2017 IEEE Conference on Control Technology and Applications (CCTA)
August 27-30, 2017. Kohala Coast, Hawai'i, USA
Energy Management System for Charging Stations with Regenerative
Supply and Battery Storage based on Hybrid Model Predictive Control
Tobias Lepold and Daniel Görges
B. State of the Art and Contribution
Abstract— This paper introduces a comprehensive approach
to smart charging at a charging station supported by a vanadium redox flow buffer battery and supplied by a photovoltaic
panel. Both increasing photovoltaic power and fast charging
of electric vehicles induce challenges for grid management.
Smart charging in conjunction with the buffer battery increases
efficiency and reduces strain on the grid. Improved yet simple
models for vanadium redox flow batteries and the electric
vehicle charging processes are are developed. The component
models for control design are formulated as mixed logical dynamical system to accommodate the limitations of the charging
process imposed by IEC 61851. From the models a hybrid
model predictive control scheme is derived and evaluated in a
test scenario.
Numerous proposals for Energy Management Systems for
different scales exist. In these proposals modeling the charging process is either done using a very simple model with
input and state constraints or models taking the theoretical
EV battery charge curve into account. [12]. In [3] hybrid
model predictive control is proposed deal with the semidiscontinuous input variables provided by IEC 61851 [5]
conforming charge points (CP). A static vanadium redox flow
battery (VRFB) efficiency model used as base for the control
design and simulation is presented in [11]. [8] investigates
the suitability of VRFBs for smart grid applications.
A control framework for charging stations with photovoltaic power plant and VRFB integration is not available
yet. This is the major contribution of the paper.
I. I NTRODUCTION
While electric vehicle (EV) avoid emissions locally, a
true clean operation of can only be achieved if renewable
energy sources are used for charging the EV. Furthermore
increasing numbers of EVs and share of volatile renewable
energy sources [10] provide an increasing challenge for grid
stability. These issues can be mitigated by organizing EV
charge points, renewable energy sources and into micro grids
with an optional buffer battery. By intelligent management
of such a micro grid efficiency can be increased while grid
strain is reduced. This paper proposes a complete control
framework for optimized operation of a charge station containing multiple charging points, at least one photovoltaic
power plant and at least one buffer battery. The component
models for control design are formulated as mixed logic
dynamics to accommodate the limitations of the charge
process control as specified by IEC 61851 . Furthermore the
models of the EV charging process and the vanadium redox
flow battery (VRFB) take the state of charge dependency of
the maximum charge and discharge power into account.
II. C ONTROL O BJECTIVES
In order to optimize plant operation the goals of the
proposed control system must be considered. These goals
are listed below in descending order of priority:
1) Comply with technical and legal constraints.
2) Charge EVs to required state of charge (SoC) duly
3) Minimize of the power drawn from grid
4) Avoid losses by unnecessary use of the buffer battery
5) Maximize EV SoCs with surplus photovoltaic power
6) Maximize VRFB SoC with surplus photovoltaic power
III. M ODELING
A. General Considerations
Models are created for each component of the plant so a
complete prediction model in the standard form
X(k) = Φ · X(k) + Γ · U (k)
A. Organization of the Paper
can be synthesized at run time. For this purpose the differential equation for each model are provided in standard form
After stating the goals of the control strategy in Section II,
the models of all components are introduced in Section III.
The control strategy is then derived based on the model and
the goals in Section IV. For the model predictive primary
control a mixed integer optimization problem is synthesized.
Simulation results are discussed in Section V. Conclusions
and remarks on future work are finally given in Section VI.
ẋ(k) = A · x(k) + B · u(k).
(2)
For the prediction model of the entire system the differential
equations are collected in a single matrix equation of the
standard form. Furthermore each model must include an
appropriate set of constraints to delimit its safe operating
area. The constraints are collected into two equation systems
The authors are with the Juniorprofessorship for Electromobility, Department of Electrical and Computer Engineering, University of Kaiserslautern, Erwin-Schrödinger-Straße 12, 67663 Kaiserslautern, Germany, Email lepold| goerges@eit.uni-kl.de.
This work is supported by the German Federal Ministry for Economic
Affairs and Energy under grant 03ET6053D.
978-1-5090-2182-6/17/$31.00 ©2017 IEEE
(1)
Eeq · x(k) + Meq · u(k)
=
beq
(3)
Eineq · x(k) + Mineq · u(k) ≤ bineq
(4)
in a similar fashion to the differential equations.
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TABLE I: VRFB Parameters
Parameter
Value
CV
PV
PV
etaV,+
etaV,
usable capacity
rated charge AC power
rated discharge AC power
rated charge efficiency
rated discharge efficiency
100 kWh
34 kW
22 kW
0.8
0.75
1
0.8
0.6
SoC
Variable
u2
0.4
u1
B. Plant Description
The example plant in this paper is a EV charge station
composed of 3 controllable and one switchable charge points,
a 10 kWp photovoltaic array and a vanadium redox flow
battery with a rated discharge power 24 kWp and capacity
100 kWp as buffer storage.All elements are coupled via 3
phase 400 V AC power line.
0.2
0
-30
-20
-10
0
10
20
30
40
Power [kW]
Fig. 1: VRFB constraint polytope
C. VRFB Battery
In the considered plant the buffer battery is a vanadium
redox flow battery. This type of batteries has promising
properties for storing renewable energy such as high cycle
stability compared to lithium ion batteries. For control design
purposes it is modeled as a linear state equation (5)
X: 0.06713
Y: 0.878
X: 0.1
Y: 0.9185
(5)
with SoCV being the VRFBs state of charge and
−1
−1
BV = ηV,+ ηV,−
CV
uV,+ · CV .
uV
= u
V,−
X: 0.2
Y: 0.9672
0.8
Share of spectrum
˙ V (t) = BV · UV
SoC
1
(6)
(7)
X: 0.03335
Y: 0.7888
X: 0.01662
Y: 0.6927
0.6
X: 0.0011
Y: 0.3959
0.4
X: 0.000555
Y: 0.3366
0.2
The model also includes a set of constraints (8) to (11).
0
PV
0
M · SoCV + E · UV
≤ uV,+ ≤ PV
0
(8)
≤ uV,− ≤
≤ SoCV ≤
0
1
(9)
(10)
≤
b
(11)
0.2
0.3
0.4
0.5
Fig. 2: Cumulative spectrum of harvested photovoltaic power
available with forecasting horizons up to 7 day in advance.
These forecasts are clearly limited in both accuracy and
frequency resolution. Fig. 2 illustrates that only a small part
of the photovoltaic power frequency spectrum can be covered
by an optimizing control, whose update rate is limited by
the update rate of the photovoltaic power forecast of 15 min.
The data used for generating the spectrum is from a plant
located at in south west Germany and spans a year. In order
to mitigate these limitations a faster subsidiary controller is
used to control the VRFB battery.
0.022
0
1
1.333
0
−0.084 , b = 3.2139 .
1 ,E =
0 −0.0126
1
0.9697
The constraints are derived from precursory modeling work
[11], which was extrapolated to the manufacturers projected
specifications. Fig. 1 shows the resulting polytopes. The
mixed input-state constraints 11 represent the limitations on
charge and discharge power imposed by high/low SoCs.
The state equation has separate inputs for charging and
discharging to respect the reversion of the energy flow and
resulting losses. It also enables assigning separate priorities
when designing the cost function.
!
0.1
Frequency [Hz]
with
!
0
!
M=
E. EV Charging Process
Knowledge of the charging process is essential for optimizing. The charge process can by split into two interacting
parts: The charge point and the battery unit of the vehicle.
Many investigations have been conducted on modeling of the
battery unit with a bottom-up approach such as in [3]. While
this approach offers great insight into the battery behavior
itself it might not be practical for smart charging for several
reasons:
D. Photovoltaic Power and Forecasting
The plant is equipped with a 10 kWp photovoltaic array
as power source. In order to make best use of the available
photovoltaic power a forecast is utilized. This forecast is
delivered in form of average values with a sampling period
of 15 min. The photovoltaic power forecast are commercially
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18
Measurement
Polytope
16
0
≤ uEV ≤
0
≤ SoCEV ≤
Pcomb (13)
P (SoCEV ) = gP R · (SoC(t) − SoCbulk )
14
Charge Process
interrupted
Power (kW)
10
8
CEV · ∆SoCEV
(17)
PCP · ∆t
Note that the maximum power in the charge process Pcomb
is a result of the combination of car, charge point and the
used cable.
(18)
Pcomb = min PEV , PCP , Pcable
2
0
65
70
75
80
85
90
95
100
SoC (%)
2) Charge points: In this paper the charge points utilized
are of the type Walther Ecolektra 200 RFID and use SAE
1772 type signaling as specified in IEC 61851 to control the
maximum current which can be used by the electric car. The
actual control of the current is handled by the EV’s internal
charge controller though. The IEC 61851 standard uses a
PWM signal to control the maximum amount of current
which can be used by the electric vehicle. This signal is
also used for connection and error detection. Therefore it
is never truly zero and thus the minimum current is 6A.
Considering 3 phase AC charging using European standard
grid voltage of 230 V this leads to an minimum allowed
max. power of 4.14 kW. Given our photovoltaic power
plant has a peak power of only 10 kW not considering
this threshold might lead to significant efficiency losses. The
current reference values above 6 A are discretized in 1 A
steps. For control design purposes this region was treated as
continuous to minimize the difficulty in solving the mixedinteger programming problem. Therefore this discontinuity
is modeled in the mixed logical constraints (19) to(20).
The variable d is a binary decision variable which if set to
1 allows the EV to consume current up to the set maximum.
Fig. 3: Nissan Leaf ChargeCurve
TABLE II: EV Parameters
•
(16)
ηEV =
4
•
(15)
SoCEV is the state of charge of the EV. with ηEV being
obtained by measuring SoCEV and AC power at the chargestation PCP and calculating
X: 78.31
Y: 8652
6
•
≤ P (SoC(t))
u(t)
12
1 (14)
Variable
Parameter
CEV
PEV
ηEV
SoCbulk
gP R
rated capacity
EV rated charge power
charge efficiency
SoC bulk charging complete
gradient of charge power reduction
Modeling effort for an increasing number of electric
vehicle types and variants
CP max current setpoint to SoC measured by EV’s
internal sensor is the relevant control path
Computational effort of nonlinear models
Therefore a simple black box model based solely on
measurements of input power and SoC with the vehicles
internal SoC sensor is preferable to a theoretical model.
1) Vehicle battery: In current charging stations the charging process is controlled via a pulse-with modulated (PWM)
signal as specified in IEC 61851 [5]. This signal tells
the battery management system of the electric vehicle the
maximum amount of power it is allowed to draw. The
battery management system must react within 5 s to the new
reference value. In a typical EV the preferred charge strategy
is constant current constant voltage (CCCV). This means that
up to a certain SoC the maximum current possible is constant
and will decrease from that point. For all EVs investigated for
this paper the current decrease is proportional to the SoC.
These properties can be used to construct a linear mixed
state-input constraint in the optimization problem. In Fig. 3 a
measured charging curve from a Nissan Leaf electric vehicle
and the corresponding constraint polytope are shown. The
data was obtained by reading out the on-board diagnostics
(OBD) port [6] of the vehicle.
The charging process with respect to the electric vehicle
is therefore modeled by (12) to (16).
˙ EV
SoC
= CEV
−1
· ηEV · uEV
¬d(t) ∧ uEV (t) = 0
(19)
d(t) ∧ uEV (t) ≥ min(PCS , P (SoC(t)))
(20)
The minimum constraint in (20) can be rewritten as a set of
linear constraints
min(a, b) = arg max x
s.t. x ≤ a, x ≤ b
(21)
(22)
where x is an an auxiliary variable.
3) Grid: Naturally the system must also respect constraints imposed by the grid. To this end input the Power
transfer to and from the grid is split into to inputs for positive
uG,+ and negative uG,− power from the grid.
PG = uG,+ + uG,−
(23)
with PG being the power at the grid connection point. Thus
the grid constraints are (24) and (25)
(12)
0 ≤ uG,+ ≤ PGrid
(24)
PG ≤uG,−
(25)
≤0
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vehicle
database
booking system
Hardware
charge
requirements
solar power
forecast
charge
forecast
energy
management
SoC, Events
Software
P
SoC
P
subsidiary
control
P
P
photovoltaic
plant
an infeasible optimization problem i.e. can be fulfilled by
the existing charging infrastructure. The booking system will
inform the EMS about the time slots each car is expected to
be connected to the charge points, estimated initial SoC as
well as the EVs Parameters from a database. With the data
the EMS will select a suitable charge points to full fill the
users SoC requirement if possible. Suitability depends on
maximum power, available charge cables and fuse options
installed in the CP. If not the booking will be rejected so
that the user can try again with different parameters. Upon
creation of a car booking the Energy Management System
will check if the requested car can brought to the required
minimum SoC calculated by the Booking System depending
on route, car, etc. If the car is to return to the charge station
an SoC upon return is calculated as well. With respect to the
control problem the users SoC requirement SoCreq is added
as a constraint (28) at the time point of departure k, i.e.
Legend:
reference
value/data
forecast
measurement
power
P
CPs, EVs
P
grid connection
point
VRFB
Fig. 4: Control System Overview
SoCEV (k) ≥ SoCreq
(28)
SoCreq
(29)
<
1
Note that from (15) follows that SoCEV = 1 can mathematically not be reached in finite time.
While the schedule provided by the booking system is
theoretically sufficient for optimization some human aspects
must be considered:
• Cars arriving at CS later than scheduled might result in
infeasibility
• User might not connect recommended charge point
Before each optimization the EMS will try to identify
possible sources of infeasibility such as users coming late or
using a CP other than recommended. An appropriate warning
is given to the booking system if reaching the required SoC
is not possible. The Booking system will then inform the
user about the problem.
4) System wide constraints: While the previous compon
model include constraints based on used components itself,
some further constraints are introduced based on the coupling of the systems and it’s intended purpose. Based on
conservation of energy (26) is added. To avoid discharging
the VRFB into the grid (27) is added.
X
P V + PP V + P G +
PEV =
PP V
(26)
X
PV
≤
PEV
(27)
IV. C ONTROL D ESIGN
The proposed control system is consists of an energy
management system (EMS) based on Hybrid Model Predictive Control, which enables the optimization of the charging
process, a subsidiary controller to balance out any deviations
at the grid connection point and the hardware and user
interfaces. Inputs to the control system are the photovoltaic
power forecast, EV user requirements from a booking system
and vehicle parameters from a database. Fig. 4 shows the
interaction of these components.
B. Model Predictive Control
The model predictive control is based on a mixed-logic
optimization problem 30
maxJ(u) = uT Hu + c · u
s.t. Au ≤ b
u≤u≤u
A. User Interaction
Aineq · u ≤ bineq
In order to optimize the charging process the SoC requirements as well as the cars properties must be known.
Since these information depend on intended drive cycles it
must be supplied in some form by the user. In this example
plant this is done via a booking system which is used to
reserve a company car. The booking system was chosen since
it is the most complex form of user interaction and allows
for most optimization since arrivals at the chargestation are
known in advance. Downgraded modes of user interaction
are also possible. The calculation of the required SoC is
automated based on the selected car and the destination and
other parameters. Thus no further burden is created for the
user. Furthermore the SoC requirements must not result in
Aeq · u = beq ,
d(t) → Alog,eq · u = blog,eq
d(t) → Alog,ineq · u ≤ blog,ineq
generated from the models described above and a usersupplied charging schedule.
The sampling time TS for the optimizing control is set
to 15 min since the sampling rate is limited by the time
resolution of the photovoltaic power forecast. An update
of the optimization will also be triggered by events from
the booking system or the charge points. In order to find
and optimal input sequence and optimization problem using
the models and constraints mentioned above is formulated.
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TABLE III: Cost assignment
Process events
Cost assignment
Input
cEV
cV,+
cV,+
cG,+
cG,
uEV
u1
u2
uG,+
uG,
yes
Unprocessed
events?
no
Update SoC
measurements
−cEV < cV,− < cG,−
(32)
The rationale for these cost assignment is as follows:
• (32) makes charging the EVs directly from PV power
preferable since buffering is leads to inevitable losses.
• (32) also makes storing energy in the VRFB is preferable to feeding to the grid given current fixed prices and
discharging the VRFB is preferable to buying energy
• (32) prevents VRFB discharge and and grid power usage
unless forced by an EV SoC constraint
Note that by adjusting cG,+ , cG,− the cost for grid power
the plant can easily benefit from a flexible energy price. If the
cEV is varied among the EV soft priorities can be assigned
to individual cars.
Quadratic costs are are assigned to the inputs uV,− and
PG,+ . This reduces the peak power to the EV from sources
other than the PV array. The control design thus provides
both maximum utilization of the photovoltaic power while
avoiding reducing battery lifetime by high currents if powered from the VRFB or the grid.
Select charge periods
in prediction horizon
Charging schedule
feasibility check
Build and solve
optimization problem
Write output
yes
𝑡 ≥ 𝑇𝑆
no
yes
Unprocessed
events?
C. Inner Control Loop
The available photovoltaic power may deviate from the
photovoltaic power forecast and may have an unpredictable
higher frequency component not adequately covered by the
15 min sampling time of the model predictive controller.
Since the maximum response time of the battery management
system to changes in reference power is specified by IEC
61851 to be 5 s, it is possible to balance positive deviations
which last longer than this time span using the charging
station power reference value. Whether it is advisable to do
so is debatable since the resulting higher currents reduce
battery lifetime. Negative deviations must not be passed on
to the EV since the resulting lower SoC might cause an
infeasibility in the optimizing control loop. Therefore a PItype controller with a sampling time of 1 s is used to control
the power drawn from the grid to zero by setting the VRFB
power. The inner control loop also prevents any violations
of the German renewable energy act (EEG 2017 §9 section
(2) clause 2.b) ) [2] by ensuring that he photovoltaic inverter
is throttled in case that the output to the grid surpasses 70 %
of the peak output of the photovoltaic power plant.
Fig. 5: MPC Control Loop
To this end models are discretized with a sampling time of
15 min. If no car is connected to a charge point the respective
input is constrained to zero. The prediction model for the
entire plant is synthesized from the components models
described above with consideration of the planed charge
processes. For each EV charge process a separate SoC state
is added to the prediction model so that estimated SoCs on
arrival can be included. The prediction horizon is 3 days
which implies N = 288. Fig. 5 gives an overview of the
MPC control loop.
1) Cost function: The cost function is comprised of a
linear part and a quadratic part. Each part itself is made
of individual cost assignments for the components III. The
linear part assigns negative costs for charging EVs and the
VRFB. Positive cost are assigned to discharging the VRFB
and consuming grid power.
T
J(u) = cu + u Hu
(30)
cEV < cV,+ < cG,+ < 0
(31)
V. S IMULATION R ESULTS
In order to validate the benefits of controller simulations
runs have been performed. For the simulation detailed models of the components have been implemented in MATLAB/Simulink including VRFB efficiency curves and value
with
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TABLE VI: Financial Results
TABLE IV: EV Schedule
EV
Arrival
Departure
SoCref
Turnover
Uncoordinated
Hybrid MPC
1
2
3
16:00
17:00
16:30
08:00
15:00
15:00
0.915
0.4
0.915
grid power expenditures
grid power sales
∆ value VRFB charge
3.17 e
0.10 e
3.93 e
0.23 e
0.11 e
6.84 e
P
0.86 e
6.72 e
TABLE V: Energy Balance
R
PP V dt
P
CEV · ∆SoCEV
CV · ∆SoCV
EG,+
EG,
ηplant
Uncoordinated
Hybrid MPC
145.4
66.0
21.0
12.7
0.9
0.5
145.4
56.7
36.5
0.9
0.9
0.64
decreased due to the 6A threshold. This gain in efficiency
translates to a financial gain shown in Table VI.
C. Solver computing time
The simulations have been performed on a Microsoft
Windows 64 bit computer with an Intel i5-4670 3.4 GHz
quadcore CPU and 8 GB of RAM. The solver computing
time has been limited to 30 seconds per solver settings while
all other termination criteria where the gurobi solver defaults.
In all but 5 timesteps the algorithm terminated before the
30 seconds time limit was reached. A suitable termination
criterion other than the timelimit is still subject to ongoing
research.
discretization of the charge point hardware interface. The
optimization was handled using the YALMIP toolbox [7]
together with the GUROBI solver [4].
High resolution photovoltaic production data and corresponding forecast have been used for a existing photovoltaic
12kWp power plant referred to in subsection III-D. The
power values have been scaled accordingly.The hybrid mpc
controller is evaluated against a baseline control scheme
which involves only control of the VRFB and the default
(maximum) power set-points of the charge point. From the
simulation run an energy and financial balance is determined.
Financial results are calculated assuming current German
energy prices for purchasing from [9] and feeding [1] into
the grid, as well a assuming that the VRFB can be discharged
with ηV,− = 0.75.
VI. C ONCLUSIONS AND F UTURE W ORK
In this paper a hybrid model predictive controller for smart
charging with consideration of a buffer storage has been
presented. The model used in the controller is represented
by linear models of the batteries including constant and
SoC dependent power constraints. This makes it possible to
synthesize fairly accurate prediction models even when fast
charging requirements forces the operating point onto these
constraints. The resulting coordinated charging provides
significant gains in efficiency compared to uncoordinated
charging by utilizing the predicted photovoltaic power and
respecting buffer storage limitations. Currents at the grid connection point are kept minimal. Event-based updates in the
MPC loop provide high responsiveness to user action. The
proposed architecture with the booking system maximizes
user convenience.
The logical next step for the development is experimental
validation of the VRFB model and the control system at
the real plant which is currently under construction. Further
expansions of the control functionality might include variable
tariffs for power from the grid. In the model considering
uncertainties due to EVs lithium-ion battery aging and
temperature might offer additional reliability in charging to
the required SoC in due time. The cost function could be
modified to enable late charging to increase the battery life.
A. Scenario
In this scenario it is assumed that 3 cars arrive at the
charge station in late afternoon. One car is to depart the next
day at 8:00 the others at 15:00. Table IV shows the complete
Schedule with SoC requirements. Initial SoC was 0 for the
EVs and 0.3 for the VRFB. During the timeframe selected
for simulation a day with mixed cloudy weather was selected,
representing clearly non ideal conditions with respect to
solar power forecasting. This allows for demonstration of
the effects of the subsidiary controller.
B. Results
Fig. 6a and 6b shows the assigned component powers
during the charging time frame. Additionally predicted and
measured photovoltaic powers are shown. It can be clearly
seen how the total power of all charging stations is fitted to
the predicted solar power. Thus the available solar power
is directed to it’s target and losses in the buffer battery
are minimized whenever possible. The VRFB balances the
power at the grid connection point to zero. At the end of the
charging processes with high target SoCEV the reduction of
input power is clearly visible.
Table V shows a significant increase in system efficiency,while the total amount of energy feed into the cars
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