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Power System Considerations of Plug-In Hybrid Electric Vehicles based on a Multi Energy Carrier Model Matthias D. Galus Student Member, IEEE, G¨oran Andersson, Fellow, IEEE
Abstract— A flexible modelling technique for Plug-In Hybrid Electric Vehicles (PHEV) based on a multi energy carrier approach is presented. It is able to simulate different PHEV architectures and energy management schemes while driving and during additional grid-coupled utilization modes. In contrary to the detailed vehicle models already available, the approach simplifies the vehicle but integrates possible services for the electricity network. Hence, the model offers analysis of the consequences for PHEVs from grid interactions. Contemporaneously, due to its simplicity and flexibility, the model can be easily facilitated to generate valuable inputs for power system analysis including vast amounts of PHEVs and paving the road for an integrated transportation and power system model. Results of load curves, availability of storage and ancillary power capacity are presented. As the model is based on the energy hub approach, an integration into multi energy carrier networks is intuitive and potential interactive repercussions from the systems can be studied. Index Terms— Energy Hub, Plug-In Hybrid Electric Vehicles (PHEV), Linear Multi Step Optimization, Multi Energy Carriers, PHEV power system impacts
I. I NTRODUCTION Over the last years, climate and sociopolitical change as well as increased environmental awareness changed a specific state of mind. The quest for higher efficiencies and lower CO2 emissions has motivated interest in Plug-In Hybrid Electric Vehicles (PHEV), being an enhancement of the Hybrid Electric Vehicle (HEV). PHEVs are promising to shift energy demand for transportation from petroleum to electricity. Their main source of energy for propulsion is a large battery pack powering an electric motor and being recharged by a grid connection. For longer driving distances an internal combustion engine (ICE) can be used as an auxiliary power source while also recharging the battery [1]. The vehicles are referred to as PHEV-x, where x in the abbreviation is a value (e.g. PHEV-20, PHEV-40 etc.) denoting the total number of miles driven by electricity or the measure of petroleum displacement [2], [3]. An universal conciliation has not been found, yet. Also, [3] gives a brief introduction into PHEV specific technical terms. Different architectures and driving modes, already present for HEV, can be utilized for PHEV as well [4], [5]. The driving modes are classified in: • charge-sustaining mode: The charge-sustaining mode refers to a control scheme, that forces the battery state of charge (SOC) to stay within a narrow operating band. M.D. Galus and G. Andersson are with the Power Systems Laboratory, ETH Zurich, Switzerland
[email protected]
The depth of discharge is usually shallow. For this mode the net source is petroleum. • charge-depleting mode: The battery SOC is controlled to decrease during vehicle operation. The ICE may be on or off depending on the value of the demanded power. Often it is also referred to as blended mode [1], [5], [6]. • electric vehicle mode: This is also called the all-electric mode. Electricity is the net power source propelling the vehicle. This mode together with the charge-depleting mode is the preferable one for PHEV. • engine mode: This refers to a conventional car. The only source is petroleum often charging also the battery. Most of the past literature is dealing with the control and energy management optimization for HEV [7], [8]. Only recently more attention has been paid to model PHEV accurately using sophisticated tools [9], [10] and optimization schemes [11]– [13]. Here, global optimization schemes finding the minimum for a whole drive cycle dominate the real time optimization schemes. Promising results have been found but some of them suffer from large computational demand as they rely on complex algorithms. Implementation of simplified solutions is in progress and has shown feasibility while only investigating the exchange of power with the grid [14]. The models and techniques introduced so far are either lacking integration of grid services into the PHEV model or of integration of driving behavior into the grid-connected PHEV model. Also, introduced control schemes prove to be complex. A simple technique for holistic PHEV analysis is needed to adequately model the entities not only for vehicle applications but as well for adequate power system integration. The model to be derived in the next sections will prove feasibility and flexibility by being general, simple and integrable into power systems and their analysis. The underlying idea is to model the power system and the PHEVs with an identical approach, chosen here to be the energy hub [15]. In that way the uniform technique can be used to study repercussions on both the power and the transportation system. Implementation of interfaces is then intuitive. The approach will model the vehicle not only in driving but also for typical other modes like refuelling, charging or offering services to the grid. Crucial information on PHEV, like SOC of the battery, gasoline tank level or power demand during driving or grid service will be available for further analysis. The next paragraph introduces the energy hub approach. The third paragraph is dedicated to the derivation of the PHEV energy hub model. In paragraph IV the control scheme while
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driving is introduced for the model and simulations results are shown and explained for different utilization schemes. Also, consequences for the power system are derived by investigating new load curves, available storage and ancillary potential. The fifth paragraph finally concludes the paper.
hydrogen electricity
load
II. T HE E NERGY H UB C ONCEPT The modelling approach of energy hubs has been developed and facilitated first for power system analysis. An energy hub is defined through several attributes like inputs, outputs, energy conversion and storage [16]. With respect to inputs, the set of energy carriers is denoted by E and its members are specified by small Greek letters. Furthermore, each hub i contains a set of converters Ci . The subset Ciα ⊆ Ci contains all elements of hub i which convert α into another carrier: α, β, . . . , ω ∈ E = {electricity, hydrogen, . . .} k ∈ Ciα = {1, 2, . . . , NCiα }
(1)
The hub equation without storage is mathematically formulated through (2). Here, L, P and C are the load vector, the input vector and the conversion matrix, respectively. The conversion matrix consists of coupling factors ckαβ converting one energy carrier into another. They all include efficiencies of their respective power path.
Lω | {z }
|
Lα Lβ .. .
=
L
ckαα ckαβ .. . ckαω
ck′ βα ck′ ββ .. . ck′ βω {z C
··· ··· .. . ···
ck′′ ωα ck′′ ωβ .. . ck′′ ωω
Pα Pβ .. .
(2)
Pω } | {z } P
With respect to storage, the storage interface can be modelled similar to a converter device, with steady-state input and output power values Qα and ηα , where ηα expresses the efficiency of the charging/discharging interface expressed in equation (3). ηα =
½
ηα+ 1/ηα−
if Qα ≥ 0 (charging/standby) else (discharging)
(3)
The stored energy after a certain operating period T equals the initial storage content plus the time integral of the power. For steady-state considerations, power can be approximated by the change in energy ∆E during a time period ∆t, assuming a constant slope E˙ α = dEα /dt. Therefore, the energy in the storage in time interval T , can be expressed via equation ˜ is the power weighted by the storage interface (4), where, Q efficiency.
Eα (T ) = Eα (0) +
Z
T
˜ α (t) dt ≃ Eα (0) + ∆Eα Q
(4)
0
Adding the storage to the hub equation (2) and taking the location of the storage within the hub into account, one can rewrite the scheme in a more condensed way which is denoted in equation (5), where S is the storage coupling matrix. Its entries are the coupling factors multiplied by the storage
gasoline Fig. 1: PHEV with fuel cell modelled as Energy Hub interface efficiencies of the particular power paths. The storage vector is represented by E˙ and contains different storages and their respective power output to meet the load of the energy hub. A detailed derivation of the energy hub modelling technique can be found in [16]–[18]. ¶ µ ¡ ¢ P L = C −S (5) E˙ III. M ODELLING PHEV AS AN E NERGY H UB PHEVs, unlike to usual vehicles, can be utilized in various operating states. Potential states are introduced through equation (6). They consist of driving (D), charging (C), refuelling (RF) and possibly offering ancillary services also called regulation services (R) to the electricity network [1]. In order to integrate the states into the hub model described in the previous paragraph an operating state decision function (7) is derived. Averting redundancy, it is easily understood that the charging state can be integrated into regulation as the latter is discharging but also recharging the battery. For the rest of the paper charging will not be investigated individually. Ξ = {D, C, RF, R}
(6)
¢ ∂ ¡ D C RF R (7) ∂Ξ The kinetic load for the PHEV energy hub model while driving is calculated through Newton’s 2nd law denoted in (8) for different drive cycles constituting various behaviors and speeds [19], [20]. In this case the load is not a vector but a single value. In (8), M is the mass, v is the speed, Cr is the tire friction coefficient, Af is the cars front area, CD is the car air resistance coefficient, ρair is the air density, δ is the vehicle mass coefficient and sin(Θ) is the road’s grade. They are quantified in table II. E(Ξ) =
1 E = (M gvCr + ρair CD Af v 3 + δM v v˙ + M gv sin(Θ))∆ 2 (8) The general energy hub has to be reformulated to account for the peculiarities of PHEV. The PHEV model is denoted in equations (9)-(9c) for an architecture depicted in figure 1. The grey area in figure 1 displays the typical converter arrangement for a Series-PHEV [8] and defines the power paths through which the load can be met. The white area indicates a possible extension using a fuel cell and a hydrogen
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State D R, C RF
In-, Output Pel D Pgaso D Pgaso R Lkin Pel RF Lkin
Value 0 0 0 0 0 0
PHEV energy hub data Vehicle mass Air density Car front area Tire friction coefficient Car air resistance coefficient Vehicle mass coefficient Grade of road Gasoline storage Electric storage ICE efficiency Electric motor efficiency Electric generator efficiency Charging/discharging efficiency Regenerative breaking efficiency Battery power ICE power Battery output power derivative ICE output power derivative
TABLE I: Operating state dependency of inputs and load tank, recently investigated in [21], which shall not be under further investigations, here. In the model, the general energy hub equation is multiplied by the operating state decision function, choosing the power flow couplings within the PHEV architecture appropriate to the states. The vector P is denoting the input vector of the architecture, for which obviously only electricity and gasoline are possibly apparent. The inputs need to be differentiated for each state. There will be no inputs apparent when the vehicle is driving as it is not connected to any infrastructure. The electric input Pel can only be nonzero if the PHEV is connected to the power system. In fact, once it is connected the electric input can be positive or negative or just positive depending on whether the PHEV is in use for grid services or just charging. The kinetic load will obviously be zero in these states as the car is parked. The refuelling state is modelled accordingly but here only Pgaso will be nonzero and positive. The dissipated power Pdis is the only input being nonzero while driving as this input variable is kept always lower or equal than zero. For other states it is not relevant. Table I summarizes the load with respective inputs being zero for the operating states. µ ¶ ¡ ¢ P L = E(Ξ) C −S (9) E˙ with
cel kin D (L) cgaso kin D (L) cgaso kin R C = cel kin R cel kin RF cgaso kin RF c c (L) (L) el kin D
S=
and
ηel
cel kin R ηel cel kin RF ηel
gaso kin D
ηgaso
cgaso kin R ηgaso cgaso kin RF ηgaso
1 0 0
µ ¶ Pel Ξ E˙ el ˙ Pgaso Ξ P= E= E˙ gaso Pdis
offering grid services there cannot be a power link between the gasoline tank and the grid. The input needs to be directly related to the electric storage as the demanded/offered power from/to the grid needs to be supplied from the battery. The input while refuelling needs also to be directly related to the gasoline storage. A link to the battery is not possible. The concrete model for the PHEV is denoted (10). µ in ¶ ¡ ¢ P (10) L = E(Ξ) C −S E˙ with cel kin D (L) cgaso kin D (L) 1 1 0 0 C= (10a) 0 1 0 c c (L) (L)
In (9a), cel kin D (L) is the coupling factor from electricity input/storage to kinetic load in the driving state. It is composed of all converter efficiencies in the respective power flow path. A load dependency of the coupling factor is indicated by L. This enables integration of nonlinear efficiencies to be included into the factor. For simplicity the efficiencies of the converters are assumed constant but regenerative breaking is taken into account by mutating the factor and will be explained in the next paragraph. The other coupling factors are assumed to be independent of the load in the other operating states. The general model in equation (9) can be simplified as the coupling factors for regulation and refuelling have to be set to zero or one. These values assure a correct power flow within the hub for the specific utilization scheme. Especially while
gaso kin D
el kin D
S=
and
(9c)
gaso D
Value 1375 kg kg 1.2 m 3 2.5m2 0.015 0.4 1 0 50l 10kWh 0.21 0.90 0.75 0.7/0.9 0.3 ± 30kW 50kW ± 12kW ± 8kW
TABLE II: Simulation data
(9a)
(9b)
Symbol M ρair Af Cr CD δ Θ SOCgaso SOC ηICE ηmot ηgen ηc /ηdc ηreg ˙ E el D ˙ E gaso D P˙ el D P˙
ηel 1 ηel
ηgaso
0 1
0
ηgaso
µ ¶ Pel Ξ E˙ el P = Pgaso Ξ E˙ = E˙ gaso Pdis
(10b)
(10c)
A complete overview of the parameters, which are used to model the PHEV energy hub, is displayed in table II. They are partly assumed (e.g. specific car parameters as mass, power derivatives, etc.) and partly taken out of publications. The efficiencies of electric motors, of ICEs, for chargingdischarging batteries, regenerative breaking and power as well as energy constraints can be found [6], [22]–[26]. IV. M ULTI S TEP O PTIMIZATION FOR PHEV I NTEGRATION The model is used for multiple simulations. Determination of SOC at arrival, of load patterns or possible available storage at different nodes once the PHEV connect is relying on the anterior driving behavior of the vehicles modelled here via a multi step optimization scheme. The scheme takes the effects of past driving behavior into account by adjusting the objective function according to the actual level of the hub storages. Multiple steps are chosen for simplicity as well as to model a more realistic behavior as the individual driving cycles are not available before driving. The complete optimization scheme is denoted in (11) introducing a cost function F to be minimized
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and constraints (11a-i) imposed by the converters. The first two constraints refer to minimum and maximum power output of the ICE and the battery, respectively. Constraint (11c) refers to the SOC of the battery which needs to lie between 100% and 20%, being a value not deteriorating the battery life crucially. Constraints (11d) and (11e) refer to the power derivative bounds of the converters. Further, for the ICE usage a heuristic was chosen as the converter is regarded as an ancillary power source, only, not being in use often. The heuristic of the ICE control is implemented via constraints (11f) and (11g) and bounds the converter to a minimum of 300 seconds of running time once it is switched on. This should assure that the ICE is not intermittently switched on and off, operating inefficiently. Also, the minimum power output of the last optimization step is taken as the lower bound for the next step of the ICE in (11h). The last constraint refers to the dissipated power in each step. T ˙T min F T (E˙ el , Egaso )
s. t.
L = E(Ξ)
¡
(11)
C −S
¢
T T δgaso E˙ gaso D ≤ E˙ gaso D ˙ T ˙ ˙ E ≤E ≤E
µ
P E˙ ≤ E˙
¶ gaso D
(11a) (11b)
el D
(11c)
SOC ≤ SOC ≤ SOC T dE˙ el D ≤ P˙ el D P˙ el D ≤ dt T dE˙ gaso D P˙ gaso D ≤ ≤ P˙ gaso D dt T δgaso = 1 if E˙ gaso D ≥ 0 ∧ tgaso ≤ 300
(11d)
el D
el D
T
T +1 E˙ gaso D
T = E˙ gaso D
Pdis ≤ 0
(11e) (11f) (11g) (11h) (11i)
One of simplest and typical modes for PHEVs while driving is assumed to be all electric [5] complemented by the ones mentioned above. So far, tested control schemes for known hybrid vehicles clearly differ from this idea [27]. Here, the implemented strategy is preferring electricity for propulsion (electric mode) but switches to a blended mode if a converter bound is reached or the battery is depleted until 20%. The objective function is minimizing the cost for propulsion and is using constant prices for electricity and gasoline as denoted in equation (12). It is also incorporating a term (κ/SOC), taking deep battery discharge into account. The constant κ is chosen as such, that the electricity price is higher than the gasoline price for SOC equal or lower than 20%. dF (E˙ el ,E˙ gaso ) κ = P riceel SOC T dE˙ el ˙ ˙ dF (Eel ,Egaso ) = P ricegaso dE˙ gaso
(12)
The optimization scheme while driving needs to be adjusted for the different energy flows that can occur. Depending on the energy flow within the PHEV the efficiencies of storages and converters need to be adjusted as they behave differently in various modes, effecting the SOC of the storages vigorously. The efficiencies of the power paths are summarized in table III
PHEV driving case driving: regenerative breaking: charging:
coupling factors cel kin D = ηel mot ηdc cgaso kin D = ηICE ηgen ηel mot cel kin D = ηreg cgaso kin D = ηICE ηgen ηc cel kin D = 1/ηc cgaso kin D = ηICE ηgen
TABLE III: Coupling factors for the various energy flows possible. When recapturing energy while breaking the power path of electricity is completely defined by the regenerative breaking efficiency being different than for acceleration. The ICE might also be switched on and hence the battery will be charged by the ICE with an efficiency denoted in table II. In the charging mode the PHEV can be standing idle but the ICE could still be running due to the heuristic. Therefore the power path efficiencies have to be adjusted once more. V. S IMULATION R ESULTS Simulations were carried out for the type of car described above and specified by the data found in table II only. The first simulation is carried out for an arbitrary composition of drive cycles. Here, it consists of Urban Dynamic Drive Cycle (UDDS) with 7.9 miles sampled, Highway Fuel Economy Cycle (HWFET) with 10.26 miles sampled, New York City Cycle (NYCC) with 1.18 miles sampled and Federal Test Procedure (FTP) 75 with 11.04 miles sampled [20]. The complete cycle is visualized in figure 2 where figure 2(a) represents the speed profile with a step size of 1 second. Hence, the optimization step size T is chosen commensurately. Figure 2(b) depicts the power profile of the drive cycle determined by the specific vehicle data incorporated in equation (8). The demanded power is supplied by the battery and electric motor as well as through the ICE running a generator. The power demands from battery and ICE are displayed in figures 2(c) and 2(e), respectively. They are resulting in a decrease of gasoline and electric energy level in tank and battery, respectively, shown in figures 2(f) and 2(d). The order of subplots is kept alike for the upcoming set of plots. It is easily seen that most of the power demanded for the drive cycle composition is supplied by the battery. Only during times when the power derivative is exceeding the upper bound of the battery, the ICE is switched on to supply the rest of it. This is seen especially during the HWFET as increased power is demanded from the ICE. It is kept running for 300s supplying a part of the demand during that time but also partly recharging the battery when the vehicle is breaking or parking. After 300s it is switched off again. The SOC decreases until 42.5%. The most electricity is consumed on the highway. A total distance of 29.93 miles is driven and the fuel economy can be calculated to be 75 miles per gallon (3.1 l/100km) being considerably less than found in [6]. However, note that the battery constitutes a comparably high SOC after the PHEV energy hub has driven almost 30 miles, which is assumed to be the average day demand for transportation [22]. To display how the PHEV energy hub model is behaving once the battery is depleted, ten UDDS drive cycles have been simulated. The results are depicted in the same order
1000
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3000
4000
5000
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(c)
0 −30 −50 0
1000
2000
3000
4000
5000
1 0.8 0.6 0.4 0.2 0 0
4
(e)
3 2 1 0 0
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5000
(d) 1000
2000
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4000
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50 49.9
(f)
49.8 49.7 49.6 0
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4000
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Fig. 2: Simulation of various test driving cycles; see text (a) Vehicle Speed (b) Demanded Power (c) Demanded Power from Battery (d) SOC of Battery (e) Demanded Power from ICE (f) Gasoline Consumption
as introduced in figure 2. Clearly, it can be seen that after seven cycles or about 8000s the battery is depleted until 20% and the model switches to a charge sustaining mode, keeping the SOC of the battery constant around the threshold value. In this mode the ICE not only supplies the demanded power for propulsion but also partly recharges the battery, especially during low load times as shown in figures 3(c) and 3(e). Obviously, the battery still supplies the net transient load. The net power demanded or supplied after ICE generation is subtracted from the load is either supplied by or stored in the battery. A total of 79 miles is driven and some 1.5 gallons of gasoline are used. Only analyzing the blended mode of the PHEV model a fuel economy of 120 miles per gallon is found (1.96 l/100km). This is very similar to other publications which rely on more advanced models. The error in battery utilization time lies roughly within 10% when comparing with sophisticated models and control schemes [6]. The time of engine utilization of the PHEV is not taken into account for fuel efficiency calculations as it deteriorates the overall fuel economy and efficiency of the vehicle by and large. Figures 4(a)-(f) show a possible full day schedule incorporating utilization for grid ancillary services of the PHEV (blue) and charging it (red). For better visibility the states are individually indicated. The ancillary service signal was taken from Pennsylvania-New Jersey-Maryland (PJM) Interconnection [28] and fitted for PHEV capabilities assuming a maximal power connection of 3.5 kW. In order to account for the limited power capacity of PHEVs, the signal was put in reference to the maximal available regulation capacity at that certain time interval and weighted by the regulation capacity of the PHEV (here 3.5 kW) [29]. It is shown in figure 4(c). The signal is integrated via Pel . Negative values refer to charging and positive to discharging of the PHEV battery, respectively. Obviously, the grid power demand in the time intervals is much lower than for actual transportation. In figure 4(a) the schedule starts with driving of various cycles. The PHEV is
10000
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5000
Demanded Battery Powerfor LDV Driving Cycle 50 30
(c)
0 −30 −50 0
Gasoline Consumption for LDV Driving Cycle Gasoline Tank / l
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Vehicle Speed / km/h Battery Power / kW
(a)
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Power Demand for LDV Driving Cycle
Driving Cycle for Light Duty Vehicles (LDV) 100
Power Demand / kW
5
50 48 46 44 42 40 0
(f) 5000 10000 Total Time / s
15000
Fig. 3: Simulation of ten Urban Dynamic Drive Cycles (a) Vehicle Speed (b) Demanded Power (c) Demanded Power from Battery (d) SOC of Battery (e) Demanded Power from ICE (f) Gasoline Consumption
then connected for some hours and in the end of the connection time it is recharged, indicated through the red graph. For recharging, a connection of 3.5 kW and the charging efficiency denoted in table II are used. Then the PHEV is moving again resulting in a decrease of SOC and in the end it is charging once again. The comprehensive devolution of the SOC of the battery is depicted in figure 4(d). Palpably, the battery is recharged during the usage for grid services. The maximum SOC is not violated while recharging the PHEV at the end of grid service time. Due to the information density delivered by this model not only impacts on the vehicle can be studied. The model can furthermore be used as a valuable input for power system modelling and analysis. Being able to simulate different drive cycles conveniently and quickly, vast amounts of PHEV can be aggregated to get a realistic idea of the load which would be imposed on the electricity system by them. The vehicles are assumed to connect after driving at one node representing in an urban agglomeration supplied by one substation. Specific feeders are not under consideration as they supply areas which are not large enough to aggregate the investigated amounts of PHEVs. For the following findings the vehicles were presumed to leave their homes between 5a.m. and 9a.m. with certain probabilities peaking at 8a.m. and with different drive cycles composed of the ones introduced for figure 2 [30]. Here, the cars are presumed to connect in a business area. Uniform probability distributions for deciding the amount and composition of drive cycles are used. The expected time of driving is calculated to be 1.2h from the composition of the utilized cycles [31]. The vehicles are assumed to recharge instantaneously after arriving. No smart charging scheme is proposed, here. Figure 5 is visualizing the load imposed by several amounts of PHEVs connecting in the supposed area. The plotted time varies between 5a.m. and 2p.m. and the PHEV amounts under investigation are ranging from 100 to 1000. Clearly,
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Power Demand for LDV Driving Cycle
driving
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charging
40 20 0 0
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regulation
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0
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charging
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driving
1
charging
2 3 Total Time / s
1
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5 x 10
4
49.8
(f)
0.5
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0.25
0.4
driving
49.6
regulation
charging
49.4 49.2 49 0
1
2 3 Total Time / s
4
0 1000
5 4
x 10
Fig. 4: Simulation of driving, charging and regulation (a) Vehicle Speed (b) Demanded Power (c) Demanded Power from Battery (d) SOC of Battery (e) Demanded Power from ICE (f) Gasoline Consumption
for small amounts of PHEVs the load is not uniform and peaking earlier than for large amounts. Increasing the number of connecting PHEVs results in a more even distribution of the imposed load. The peak is found to be at 10a.m., exactly two hours after the highest departure probability is assumed. The maximum load is found to be 1.65pu. Presuming typical plugs of 3.5 kW power capacity (single phase connection, 240V, 16A) and a linear recharging curve of the batteries utilizing a 70% efficiency results in a total load of 1.65MW. Investigating larger amounts in figure 6, it is easily seen that the maximum load is still found at 10a.m. and the load curve does not change its gaussian shape anymore. Numbers of up to 50.000 PHEVs are simulated. The maximum load for 50.000 connected PHEVs, a realistic amount for large areas including commercial buildings or plants, is found to be 82.8MW. Extraction of the load for lower PHEV amounts at different times is straightforwardly done with figure 6. Also, simulations for a higher power connection can easily be performed (three phase connection, 6.4kW, 400V, 16A). They would result in a slimmer but higher load curve. Deriving the relation of maximum imposed load and amount of PHEV, one finds obviously an almost perfect linear dependence. Figure 7 is plotting the maximally imposed load of various amounts of PHEVs. The different peaking times are not indicated, here. However, 10a.m. is found for all amounts above 750 PHEVs. The linear fitting is indicated by the red solid graph and the simulation points by diamonds. It can be seen that the simulation findings are perfectly fitted by a linear dependence found to be L(P HEV ) = 0.0016P HEV + 0.038 [pu] also displayed in the upper left hand corner of the graph. Intuitively, for investigations of loads imposed from more than 50.000 PHEVs, the linear fitting can conveniently by used. Lastly, due to the micro-information delivered by the model, it is able to deliver the total available stored energy within the area under investigation. Here, the maximal deliverable
0.2 750
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9 10 Time [h]
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Fig. 5: Load development over time and PHEV amount at one node for a maximum of 1000 PHEV (1pu = 1MW)
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Fig. 6: Load development over time and PHEV amount at one node for a maximum of 50000 PHEV (1pu = 1MW)
90
Simulation Fitting
y = 0.0016 PHEV + 0.038 80
Maximum Load [pu]
Gasoline Tank / l
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charging
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Fig. 7: Maximum load imposed from PHEV (1pu = 1MW)
7
130
Storage [MWh]
160 200 180 160 140 120 100 80 60 40 20 0 5
140 120 100 80 60 40
4 3 4 Amount x 10of PHEV [x 10k] 2
1 0
5
6
7
8
9 Time [h]
10
11
12 20 0
Fig. 8: Available storage at one node over time and PHEV amount without taking recharging into account energy from batteries (battery minimum SOC of 20% for each PHEV) was taken into account. Figure 8 displays the development of total available storage over time and PHEV number. The vehicles are assumed not to recharge at all in this case. The total available storage from 50.000 PHEVs is found to be 175MWh. This results in an average storage capacity of 3.5kWh which could be utilized for the system. It is also obvious for this plot that the dependence of maximal available storage scales linearly with the PHEV number. The plot proving this dependence is not included due to space restrictions in this paper. However, the dependence for available storage S can be expressed through
Regulation up/down capacity [pu]
160
100
120 80
50
40 0
0
−40 −50
−80 −120
−100
−160 5
4
3 4 PHEV [x 10k] Amount x 10
2
1
0 5
6
7
8
12 9 10 11 Time [h]
−150
Fig. 9: Potential available power for grid ancillary services (regulation up/down) over time and PHEV amount. Power for grid infeed is denoted positive (1pu = 1MW) is lower than the found 175MWh stored in all vehicles. For regulation up and down, one can calculate 2.6kW and 3kW as an average power capacity for each car. The time dependency of the power capacities to be used for ancillary services can also be extracted from figure 9. Again, the maximum ancillary capacity is linearly dependent on PHEV amount. Here, positive ancillary P A (PHEV feed into grid) and negative ancillary N A (PHEV are recharged) potential can be expressed through P A(P HEV ) = 0.0026P HEV − 0.024 [pu] N A(P HEV ) = −0.003P HEV − 0.01 [pu]
S(P HEV ) = 0.0035P HEV − 0.054 [pu]
VI. C ONCLUSIONS AND O UTLOOK
The intuitive idea to use the storage plotted in figure 8 for grid ancillary services leads to investigations of possible obstacles for it. The maximum storage to be available for the grid was found to be 175MWh for 50.000 PHEV. That does not necessarily mean, that all of it can be utilized. Further, the contracted and requested power for possible ancillary services has to be available at a very high security grade. A breakdown is not bearable. This breakdown of requested power could be due to several reasons like PHEVs leaving, but for now, running out of energy shall only be included in the investigations. Some PHEVs might have more power stored than can be delivered in one hour due to their power connection. Others might have less energy stored than can be delivered in one hour due to a very low SOC. The further calculations for ancillary services need to take into account that maximum delivery time for grid service might be one hour. Therefore, calculation of possible ancillary capacity has to include minimal and maximal charging levels of batteries (20% minimal-, 100% maximal charge) and maximal power output of the connection for up and down regulation, respectively. Figure 9 visualizes the aggregated power (plug power capacity) dependent on daytime and amount of PHEVs. It can be extracted that maximal possible power which can be fed into the grid is 130 pu for 50.000 PHEV. The maximal power which can be imposed on the grid for one hour acting as a load is found to be 150pu, where 1pu = 1MW. Obviously this
The paper introduces the concept of energy hubs for PHEV modelling. The approach offers the possibility to model a PHEV in different states as it can be utilized for more than driving. Further, it is easily extendable to incorporate different architectures and propulsion schemes. An optimization scheme for the driving states preferring electricity before gasoline while incorporating converter constraints is presented. The scheme offers the flexibility to analyze different day schedules obtaining results close to well known, sophisticated vehicle models. The approach is also capable to give implications for the SOC of the battery at different day times after the PHEV has been used for transportation. Furthermore the model can be used to validate so far assumed values for PHEV energy consumption. Additionally, the impacts on PHEV when utilizing it for grid ancillary services can be studied. Particularly, the model is not limited for vehicle investigations. Due to the simplicity and computationally fast procedure it can be used to simulate vast amounts of different PHEVs and use the individual data like SOC and fuel tank level as inputs for power system simulations. Here, load curves, storage availability and ancillary service capacities were investigated and presented for different amounts of PHEVs and various times, resting upon assumed departure patterns. Furthermore, important dependencies for maximally imposed load, available storage and grid ancillary capacities are derived from the simulation results. Publications [30] and [31] are
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based on the presented PHEV hub model, proving to be a stable fundament and a valuable tool for in-deep power system and grid investigations. The findings can be extrapolated for larger quantities and other time dependencies. Future work will focus on model enhancements by integrating nonlinearities and adding of various vehicle architectures. Also, integration of the model in a multi energy carrier power system approach including smart management schemes will be performed. VII. ACKNOWLEDGEMENTS The work is sponsored by the Swiss Federal Institute of Technology (ETH) Zurich under research grand TH 22073. The author would like to thank all colleagues and especially Antonis Papaemmanouil at the power systems laboratory (PSL) for helpful discussions. R EFERENCES [1] T. H. Bradley and A. A. Frank. Design, demonstrations and sustainability impact assessments for plug-in hybrid electric vehicles. Renewable and Sustainable Energy Reviews, In Press, Corrected Proof:2–7, 2007. [2] J. Gonder and A. Simpson. Measuring and reporting fuel economy of plug in hybrid electric vehicles. Plug-In Hybrid Electric Vehicle Analysis, NREL Milestone Report NREL/MP-540-40609, 2006. [3] T. Markel and A. Simpson. Plug-in hybrid electric vehicle energy storage system design. In Advanced Automotive Battery Conference, Baltimore, MD, 2006. National Renewable Energy Laboratory (NREL), Golden, CO,USA. [4] D. Karner and J. Francfort. Hybrid and plug-in hybrid electric vehicle performance testing by the us department of energy advanced vehicle testing activity. Journal of Power Sources, In Press, Corrected Proof:1–7, 2007. [5] J. Gonder and T. Markel. Energy management strategies for plug-in hybrid electric vehicles. In SAE World Congress, 2007, pages 1–5, Detroit MI, 2007. [6] A. F. Burke. Batteries and ultracapacitors for electric, hybrid, and fuel cell vehicles. Proceedings of the IEEE, 95(4):806–820, 2007. 00189219. [7] L. Guzzella and A. Sciaretta. Vehicle Propulsion Systems. Springer, 2nd edition, 2007. [8] K. T. Chau and Y. S. Wong. Overview of power management in hybrid electric vehicles. Energy Conversion and Management, 43(15):1953– 1968, 2002. [9] J. Wu, A. Emadi, M. J. Duoba, and T. P. Bohn. Plug-in hybrid electric vehicles: Testing, simulations, and analysis. In IEEE Vehicle Power and Propulsion Conference, 2007. VPPC 2007., pages 469–476, 2007. [10] T. Markel and K. Wipke. Modeling grid-connected hybrid electric vehicles using advisor. In The Sixteenth Annual Battery Conference on Applications and Advances, 2001., pages 23–29, 2001. [11] A. Pagerit S. Sharer P. Karbowski, D. Rousseau. Plug-in vehicle control strategy: From global optimization to real-time application. In EVS-22, pages 1–12, Yokohama, Japan, 2006. [12] Pagerit S. Gao D. Rousseau, A. Plug-in hybrid electric vehicle control strategy parameter optimization. In EVS 23, pages 1–14, Anaheim California, USA, 2007. [13] Q. Gong, Li Yaoyu, and Peng Zhong-Ren. Trip based power management of plug-in hybrid electric vehicle with two-scale dynamic programming. In IEEE Vehicle Power and Propulsion Conference, 2007. VPPC 2007., pages 12–19, 2007. [14] J. T. B. A. Kessels and P. P. J. van den Bosch. Plug-in hybrid electric vehicles in dynamical energy markets. In IEEE Intelligent Vehicles Symposium, 2008, pages 1003–1008, 2008. [15] M. Geidl, G. Koeppel, P. Favre-Perrod, B. Kloeckl, Andersson G., and K. Froehlich. Energy hubs for the future. IEEE Power and Energy Magazine, 5(1):24–30, 2007. 1540-7977. [16] M. Geidl and G. Andersson. Optimal power flow of multiple energy carriers. IEEE Transactions on Power Systems, 22(1):145–155, 2007. 0885-8950. [17] M. Geidl and G. Andersson. Optimal power dispatch and conversion in systems with multiple energy carriers. In 15th Power Systems Computation Conference (PSCC), volume 15, Liege, Belgium, 2005.
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Matthias D. Galus was born in Swientochlowitz, Poland. He received a Dipl.-Ing. degree in electrical engineering and a Dipl.-Ing. degree in industrial engineering from the RWTH Aachen, Germany, in 2005 and in 2007, respectively. He joined the Power Systems Laboratory of ETH Zurich, Switzerland in 2007 where he is working towards a PhD. His research is dedicated to modeling, optimization and efficient integration of PHEV into power systems. He is a student member of the IEEE and VDE (German society of electrical engineers).
G¨oran Andersson was born in Malm¨o, Sweden. He obtained his MSc and PhD degree from the University of Lund in 1975 and 1980, respectively. In 1980 he joined ASEA, now ABB, HVDC division in Ludvika, Sweden, and in 1986 he was appointed full professor in electric power systems at the Royal Institute of Technology (KTH), Stockholm, Sweden. Since 2000 he is full professor in electric power systems at ETH Zurich, Switzerland, where he heads the Power Systems Laboratory. His research interests are in power system analysis and control, in particular power system dynamics and issues involving HVDC and other power electronics based equipment. He is a member of the Royal Swedish Academy of Engineering Sciences and Royal Swedish Academy of Sciences and a Fellow of IEEE.
