Data Communication Over the Smart Grid

Data Communication over the Smart Grid G. N. Srinivasa Prasanna1, Amrita Lakshmi2, Sumanth. S1, Vijaya Simha1, Jyotsna Bapat1 , and George Koomullil2 1

2

Department of Information Technology, IIITB, Electronics City, Bangalore, India. Corporate Innovation & Technology, NXP Semiconductors India Pvt Ltd, Nagawara, Bangalore, India

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 timevarying, 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.

This Multi-user communication over the low-voltage powerlines 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.

Keywords—Smart grid, channel modelling, OFDMA, sub-band allocation

I. INTRODUCTION

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 transmitterreceiver pairs, aggregate and minimal capacity) in implementing ubiquitous sensing in a smart grid.

T

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 twoway 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.

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

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.

273

II. CHANNEL MODEL

and

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. A

B

Z2(t)

(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.

C

Z3(t)

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 nonRayleigh 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.

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.

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.

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 Zieq(f,t), can be calculated. Hi+1(f)

H(i)(f)

Head End Z1(f)

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]

− Z sinh(γ l )   V  V   cosh(γ l ) 0 L   S    = −1 sinh(γ l ) cosh(γ l )   I   I  L  Z  0  S 

where f is the frequency. The input impedance

 Z cosh(γ l ) + Z 0 sinh(γ l )  Z in = Z 0  L   Z 0 cosh(γ l ) + Z L sinh(γ l ) 

Head end Z1(t)

ω = 2πf

is given by

Z ieq(f)

Z i+1eq(f)

ZLi (f)

ZLi+1 (f)

ZL(f)

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,

(1)

V

i

( f ) = Z Li ( f , t ) I i ( f )

(3)

Hi(f) can be calculated. We have explicitly indicated the time varying and frequency-dependent nature of the impedance

γ = ( R + jωl )(G + jωC ) = α + j β where α is the propagation constant and β is the phase constant

274

as Z

i +1

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],

( f , t ) above. Under quasi-static assumptions, the

L

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 Z

i +1 L

( f ) . Using equations 1, 2, and 3, it is

N ( f ) = 10 ( K −3.95 x10

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

 Z i + 1 ( f ) * Cosh (γ l ) + Z * Sinh (γ l )  0  eq  Z (f)= in  Z * Cosh(γ l ) + Z i + 1 ( f ) * Sinh (γ l )   0  eq i eq

(f)=Z

i Z L in

( f )/

(

Z

i L

( f ) + Zi ( f ) in

Z H

where

i

( f ) = Hi −1

Z

i +1 eq

(f)

(

Z

i eq

i eq

0

)

sinh ( γ l )

W / kHz

(5)

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.

(4)

(f)

( f ) cosh ( γ l ) + Z

f / Hz )

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.

i

Z

−5

)

III. MODEL RESULTS Equations 1 through 4 characterize the performance of the system of multiple nodes (meters) communicating to a headend 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.

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.

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.

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.

275

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.

A. Channel Dynamics: Mean Attenuation & Capacity

Figure 3: Transfer function bounds (min, average, max) as a function of frequency for 10 meter section

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 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

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 K ij

 i   H ( f ) − E H i ( f ) * H j ( f )− E H j ( f )   Var H i ( f ) Var H j ( f )    

( f ) = E (

(

(

)) ( ) (

))

(

)

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.

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 ˆj to

IV. OFDMA SYSTEM

user i such that the metric Γ is maximized. For simplicity, it is assumed that N m = N s or one sub-band is available per meter.

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.

Xij is the SNR seen by meter i in subband j. 1) Initialization I = {1,..., N m} , J = {1,..., N s } , Xij = zeros(Nm,Ns)

X ij = SNRij , ∀i ∈ I , ∀j ∈ J 2) For: i = 1,..., N m Ns

X itotal =

3) while I ≠ Ø, J ≠ Ø Piˆ = min i ( X itotal ) min

Qˆ i

ˆ = max j ( X iˆ

min , j

min j

)

I = I − {iˆmin } J = J − { ˆj} 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.

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:

µ SNR

ij

j =1

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.

Γ=

∑X

(6)

2 1 + σ SNR

  Q = Q ^ , Q ^ ,........, Q ^  N m , jN m   1, j1 2, j2

µ SNR = E (Q ) =

1 Nm

Nm

∑Q

i , ˆj

i =1 2

2 σ SNR = E[(Q − µ SNR ) ], i = 1,..., N m , j = 1,..., N s

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 ˆj is selected with effective

Figure 7. Block diagram of an OFDMA system for simultaneous transmission of data from meters to the head-end

SNR of Qi , ˆj . µSNR is the average of the effective SNRs seen by

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. Z8 122m

Z4

T9 135m

398m

Z19

Z9

399m 197m

Z1

Z3

293m

T4

Z7

120m

Z14

106m

Z18

T8 137m

333m

Zs

T1 277m

448m

T2 224m

452m

T5

T7

481m

454m

T10 155m

485m

T14 368m

T15 334m

T6

Z6

T11

122m

Z --- Meter Impedances

Z5

338m

412m

Z15 104m

417m

257m

T12

T --- Taps

T16

Z10 411m

208m

442m

T18

123m

219m

321m

Z2

453m

150m

T3

T19

148m

T13

Z13

T17

372m

Z16

367m

Z1 - 141 Z2 - 493 Z3 - 300 Z4 - 142 Z5 - 654 Z6 - 554 Z7 - 428 Z8 - 255 Z20 Z9 - 410 Z10 - 443 Z11 - 655 Z12 - 647 Z13 - 549 Z14 - 528 Z15 - 690 Z16 - 638 Z17 - 335 Z18 - 224 Z19 - 562 Z20 - 133

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

VI. SIMULATION RESULTS

142m

Z11

Z12

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.

Z17

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.

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

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

278

[5]

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.

[6]

[7] [8]

[9] [10] [11]

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

[12]

M1 M2 M3 M4 -1

M5 M6

10

[13]

M7 M8 M9

BER

-2

[14]

M10

10

M11 M12 M13

[15]

M14 M15 M16

-3

10

M17

[16]

M18 M19 M20

-4

10

-10

-5

0

5 10 15 Transmit power(dBm)

20

25

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

0

10

M1 M2 M3 M4 -1

M5 M6

10

M7

BER

M8 M9 M10

-2

10

M11 M12 M13 M14 M15 M16

-3

10

M17 M18 M19 M20

-10

-5

0

5

10 15 20 Transmit power(dBm)

25

30

35

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

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[2]

[3]

[4]

D. Cooper and T. Jeans, “Narrowband, low data rate communications on the low-voltage mains in the CENELEC frequencies-part I: noise and attenuation,” IEEE Tr. Power Delivery, vol. 17, no. 3, July 2002. M. Zimmerman, K. Dostert, “A Multipath Signal Propagation Model for the Power Line Channel in the High Frequency Range”, Proc. of 3rd Int’l Symp. Power Line Comm. and its Applications, 1999, pp. 45-51. O. G. Hooijen, “A channel model for the residential power circuit used as a digital communications medium,” IEEE Tr. Electromagnetic Compatibility, vol. 40, no. 4, pp. 331-336, November 1998. “Signalling on low-voltage electrical installations in the frequency range 3 kHz-148.5kHz, BS Standard EN50065-1:1992, 1992.

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