Abstract—The emerging smart grid system requires high speed

sensing of data from all the sensors on the system within a few

power-cycles. The Advanced Metering Infrastructure is a simple

example of such a system where all the meters on a certain grid

must be able to provide the necessary information to the master

head end within a very short duration (fraction of a second for

real time load control). Wireless solutions for the smart grid

systems have been implemented, but cannot access all grid

locations, especially enclosed ones. In this paper, we present an

interactive, OFDMA based communication system optimized for

operation over the low voltage power lines in the CENELEC

bands A and B. A channel model representing statistical time-

varying, and frequency selective powergrid channels and noise is

presented. Using this model, an OFDMA based transceiver is

developed that is capable of providing smart grid like access

capacity to the head end connected to multiple meters. The

transceiver is optimized based on the channel model and the

characteristics derived from the structure of the grid. Keywords—Smart grid, channel modelling, OFDMA, sub-band

allocation

I. INTRODUCTION

HE efficiency, safety and reliability of the electricity

transmission and distribution system can be improved by

transforming the current electricity grids into an interactive

(customers/operators) service network or the smart grid [11].

Advanced Metering Infrastructure (AMI) provides consumers

with the ability to use electricity more efficiently and provides

utilities with the ability to monitor and repair their network in

real time. Smart grid communication technologies must allow

the powergrid control center to access each meter connected to

it interactively several times in a second, offering dynamic

visibility into the power system. Some implementations exist

of this infrastructure using wireless technologies. In this paper

we explore the use of the existing infrastructure; i.e. the low

voltage power-lines for high speed, reliable simultaneous two-

way communication between the head end (i.e. the nearest

powergrid communication hub) and meters located on

different parts of the network. Data communication through

the power grid offers several advantages in that new

infrastructure is not required, and in principle even enclosed

sensors not accessible by wireless technologies can be read.

This Multi-user communication over the low-voltage power-

lines must deal with several issues such as, large number of

sensors, time varying circuit behaviour, high

background/impulsive noise and varying grid topologies.

In the first part of this paper, we present a channel model

representing statistical time-varying, and frequency selective

powergrid channels. The model views the current grid

configuration as a MIMO/MISO (Multiple Input

Multiple/Single Output) channel. In the second part of the

paper, we use this channel information to develop an OFDMA

based transceiver. For multi-access, the sub-band based carrier

allocation is made based on the uplink channel seen by each

meter. The nature of the uplink channel changes depending

upon location of the meter with respect to the head end and

this adaptation allows us to construct a system that can provide

reliable and fair communication between the meters and the

head end, irrespective of the meter’s location.

Our work extends previous work on integrated meters by Choi

et. al [16] and others by tightly integrating a statistical channel

model with the design of the multi-access physical layer. We

extend Barmada et al [5]’s analysis to include statistical

correlated variations in the channel as seen by the meters in a

smart grid. Compared to multi-access schemes in low voltage

powerline network in the frequency range of 1-20 MHz [15],

we consider the CENELEC bands A and B,. While we

primarily discuss meter reading, our approach actually treats

fundamental communication issues (channel responses,

correlations amongst responses between different transmitter-

receiver pairs, aggregate and minimal capacity) in

implementing ubiquitous sensing in a smart grid.

The paper has been organized as follows. Section II discusses

the MIMO nature of the channel and the correlation between

frequency responses seen by various meters. Section III

analyzes a representative channel in detail. Section IV presents

the OFDMA based transceiver that utilizes the channel

information for sub-band allocation to individual meter.

Section V and VI discuss the simulation environment and

results, followed by conclusions in section VII.

Data Communication over the Smart Grid

G. N. Srinivasa Prasanna1, Amrita Lakshmi

2, Sumanth. S

1, Vijaya Simha

1, Jyotsna Bapat

1 , and

George Koomullil2

1Department of Information Technology, IIITB, Electronics City, Bangalore, India.

2Corporate Innovation & Technology, NXP Semiconductors India Pvt Ltd, Nagawara, Bangalore, India

T

978-1-4244-3790-0/09/$25.00 ©2009 IEEE 273

II. CHANNEL MODEL

Figure 1 depicts the key challenge in simultaneous data

communication over the grid. A grid bus is shown with time

varying loads Z1(t), Z2(t), and Z3(t). The time-variation of

these loads represent primarily the complex frequency

dependent, switching behavior in the CENELEC bands of

residential and commercial powered equipment.

Fig. 1. Time Varying Grid Bus – Only Vertical Impedances Named

For the analysis, these time varying loads are modeled as

random variables. It is assumed that meters/sensors exist at

these same loads, and their (typically large) impedance is

subsumed in the impedances presented by these loads.

Communication has to be simultaneously established between

the meters and the head end located at say, a step down

transformer. The analysis determines the channel responses to

A, HA(f), to B, HB(f), and to C, HC(f), and shows that they are

correlated and time-varying, exhibiting in general non-

Rayleigh fading behaviour. This extends the work of Barmada

et al, [5] where bounds on time-varying channel responses

using wavelets are presented, but correlations are not

discussed.

We shall analyze this MISO channel based on transmission

line theory. Our analysis treats MISO communication between

the root and the leaves of a tree structured bus with branches.

Now, any node in a tree can be treated as the root. Hence the

same analysis is applicable to the MIMO channel - when

meters/sensors talk to each other simultaneously. The signal is

additionally impacted by colored background noise and

impulse noises in time and frequency domains. Details of these

models are discussed next.

A. Channel Frequency Selectivity

From transmission line theory, the propagation of the

incident and reflected waves is governed by the matrix

equations relating the sending and receiving end voltages and

currents Vs, Is and VL, IL, as [7]

cosh( ) sinh( )0

1 sinh( ) cosh( )

0

l Z lVV

SLl lI IZL S

γ γ

γ γ

−

= −

(1)

( )( )R j l G j C jγ ω ω α β= + + = +

where α is the propagation constant and β is the phase constant

and fπω 2= where f is the frequency. The input impedance

is given by

cosh( ) sinh( )

00 cosh( ) sinh( )

0

Z l Z lLZ Zin

Z l Z lL

γ γ

γ γ

+=

+

(2)

Propagation in tree networks (Figure 2) can be analyzed using

this matrix equation to recursive propagate the leaf

impedances to the source, and the signals to the leaves from

the source using voltage/current division (Equation 4 below).

Given the wide variety of power-grid topologies, the channel

responses are variable, and details are presented in Section II

and III. Given LT grid dimensions of a few kilometers

between transformers and the load, multiple nulls can be

expected in the CENELEC band stretching to 125KHz.

Impulse responses ranging to 0.5 milliseconds or more can

occur. Signal attenuations can be easily 60+ dB. The

transceiver system has to robust to these impairments.

B. Channel Statistical Behavior and Dynamics

Not only is the channel frequency selective, but the

switching on/off of loads causes fading. This fading is

however, unlike the classical Rayleigh fading, since it is due to

time-varying circuit elements. Strictly speaking, time-varying

loads cause nonlinear behaviour, and Fourier analysis is not

directly applicable. However, if the nonlinearity changes

slowly relative to the frequencies of interest, then we can use a

quasi-static approximation, and use Fourier analysis, with

time-varying and stochastic impedances. Our analysis below is

based on this quasi-static approximation.

Figure 2 shows signal propagation through the ith node (load

and meter) (i=0,1,2, …) of a tree branch. Using Equations 1,

and 2, the complex transfer function Hi(f) from the head-end

to the ith node, and equivalent impedance Z

ieq(f,t), can be

calculated.

Figure 2 Recursive Analysis of a Tree Branch, H(i)(f) is the transfer function

from the source to node i at frequency f. All impedances are time-varying.

Using the relations between voltage and current at node i,

( ) ( ) ( ),i i i

V f Z f t I fL= (3)

Hi(f) can be calculated. We have explicitly indicated the

time varying and frequency-dependent nature of the impedance

Z1(f) Z

i+1eq(f)

Head

End

ZLi+1

(f) ZL(f)

Z ieq(f)

ZLi (f)

H(i)(f)

Z1(t) Z2(t) Z3(t)

A B C

Head

end

Hi+1(f)

274

as ( )1,

iZ f t

L

+above. Under quasi-static assumptions, the

impedance will be modeled as a sample of a time-invariant

impedance ensemble, drawn from an appropriate distribution.

We shall denote this random variable (which is a function of

frequency), as ( )1iZ f

L

+. Using equations 1, 2, and 3, it is

easy to show that, Hi(f) is given recursively (voltage division

in Equation 1) in terms of transfer function to the (i-1)th node,

Hi-1

(f) as

( )( )

( )

( ) ( ) ( ) ( )( )

( )( )

( ) ( ) ( )( )

1* ( ) * ( )

0

1* ( ) * ( )

0

1

cosh sinh0

/

iZ f Cosh l Z Sinh l

eqiZ f

in iZ Cosh l Z f Sinh l

eq

i i i iZ f Z Z f Z f Z f

eq L in L in

iZ f

eqi iH f H

iZ f l Z l

eq

γ γ

γ γ

γ γ

++

=+

+

= +

−=

+

(4)

where ( )1i

eqZ f+ is the equivalent impedance seen towards

the leaves at the (i+1)th node (Figure 2). The impedances are

calculated in the backward recursion, and the transfer

functions in the forward direction. We reiterate that our

analysis is a quasi-static approximation, since all the

impedances in Equations 3 and 4 are time-varying.

Since the impedances in Equation 4 are random, so is the

transfer function. Furthermore, due to the recursion, the

channel response at different meters is correlated, and exhibits

complex fading dynamics. The correlation is also frequency

dependent. It should be noted that the same equation can be

used for branched structures. The correct statistical behaviour

of the equivalent impedance at each branch point has to be

determined, and the recursion executed. If two branches are

statistically similar, they each lose 3dB in signal, and hence 1

bps/Hz in the maximal (Shannon) capacity.

Equations 3 and 4 can be numerically solved to determine the

joint probability distribution of the (complex) transfer function

at some or all points. Alternatively, Monte-Carlo simulations

can be used to estimate various parameters of interest (mean,

correlations, etc - our work has used this approach).

Additionally, under special cases of the probability distribution

of the loads, ranging from a 2-state Markov process (on-off

loads) to a uniform load, closed-form solutions are possible for

single stage networks. If the load is 2-state Markov, so is the

transfer function, but in other cases, the p.d.f of the transfer

function differs from that of the load. Details are skipped for

brevity. These equations are used in Section III to get

theoretical insight into the communication potential of the grid

in the CENELEC band.

C. Channel Noise

Noise measurements on power lines Hooijen [3] have shown

that the background noise in power line channels is colored,

with the noise power spectral density (PSD) decreasing with

increasing frequency. The PSD of the background noise can be

approximated as in [3],

kHzWfN HzfxK /10)( )/1095.3( 5−−= (5)

where, K follows a Gaussian distribution with mean µ = -5.4

and standard deviation, σ = 0.5. This is used to model the

colored noise in the simulations.

D. System Capacity Estimation

Based on the channel responses to different nodes as per

equation (4), the noise as per equation (5) and a given transmit

power, the received SNR at each node, and hence the

(frequency dependent) limiting channel capacity can be

calculated as per Shannon’s formula. These results are used to

evaluate the actual implementation of our OFDMA system

with respect to the theoretical bounds.

III. MODEL RESULTS

Equations 1 through 4 characterize the performance of the

system of multiple nodes (meters) communicating to a head-

end over the power-grid. We reiterate that while the equations

have been written for a single branch, the recursive

decomposition of a tree structure enables them to be used for

arbitrary trees. Since any tree node can be treated as the root,

the same can be used, for estimating channel performance

between any two points, in either direction. Hence Equations 1

through 4 represent a general MIMO channel, where the

impedances at the ith

node are computed from a leaf node to

the node chosen as the root.

For analyzing the fundamental properties of this channel, a

representative structure has to be chosen. We chose to analyze

a section with 10 meters, corresponding to the longest branch

in the structure used in Section IV (corrections for transmit

power at each branch are 3dB, as already mentioned). We

assume that the transmitter uses 1 Watt of power over the

entire CENELEC band, corresponding to a per channel power

of 0 dBm in our 1024 channel OFDMA system described later.

The noise is as per Equation 5 from [3]. Equations 3 and 4 are

used in a Monte Carlo simulation for channel analysis. Loads

are randomly selected from a uniform distribution, with a

maximum up to ten times the characteristic impedance.

Statistical parameters like min/mean/max of the transfer

function, Shannon capacity, etc are estimated from the

simulation. We also estimate the minimum simultaneous rate

of transmission between all the meters and the head-end, by

allocating larger spectrum to meters with high

attenuation/poorer SNR.

275

A. Channel Dynamics: Mean Attenuation & Capacity

Figure 3: Transfer function bounds (min, average, max) as a function of

frequency for 10 meter section

Figure 4. Received SNR and spectral density (Bps/Hz) in CENELEC band

Figure 3 shows the minimum, average, and maximum of the

transfer function as a function of frequency in the CENELEC

band,. Figure 3 shows that while the mean attenuation for the

1st meter is less than 10 dB, the maximum attenuation can go

as high as 50 dB. For the last meter in the span, attenuation

ranges from 25 dB to 80 dB at the lower band edge, and from

40 to 140 dB at 125 KHz. Note that these are the limits of

channel responses, and do not necessarily correspond to any

specific channel. Indeed resonant loads can cause the response

to increase with frequency, and this will be shown in Section

IV. Figure 3 shows that attenuation can be excessive in bad

cases, for spans 10 meters or more deep. Mesh architectures

may have to be used in these cases.

Figure 4, which plots average system spectral density

(bps/Hz) shows that the close by meters can reach very high

spectral densities of 15 Bps/Hz at the higher band edge, while

far off meters can manage 1-2 bps/Hz at the lower band only.

Figure 5 shows aggregate system capacity. It shows that the

aggregate capacity can be as high as 1 Mbps+ for the closest

meter, decreasing to less than 20 Kbps for the last meter, if the

entire CENELEC band is allocated to the respective meter.

The cumulative capacity over all 10 meters is about 5 Mbps.

Figure 6 shows minimum rate available over all meters,

decreases from 1 Mbps+ to about 7 Kbps if 10 meters are

transmitting simultaneously. If even more meters communicate

simultaneously, capacity drops dramatically. These results

indicate that powergrid with sections composed of more than

about 10-15 meters have to adopt mesh architectures, with

multi-hop communication.

Figure 5: Available Total Capacity at each Meter While we have discussed a sample grid configuration, clearly

the approach using the recursive equations is valid for general

structures.

Figure 6: Minimum rate (Kbps) at which all meters can simultaneously

transmit, as a function of number of meters simultaneously transmitting.

B) Channel Correlations

From the classical results of Foschini et al [6], MIMO

channels are characterized by the correlation between the

transfer functions of different channels. Since the signal

propagates sequentially down the grid, the transfer function to

different taps is correlated, impacting MIMO performance. We

can compute the covariance coefficient to different taps as

( )( ) ( )( )( ) ( ) ( )( )( )

( )( ) ( )( )

*i i j j

ij i j

H f E H f H f E H fK f E

Var H f Var H f

− −

=

Monte-Carlo simulations based on Equations 3 and 4, using

random impedances, are used to determine Kij(f). The results

276

indicate that correlation is high between different nodes at low

frequency (9 KHz), where the correlation coefficient is close

to unity everywhere. At such a low frequency, the entire

network behaves like a resistive system. Correlation

progressively decreases as frequency increases (125 KHz),

with a minimum less than 40%. Details are skipped for brevity.

IV. OFDMA SYSTEM

Orthogonal frequency division multiple access (OFDMA)

systems have been in use for various wireless systems

including WiMax and 3GPP systems for optimizing the

simultaneous use of available bandwidth for data transmission

from mobile stations to the base station. A unique subset

(referred to as a sub-band) of the available subcarriers is

assigned to each user in an OFDMA system for the

simultaneous transmission of data. The most prominently used

allocation schemes are interleaved OFDMA and sub-band

based OFDMA. Though the interleaved assignment benefits

from frequency diversity, it is shown to be more sensitive to

errors in frequency offset estimation [12]. The sub-band based

assignment divides the available bandwidth into a number of

sub-bands and assigns them to different users. This scheme

may see performance degradation when any of the sub-bands

sees a long, deep null.

We propose an OFDMA system (Fig. 7) for the smart grid

with multiple meters, which uses an allocation algorithm based

on the SNR seen by each meter in individual sub-bands during

channel estimation and aims to maximize the data rate of all

meters fairly and uniformly. It should be noted that the goal of

the algorithm is uniform access capability for all meters and

not maximizing the overall data rate.

The performance metric to be maximized for sub-band

allocation attempts to simultaneously increase SNR, as well as

reduce differences between SNR seen by different meters. One

possible metric achieving this can be defined as:

21 SNR

SNR

σ

µ

+=Γ (6)

smSNRSNR

N

i

jim

SNR

jNjj

NjNiQE

QN

QE

QQQQ

m

mNm

,...,1,,...,1],)[(

1)(

,........,,

22

1

ˆ,

,,2,1^^

2

^

1

==−=

==

=

∑=

µσ

µ

where Nm denotes the number of meters in the grid, Ns denotes

the number of available sub-bands . The average SNR for ith

meter in jth

sub-band is denoted as SNRij. For each meter i, the

best possible sub-band of index j is selected with effective

SNR ofji

Q ˆ,. µSNR is the average of the effective SNRs seen by

each meter over its assigned sub-band of operation.

Maximizing Γ is a balance between high average SNR, and

low variance between quality of communication link seen by

different meters on the grid irrespective of their distance from

the head end.

SNR based sub-band allocation algorithm:

The sub-band allocation function allocates sub-band j to

user i such that the metric Γ is maximized. For simplicity, it is

assumed that sm NN = or one sub-band is available per meter.

Xij is the SNR seen by meter i in subband j.

1) Initialization

},...,1{ mNI = , },...,1{ sNJ = , Xij = zeros(Nm,Ns)

ijij SNRX = , JjIi ∈∀∈∀ ,

2) For: mNi ,...,1=

∑=

=sN

j

ijtotali XX

1

3) while ≠I Ø, J ≠ Ø

)(minminˆ

totaliii

XP =

min min

max ( )ˆ ˆ ˆ,Q Xji j i j

=

}ˆ{

}ˆ{ min

jJJ

iII

−=

−=

The algorithm first selects the meter with lowest total SNR

across all sub-bands and assigns the sub-band with highest

SNR to that meter. The meter and the sub-band thus assigned

to it are removed from the set of meters and sub-bands and the

process continues till all the meters are assigned a sub-band.

Faraway meters experiencing hostile channel characteristics

are allowed to choose first and are allocated best sub-bands for

the channel they are facing, thereby achieving the goal of best

possible connectivity for all meters, irrespective of their

physical location.

Figure 7. Block diagram of an OFDMA system for simultaneous transmission

of data from meters to the head-end

277

V. A SAMPLE GRID

The configuration of the power line grid used in the current

study is given in Figure 8, with meter Mi having (resistive)

impedance Zi. For clarity, we label the meter by its impedance

only.

Zs

Z1

T1 T10T7T5T3T2 T18T14 T15 Z20

Z14

Z11

Z8

Z3

Z4

Z15

Z17

T16Z6

Z5

T6

T17 Z16

T8Z7

T12

T11 Z10

Z12

T13 Z13

T19Z18

Z19T9 Z9

277m

333m

452m224m

Z2

321m

481m

448m

293m

485m

208m

122m

454m

399m

197m

150m

398m

122m

155m

219m

411m

257m

367m338m

148m

368m 334m

137m

123m

417m

142m

372m

104m

442m

453m

106m

120m

412m

T4

135m

T --- Taps

Z --- Meter Impedances

Z1 - 141

Z2 - 493Z3 - 300

Z4 - 142

Z5 - 654

Z6 - 554Z7 - 428

Z8 - 255

Z9 - 410

Z10 - 443Z11 - 655

Z12 - 647

Z13 - 549

Z14 - 528Z15 - 690

Z16 - 638

Z17 - 335

Z18 - 224Z19 - 562

Z20 - 133

Figure 8. The grid configuration used in the current study.

This sample powergrid consists of 20 meters downstream of

a transformer Zs. The available frequency band from 9 kHz to

125 kHz has been divided into 1024 channels, with channels

width of 113.28 Hz. Of the 1024 channels, 800 channels are

used for upstream data transmission by 20 meters (from which

sub-bands consisting of 40 distinct carriers each are assigned

to each meter). Two preamble OFDM symbols are used for

channel estimation and carrier acquisition. With inclusions of a

cyclic prefix of 256 samples, the total transmission time per

burst with two preamble symbols and two OFDM symbols is

approximately 44 ms. It should be noted that the difference in

propagation time from different meters is in microseconds and

is considered negligible in comparison to the RMS delay

spread due to signals reflections of multipath channels.

The responses of the channels from each meter placed on

the leaf node of the grid configuration to the concentrator are

estimated using Equations 3 and 4 in Section III. The impulse

and frequency responses of these channels are plotted in

Figures 9 and 10.

Figure 9. Impulse responses of all channels obtained for the grid

configuration.

Figure 10. Frequency responses of all channels obtained for the grid

configuration.

VI. SIMULATION RESULTS

Simulations were conducted using Matlab with the

parameters of the OFDMA system as discussed in previous

section. A sub-band of 40 adjacent subcarriers, is assigned to

each meter using two types of sub-band allocation techniques.

The first technique uses the sub-band allocation algorithm

discussed in section IV to allocate appropriate sub-bands to

the meters. The second one allocates the sub-band randomly.

Background colored noise, as discussed in [3] is used in the

simulations.

The minimal bit rate achieved at a BER of 10-3

is about 2

Kbps/meter, which is 30% of the predicted bound of 7Kbps

from our model in Figure 6. The total available capacity

(entire band) at each meter (Mi with impedance Zi from Figure

8) is about 1Mbps at the first meter, consistent with Figure 5.

This shows that even simple systems like the one proposed can

perform reasonably well.

The BER performance for each meter using both mappings

are plotted versus the transmit power for each meter in figures

11 and 12. The figures show a more consistent BER

performance for each meter using the sub-band allocation

technique. The metric for SNR-based allocation algorithm was

found as 1.7489 and for the random allocation as 0.0980.

These results are consistent with the goal of the system, which

is uniform and fair access for all the meters, rather than high

overall bit rate. Further improvements can be achieved by

uneven sub-band allocation to the meters and powerful error

correction codes such as LDPC [14]. It should be noted that

current results are for un-coded BPSK data, coding techniques

yield even better results.

VII. CONCLUSIONS

We have investigated the potential of Low Voltage Power

Lines for real time communication, satisfying the requirements

of a smart grid monitoring system. A statistical time-varying

channel model has been developed, and using which, a

multiple access scheme in the form of OFDMA with

appropriate sub-band allocations has been proposed.

Appropriate sub-band allocation has been shown to be of

278

paramount importance in gaining access to all the meters

simultaneously. Channel capacity bounds have been evaluated

using the model, and the transceiver performance is shown to

approach those bounds. For realistic channel topologies,

minimal capacities of a few Kbps per second per meter can be

achieved with 20 meters simultaneously transmitting at a total

channel power of 1 W. Further improvements using

sophisticated bit loading techniques and FEC codes are

currently under investigation. Our analysis yields insight into

the general MIMO problem, encountered when ubiquitous grid

sensors communicate with each other.

-10 -5 0 5 10 15 20 2510

-4

10-3

10-2

10-1

Transmit power(dBm)

BE

R

Performance of 20 meters using OFDMA with SNR-based sub-band allocation

M1

M2

M3

M4

M5

M6

M7

M8

M9

M10

M11

M12

M13

M14

M15

M16

M17

M18

M19

M20

Figure 11. Performance of 20 meters with SNR-based sub-band allocation.

-10 -5 0 5 10 15 20 25 30 35

10-3

10-2

10-1

100

Transmit power(dBm)

BE

R

Performance of 20 meters using OFDMA with random sub-band allocation

M1

M2

M3

M4

M5

M6

M7

M8

M9

M10

M11

M12

M13

M14

M15

M16

M17

M18

M19

M20

Figure 12. Performance of 20 meters with random sub-band allocation

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