Reliability Engineering for WirelessCommunications in Special Protection Schemes of

Smart GridHusheng Li and Aleksandar D. Dimitrovski

Abstract— Special protection scheme (SPS) is an importanttechnology to enhance the reliability of power grid. In SPS,communications are needed to convey information and coordinatethe actions. In this paper, wireless communications are proposedfor the SPS system due to its low cost and fast deployment.Due to the high requirement on the reliability of SPS system,it is of key importance to improve the reliability of the wirelesscommunication infrastructure in SPS, since wireless communica-tions are subject to various random factors such as noise, fadingand interference. Hence, the framework of reliability engineeringis applied to the resource allocation of wireless communicationlinks, i.e., how to allocate the spectrum bandwidth to various linkssuch that the overall system reliability is maximized. To that goal,a general model of SPS is adopted and the resource allocationis modeled as constrained optimization problems. Both cases ofexclusive resource allocation and spectrum reuse are considered.Numerical simulations show that the reliability engineering forthe wireless communication links can significantly improve thereliability of SPS systems.

I. INTRODUCTION

The reliability of power system is of the first prioritysince accidents such as system instability or even blackoutin power grid may cause substantial damages. Hence, theprotection of power grid is an important component of thewhole system. Among various protection mechanisms, theSpecial Protection Scheme (SPS) [6] is an automatic protectionmechanism that detects abnormalities in power grid and takescorrective actions to recover the system reliability. Since theoutage of SPS may result in the loss of protection on the powersystem, the reliability of the SPS itself is also very important.

The reliability of SPS or many other protection systems hasbeen extensively studied [4] [7] [10] [16]. In SPS an importantcomponent is the communications among different units suchas merging unit which carries out measurements in substationsor logic solver which actuates the control actions. For example,the communication could be an Ethernet with the standard IEC61850 [3]. The communication schemes and the correspondingimportance in protection systems have been studied in [9][14]. In the future development of smart grid, communicationtechnology will play a more important role since it serves asthe ‘nerve’ of the whole power system. However, there have

H. Li is with the Department of Electrical Engineering and Com-puter Science, the University of Tennessee, Knoxville, TN (email:husheng@eecs.utk.edu). A. D. Dimitrovski is with Oak Ridge National Lab,Oak Ridge, TN (dimitrovskia@ornl.gov). This work was supported by theNational Science Foundation under grants ECCS-0901425 and CNS-1116826,as well as and UT-ORNL Science Alliance JDRD Award.

Fig. 1: An illustration of the components in SPS system

been very few studies on the reliability of the communicationinfrastructure for the protection systems.

In this paper, we study the resource allocation in the com-munication infrastructure in order to maximize the reliabilityof SPS system. In contrast to many existing studies, our studyis characterized by the following features:

• We consider wireless communications instead of wiredones. Although not widely deployed, there have been pro-posals on using wireless communications such as LongTerm Evolution (LTE) [15] or Worldwide Interoperabilityfor Microwave Access (WiMAX) [1] for smart grid, dueto their low cost, fast deployment and plug-and-playnature.

• There have been many studies on the resource allocationin wireless communication networks [8]. However, thevast majority of them are focused on maximizing theutility function measured in throughput with certain con-straints on the fairness. In a sharp contrast, in this paper,the resource allocation is to maximize the reliability, sincethe main challenge for communications in SPS is thereliability, not capacity.

We will adopt the general model for the SPS system [10],instead of a concrete example, as well as a general model forthe wireless communication infrastructure. Then, we considerthe sub-carriers in the spectrum as the system resource, andapply the theories in the reliability engineering [11] as if thesub-carriers are parts like bolts or transistors. We will considerboth cases in which the spectrum should be either exclusivelyassigned or can be shared by different communication links.To our best knowledge, there have not been studies on theresource allocation in wireless communication for smart grid

IEEE SmartGridComm 2012 Symposium - Communication Networks for Smart Grids and Smart Metering

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from the viewpoint of system reliability1. Meanwhile, thestudy also significantly helps the application of wireless com-munications in the protection systems in future smart grids.

The remainder of this paper is organized as follows. InSection II, the system model, including both the models ofSPS and wireless communications, is briefly introduced. Then,the resource allocations in both cases of exclusive assignmentand spectrum sharing will be studied in Sections III and IV,respectively. Finally, the numerical results and conclusions aregiven in Sections V and VI, respectively.

II. SYSTEM MODEL

In this section, we introduce the system model, includingboth the models of the SPS and the communication infrastruc-ture.

A. SPS Model

We follow the general framework in [10] to model theSPS system in smart grid. An illustration is shown in Fig. 1,which consists of two independent and redundant functionalsets. Each set has a phasor measurement unit (PMU), a timesynchronization source (TS), a merging unit (MU), a digitallogic solver (LS) and a switch (SW). Note that the two PMUsand TS’s can be shared by both sets; i.e., if one of the PMUs(TS’s) fails, the other PMU (TS) can still work for both sets.We assume that the LS’s, SWs and MUs in different sets arelocated in different places in order to avoid mutual interferenceand fire spreading.

Among the PMU, SW, LS and MU, a communicationinfrastructure is used to convey the corresponding information.In [10], an Ethernet communication media is used for the com-munication infrastructure, e.g., using the IEC 61850 standard[3]. In this paper, we assume that all the communication linksare realized using wireless communication technologies. Thetwo switches play the roles of base stations that exchangemessages among the different components in the system. Forsimplicity, we assume that there is only one transceiver in eachMU and each LS.

We denote by P ecomponent the failure probability of a

certain component which could be PUM, LS, TS or MU. Forsimplicity, we assume that the failure probability of the samecomponent is the same for both SPS sets. It is straightforwardto extend to the case of asymmetric failure probabilities.

B. Communication Model

We assume that an orthogonal frequency division multiplex-ing (OFDM) system is used for the communications, whichcould be LTE or WiMAX systems. There are totally N sub-carriers in the spectrum and each transmission can use MOFDM symbols. For simplicity, we assume that the binaryphase shift keying (BPSK) is used. For the six communicationlinks, we assign Nk sub-carriers to link k. Hence, in eachtransmission, we can use MNk bits to convey one packet. For

1A reliability engineering study is carried out for cognitive radio networksin [12]

Fig. 2: An illustration of the communication system model

simplicity, we do not consider the details of possible interfer-ence across different sub-carriers. We also do not consider thedifference of the channel qualities on different sub-carriers.Each sub-carrier looks the same for each communication link.We assume that L information bits, including the header,payload and security signature, are included in each packet. Ifa transmission fails, the link will retransmit the packet. If thetransmission fails for T times, we claim that the packet is lostsince it has missed the deadline. For simplicity, we assumethat the decoding procedures of different retransmissions aremutually independent. It can improve the performance ifwe consider hybrid-ARQ which collects the information indifferent transmissions; however, it makes the analysis morecomplicated. Hence, it is out of the scope of this paper.

Note that it is not necessary to allocate different sub-carriersto different links. If two links are far away from each other,we can assign the same set of sub-carriers to them. In thispaper, we consider the following two cases:

• Exclusive resource allocation: In this case, we assumethat all communication links are close to each other.Hence, two communication links cannot share the samesub-carrier due to the mutual interference.

• Resource allocation with spectrum sharing: In this case,two communication links that are far away from eachother can share the same sub-carrier. We can use a graphto represent the relationship of spectrum sharing.

The resource allocation of both cases will be discussed in thesubsequent two sections.

C. Possible ExtensionsNote that the system model considered in this paper is a

simplified and generic one. In our future study, we will extendthe model to more practical and more concrete cases in thefollowing aspects:

• Some of the communication links could be hard wired,e.g., via Ethernet.

• There could be multiple MUs or multiple LS’s, thusincreasing the number of communication links.

• Consider more practical communication systems such asLTE or WiMAX, as well as different channel qualitiesover different sub-carriers.

III. EXCLUSIVE RESOURCE ALLOCATION

In this section, we discuss the resource allocation withexclusive spectrum assignment. As we have mentioned, thisis reasonable when different communication links are close to

241

Fig. 3: The block diagram for risk analysis

each other compared with the wireless interference range. Wewill first carry out the risk analysis for the whole SPS system.Then, we study the resource allocation to minimize the risk.

A. Risk Analysis

Due to the model of SPS introduced in Section II, wecan draw the block diagram of the system in Fig. 3. Weobserve that the PMUs and TS’s are parallel due to theredundancy. In each set of SPS, the components, which includethe three communication links, are serial since the failure ofany component will make this set out of function. The twoserial components then form a parallel one since the protectionmessage can be conveyed if one (or both) of the sets worksnormally.

Now, we need to look into each communication link. Wecan consider each sub-carrier in each OFDM symbol as acomponent as well, which is coined bit-component in order todistinguish from the physical component in SPS. Recall thatwe have assumed that communication link k is assigned MNk

bits (M OFDM symbols and Nk sub-carriers). For simplicity,we assume that a hard decoding is used; i.e., each receivedbit is demodulated first and then the hard demodulation resultis used for channel decoding. When the noise over differentsub-carriers and different OFDM symbols is independent (thisis valid for white noise), it is reasonable to assume that thefailures of these bit-components are mutually independent, orequivalently the event of demodulation error is independentfor different bits. Then, the bit demodulation error probabilityis denoted by pke for communication link k, which depends onvarious factors such as shadowing and the distance betweenthe transmitter and receiver.

The packet error rate is a function of pke , L (the number ofuncoded information bits) and MNk (the number of encodedbits), whose exact expression could be very complicated oreven mathematically intractable (e.g., for turbo codes). Forsimplicity of analysis, we assume that the packet error rate isdetermined by the minimum Hamming distance dmin betweenany two codewords, which is reasonable in the high signal-to-noise ratio (SNR) regime. Furthermore, we assume thatdmin in the codes used for the communication is a maximum-distance code, which achieves the singleton bound [2], i.e.,

dmin = MNk ! L+ 1, (1)

which is reasonable for the Reed-Solomon codes. With thisassumption, we can approximate each packet as an mk

0-out-

of-nk0 system [13], where

mk0 = MNk !

!MNk ! L+ 1

2

"

" MNk + L

2, (2)

and nk0 = MNk; i.e., if mk

0 or more bit-components aredemodulated correctly, the packet can be decoded correctly.Furthermore, since we assume that each packet has T op-portunities of independent transmissions, each communicationlink can then be modeled as a system with T parallel sub-systems and each sub-system is a an mk

0-out-of-nk0 one with

component failure rate pke .Summarizing the above discussion, we obtain the probabil-

ity that the SPS system works normally, which is given by

Pr =!1! (P e

PMU )2"!

1! (P eTS)

2"

"#1!

$1! (1! P e

MU ) (1! P eSW ) (1! P e

LS)

"3%

k=1

(1! P ec,k)

&"

$1! (1! P e

MU ) (1! P eSW ) (1! P e

LS)

"6%

k=4

(1! P ec,k)

&', (3)

where the failure probability of communication link k, P ec,k,

is given by

P ec,k =

#

$nk0%

l=nk0!mk

0+1

&pke'l &

1! pke'nk

0!l(

nk0

l

)*

+T

. (4)

We can simplify (3) to

Pr = A

,1!

-1!B

3.

k=1

(1! P ec,k)

/

#-1!B

6.

k=4

(1! P ec,k)

/0, (5)

where the coefficients A and B can be computed using thefailure probabilities of various components, which are givenby

1A =

21! (P e

PMU )232

1! (P eTS)

23

B = (1! P eMU ) (1! P e

SW ) (1! P eLS)

. (6)

B. Resource AllocationThe purpose of resource allocation for the wireless com-

munications in SPS system is to maximize the reliabilityprobability, i.e.,

{N"k}k=1,...,6 = arg max

{Nk}k=1,...,6

Pr

2{Nk}k=1,...,6

3. (7)

Since the variables Nk, k = 1, ..., 6, are discrete, theoptimal solution can only be obtained by an exhaustive search.However, such an exhaustive search is not scalable whenthere are many communication links. Hence, in this paper wepropose an approximate algorithm by considering the spectrumallocations as continuous variables. This approach is valid

242

when L and N are both large, which is reasonable for practicalsystems.

First, we notice that the number of demodulation errors atcommunication link k can be written as

Ek =MNk%

p=1

ep, (8)

where ep is the random variable indicating the demodulationresult of the p-th bit: ep = 1 when the correspondingdemodulation is incorrect; ep = 0 otherwise. As we haveassumed, {ep}p=1,...,MNk

are mutually independent binaryrandom variables with expectation pke and variance pke!

&pke'2.

According to the central limit theorem, Ek!MNkpke!

MNk(pke!(pk

e )2)

satisfies Gaussian distribution with zero expectation and unitvariance, as Nk $ %. Then, the packet decoding errorprobability is given by

P (packet decoding error at link k)

= P&Ek > nk

0 !mk0

'

= P

#

44$Ek ! nk

0pke5

nk0

2pke ! (pke)

23 >

nk0

&1! pke

'!mk

05nk0

2pke ! (pke)

23

*

66+

" 1! !

#

44$nk0

&1! pke

'!mk

05nk0

2pke ! (pke)

23

*

66+ , (9)

when MNk and L are sufficiently large, where ! is thecumulative distribution function (CDF) of standard Gaussiandistribution.

Since the wireless communications for power system pro-tection should be very reliable, it is reasonable to assume thatthe argument in function ! is large. Hence, we can use thefollowing approximation:

1! !(x) " 1&2!

1

xe!

x2

2 , (8)

when x is sufficiently large. Then, we denote by xk theproportion of spectrum allocated to communication link k.Although xk can only take discrete values, we assume thatxk is continuous in order to simplify the analysis. We definefunction z as

zk(x) =MNx(1! pke)! MNx+L

25MNx

2pke ! (pke)

23 . (9)

Summarizing the above approximations and definitions,we can rewrite the optimization problem for the resource

allocation as

minx1,...,x6

71!B

3.

k=1

(1!

(1&2!

1

zk(xk)e!

z2k(xk)

2

))T8

#71!B

6.

k=4

(1!

(1&2!

1

zk(xk)e!

z2k(xk)

2

))T8

s.t. xk ' 0, k = 1, ..., 66%

k=1

xk = 1. (10)

It is easy to verify that the optimal solution to (10) satisfies(11) (on the top of the next page), where " > 0 is a constantplaying the role of Lagrange factor. The physical meaningof the above equations is that, at the optimal solution, thesensitivity of reliability for each communication link should bethe same; otherwise, it can achieve a higher reliability to swapsome bandwidth among the communication links. Note that itis impossible to solve the equations analytically. However, itcan be solved numerically; or, a numerical approach can beapplied directly to the optimization problem in (10).

After obtaining the optimal solution to the optimizationproblem (10), denoted by x"

k, k = 1, ..., 6, we can assign Nk =(Nxk) sub-carriers to communication link k. There could beat most 6 sub-carriers unassigned due to the ceil operation.These leftover sub-carriers can be randomly assigned to anycommunication links.

Note that the optimization problem (10) may not resultin the optimal solution of the original problem, due tothe approximation of Gaussian distribution, the approximateexpression of !(x) and the continuous assumption of x.However, the approximation simplifies the expression of thereliability probability and converts the discrete optimizationproblem to a continuous one, thus making the computationfeasible in practice.

IV. RESOURCE ALLOCATION WITH SPECTRUM SHARING

In the previous section, we assume that each sub-carriercannot be shared by two or more communication links in theSPS system, which is due to the co-channel interference andis valid when all communication links are close to each other.When two communication links are far away from each other,they can share the same sub-carrier in the spectrum. In thissection, we discuss how to allocate the spectrum with spectrumsharing. Note that this has not been studied in traditionalreliability engineering since the same bolt cannot be placedat two locations of a spacecraft.

A. Interference GraphWe use an interference graph to represent the conflict rela-

tionship among the communication links, as in many studieson wireless networks. In this graph, each node represents acommunication link. If two nodes are connected by an edge,the corresponding two communication links cannot share thesame spectrum. In practice, this conflict relationship maybe different in different frequency bands due to differentpropagation characteristics. For simplicity, we assume that the

243

dP ec,k(xk)

dxk=

9:

;

!B

"l !=k,l"3(1!P e

c,l(xl))(1!B"6

l=4(1!P ec,l(xl)))

, k = 1, 2, 3!

B"

l !=k,l>3(1!P ec,l(xl))(1!B

"3l=1(1!P e

c,l(xl))), k = 4, 5, 6

. (11)

Fig. 4: An example of interference graph

conflict graph is the same throughout the whole spectrumband. An illustration is given in Fig. 4, where we can see thatonce a sub-carrier is allocated to link 1, it cannot be assignedto links 2, 3 and 4. We denote by k * j if communicationlinks k and j interfere each other.

B. OptimizationFor the case with spectrum sharing, it is difficult to approxi-

mate the optimization problem by a continuous one, since it isdifficult to express the constraint. The constraint

<6k=1 xk = 1

may no longer hold since two communication links may sharethe same band such that the sum of the proportions could belarger than 1.

To address the challenge, we focus on the discrete opti-mization and divide the total N sub-carriers into Q > 6groups having equal numbers of sub-carriers (we assumethat Q divides N ). The sub-carriers are allocated to thecommunication links in groups. The larger Q is, the moregranularity the optimization problem can achieve, and themore the computational cost is. We denote by zlk the allocationof the l-th group for communication link l. zlk = 1 if group lis allocated to link k; zlk = 0 otherwise.

Then, the resource allocation problem is formulated as

min{zlk}l=1,...,Q,k=1,...,6

O({zlk}l=1,...,L,k=1,...,6)

s.t. zlk = 0, 1.

zlj + zlk + 1, ,j * k, (12)

where O is the objective function in (10) where xk =#Q

l=1 zlkQ .

V. NUMERICAL RESULTS

In this section, we use numerical results to illustrate theanalysis in this paper. Following the setup in [10], we assumethat the failure rates for the TS, MU, EM, SW and LS are all0.1 per year while the failure rate of PMU is 0.65 per year.The bit demodulation error rates of the six links are 0.1, 0.02,0.01, 0.08, 0.03 and 0.09, respectively. We assume N = 2048,T = 1 and L = 200.

1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

link

chan. allocationerror prob.

Fig. 5: Channel allocation after optimization.

205 210 215 220 225 230 235 240 245 2500

50

100

150

L

perfo

rmen

ce g

ain

(dB)

M=1M=2

Fig. 6: Performance gain when M = 1 and M = 2.

A. Exclusive Allocation

We first test the case in which the channels are allocated inan exclusive way. The optimization problem in (10) is solvedby using the gradient algorithm. The channel allocation after20 iterations is shown in Fig. 5, together with the bit errorprobability of each link. We observe that a link with a higherbit error rate receives more spectrum, in order to balance thereliability.

In Fig. 6, we show the performance gain, defined as theratio of the error rates of optimized sub-carrier allocationand equal sub-carrier allocation (in dB scale). We tested bothcases in which M = 1 and M = 2. We observe that theperformance gain of the spectrum optimization is significantwhen M = 1. However, there is no performance gain whenM = 2. The reason is that, when M = 2, the communicationis sufficiently reliable and the overall reliability is dominatedby other components.

244

1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

link

channel proportionbit error rate

Fig. 7: Channel allocation after greedy algorithm with spec-trum sharing.

0 10 20 30 40 50 60 70 80 90 100−22

−20

−18

−16

−14

−12

−10

−8

group index

log 10

(err

rate

)

greedy algorithmrandom 1random 2random 3

Fig. 8: The evolution of error rate when more channels areallocated.

B. Channel Allocation with Sharing

We assume that the interference graph is given in Fig.4. It is difficult to solve the integer programming in (12).Hence, we used a greedy algorithm to obtain a suboptimalsolution to (12). We first allocate 1.5L sub-carriers to eachlink. Then, we divide the remaining sub-carriers into groups,each having 4 sub-carriers. Each group is allocated to amaximum independent set (there are three maximum matchingsets: {1, 5, 6}, {2, 3, 5, 6}, {2, 3, 4}) which minimizes the errorprobability. The final proportion of spectrum is given in Fig. 7,in which we observe that links 1, 5 and 6 receive much morespectrum. The evolution of the error rate as more sub-carriergroups are allocated is shown in Fig. 8, in which the evolutionsof three realizations of random allocation are also shown.We observe that the greedy algorithm can decrease the errorrate much faster. The error rate finally saturates because thereliability is dominated by other components when sufficientsub-carriers have been allocated.

VI. CONCLUSIONS

In this paper, we have studied the resource allocationfor wireless communication systems in the SPS system ofpower grid, from the viewpoint of reliability engineering.We have proposed to use wireless communications to conveythe messages in SPS systems, rather than traditional wirednetwork, due to the low cost and fast deployment of wirelesscommunications. Then, we have considered the spectrumresource allocation for the wireless communication links withthe purpose of maximizing the overall system reliability. Byusing a general model of SPS systems, we have obtainedthe expression of the probability of normal operation of thesystem, based on which we have formulated an optimizationproblem with constraints of spectrum conflict. Then, we haveadopted a large system approximation such that the discreteoptimization problem is converted into a continuous one,thus facilitating the numerical solution. Both cases of exclu-sive spectrum allocation and possible spectrum sharing havebeen studied. Finally, we have used numerical simulations todemonstrate the validity of the proposed resource allocationscheme.

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