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QoS Routing in Smart GridHusheng Li and Weiyi Zhang

Abstract— Smart grid is an emerging technology which is ableto control the power load via price signaling. The communicationbetween the power supplier and power customers is a key issuein smart grid. Performance degradation like delay or outagemay cause significant impact on the stability of the pricingbased control and thus the reward of smart grid. Therefore,a QoS mechanism is proposed for the communication system insmart grid, which incorporates the derivation of QoS requirementand applies QoS routing in the communication network. Forderiving the QoS requirement, the dynamics of power load andthe load-price mapping are studied. The corresponding impactsof different QoS metrics like delay are analyzed. Then, the QoSis derived via an optimization problem that maximizes the totalrevenue. Based on the derived QoS requirement, a simple greedyQoS routing algorithm is proposed for the requirement of highspeed routing in smart grid. It is also proven that the proposedgreedy algorithm is a K-approximation. Numerical simulationshows that the proposed mechanism and algorithm can effectivelyderive and secure the communication QoS in smart grid.

I. I NTRODUCTION

In recent years, power grids are experiencing a revolution-ary technological transformation. One significant featureisthat electric appliances can receive realtime power price viacommunication networks and optimize its power consumptionlevel according to the current power price. Then, the powerutilization efficiency is significantly improved and the globalenergy consumption is reduced to combat the crisis of energyresource.

In smart grid, a key challenge is how to adapt the commu-nication network to the context of power price transmission.Obviously, the data flow of power price cannot be elastic sinceit should be realtime; otherwise, it may incur a significantloss if the expired power price is used. Therefore, the datatransmission of power price must be equipped with quality ofservice (QoS) guarantee. This incurs two important questionsunique to smart grid:

• How to define the QoS requirement in the context of smartgrid?

• How to ensure the QoS requirement from the homeappliance in the communication network?

In this paper, weanswer the above two questions by proposinga QoS system for smart grid.The proposed QoS frameworkplays the role of interface between the power market andthe communication networks. Once a set of reasonable QoSmetrics can be derived in the context of smart grid, manyQoS ensuing approaches can be applied to guarantee theperformance gain introduced by the technology of smart grid.

H. Li is with the Department of Electrical Engineering and Com-puter Science, the University of Tennessee, Knoxville, TN,37996 (email:husheng@eecs.utk.edu). W. Zhang is with the Department of ComputerScience, North Dakota State University, Fargo, ND, 58105. This work wassupported by the National Science Foundation under grants CCF-0830451 andECCS-0901425.

Fig. 1: The network perspective of smart grid

To answer the first question, we need to study the detailedmechanism of power price. Take video streaming for instance.To propose a QoS requirement for video streaming, the sourcecoder must be aware of the impacts of different factors likedelay or jitter on the video quality and then derive a suitableQoS requirement. Therefore, we study the impact of QoSparameters on the reward of home appliance. For simplicity,we study only two QoS parameters, namely the delay andoutage probability. The framework proposed in this paper alsoapplies to many other QoS metrics. We first introduce themechanism of power price based on the dynamics of load.Then, we build a reward system for the home appliance basedon the power price and the utility function of the appliance,thus obtaining the impact of delay and outage on the rewardof home appliance. Finally, the QoS requirement is derived byoptimizing the reward.

To answer the second question, we focus on routing method-ologies meeting the derived QoS requirement. We focus onproviding multiple QoS-aware routing within multiple (morethan 2) constraints. Given the heterogeneity of the smart grid,traditional schemes, such as fully polynomial-time approx-imations [12] [5] [13], cannot be directly applied due tothe requirements of high computing and storage capabilities.An efficient, which can be implemented by both powerfuland resource-limited devices, and effective, which providesprovably-good performance, algorithm is needed for the QoSrouting in smart grid. In this part, we present a simple greedyalgorithm for the multi-constrained QoS routing. Moreover,we prove that our greedy algorithm is aK-approximation (Kis the number of constraints). In addition, our solution canbeimplemented in a distributed manner.

The remainder of this paper is organized as follows. Thesystem model is introduced in Section II. Then, the QoSrequirement is derived in Section III while the QoS routingis discussed in Section IV. Numerical results and conclusionsare provided in Sections V and VI, respectively.

II. SYSTEM MODEL

We consider a simplified model for smart grid by consid-ering only the QoS requirement in the power price inquiry.

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We assume that a home appliance receives power price fromthe power market. A QoS requirement is sent from the homeappliance to the control center of the communication network.Then, the control center assigns one or more route for thehome appliance to guarantee the QoS requirement. Smartdevices, such as smart meter, and electricity generator canbeviewed as the nodes throughout a network. All the transmis-sion medium, such as fiber, wireless, broadband over powerline, WiMax, GPRS, Ethernet, and radio, form the links in anetwork. As shown in Fig. 1, the whole infrastructure of smartgrid can be represented by a communication network structure,which is designed to optimize a smart grid investment.

It is worth noting that smart gird is a heterogeneous network.Various electric equipments, with dramatically differentre-source limits, such as computing power, storage capability, areintegrated in the grid. Meanwhile, wireless network technologyis utilized in combination with a utilities fiber or Ethernetcommunications infrastructure. To provide QoS-aware routingfor smart grid, we must consider the heterogeneity of thenetwork and provide solutions that could be applied for allthe devices in the networks.

III. D ERIVATION OF QOS REQUIREMENT

A QoS requirement usually includes specifications likeaverage delay, jitter and connection outage probability. Toderive the QoS requirement, the following problems shouldbe addressed in the study:

• How to describe the probabilistic dynamics of the powersystem?

• How to evaluate the impact of different QoS specifica-tions on the smart grid system? For example, how doesa long communication delay affect the system perfor-mance?

• How to derive QoS requirement due to the correspondingimpact?

In this section, we provide an approach to address the abovethree key questions and thus derive the QoS requirements fordelay and outage probability.

A. Probabilistic Dynamics of the Power System

Power price is typically determined by locational marginprice (LMP) [1] driven by the load which varies with time.A constrained optimization problem can be used to derive theLMP from the load and other parameters, where the Lagrangefactors of the constraints are considered as prices [9]. Inpractical systems, we can use a piecewise curve, as illustratedin Fig. 2, to accomplish the mapping between the load and theprice. Note that, we have finite numbers of prices, denoted byQ, in Fig. 2. Therefore, we denote byq1, q2, ..., qQ theseprices. The intervals of loads corresponding to the pricesq1,..., qQ are denoted byJ1, ..., JQ, respectively. We assumedthat the load is uniformly distributed within the correspondinginterval given the price.

The load is random due to many random factors like thepower generation and consumption level. We can model it

Fig. 2: An illustration of the mapping between load and LMP.

as the positive part of a Gaussian random variable, whoseprobability density function (PDF) is given by

f(Dt) =exp

(

− (Dt−µt)2

2σt

)

∫Dmax

0exp

(

− (y−µt)2

2σt

)

dy, (1)

whereDt is the load at time slott, Dmax is the maximalpossible load,µt andσt are the expectation and variance.

Then, we model the Gaussian distribution parameters asfunctions of the elapsed time. Suppose that, at time slot 0,the true value of the load isD0. Then, we assume that theload distribution at time slott satisfies that following laws:

• The expectationµt of the Gaussian distribution is equalto D0. The rationale is that the prediction should beunbiased.

• The varianceσt satisfiesσt = θt, whereθ is a parameterand can be estimated from measurements, i.e. the varianceincreases linearly with the elapsed time, which is similarto a Brownian motion.

B. Impact of Delay

At time slot t, the power price and power consumption aredenoted bypt andxt, respectively. We assume a time-invariantutility function for the power consumption and denote it byU(xt). The decision of power consumption is based on theknown power price, which means thatxt is a function ofpτt .For simplicity, we assume that the optimal power consumptionlevel maximizes the following metric:

xt(p) = argmaxx

(U(x) − px) , (2)

wherep is the price adopted by the home appliance. It couldbe different from the true value due to delay. We assumethat U is an increasing, strictly concave and continuouslydifferentiable function. We also assume that the first orderderivative ofU , denoted byU̇ , ranges from∞ to 0. Basedon these assumptions, the optimal power consumption level isthus given byxt(p) = U̇−1(p), which is derived from the firstorder condition of optimality, i.e.̇U(x)− p = 0.

Suppose that the communication delay isd time slots.Then, at time slott, the price used for optimizing the powerconsumption level ispt−d. Hence, the cost incurred by thecommunication delay, as a function of the delay, is given by

C(d) = E [U(x(pt))− ptx(pt)

− (U(x(pt−d))− ptx(pt−d))] , (3)

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where the expectation is over all realizations of the powerprice and can be computed using the probabilistic dynamicsof the power price discussed in Section III. A.

C. Impact of Outage

It is also possible that the communication link experiencesan outage such that the home appliance cannot obtain therealtime power price. In such a situation, the home appliancecan only use a default power price, which is independent ofthe time. We assume that the default power price equals theaverage power price, which is denoted byp̄. Then, the expectedloss incurred by the outage is given by

L(ζ) = ζE [U(x(pt))− ptx(pt)− (U(x(p̄))− ptx(p̄))] , (4)

whereζ is the outage probability.

D. Derivation of QoS Requirement

If there is no constraint on the delay, the delay require-ment of the home appliance should be as low as possible.However, it is expensive for the network to achieve a verylow communication delay. Therefore, the system can controlthe delay requirement using a delay dependent price, namelyP (d). Then, the delay requirement of the home appliance isto minimize the total cost, i.e. the average loss incurred byusing the old price and the price taxed by the communicationnetwork. The optimal delay requirement is then given by

d∗ = argmind

(C(d) + P (d)) . (5)

Similar approach can be applied for deriving the require-ment of outage probability. Suppose that there is a tax for thecommunication with outage probabilityζ, which is denotedby T (ζ). Then, the optimal requirement of outage probabilityis given by

ζ∗ = argminζ

(ζL(ζ) + T (ζ)) . (6)

When the QoS specification includes both delay and outageprobability, the optimal QoS requirement is then given by

(d∗, ζ∗) = argminλ,ζ

(1− ζ)C(d) + ζL(ζ) + P (d) + T (ζ). (7)

IV. QOS ROUTING ALGORITHM

After deriving the QoS requirements, we will study how todeliver transmission in smart grid with multi-constrainedQoSrouting problems withK ≥ 2 additive QoS parameters.

A. MCR Problem

A smart grid is modeled by an edge weighted directed graphG = (V,E, ω), whereV is the set ofn nodes, including endusers, smart meters and other electric devices,E is the set ofm edges, andω = (ω1, ..., ωK) is an edge weight vectorsothat ωk(e) ≥ 0 is the kth weight of edgee. For a pathp inG, the kth weight of p, denoted byωk(p), is the sum of thekth weights over the edges onp: ωk(p) =

∑

e∈pωk(e).

Definition 1 (Multi-Constrained Routing (MCR)): Givenan edge weighted directed graphG = (V,E, ω), with K

Fig. 3: Illustration of the MCR problem

nonnegative real-valued edge weightsωk(e) associated witheach edgee, a constraint vectorW = (W1, ...,WK) whereeachWk is a positive constant; and a source-destination nodepair (s, t). The MCR problem seeks ans → t path p suchthatωk(p) ≤ Wk, 1 ≤ k ≤ K. �

The inequalityωk(p) ≤ Wk is called the kth QoS con-straint. A path p satisfying allK QoS constraints is calleda feasible path or a feasible solutionof MCR problem. AnMCR problem is said to befeasibleif it has a feasible path,and infeasibleotherwise.

To see the incidences of this problem in smart grid, asshown in Fig. 3, one can consider that on each transmissionline, there are differentweightsassociated with it, representingthe energy consumption for the transmission, edge delay, edgereliability, etc. In smart grid, a transmission is required tosatisfy several constraints, such as delay, energy consumption,and transmission reliability. Assume that Electric generator (S)needs to provide QoS transmissions to the user (D). On eachlink, two different QoS metrics:costanddelay, are considered.If the constraint vectorW is (3, 5), in other words, if usersaim to find a path such thatcost ≤ 3, delay ≤ 5, path (1,2, 5), marked by dotted red links, is a feasible path. For theconstraint vector (4, 4.5), path (1, 3, 4, 5), marked by solidblue links, is a feasible solution. However, there is no feasiblesolution in this network for constraint vector (3, 4).

The MCR problem is known to be NP-hard [11], even forthe case ofK = 2. Although QoS routing in networks hasbecome an active area in recent years, little work, particularlyon performance-guaranteed multi-constrainedQoS routing,has been done in smart grid. Given the characteristics of smartgrid, there are several unique challenges for providing multi-constrained QoS routing. Among them, one of the biggestconcerns is routing for a heterogenous system like smartgrid. Various devices with different resources and capabilities,from powerful large electrical generator to resource-limitedsensors, are collaborated together. Most previous performance-guarantee QoS routing schemes requires strong computing ca-pability [2] [6] [5] [13]. However, these sophisticated schemescannot be directly applied in smart grid due to the stringentre-quirements on the memory and computing capability. Second,A smart grid is a large distributed system. Most of the time,QoS routing decision must be made locally by each devicebased on its local information. For example, a smart meterneeds to decide whether to accept a QoS request based on itslocal reading and expectations. Most previous work, especiallywith performance guarantee, requires the globe knowledge ofthe network, and could not be directly applied to smart grid.Tobuild a scheme for diverse heterogeneous system, simple andefficient QoS routing scheme, which could be implemented by

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various devices, is needed. Our goal is to find a simple andeffective routing solution for smart grid.

B. Effective Scheme for QoS Routing in Smart Grid

To find simple and efficient solution that can be implementin a distributed manner, we target the problem from a differentperspective. Instead of studying theMCR problem directly, letus formulate anoptimizationversion multi-constrained QoSrouting problem.

Definition 2 (OMCR(G, s, t,K,W )): Given an undirectednetwork G=(V,E), with K nonnegative real-valuededgeweightsωk(e), 1 ≤ k ≤ K, associate with each edgee ∈ E; apositive vectorW = {W1, . . . ,WK}; and a source-destinationnode pair (s, t), MCR seeks ans − t path po such thatωk(po) ≤ δo · W, 1 ≤ k ≤ K, whereδo is the smallest realnumberδ ≥ 0 such that there exists ans− t pathp satisfyingωk(p) ≤ δ ·WK , 1 ≤ k ≤ K. �

We call δo the optimal valueof MCR and po ad optimalpath of MCR. Note that δo ≤ 1 if and only if MCRproblem is feasible. Sinceδo could be smaller than 1, theoptimization problemOMCR also introduces a metric tocompare two feasible solutions toMCR − the one with thesmaller correspondingδ value is regarded as a better solution.

A very simpleK-approximation algorithm, namedOMCR,is presented in Algorithm 1. The algorithm computes an aux-iliary edge weightωA(e) as the maximum of all edge weightsω1(e), . . . , ωK(e) divided by W1, . . . ,WK , respectively. Itthen computes a shortest pathPA using this auxiliary edgeweight. The pathpM is guaranteed to be aK-approximationof OMCR. Note that the auxiliary edge weights can becomputed locally at each node, and the shortest path can becomputed using Bellman-Ford algorithm. Therefore, ourK-approximation algorithm can be implemented as a distributedalgorithm, and can be used by existing routing protocols suchas OSPF [3].

Algorithm 1 OMCR(G, s,K, ~W, ~ω)

1: for each edgee ∈ E of G do2: Compute an auxiliary edge weightωA(e) = max

1≤k≤K

ωk(e)Wk

;

3: end for4: Compute a shortest pathPA from s to t with the auxiliary edge

weight functionωA

Theorem 1:The pathpA found by Algorithm 1 is aK-approximation toOMCR. In other words,

ωk(pA) ≤ K · δo ·Wk, 1 ≤ k ≤ K,whereδo is the optimal value ofOMCR. �

Proof: Sinceδo is the optimal value ofOMCR, there existsan pathpo such thatωk(po) ≤ δoWk. This means that

∑

e∈po

ωk(e) ≤ δoWk, 1 ≤ k ≤ K (8)

(8) can be presented as

∑

e∈po

ωk(e)

Wk≤ δo, 1 ≤ k ≤ K (9)

Summing (9) overK constraints, we have

∑

e∈po

K∑

k=1

ωk(e)

Wk≤ K · δo (10)

SinceωA(e) = max1≤k≤K

ωk(e)Wk

≤K∑

k=1

ωk(e)Wk

, we have

∑

e∈po

ωA(e) ≤∑

e∈po

K∑

k=1

ωk(e)

Wk≤ K · δo (11)

SincepA is the shortest path with respect to edge weightfunctionωA, we haveωA(pA) ≤ ωA(po). Therefore,

∑

e∈pA

ωA(e) ≤∑

e∈po

ωA(e) ≤ K · δo (12)

Since ω(e)Wk

≤ ωA(e), 1 ≤ k ≤ K, we have

ωk(pA)

Wk=

∑

e∈pA

ω(e)

Wk≤

∑

e∈pA

ωA(e) ≤ K · δo, 1 ≤ k ≤ K

(13)Therefore, we know thatωk(pA) ≤ K ·δo ·Wk(1 ≤ k ≤ k),

and consequently, thatpA is aK-approximation toOMCR.

V. NUMERICAL RESULTS

In this section, we use numerical simulations to demonstratethe proposed mechanism and algorithm in this paper.

A. Simulation Setup

The PJM five-bus system [8] is used for simulations, asillustrated in Fig. 4. The mapping between LMP and load(one curve for each bus) is given in Table I (the first columnshows the lower boundary of the corresponding load interval{qi}q=1,...,8) [4].

$10600MW

$1440MW

$15170MW

Brighton

Alta

Park City

E

A

B C

Solitude

$30520MW

Sundance

$35200MW

Generation Center Load Center

Limit = 240MW

Limit = 400MW

D

300MW

300MW

300MW

Fig. 4: The base case modified from the PJM five-bus system.

We assume that utility function isU(x) = 1000 logx andthe price for communication delay isP (d) = e4/d. Note thatthese functions are chosen arbitrarily for illustrative purpose.For practical systems, they can be estimated from historicaldata.

5

TABLE I: LMP ($/MWh) versus load (MW)Load (MW) LMP(A) LMP(B) LMP(C) LMP(D) LMP(E)

0.00 10.00 10.00 10.00 10.00 10.00600.00 14.00 14.00 14.00 14.00 14.00640.00 15.00 15.00 15.00 15.00 15.00711.81 15.00 21.74 24.33 31.46 10.00742.80 15.83 23.68 26.70 35.00 10.00963.94 15.24 28.18 30.00 35.00 10.001137.02 16.98 26.38 30.00 39.94 10.001484.06 16.98 26.38 30.00 39.94 10.00

B. QoS Requirement

Fig. 5 shows the curves of cost versus different delays(measured in time slots) for homes served by the five buses,respectively. We observe that, for some buses, the cost in-creases monotonically with delay while the minimal cost isnot achieved by the minimal delay for other cases. Comparingthe results with Table I, we observe that, the higher the LMPis, the more sensitive the cost is to the delay. The curvesof cost versus different outage probabilities are shown inFig. 6. Again, we observe the non-monotonicity of the cost,which demonstrates the existence of the optimal requirementof outage probability.

0 2 4 6 8 100

50

100

150

200

250

300

350

delay

tota

l cos

t

ABCDE

Fig. 5: The curves of cost versus delay.

0 0.02 0.04 0.06 0.08 0.10

2

4

6

8

10

12

14

16

18

20

outage probability

tota

l cos

t

ABCDE

Fig. 6: The curves of cost versus outage probability.

The optimal requirements of delay and outage probabilitiesusing the joint optimization in (7) are shown in Figures 7and 8, respectively, for various values ofθ. Note that therange of the outage probability is confined between 0 and 0.1.We observe that there exists some fluctuation in the optimal

values. Particularly, the optimal QoS requirements of bus Eare quite loose. An explanation is that the power price changesmarginally for bus E. Therefore, home appliances served bybus E can degrade their QoS requirements to avoid the costfor communication.

60 80 100 120 140 160 180 2000

1

2

3

4

5

6

7

8

9

10

θ

optim

al d

elay

ABCDE

Fig. 7: The optimal delay requirement when the delay andoutage probability are jointed optimized.

C. QoS Routing

In this section, we present some numerical results to showthe performance of our simple greedy algorithm. We imple-mented our greedy algorithm of this paper (denoted byOMCRin the figures), and compared it with previous sophisticatedapproximation algorithmFPTAS of [12] (denoted byFPTASin the figures), which is the best approximation solution tothe OMCR problem. Our numerical results are presented inFigs. 9 and 11, where each figure shows the average of100runs.

First, to compare the routing performance, we define the

lengthof a found pathp is l(p) = max1≤k≤K

ωk(p)

Wk. We say path

p1 is better than pathp2 is l(p1) < l(p2).In Fig. 9, we show thequalitative comparison of the

performances ofOMCR and FPTAS using the metric ofpath length. We setǫ = 0.5 for FPTAS, which means thatFPTAS returns a 1.5-approximation to theOMCR problem.We observed that for all test cases,FPTAS generally provides

60 80 100 120 140 160 180 200

10−2

10−1

θ

optim

al o

utag

e pr

obab

ility

ABCDE

Fig. 8: The optimal requirement of outage probability whenthe delay and outage probability are jointed optimized.

6

Case 1 Case 2 Case 30

5

10

15

20

25

30

35

40

Com

paris

on o

f pat

h le

ngth

s

OMCPGreedy

Fig. 9: Comparison of number of better paths

better results. In among the 100 connections, in 30% to 43%of the test cases (30% for the tight scenario, 35% for themedium scenario, and 43% for the loose scenario), the pathcomputed byFPTAS is better than the path computed byOMCR. Meanwhile, in 20% to 35% of the test cases(20% forthe tight scenario, 25% for the tight scenario, and 35% for theloose scenario), the path computed byOMCR is better thanthe path computed byFPTAS. We can conclude thatOMCRhas similar performance asFPTAS.

infeasible tight loose

0

0.5

1

1.5

2

Ru

nn

ing

Tim

e (

se

c)

GreedyOMCP

Fig. 10: Comparison of running times

Next, we compare the running times between theOMCRand FPTAS in Fig. 10. As we expected, the running timeof OMCR is much shorter than the running time ofFPTAS,while the two algorithms computed paths with comparablelengths.

80 100 120 140 1600

5

10

15

20

25

30

35

40

45

Run

ning

Tim

e (s

ec)

OMCPGreedy

Fig. 11: Scalability of the schemes

To study the scalability ofFPTAS and OMCR with thenetwork size, we used four more random network topologies

with the following sizes: 80 nodes with 314 edges, 120 nodeswith 474 edges, 140 nodes with 560 edges, 160 nodes with 634edges, to test the computational scalability of the algorithms.Here we have usedǫ = 0.5 and medium scenario for thesetest cases. The running times of these two algorithms areshown in Fig. 11. We can see that the running time ofFPTAS increased dramatically with the increased networksize. Meanwhile,OMCR requested much less amount of timeand is not affect much by the size of the networks. This provesthat our solution will be more adaptable in fast-developingsmart grid enviroment.

VI. CONCLUSIONS

We have addressed the QoS routing in smart grid. To derivethe QoS requirement, we have analyzed the dynamics ofpower market and the impact of communication metrics likedelay and outage on the revenue of home appliances. Then,we model the QoS derivation as an optimization problemthat maximizes the total reward. Based on the derived QoSrequirement, a simple greedy routing algorithm has beenapplied to secure the QoS and address the strict realtimerequirement. We have shown that the proposed algorithm is aK-approximation. We have run numerical simulations whichdemonstrated the effectiveness of the proposed mechanism andalgorithm.

ACKNOWLEDGEMENT

The authors would like to thank Prof. Fangxing Li in theDept. of EECS in the University of Tennessee, Knoxville, forthe discussion on the load-price mapping in power market.

REFERENCES

[1] R. Bo and F. Li, ”Probabilistic LMP forecasting considering loaduncertainty”, IEEE Trans. Power Syst., vol.24, pp.1279–1289, Aug.2009.

[2] R. Guerin and A. Orda, “QoS routing in networks with inaccurate infor-mation: theory and algorithms,”IEEE/ACM Transactions on Networking;vol. 7, pp. 350-364, 1999.

[3] C. Huitema, Routing in the Internet2nd ed. Englewood Cliffs, NJ:Prentice-Hall PTR, 2000.

[4] F. Li, “Continuous locational marginal pricing (CLMP),” IEEE Trans.Power Syst., vol.22, pp.1638–1646, Nov. 2007.

[5] D. H. Lorenz and D. Raz, “A simple efficient approximationscheme forthe restricted shortest path problem,”Operations Research Letters, vol.28, pp. 213-219, 2001.

[6] J. M. Jaffe, “Algorithms for finding paths with multiple constraints,”Networks, vol. 14, pp. 95-116, 1984.

[7] K. Moslehi and R. Kumar, “Smart grid - A reliability perspective,” inProc. of IEEE Innovative Smart Grid Technologies Conference (ISGT),2010.

[8] PJM, PJM Training Materials (LMP101). [Online]: Available:http://www.pjm.com/services/training/train-materials.html.

[9] S. Stoft,Power System Economics – Designing Markets for Electricity,IEEE/Wiley, 2002.

[10] J. Wen, P. Arons and E. Liu, “The role of remedial action schemes inrenewable generation integrations,” inProc. of IEEE Innovative SmartGrid Technologies Conference (ISGT), 2010.

[11] Z. Wang and J. Crowcroft, ”Quality-of-service routingfor supportingmultimedia applications,”IEEE J. Sel. Areas Commun., vol. 14, no. 7,pp. 1228-1234, Sep. 1996.

[12] G. Xue, A. Sen, W. Zhang, J. Tang and K. Thulasiraman, “Finding apath subject to many additive QoS constraints,”IEEE/ACM Transactionson Networking; vol. 15, pp. 201–211, 2007.

[13] G. Xue, W. Zhang, J. Tang, and K. Thulasiraman, “Polynomial time ap-proximation algorithms for multi-constrained QoS routing,” IEEE/ACMTransactions on Networking, vol. 16, pp. 656-669, 2008.

A

B

C

D

E

0

5

10

15

20

25

30

35

40

45

450 550 650 750 850 950 1050 1150 1250 1350

Load (MW)

LMP ($/MWh)

A B C D E

Load (MW) Price ($/MWh)Power

consumption level (MWh)

environment power supplier home appliance

LMP

Load

J1 J2 J3 J4 J5

p1

p2

p3

p4

p5

p6

Power / Price

Price Inquiry

Power Source Home

80 100 120 1400

5

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35

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45

Run

ning

Tim

e (s

ec)

OMCPGreedy

Power supplier

Smart meter

report

Power price

L, 0 L, 1 L, 2 L, T

H, 0 H, 1 H, 2 H, T

...

...

Communication

networks

Home appliance

Power market

Communication

control centerPower

price

QoS requirement

Power Price

Adjustment

Price Inquiry

(optional)

Power

Consumption

Adjustment

Power supplier Home appliance