PLoss(h) is the instant active power loss in the grid at t ¼ h (hour), and is found as:
24 X
PLoss ðhÞ
h¼1
¼
(4)
NB 24 X X X
0:5rkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
h¼1 m2Sk k¼1
(11)
Similarly, the instant reactive powers distributed in the grid should satisfy the following equation at t ¼ h (hour):
2.1. Limitations There are several limitations in a grid consisting of DGs, EVs and CPGs that should be satisfied during normal operation of the grid. For DGs, the following limitation should be considered:
PDG ðk; hÞ PDGMax ðk; hÞ
(5)
where k ¼ 1, 2,..., NDG and h ¼ 1, 2,..., 24. Similar limitation should be considered for CPGs as following:
PCPG ðk; hÞ PCPGMax ðk; hÞ
(6)
where k ¼ 1, 2,..., NCPG and h ¼ 1, 2,..., 24. The rechargeable battery of each EV (electric vehicle) should satisfy the following balance equation:
PStore ðk; hÞ ¼ PStore ðk; h 1Þ þ PCharge ðk; hÞ PUsed ðk; hÞ PDischarge ðk; hÞ
NB X xkk jVB ðk; hÞj2 k¼1
¼
jzkk j NDG X k¼1
2
NB X X
þ
0:5xkm
jVB ðk; hÞ VB ðm; hÞj2 jzkm j2
m2Sk k¼1
QDG ðk; hÞ þ
N CPG X k¼1
QCPG ðk; hÞ
NB X
QLoad ðk; hÞ
It is worthwhile to note that EVs charging and discharging both only consist of active power transmission, so they do not produce any positive or negative reactive power. On the other hand, all the bus voltages should be more than an acceptable minimum voltage, and also less than an acceptable maximum voltage at any time as below:
VBp:u:Min VBp:u: ðk; hÞ VBp:u:Max (7)
(12)
k¼1
(13)
where k ¼ 1, 2,..., NB and h ¼ 1, 2,..., 24.
where k ¼ 1, 2,..., NEV and h ¼ 1, 2,..., 24. The following limitations should be considered when Eq. (7) is numerically solved:
8 24 > P > > PStore ðk; hÞ 1 hour PBatCapacity ðkÞ < h¼1
> PDischarge ðk; hÞ PDischargeMax ðkÞ :X > > :P ðk; hÞ P ðkÞ :Y Charge
2.2. Objective function
(8)
ChargeMax
where X and Y are binary variables (X, Y 2{0,1}), so that X. Y ¼ 0 because battery charging and discharging can not be simultaneously performed. Eq. (7) presents the systematic power balance for the rechargeable battery of each EV during daily activities consisting of the battery charging, discharging, electric power consumption, and the electric energy previously stored in the battery. Eq. (8) similarly gives the related limitations. Thus, Eqs. (7), (8) do not depend on the battery model type, and are valid for all the rechargeable battery models [35]. The instant active powers distributed in the grid should satisfy the following equation at any time such as t ¼ h (hour):
In this study, the main objectives are as below: Minimizing the total cost of the electric energy produced in the grid during 24 h (Ctotal) Minimizing the active power loss in the grid during 24 h (PLoss24h) Minimizing the deviation of all the bus voltages (voltage profile) in per unit (p.u.) from 1 p.u. Thus, there are three objectives that should be considered to form the objective function. In the objective function, each objective has a weight coefficient the value of which shows the relative importance of that objective compared to the other two objectives. Considering the three mentioned objectives, and using Eqs. (1) and (11), the objective function is defined as:
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H. Fathabadi / Energy xxx (2015) 1e11
NB X 2 2 F Ctotal ; PLoss24h ; VBp:u: ðk; hÞ ¼ w1 Ctotal þ w2 PLoss24h þ w3 k¼1 24 X VBp:u: ðk; hÞ 12
It can be summarized that to configure an optimal power grid, the objective function F(Ctotal, PLoss24h, VBp.u.(k,h)) presented with Eq. (16) should be minimized while the limitations expressed with Eqs. (5)e(10) and Eqs. (12) and (13) should be simultaneously satisfied.
h¼1
(14) where w1, w2 and w3 are the weight coefficients related to the total cost of the electric energy production, active power loss, and voltage profile deviation, respectively. They should also satisfy the following criteria:
w1 þ w2 þ w3 ¼ 1
(15)
The value of each weight coefficient should be chosen by the user based on the relative importance of its related objective that should be minimized. For example, choosing w1 ¼ 0.60, w2 ¼ 0.25, w3 ¼ 0.15 means that minimizing the electric energy production cost the weight coefficient of which is w1 has more importance compared to minimizing the active power loss and voltage profile deviation that their related weight coefficients are w2 and w3, respectively, and also minimizing the active power loss has more importance compared to minimizing the voltage profile deviation. In this research, the value of the three weight coefficients have been chosen as w1 ¼ 0.60, w2 ¼ 0.25 and w3 ¼ 0.15 by Iranian governmental Niroo Corporation which is the exclusive corporation in Iran that produces, distributes and sells electric power because the results of this research will be used by Niroo Corporation for the power distribution network of Manjil city in Iran. Thus, the objective function can be rewritten as:
2 2 F Ctotal ; PLoss24h ; VBp:u: ðk; hÞ ¼ 0:6 Ctotal þ 0:25 PLoss24h þ 0:15
NB X 24 X VBp:u: ðk; hÞ 12 k¼1 h¼1
(16)
3. Minimizing objective function, power flow and simulated results In this study, the 33-bus power distribution network shown in Fig. 1 has been considered to provide simulated results. The mentioned power distribution network is the urban power distribution network of Manjil city in Iran. The 33-bus distribution network includes 10 DGs consisting of 3 PV (photovoltaic) power generation systems, 4 WTs (wind turbines), and 3 FCs (fuel cells). The electric power produced by all the CPGs is injected into the distribution network through the bus marked with the number of 0. The specifications of the 33-bus power distribution network are summarized in Table 1. The battery charging and discharging of EVs are performed in the parking lots. The curve of the average annual load demand in the network during 24 h reported by Iranian governmental Niroo Corporation is shown in Fig. 2. In Manjil city, the load demands in winter, autumn, and spring are very similar to the average annual load demand curve shown in Fig. 2, the only important difference is in the power amounts, not in the shape and slopes of the load demand curve. Thus, the load demand optimization for the three seasons consisting of winter, autumn, and spring is similar to the load demand optimization for the average annual load demand that is performed in the rest of this section. In this research, the average annual load demand curve has been used because of extending the results of this research to the whole of the year, although a separate load demand optimization is also performed for summer season in Sub-section 3.6. The price of the electric energy delivered by the CPGs during 24 h has been summarized in Table 2. The amount and price of the electric power produced by the DGs during 24 h are also reported in Appendix 1.
Fig. 1. 33-bus power distribution network.
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H. Fathabadi / Energy xxx (2015) 1e11
produced by the CPGs and DGs as reported in Table 2 and Appendix 1. To highlight the impacts of the 10 DGs and 60 EVs, and to perform a comparative study, four cases are considered in this section. For all the cases, power flows are obtained using NRA (NewtoneRaphson algorithm) [36e38], the maximum output power of the CPGs in Eq. (6) is assumed asPCPGMax(k,h) ¼ 6 MW, and the limitations for the bus voltages are considered as0.9 V Bp.u.(k,h) 1.1, where k ¼ 1, 2,..., NB and h ¼ 1, 2,..., 24. The four cases are as below:
Table 1 Specifications of 33-bus power distribution network. Branch number
Output bus
Input bus
rij (U)
xij (U)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
0 1 1 2 2 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20 22 23 25 26 27 28 29 30 31
1 2 18 3 22 4 5 6 25 7 8 9 10 11 12 13 14 15 16 17 19 20 21 23 24 26 27 28 29 30 31 32
0.1332 0.7122 0.2699 0.3890 0.6039 0.1911 0.7262 1.0514 1.0656 0.2007 0.3822 1.4984 0.5528 0.6033 0.7618 1.3157 0.7472 0.3280 3.0084 0.8190 1.0241 0.6518 1.2973 1.2944 0.1497 0.2901 1.0810 0.8209 0.5180 0.9946 0.3169 0.3481
0.0471 0.2517 0.0954 0.1048 0.2134 0.0515 0.1957 0.2833 0.2872 0.0541 0.1030 0.4038 0.1488 0.1626 0.2053 0.3546 0.2014 0.0884 0.8107 0.2207 0.3620 0.2304 0.4585 0.4575 0.0529 0.0782 0.2913 0.2212 0.1396 0.2680 0.0854 0.0938
5
Case 1: The 33-bus power distribution network with the CPGs. Case 2: The 33-bus power distribution network with both the CPGs and 10 DGs. Case 3: The 33-bus power distribution network with both the CPGs and 60 EVs. Case 4: The 33-bus power distribution network with the CPGs, 10 DGs and 60 EVs.
3.1. Minimizing objective function and simulated results for case 1 The produced power by the CPGs during 24 h, total cost of the electric energy production in the grid during 24 h (Ctotal), 24-h power loss (PLoss24h), and bus voltages are obtained using NRA, the load demand shown in Fig. 2, and minimizing the objective function F(Ctotal, PLoss24h, VBp.u.(k,h)) expressed with Eq. (16) while the limitations presented with Eqs. (6), (9)e(10) and Eqs. 12 and 13 are satisfied. The flow chart of the optimization process implemented for this case is shown in detail in Fig. 3. The electric power produced by the CPGs during 24 h and the voltage profile are shown in Fig. 4 and Fig. 5, respectively. The total cost of the electric energy production in the grid and power loss during 24 h are also reported in the first row of Table 4. 3.2. Minimizing objective function and simulated results for case 2 In this case, the produced power by the CPGs and 10 DGs, total cost of the electric energy production in the grid, power loss, and bus voltages are similarly obtained using NRA, the load demand shown in Fig. 2, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. (6), (9)e(10), Eqs. 12 and 13, and Eq. (5) in which PDGMax(k,h) is substituted from Appendix 1 are satisfied. The electric power produced by the CPGs and 10 DGs during 24 h, and also the voltage profile are shown in Fig. 6 and Fig. 5, respectively. The total cost of the electric energy production and power loss are also presented in the second row of Table 4. As mentioned, the DGs are three types of renewable energy sources, PV (photovoltaic), WT (wind turbine), and FC (fuel cell) that the output power of each type is shown in Fig. 7.
Fig. 2. Average annual load demand in the network during 24 h.
Sixty EVs have been considered, and all the EVs use similar rechargeable Li-ion battery the specifications of which are summarized in Table 3. It is clear that the battery charging cost of the EVs during 24 h is determined by the price of the electric energy
3.3. Minimizing objective function and simulated results for case 3 In case 3, the 33-bus power distribution network is supplied with the electric power produced by the CPGs and recharging 60
Table 2 Price of the electric power produced by the CPGs during 24 h. Hour Price (V/kWh) Hour Price (V/kWh)
1
2
3
0.07
0.06
13 0.09
14 0.09
4 0.06
15 0.1
5 0.06
16 0.1
6
7
8
9
10
11
12
0.06
0.07
0.07
0.08
0.09
0.1
0.1
0.1
17 0.12
18 0.13
19 0.15
20 0.16
21 0.16
22 0.15
23 0.13
24 0.1
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H. Fathabadi / Energy xxx (2015) 1e11
Table 3 Specifications of the Li-ion battery used in the 60 EVs. Charge rate
Discharge rate
Battery capacity (PBatCapacity)
Transportation distance
Discharge price
5.4 kW/h
2.8 kW/h
22 kWh
160 km
0.07 (V/kWh)
Fig. 3. Flow chart of the optimization process implemented for case 1.
Fig. 4. Electric power produced by CPGs during 24 h in case 1.
Fig. 5. Comparative voltage profiles in case 1 and case 2.
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H. Fathabadi / Energy xxx (2015) 1e11
7
Table 4 Simulated results for the average annual load demand optimization: Total cost of the electric energy production and power loss for each case. Case Case Case Case Case
1 2 3 4
Ctotal (V)
CPGs (V)
V2G (V)
DGs (V)
Power loss (kW)
7606.35 7453.45 7345.30 7192.45
7606.35 6997.80 7303.85 6775.25
e e 41.45 28.75
e 455.65 e 388.45
2583.62 2246.36 2446.71 2298.48
Fig. 8. Charging/discharging the batteries of the 60 EVs during 24 h in case 3.
Fig. 6. Electric power produced by CPGs and DGs during 24 h in case 2.
EVs. The electric energy consumed by each EV for daily trip is generally between 30% and 45% of the battery capacity that is enough for a daily trip with an EV between 48 km and 72 km. The EVs are charged by the grid between 1 and 6 A M., and are discharged into the grid using V2G connection capability between 6 and 12 P M.. The electric powers absorbed/delivered during charging/discharging the batteries of the 60 EVs are shown in Fig. 8. In this case, the electric energy needed for charging the batteries of the EVs should be provided by the grid, so the load demand increases as shown in Fig. 9. It is important to note that batteries charging is perform between 1 and 6 A M. when the load demand is low, and batteries discharging is performed between 6 and 12 P M. when the load demand increases. Thus,
Fig. 7. Power produced by each type of DGs during 24 h in case 2.
Fig. 9. New load demand in the grid during 24 h in case 3.
charging and discharging the batteries effectively improves the load demand curve. The produced power by the CPGs and discharging the 60 EVs, the total cost of the electric energy production in the grid, power
Fig. 10. Electric power produced by the CPGs and discharging the EVs during 24 h in case 3.
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H. Fathabadi / Energy xxx (2015) 1e11
Fig. 13. Comparative voltage profiles in case 1 and case 4.
3.5. Analysis of the simulated results Fig. 11. Comparative voltage profiles in case 1 and case 3.
loss, and bus voltages are again obtained using NRA, the new load demand shown in Fig. 9, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 6e10 and Eqs. 12 and 13 are satisfied. The electric power produced by the CPGs and discharging the 60 EVs, and also the voltage profile are shown in Fig. 10 and Fig. 11, respectively. The total cost of the electric energy production and power loss related to case 3 are reported in the third row of Table 4. 3.4. Minimizing objective function and simulated results for case 4 In this case, the electric power consumed by the 33-bus power distribution network is provided by the CPGs, 10 DGs and recharging the 60 EVs. The produced power by the CPGs, 10 DGs and discharging the 60 EVs, total cost of the electric energy production in the grid, power loss, and bus voltages are obtained using NRA, the new load demand (loads and the power needed for charging EVs) which is shown in detail in Fig. 12, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 5e10 and Eqs. 12 and 13 are satisfied. Power balance in the grid consisting of the power loss, new load demand, electric power produced by the CPGs, 10 DGs and recharging the EVs are shown in Fig. 12. The voltage profile is shown in Fig. 13, and the total cost of the electric energy production and power loss related to the case 4 are also reported in the fourth row of Table 4.
Fig. 12. Power balance in the grid in case 4.
Comparing the simulated results obtained in the four cases for the average annual load demand in the network highlights the following items: 1) Utilizing DGs in a grid (case 2) not only decreases the total cost of electric power production but also improves the voltage profile of the grid. In this case, there is a significant reduction in the power loss of the grid that is less than all the other cases. 2) Utilizing EVs with V2G connection capability (case 3) in a grid not only decreases the power production cost and power loss but also improves the voltage profile. 3) Utilizing both DGs and EVs in a grid (case 4) effectively decreases the power production cost, and significantly improve the voltage profile. In this case, there is also a reduction in the power loss of the grid compared to case 1 and case 3. Thus, it can be summarized that the lowest power production cost and the best voltage profile are obtained by utilizing CPGs, DGs and EVs in a grid while the lowest power loss is obtained by utilizing CPGs and DGs. 3.6. Minimizing objective function and simulated results for all cases in summer In Manjil city, the load demands in winter, autumn and spring are very similar to the average annual load demand curve shown in Fig. 2, the only important difference is in the power amounts, not in the shape and slopes of the load demand curve. Thus, the load demand optimization for the three seasons, winter, autumn, and spring does not add any new results to the research, and is similar to what performed in this research for the average annual load demand. But in summer, the load demand in the power distribution network of Manjil city is considerably different from the average annual load demand because the average temperature of Manjil city is 42C+ in summer, and thus, the cooling systems consume a large amount of electric power. To make clear the point, the load demand in the power distribution network of Manjil city in summer reported by Iranian governmental Niroo Corporation is shown in Fig. 14. Similar to Sub-sections 3.1e3.4, for the four mentioned cases, the load demand optimization in summer is again performed in this Sub-section. Similarly, the electric powers absorbed/delivered during charging/discharging the batteries of the 60 EVs are again same as that shown in Fig. 8. The produced power by the CPGs, 10 DGs and discharging the 60 EVs, total cost of the electric energy production in the grid, power loss, and bus voltages are
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9
Comparing the simulated results for the summer season summarized in Table 5 with the simulated results for the average annual load demand in the network reported in Table 4 again verifies the three conclusive items highlighted in Sub-section 3.5. 4. Conclusion
Fig. 14. Load demand in the power distribution network of Manjil city in summer. Table 5 Simulated results for the load demand optimization in summer: Total cost of the electric energy production and power loss for each case. Case Case Case Case Case
1 2 3 4
Ctotal (V)
CPGs (V)
V2G (V)
DGs (V)
Power loss (kW)
9617.40 9311.65 9176.95 8944.60
9617.40 8702.25 9135.50 8432.10
e e 41.45 28.75
e 609.40 e 483.75
3208.92 2803.11 3017.86 2889.33
again obtained using NRA, the new load demand in summer shown in Fig. 14, and minimizing F(Ctotal, PLoss24h, VBp.u.(k,h)) while the limitations given with Eqs. 5e10 and Eqs. 12 and 13 are satisfied. The total cost of the electric energy production and power loss related to the four cases are reported in Table 5.
DG number
Bus
In this paper, the effects of charging/discharging EVs/PHEVs and renewable energy sources used as DGs on a power distribution network were evaluated. The urban power distribution network of Manjil city in Iran that includes CPGs, 60 EVs with V2G connection capability, and 10 DGs consisting of 3 PV power generation systems, 4 WTs and 3 FCs was considered. Four cases that are the grid with only CPGs, the grid with CPGs and DGs, the grid with CPGs and EVs, and the grid with CPGs, DGs and EVs were analyzed. The load demand optimization was separately performed for both the average annual load demand and load demand in summer. The theoretical and simulated results explicitly showed that the minimum cost of power electric production and the best voltage profile are obtained by simultaneously utilizing CPGs, renewable energy sources used as DGs and EVs, while the lowest power loss is obtained by utilizing CPGs and DGs. As mentioned, this research work analyzed the effects of charging/discharging EVs/PHEVs and distributed renewable energy sources on the power distribution network of Manjil city in Iran that is an urban power distribution network. As likely future work, evaluating different effects of EVs/PHEVs and DGs on a continuous power distribution network of a specific country in which different cities have different load demands can be considered. Appendix 1. Amount and price of the electric power produced by the DGs during 24 h.
Energy type
Power (p.u.) Price (V/kWh)
Hour 1
2
3
4
5
6
7
8
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085 0.1
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
(continued on next page)
Please cite this article in press as: Fathabadi H, Utilization of electric vehicles and renewable energy sources used as distributed generators for improving characteristics of electric power distribution systems, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.063
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H. Fathabadi / Energy xxx (2015) 1e11
(continued ) DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour
DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price
9
10
11
12
13
14
15
16
9
10
11
12
13
14
15
16
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.085 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045 0.1
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
DG number
Bus
Energy type
Power (p.u.) Price (V/kWh)
Hour 17
18
19
20
21
22
23
24
Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max Price Min Max
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0.03 0.21 0 0.03 0.178 0 0.03 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.06 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.045 0.074 0 0.045 0.136 0 0.01 0.098 0 0.045
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
0 0.01 0.102 0 0.025 0.095 0 0.125 0.085 0 0 0.21 0 0 0.178 0 0 0.156 0 0.085 0.074 0 0.085 0.136 0 0.01 0.098 0 0.085
1
2
FC
2
5
FC
3
7
Wind
4
14
PV
5
15
PV
6
18
PV
7
20
Wind
8
24
Wind
9
27
FC
10
30
Wind
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Please cite this article in press as: Fathabadi H, Utilization of electric vehicles and renewable energy sources used as distributed generators for improving characteristics of electric power distribution systems, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.06.063