Lauteletraffic for smart_grids

Teletraffic Engineering
for Smart Grids
Laura Giarr´e,
Giovanni Neglia, Giuseppe Di Bella and Ilenia Tinnirello
L. Giarr´e October 2nd, 2014

Goal
I Energy demand and production need to be constantly
matched in the power grid.
L. Giarr´e - Teletraffic for Smart Grids October 2nd, 2014 - 2

Goal
I The traditional paradigm: to continuously adapt the
production to the demand

Goal
I is challenged by more variable and less predictable green
energy sources

Goal
energy sources
I Direct control of deferrable loads to shape the demand.

Goal
energy sources
I Analogies with flow admission control: A request for network
resources (bandwidth or energy) delayed on the current
network status to guarantee performance metrics.

Goal
energy sources
I Analogies with flow admission control: A request for network
resources (bandwidth or energy) delayed on the current
network status to guarantee performance metrics.
I A family of control schemes to achieve the desired trade-off
among resources usage, control overhead and privacy leakage.

Traditional Power Grid: Dumb?
Guarantee
I continuous matching between energy demand and production
I same frequency
I voltage and power constraints at each point
[Jeff Taft, Cisco]

Why smarter?
smarter = more communication + more computation
1. improve network resources utilization, by reducing the security
margin

Why smarter?
margin
I increasing energy demand but less money for infrastructure...

Why smarter?
margin
2. add new value-added services

Why smarter?
margin
2. add new value-added services
3. deal with renewable energies

Traditional Power Grid
transport
distribu-on
distribu-on
SMART
STUPID

Renewables: the challenge of location
transport
distribu-on
distribu-on

Renewables: the challenge of variability
[Barnhart et al, Proc. Energy and Environment, 6:2804, 2013]
Production more variable than demand
I EU renewable penetration target: 20% by 2020

Need to adapt demand to production
Possible approaches
I Smooth demand through storage (buffer...)

Possible approaches
I Demand-response

Possible approaches
I Demand-response
I Direct load control

Direct Load Control
Direct Load Control (DLC)
I Allows energy utilities to control electric loads at the
customers’ premises.

Direct Load Control
I DLC was used in critical situations to prevent blackouts by
shutting down these loads.

Direct Load Control
I DLC was used in critical situations to prevent blackouts by
shutting down these loads.
I Recently DLC has been used as a way to shape energy
demand peaks

Shaping the aggregated power demand
T_s T_e
Time t
Power Demand
Expected Power Demand
Peak Demand Controlled Power Demand
P
g
Shaped Peak
Demand
I Load control does not change the total energy demand on a
long time interval
I it can shape the instantaneous power demand by postponing
the operation time of some appliances

Our target
t
PD(t)
w/o
control
w/
control
P*
PD(t)<P*

Our target
t
PD(t)
w/o
control
w/
control
P*
PD(t)<P*
Limited intelligence
I user decides when the appliance should start
I smart plug asks and turns on/off

Our target
t
PD(t)
w/o
control
w/
control
P*
Prob{PD(t)>P*}<ε
Unknown energy demand

Our target
t
PD(t)
w/o
control
w/
control
P*
Prob{PD(t)>P*}<ε
Large number of loads

Our target
I Determine the control policy: how many appliances to admit?
I Quantify the QoS experienced by the user: average delay?
t
PD(t)
w/o
control
w/
control
P*
Prob{PD(t)>P*}<ε

Control Mechanism
I A simple control mechanism that guarantees that the
instantaneous power demand exceeds a given bound with
probability smaller than .

Control Mechanism
I Only a stochastic characterization of the power demand for
each class of appliances is required.

Control Mechanism
I Two different operation paradigms:

Control Mechanism
I deterministic: appliances need to ask a controller the
permission to start, and the controller will limit the number of
simultaneously active appliances to n(t).

Control Mechanism
I deterministic: appliances need to ask a controller the
permission to start, and the controller will limit the number of
simultaneously active appliances to n(t).
I probabilistic: an activation probability function—p(t)—is
broadcast periodically to all the appliances; appliances do not
notify the controller but they start with probability p(t) and
postpone their decision to the time t + T with probability
1 p(t).

p(t)

Control Mechanism
I 1st paradigm:

Control Mechanism
I 1st paradigm:
I requires more communication exchanges between the
appliances and the controller.

Control Mechanism
I 1st paradigm:
I requires more communication exchanges between the
appliances and the controller.
I reveals more information about the customers’ habits.

Control Mechanism
I 2nd paradigm:

Control Mechanism
I 2nd paradigm:
I works in an open-loop fashion

Control Mechanism
I 2nd paradigm:
I does not disclose any private information.

Control Mechanism
I 2nd paradigm:
I does not disclose any private information.
I The lack of an exact knowledge of the current number of
active appliances causes a lower average utilization of the
resources in order to satisfy the constraint.

w.
prob.
q
Turn
on?
YES

Control Mechanism
I We combine the two paradigms by means of a probability q:

Control Mechanism
I when an appliance wants to start operating, it will ask the
permission to the controller with probability q,

Control Mechanism
I it will decide autonomously using the function p(t) with
probability 1 q.

Control Mechanism
I it will decide autonomously using the function p(t) with
probability 1 q.
I The parameter q can then be chosen in order to achieve the
wished trade-off among resources’ usage, control overhead
and privacy leakage.

Mixed Approach
w.
prob.
1-‐q
w.
prob.
p(t)
START
POSTPONE
w.
prob.
1-‐p(t)

query
ON
Start
attempt
1-q
q
1-p(t)
t=t+T
p(t)
Start
Coin toss
Rx ON

Interplay of privacy and control overhead
By increasing q we gradually:
I reduce privacy by exposing more the energy profile of each
user
I increase control overhead because the controller needs to
directly interact with a larger number of appliances
I increase the efficiency.

Interplay of privacy and control overhead
Privacy
Efficiency
Control
overhead
q=0
q=1

Publications
Related publications
I Modeling Energy Demand Aggregators for Residential
Consumers, CDC13
I Unidirectional Probabilistic Direct Control for Deferrable
Loads, Infocom14 workshop CCSES
I Unidirectional Direct Load Control through Smart Plugs,
CDC14
I Smart Plugs: a Low Cost Solution for Programmable Control
of Domestic Loads, AEIT14
I Scalable and Privacy-Preserving Admission Control for Smart
Grids, Infocom15

Teletraffic tools
I Our main goal:
I to show how teletraffic tools
I can be effectively used to achieve a large scale deployment of
DLC to shape energy demand peaks.

Admission Control for Integrated Services
t
R(t)
w/o
control
w/
control
C*
Prob{R(t)C*}ε
C*

How many appliances to admit?
Determine the maximum value n such that:
ProbfPD(t) Pg
I Xi (t) random power consumption from appliance i at time t

ProbfPD(t) Pg
I MX (s) = log(E[esX ])

ProbfPD(t) Pg
I PD(t) =
Pni
=1 Xi

ProbfPD(t) Pg
I PD(t) =
Pni
=1 Xi
I Cramer theorem:
ProbfPD(t) Pg exp (infs0[nMX (s) sP])

ProbfPD(t) Pg
I PD(t) =
Pni
=1 Xi
I Cramer theorem:
ProbfPD(t) Pg exp (infs0[nMX (s) sP])
I simple calculations, easy to generalize to different classes of
appliances

A different constraint (time duration of violation)
Rate
Energy
Bucket
of
size
B
Rate
P*
PD(t)
L(t)
ProbfL(t) = 0g

A different constraint
Rate
Energy
Bucket
of
size
B
Rate
P*
PD(t)
Data
Rate
PD(t)
Service
Rate
P*
Data
Buffer
of
size
B
L(t)
Q(t)
ProbfL(t) = 0g = ProbfQ(t) = Bg

A different constraint (time duration of violation)
Rate
Energy
Bucket
of
size
B
Rate
P*
PD(t)
Data
Rate
PD(t)
Service
Rate
P*
Data
Buffer
of
size
B
L(t)
Q(t)
ProbfQ(t) = Bg exp

sup
t0
inf
s0

[stn(s; t) s(B + Pt)]
(s; t) =
1
st log E
h
esX(0;t)
i

Average delay?
Tsc
Ts
n
D
Acve
appliances
#
me
M(t)/D/∞
M(t)/D/n
1. Quantify for a given number of aggregated users N and a
given energy supplier’s request (K,[Ts ,Te]) the average delay
experienced by the users during the control period
2. Which scale should the aggregator reach in order to be able to
produce significant power load reduction with tolerable service
delays for the users?

Queueing model: Analysis Challenges
I time-varying system
- non-homogeneous arrival process (assumed to be Poisson)
- change of servers’ number
3000
2500
2000
1500
1000
500
0
6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6
time t [h]
active users u(t)

Queueing model: Analysis Sketch
Tsc
Ts
c
Ac$ve
appliances
#
$me
M(t)/D/∞
M(t)/D/c
Calculate:
1. probability distribution of the number of appliances active in
Tsc (Poisson distributed with parameter
R Tsc
TscD (x)dx)
2. queue probability distribution in [Tsc ;Tsc + D],
[Tsc + D;Tsc + 2D],. . . and then the delay for an activation
request arriving in t Tsc
(PfW(t) kD xg =
P1p
=0 qp(t x)
Pkcp1
j=0 dj (t x; t))
3. the average delay W (Tsc ;Te) =
R Te
Tsc (t)E[W(t)]dt
R Te
Tsc (t)dt

Numerical Results:
Ts = 10AM, D = 90min.
Reductions related to mean requested power
60
90
120
150
3000
5000
180
100
200
300
400
120
100
80
60
40
20
0
500
control time interval [min]
mean queue delay [min]
power reduction [KW]
10000

Numerical Results:
Ts = 10AM, D = 90min.
120
100
80
60
40
20
0
100 KW 200 KW 300 KW 400 KW 500 KW
power reduction
mean queue delay [min]
3000
10000
Ts-Te=180min
Ts-Te=150min
Ts-Te=120min
Ts-Te=90min
Ts-Te=60min

Open loop control
t
PD(t)
w/o
control
w/
control
P*
Prob{PD(t)P*}ε

Open loop control
t
PD(t)
w/o
control
w/
control
P*
p(t)
Prob{PD(t)P*}ε
If the appliance starts operating at time t, the plug lets it work
with prob. p(t) and postpone the decision by time T with
prob. 1 p(t)

Activation Request Process
t
λ(t ) × × × × × × × × × ×
λ(t ) p(t )
t
×
× × × ×
Tsc Te
T
λ(t )(1−p(t )) p(t+T )
λ(t )(1−p(t ))(1−p(t+T )) p(t+2T)
t
t
t
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
λc (t ) × × ×× ×× × ×× ×
×
× × × ×
Tsc Te

t
λ(t ) × × × × × × × × × ×
λ(t ) p(t )
t
×
× × × ×
Tsc Te
T
λ(t )(1−p(t )) p(t+T )
λ(t )(1−p(t ))(1−p(t+T )) p(t+2T)
t
t
t
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
λc (t ) × × ×× ×× × ×× ×
×
× × × ×
Tsc Te
I The process of admitted requests is Poisson

t
λ(t ) × × × × × × × × × ×
λ(t ) p(t )
t
×
× × × ×
Tsc Te
T
λ(t )(1−p(t )) p(t+T )
λ(t )(1−p(t ))(1−p(t+T )) p(t+2T)
t
t
t
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
λc (t ) × × ×× ×× × ×× ×
×
× × × ×
Tsc Te
- with rate c (t) = p(t)
PKmax
k=0 (t kT)
Qki
=1(1 p(t iT ))

t
λ(t ) × × × × × × × × × ×
λ(t ) p(t )
t
×
× × × ×
Tsc Te
T
λ(t )(1−p(t )) p(t+T )
λ(t )(1−p(t ))(1−p(t+T )) p(t+2T)
t
t
t
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
×
× × × ×
Tsc Te
λc (t ) × × ×× ×× × ×× ×
×
× × × ×
Tsc Te
- with rate c (t) = p(t)
PKmax
k=0 (t kT)
Qki
=1(1 p(t iT ))
- The number of active appliances at time t is a Poisson
r.v. with parameter nc (t) =
R t
tD c ( )d

Power
I PD(t) =
PNi
=1 Xi (t) where N Pois(nc (t))
I ProbfPD(t) Pg ! nc (t) n

The control policy
Goal: determine the control probability p(t) that
I guarantees nc (t) n in [Ts ;Te]
I and minimizes the delay
Policy
I admit new requests if nc (t) n
I block them if nc (t) n
I admit requests at the same rate active appliances terminate if
nc (t) = n
p(t) =
8
:
0 if nc (t) n
min1ptDtD(;
()eq()
eq(t) ) if nc (t) = n
1 if nc (t) n
(1)

Activation Delay Analysis
N (t )
Nc (t )
t
N (t )≥Nc(t)
Tsc Te Te+T
I Total delay=
R Te+T
Tsc (N( ) Nc ( )) d;
I #appliances experiencing the delay =N(Te) N(Tsc )
I
E[W] = lim
S!1
PSi
=1
R Te+T
Tsc

N(i)( ) N(i)

d
c ( )
PSi
=1

N(i)(Te) N(i)(Tsc )

=
R Te+T
Tsc
R
Tsc ((x) c (x)) dxd
R Te
Tsc (x)dx
;

Numerical Results
40
35
30
25
20
15
10
5
0
1000 1200 1400 1600 1800 2000
maximum Power P
g
[KW]
activation delay [min]
U=2500, 3000, 3500 T=5min
U

Numerical results
60
50
40
30
20
10
0
=1.4MW
4 12 20 30 50 70 90
T [min]
activation delay [min]
U=3000, 3500, 5000 P
g
U

More...
This approach holds also for
I random activation time
I variable power bound

Thanks, questions?
DEIM- University of Palermo- Italy
laura.giarre@gmail.com
giarre.wordpress.com

Interplay of Rates Control Policy
20
15
10
5
(t)
(t)
9 9.30 10 11 12 13 13.35
time t [h]
activation rates [users/min]
1
0.5
0
activation probability
U=3000 n*=895 T=5min
lambda
c
lambda
eq
lambda(t)
p(t)
T
sc
T
e
+
_

Instantaneous Number of Active Appliances
900
800
600
400
200
*
=895 T=5min
9 9.30 10 11 12 13 13.35
time t [h]
active appliances
U=3000 n
without admission control
with probabilistic admission control
T
e
T
sc
T
e
+D+T

Lauteletraffic for smart_grids

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