Mads Almassalkhi1 ([email protected]), Ralph
Hermans2, and Ian Hiskens1 1
Department of Electrical Engineering
and Computer Science, University of
Michigan, Ann Arbor, USA
2 Department of Electrical Engineering:
Control Systems, Eindhoven University
of Technology, Eindhoven, The
Netherlands
Mo#va#on and Objec#ve • Plug-‐in
electric vehicles (PEV) are
forecasted to gain significant market
share in coming years
• UIliIes are aware that their
networks may struggle to accommodate
en masse uncoordinated charging.
• Overloading of transformers may
result in transformer failure and
black-‐out of full residenIal areas.
• Centralized charging control schemes
are unrealisIc • PEV-‐owners desire
autonomy
• Research objec#ve
Solu#on: Coordinated Charging Control •
Open-‐loop Centralized Charging:
• Open-‐loop Incen#ve-‐based Coordinated
Charging:
• Centralized soluIon is recovered in
non-‐centralized way as • To
increase robustness, close the loop
with a model-‐predicDve control (MPC)
scheme:
Future Work • Improve rate of
convergence of incenIve-‐based method
• InvesIgate robustness of MPC
scheme • Study nonlinear representaIons
of temperature dynamics
Physical System Model
• Local PEV charging:
• Linearized transformer temperature (about
i = i*):
Case-‐study • IncenIve-‐based charging
control saIsfies thermal constraint
and achieves near-‐op#mal performance
Lagrangian Relaxation +
Dual Ascent Method
Exogenous disturbances
Complicating constraint prevents full separability!
Penalizes charging rates and deviations from reference charge
level (quadratic)
Disturbance forecast
Control (pseudo-price) signal
λ(p+1)
Iteration-dependent step-size parameter
Architecture of coordinated predicDve
PEV control
Formulate a non-‐centralized coordinated
PEV charging scheme that respects
thermal restricIons of transformer at
all Imes.
€
p→∞
Price Manager
20:00 22:00 24:00 02:00 04:00 06:00 08:00365
370
375
380
385
390
395
400
405
410
415
Time (hr)
Tem
per
atur
e,T
(K)
TmaxCentralizedIncentive-basedUncoordinated
20:00 22:00 24:00 02:00 04:00 06:00 08:0040
45
50
55
60
65
70
75
80
85
90
Time (hr)
Tot
alD
eman
d(k
W)
Inelastic Demand, d(t)Total demand - centralizedTotal demand -
incentive-basedTotal demand - uncoordinated
20:00 22:00 24:00 02:00 04:00 06:00 08:000
0.1
0.2
0.3
0.4
0.5
Time (hr)
Avg
.C
harg
ing
rate
(kW
)
CentralizedIncentive-basedUncoordinated
20:00 22:00 24:00 02:00 04:00 06:00 08:000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (hr)
Avg
.SO
C UncoordinatedCentralizedIncentive-basedAvg. SOC
requirement
Temperature Responses Load Profiles
Avg. PEV charging rates
Avg. SOC profiles
sn[k + 1] = sn[k] + ηnin[k] ∀n ∈ {1, . . . , N}sn[k] ∈ [0,
1]sn[k] ≥ Sn ∀k ≥ Knin[k] ∈ [in,min, in,max]
mini1[k],...,iN [k]
N�
n=1
Jn(in)
subject to
in[k] ∈ Πn�sn[0]
�∀k
ΦT [0]+Ψ
�N�
n=1
in[k]
M
�+Ψdv̂≤Tmax1K+1
Set of all in that satisfy above := Πn(sn[0])
Local Charging Problem
i(p)n [k] = argminin∈Πn(sn[0])
Jn�in�+�λ(p)[k]
��Ψin[k] ∀n
i(p)n
λ(p+1)[k] =
�λ(p)[k] + α(p)
�ΦT [0] +Ψ
�N�
n=1
i(p)n [k]
M
�+Ψdv̂ − Tmax1K+1
��
+
PEVs{1, 2, ..., N}
Substation Transformer
Price Manager / Coordinator
T [k]
{π(p)i }Ni=1
π[k]
λ(p)
v[k] ControlCommunication
{i(p)n }i∈Nin[k]
M
...
π1
π2
ππN−1
πN
...
Distribution-levelSubstation
Transformer
Distribution feeders
Load Aggregator
andPrice
Manager
��� ���
...
T
sN
s2
s1
sN−1
λ
i1
i2
iN−1
iN
i
M
M
sn state of chargein charging rateηn constant charging
parameterKn requested SOC target timeT transformer temperatureTmax
temperature limitTamb ambient temperatured inelastic background
demandM step-up voltage conversion factorτ, γ, ρ constant
transformer parameters
T [k + 1] = τT [k] + γ
��
n∈N
in[k]
M+ id[k]
�+ ρTamb[k]−
γ
2i∗
T [k] ≤ Tmax
