The effect of a smart meter on congestion and stability in a powermarket

Arman Kiani and Anuradha Annaswamy

Abstract— The efficiency, safety, and reliability of the elec-tricity transmission and distribution system of a power gridis expected to be significantly improved via a cyber-enabledenergy management. By using smart grid communication tech-nologies that offer dynamic information, the ability to useelectricity more efficiently and provide real-time informationto utilities is expected to be significantly improved. The specificmetering infrastructure that we study in this paper is a smartmeter located in suitable places in a power grid offering twoway communication regarding various data. In particular, westudy the effect of a smart meter with real time monitoring ofconsumption on energy imbalance, congestion due to constraintson transmission capacity, and the overall stability of thedynamic power market. A market with an elastic consumeris used to evaluate the results. Numerical studies of an IEEE30-bus are reported to illustrate the overall impact of a smartmeter.

I. INTRODUCTION

Energy generation, transmission and distribution in futurepower networks will be controlled by a new generationof ”cyber-enabled” and ”cyber-secure” energy managementsystems [2]. Figure 1 shows a conceptual architecture of thesmart grid [3] and illustrates the synergism of an informationnetwork with several sensors and actuators and the powersystem infrastructure, the combination of which will operateinteractively on different levels of generation, transmissionand distribution. The efficiency, safety, and reliability ofthe electricity transmission and distribution system of theresulting smart grid are expected to be significantly improved[7]. Smart grid communication technologies allow the powergrid control center to access each meter connected to itinteractively several times in a second, offering dynamicvisibility into the power system. Grouped under the rubric ofAdvanced Metering Infrastructure (AMI), these technologiesprovide consumers with the ability to use electricity moreefficiently and utilities with the ability to monitor and repairtheir network in real time. The introduction and availabilityof such technologies have fundamentally altered the mannerin which we must view and analyze power markets.

The specific metering infrastructure that we study in thispaper is a smart meter that may be typically deployed in

This work was supported by the Technische Universitat Munchen - Insti-tute for Advanced Study, funded by the German Excellence Initiative andby Deutsche Forschungsgemeinschaft (DFG) through the TUM InternationalGraduate School of Science and Engineering (IGSSE).

Arman Kiani is with the Institute of Automatic Control Engi-neering, Technische Universitt Mnchen, D-80290 Munich, Germany.arman.kiani@tum.de

Anuradha Annaswamy is with the Department of Mechanical Engineer-ing, Massachussets Institute of Technology, Cambridge, MA 02319, USA.aanna@mit.edu

a smart grid at a customer service location. This meterwill have two way communication, be able to remotelyconnect and disconnect services, record waveforms, monitorvoltage and current, and support time-of-use and real-timerate structures [2].

In a typical power grid, electricity pricing usually peaksat certain predictable times of the day and the season. Thisoccurs if generation is constrained at times when demandspeak causing more costly generation brought online. Theintroduction of a smart meter with real time monitoringof consumption as well as billing can cause the pattern ofconsumers energy usage to be more responsive to marketprices.

Power markets include a variety of participants includinggenerators, consumers, and Independent System Operators(ISO). The ISO is responsible for the pricing of the marketas well as the transmission lines. Consumers, in this paper,denote large load-serving entities. In general, market equilib-rium including the Locational Marginal Price is determinedby the above three participants [1]. In a market with real-timepricing, generators and consumers continuously adjust theirgenerated power quantities and consumptions, respectively,based on supply-demand data as well as the price of electric-ity. The price in turn is affected the available and consumedpower, and the overall energy imbalance. The dynamics ofthe power market therefore includes the dynamic evolution ofgenerated power and consumption as well as the electricityprice. It is therefore useful to analyze this overall dynamicsso as to determine effective rules to operate the power marketand transactions that allow power producers to maximizetheir profit.

Different market models have been used in the literature tocapture various aspects of power market dynamics includingbilateral contracts, power exchanges, and Poolco markets[10]. Markets are becoming more transparent and priceupdates within these markets are becoming more frequent.Therefore, when designing electricity markets, it is importantto study not only the impact of a particular market designon the resulting equilibrium point, but also on the globalstability of the resulting market [6]. References [5] and [6]address the stability properties of dynamic markets and thenature of their convergence to an equilibrium. The effectof energy imbalance and congestion is examined in thesepapers. In Reference [8], the authors use difference equationsto study the evolution of the price of electricity. In [5]and [6], it is assumed that both generators and consumersparticipate only in a real-time market.

Generally speaking, we can categorize power markets as

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being elastic or inelastic depending on their ability to allowa consumer to adjust its demand in response to the electricityprice. In a market that has a demand, market clearing price(MCP) [10] for energy is determined by the price structureof supply offers. The concept of inelastic demand is directlyrelated to the concept of firm load, which formed the basisof former electricity industry for many decades before theintroduction of open access and energy market [10].

In this paper, we consider an elastic market similar to thatin [4] and make the same assumptions therein, which include:

1) Production costs are quadratic functions of generatedpower, implying that the marginal production costs arelinear functions of generator output.

2) Consumers marginal benefit functions are negativelysloping linear functions of power consumption.

3) Demand is a function of marginal benefit and powerprice.

We introduce a smart meter into this market that is thesimplest example of a smart grid communication technology.It is assumed that this meter provides access to the powergenerated and consumed, but with a time-delay.

One of the important factors that affect the economy ofthe power market is congestion, which refers to the conditionwhen overloads occur in the transmission lines. Congestionmay result in preventing new contracts, cause additional out-ages, monopoly of prices in some regions of power systems,and damages to system components. The introduction of asmart meter can cause these harmful effects of congestionto be alleviated. We expand the market model to includecongestion effects by representing them as constraints on thetransmission capacity.

The effect of a smart meter on the resulting model isanalyzed. It is shown in particular that a smart meter canmitigate the effect of congestion by suitably redistributing thepower generation between peak and off-peak times therebyincreasing the amount of Social Welfare [13].

The presence of a time-delay in the smart meter also raisesthe question of stability of the underlying power market. Byanalyzing the dynamics of the resulting power market, westudy the effect of stability in the presence of such a delay. Itis shown that the resulting market exhibits a stable behaviorprovided the time-delay does not exceed a certain bound.

This paper has been organized as follows: In sectionII, the overall power market model with a smart meter ispresented. In section III, we study the effect of smart meteron congestion, and evaluate the impact of a smart meterthrough a numerical simulation study of the IEEE 30-bussystem. Finally section IV addresses the stability analysis ofthe electricity market with a time delay. In Section V, weprovide a summary and concluding remarks.

II. DYNAMICS OF A SIMPLE POWER MARKET WITHSMART METER

In this paper we consider a simple supply and demandmodel which is based on price, utility, and quantity of powerdemand in a real time market. In a competitive market,the price will fluctuate so as to equalize the quantity of

Fig. 1. Architecture of Integrated Smart Grid [3]

power demanded by consumers, and the quantity supplied byproducers which results in an economic equilibrium of priceand quantity. Generally speaking, if a generator observes amarket price λ above the marginal cost λgi , it is assumedthat the generator will expand production until the marginalcost of production equals the price. This rate of increaseis proportional to the difference between the observed priceand actual production cost. The speed of response in thegeneration output Pgi is dependent on the dynamics ofgenerator-response, and can be captured by a dynamic model,for supplier i = 1, ...,M , as shown below [4]:

τgi˙Pgi = λ− bgi − cgiPgi − kE (1)

where τgi denotes the time constant of the generator, bgi +cgiPgi is the marginal cost λgi of generator i, and E is theaccumulated energy imbalance which is defined later. λ in(1) denotes the market price at a time t, and approximatelyequals the locational marginal price at market equilibrium.If a supplier observes a market price λ above the marginalcost λgi , it is assumed that the supplier will increase pro-duction until the marginal cost equals the market price. Thegeneration cost function is the integration of the marginalcost function. The cost function of each generators unit isdefined:

C(Pgi) = bgiPgi +cgi2P 2gi (2)

On the consumer side, a demand Pdj with a marginalbenefit above the marginal price will lead to an expansionin consumption until equilibrium is attained. Just as on thegenerator side, if the speed of expansion is characterized bya consumer time constant τdj , the following equation can beused to describe the behavior of consumer j = 1, ..., N :

τdj˙Pdj = bdj + cdjPdj − λ (3)

where λdj = bdj + cdjPdj is the marginal benefit. Theconsumers cost function is also defined as:

U(Pdj ) = bdjPdj +cdj2P 2dj (4)

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Remark 1: The generator model in Eq (1) is fairly simple,and does not include rate constraints on generation. We notethat costs due to shutdown or startup are not included either.The consumer model in Eq (3) is simple as well. In orderfor Pdj to represent demand, a constraint that Pdj > 0 willneed to be additionally imposed.

The final condition required to characterize the marketsituation is the balance between supply and demand. If thereis an energy imbalance E, using the definitions of Pgi andPdj , we can derive the differential equation

E = Pg1 + Pg2 + ...+ PgM − Pd1 − Pd2 − ...− PdN (5)

In a power grid with several coupled synchronous gener-ators and unknown demand, energy imbalance must be re-duced and driven to zero to satisfy consumption of all loads.In restructured electrical power systems, market mechanismsshould force the energy imbalance to zero via a PricingProcedure [5]. Therefore it is reasonable that the price ofenergy reflects the degree of energy imbalance. A simplemodel of the price dynamics is given by

τλλ = −E (6)

where τλ is the time constant of the price updates. Forinstance, in real time pricing market τλ may be in orderof 1 to 5 minutes [14], and for a one-day-ahead marketτλ = 24hrs.

Remark 2: Unlike the model in Eqs. (1), (3), (5) and (6),real time balancing of E is typically achieved in a powermarket by methods based on frequency regulation, spinningreserve and also direct load control [11]. The third method,for instance, views the load as a variable, uncontrolleddemand that the generation must constantly adjust to reliablymeet. Therefore the load is only controlled under severeconditions such as under- frequency load shedding and cancause the utilities to shed remote customer loads unilaterally[15]. The proposed model suggests a method that is differentfrom any of the above, and perhaps can be viewed as animplicit load control method. This load control is achievedby λ responding to an energy imbalance (as in Eq. (6)), andPgi and Pdj responding in turn to change in λ (as in Eq.(3) and (1)) which in turn responses a balance E (using Eq.(5)).

It should be noted that the right hand side of Eq. (5)cannot be computed in real time. While Pgi can be measuredinstantly and is available to the ISO (Independent SystemOperator), Pdj may not be measurable in real-time. Typicallyan approximation is used for the right hand side of Eq.(5)such as those based on weighted sum of frequency errorsused in [4]. Instead, we propose a realistic alternative, whichis the use of a smart meter to measure Pdj . It is also assumedthat this measurement is available to ISO with a delay τ ,therefore the energy imbalance E is determined as

E =

M∑i=1

Pgi(t) −N∑j=1

Pdj (t− τ) (7)

We show in section IV that even with a delayed measurementof E as in (7), it is possible to ensure the stability of the

overall power market. It should be noted that in the above,we have modeled a smart meter as a pure time-delay andotherwise have ignored its dynamics. We note that the modelof the market in Eqs. (1), (3), (6) and (7) does not representany particular power market, but a generic model of thefuture market with smart meters.

III. EFFECT OF SMART METER ON CONGESTION

As mentioned in Section I, congestion can directly affectthe economy of the power market. For instance, congestionmay result in preventing new contracts, as well as causeadditional outages, monopoly of prices in some regionsof power systems,or damages to system components [10].Congestion can be corrected by applying controls such asphase shifters, tap transformers, reactive power control andre-dispatch of generators. In this paper we address congestioncontrol by introducing Price elasticity demand (PED), whichcorresponds to the responsiveness of the quantity demandedof electricity to a change in its price [16]. To accomplish thisgoal, we expand the model proposed in Section II to includeconstraints on the capacity of transmission lines and evaluatethe impact of smart meters on congestion.

We begin with a model with m suppliers and n consumersgiven in section II, in Eqs. (1), (3), (6) and (7), and includeconstraints. This model can be written compactly as

x = A0x(t) + A1x(t− τ) +B (8)

where

x =[Pg1 · · · Pgm Pd1 · · · Pdn E λ

]T(9)

A0 =

−cg1τg1

0 . . . 0 0 . . . 0 −kτg1

1τg1

0−cg2τg2

. . . 0 0 . . . 0 −kτg2

1τg2

.... . .

...... . . .

......

...0 . . . 0

−cgmτgm

0 . . . 0 −kτgm

1τgm

0 . . . 0 0cd1τd1

. . . 0 0 −1τd1

......

......

.... . .

......

...0 . . . 0 0 0 . . .

cdnτdn

0 −1τdn

1 . . . 1 1 0 . . . 0 0 00 . . . 0 0 0 . . . 0 −1

τλ0

(10)

A1 =

0 0 . . . 0 0 . . . 0 0 00 0 . . . 0 0 . . . 0 0 0...

. . ....

... . . ....

......

0 . . . 0 0 0 . . . 0 0 00 . . . 0 0 0 . . . 0 0 0...

......

......

. . ....

......

0 . . . 0 0 0 . . . 0 0 00 . . . 0 0 −1

τd1. . . −1

τdn0 0

0 . . . 0 0 0 . . . 0 0 0

(11)

B =[− bg1τg1

...−bgmτgm

bd1τd1

... bdnτdn

0 0]T

(12)

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We now introduce constraints that occur due to the presenceof congestion. Denoting the capacity of the transmission linethat connects bus b and bus k as C(MW )

bk , the constraints dueto congestion can be represented for all connected buses b,kas

−Cbk <θb − θkxbk

< Cbk (13)

where θb and θk denote the phase angles of buses b andk, respectively, and xbk is the reactance of the transmissionline. These phase angles can be expressed in terms of thepower injected as

N∑k=1

θb − θkxbk

= Pgb − Pdb for b = 1, ..., N (14)

where Pgb and Pdb represent generator and load connectedto bus b and N is the number of buses in the network.

Remark 3: While no transmission loses have been in-cluded in Eq. (14), they could be represented by replacingPgb by γPgb where (1 − γ) denotes the transmission loss inpercentage.

We introduce an additional constraint that may be presenton the power generated. Both lower and upper bounds P giand P gi may exist with

P gi ≤ Pgi ≤ P gi (15)

In order to best illustrate the advantage of using a smartmeter, we consider four different scenarios according tothe changes of the demand during a day. Two of thesescenarios correspond to the cases when the consumer demandoccurs during Peak Time and Off-Peak Time. The other twoscenarios are based on whether or not a smart meter is used.The case when the smart meter is used corresponds to thesolution of Eq. (8) which includes Eq. (7) that correspondsto the use of a smart meter. The case when a smart meteris not used is simulated as follows. Choosing an objectivefunction

F (Pgi , Pdj ) =

M∑j=1

U(Pdj ) −N∑i=1

C(Pgi) (16)

where U(Pdj )($/h) and C(Pgi)

($/h) are defined in Eq. (4)and Eq. (2) respectively, Pgi and Pdj are determined assolutions of an optimal load flow problem with (16) as theobjective function subject to constraints (13) and (15). Theresulting four scenarios, described below, are simulated anddiscussed further.

1) peak time without using smart meter2) peak time with smart meter3) off-peak time without smart meter4) off-peak time with smart meter

An IEEE 30-bus case is used for all simulation studies,whose interconnections are shown in Figure 1. Relevantparameters of the generators and consumers are shown inTable I and Table II, respectively. The reactance xbk of theline connecting bus b and bus k can be found in [13]. Theupper bound Cbk of all transmission lines is chosen to be100MW .

TABLE IPARAMETERS OF COST FUNCTIONS AND THE UPPER AND LOWER

BOUND OF GENERATORS

Name Lower Bounds Upper Bounds τg cg bgP gi

P gi

Pg1 0 100 MW 0.2 0.38 47.2Pg2 0 100 MW 0.2 0.25 48.8Pg5 0 150 MW 0.2 0.15 40Pg11 0 150 MW 0.2 0.15 40Pg13 0 100 MW 0.2 0.15 30

TABLE IIPARAMETERS OF COST FUNCTIONS OF CONSUMERS

Name Demand Level τd cd bdPd3 ,Pd19 off-peak 0.1 -0.2 87.2

peak 0.1 -0.3 90Pd7 ,Pd20 off-peak 0.1 -0.5 85.5

peak 0.1 -0.4 87Pd8 ,Pd21 off-peak 0.1 -0.15 70

peak 0.1 -0.2 90Pd9 ,Pd23 off-peak 0.2 -0.35 70

peak 0.2 -0.4 90Pd14 ,Pd24 off-peak 0.2 -0.2 50

peak 0.2 -0.3 80Pd15 ,Pd26 off-peak 0.2 -0.3 60

peak 0.2 -0.3 70Pd16 ,Pd29 off-peak 0.2 -0.1 65

peak 0.2 -0.2 90Pd17 ,Pd30 off-peak 0.2 -0.5 68

peak 0.2 -0.5 90

The results obtained are tabulated in Table III for thefour scenarios (1)-(4) listed above. In each case, the totalgeneration, total consumption are indicated. In Table IV, thecongestion status of each transmission line is computed forthe same four scenarios. Congestion status is defined as thepower flow for the line connecting bus b and bus k and isgiven by θb−θkxbk

. Negative numbers imply that the power flowis from bus k to bus b. Noting that the transmission linecapacity is 100MW , all congested lines are indicated in boldfont. The results in Table III and IV lead to the followingobservations.

Table III shows that the total consumption drops from373.7MW in Peak-time to 130.7MW in off-peak withoutsmart meter corresponding to scenarios (1) and (3). Thesenumbers change to 270.8MW in scenario (2) and 269.8MWin scenario (4), respectively, showing that the demand isdistributed uniformly over these two times with a smartmeter.

This spreading effect can also be observed in Table IV inthe congestion status. It can be seen that the transmissionlines connecting buses 9 and 11 and buses 12 and 13 havereached their transmission capacity limits. These two linesare the only paths through which the power of low-costgenerators g13 and g11 can be delivered. Since they arecongested, the only way to improve network performanceis by adding new transmission lines, if no smart meter isused. In the same transmission line connecting buses 9 and11, with smart meter, we see that the congestion status hasdropped to 66.27MW , thereby eliminating the need for any

197

Fig. 2. IEEE 30-bus case study

TABLE IIITOTAL GENERATION AND CONSUMPTION FOR OFF PEAK AND PEAK

TIME USING SMART METERS WITH WITH TIME-DELAY τ = 4

Total Peak Time Peak Time Off Peak Off PeakWithout With Without With

AMI AMI AMI AMIGeneration 373.7 270.8 130.7 269.8

Consumption 373.7 270.8 130.7 269.8

additional transmission lines. The smart meter accomplishesthis by essentially shifting the consumer demand from Peak-time to Off-Peak Time. This shift, in turn, has occurreddue to the elasticity of the consumer demand in responseto the price fluctuations. It can be seen from Table IVthat no transmission congestion occurs in Peak-time withsmart meter anywhere in the overall network. The congestionthat can occur during Peak-time is alleviated by the smartmeter by shifting the consumption to the Off-peak time.This is done, obviously, at the expense of increasing theconsumption during Offpeak time, but is done so withoutexceeding the available transmission capacity

We now compare the same four scenarios using anothermetric, which corresponds to Social Welfare [13]. Denotingthis as SW , we define, as in [13],

SW =

N∑i=1

SPgi +

M∑j=1

SPdj − CT (17)

where SPgi and SPdj denote the surplus of generator i and

TABLE IVCONGESTION CONDITION FOR OFF PEAK AND PEAK TIME USING SMART

METERS WITH WITH TIME-DELAY τ = 4

bus bus Peak Peak off-Peak off-Peakb k Without With Without With

AMI AMI AMI AMI9 11 -100 -66.27 -31.16 -66.02

12 13 -100 -99.6 -64.49 -99.35

TABLE VSOCIAL WELFARE CHANGES IN DIFFERENT SCENARIOS

Without Withsmart meter smart meter

SW 19873.78 13182.74in Peak time

SW 5531.2 13122.9in off-Peak time

Total SW 25404.98 26305.64in Peak and off-peak

consumer j, respectively. These in turn are defined as

SPgi = [−C(Pgi) + Pgiλ] (18)

SPdj =[U(Pdj ) − Pdjλ

](19)

where U(Pdj )($/h) and C(Pgi)

($/h) are defined in Eq. (4)and Eq. (2) respectively and C($/h)

T = Pgiλ−Pdjλ is denotedas a transmission cost. With this definition, SW is identicalto the objective function defined in (16).

In table V, SW corresponding to scenarios (1)-(4) areshown. It can be seen that the total Social Welfare hasincreased from 25404.98($/h) to 26305.64($/h) due to theuse of a smart meter. Stability of the interconnected powermarket and power network has been previously studied in [4]and [5]. In turn, in the next section, the stability of powermarket subjected to smart meter is analyzed.

IV. STABILITY OF POWER MARKET WITH TIME DELAY

The results of section III clearly establish the advantagesof a smart meter. In particular, it was shown that a smartmeter alleviates congestion, uniformly distributes demand,and leads to increased Social Welfare. These advantages stemprimarily due to two factors. One is the use of the smartmeter which enables real-time measurement of the energyimbalance, modeled through Eq. (7). The second is due to theelasticity of the power market, where the price λ is allowedto fluctuate as a function of the energy imbalance, quantifiedthrough Eq. (6).

In this section, we address the flip side of these two factors,which is their impact on stability of the overall market. InEq. (7), we assumed that the smart meter obtains informationabout the power consumed after a time-delay τ . The questionthat can be posed here is if there are any limits on thisdelay. If this delay becomes excessive, it may be possiblefor the overall market to become unstable. We carry out astability analysis of the overall market and show that indeedthe stability is dependent on τ . In particular, we derive anupper bound on τ for which stability can be guaranteed.

Our focus is on the overall market dynamics, whichis determined by Eqs.(1), (3), (6), and (7). Shifting theequilibrium of the state x defined in section II, we then obtaina linear time-delay system. For simplicity, we consider thecase when there is a single consumer and a single generator,

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which leads to the following equations:

τgi˙Pgi = λ− cgiPgi − kE

τdj˙Pdj = cdjPdj − λ

E =

M∑i=1

Pgi(t) −N∑j=1

Pdj (t− τ)

τλλ = −E

(20)

Eq. (20) can be rewritten as

x = A0x(t) +A1x(t− τ) (21)

where x = [Pg, Pd, , E , λ]T . The next question if an upperlimit for the time-delay can be found for which (21) is stable.This is discussed in the theorem below.

Theorem 1: Electricity market model described in Eq.(21) is asymptotically stable if there exist real symmetricmatrix P > 0 such that: M −PA1A0 −PA2

1

−AT0 AT1 P −P 0−(A2

1)TP 0 −P

< 0 (22)

whereM =

1

τ

[PA0 + AT0 P + 2P

]and A0 = A0 +A1

Proof: The proof is established by showing that Vdefined as V = xTPx where P is positive definite is aLyapunov function. This in turn is shown by using Eq. (22)and the existence of a symmetric matrix R(θ) that along withP satisfies the conditions

PA0 + AT0 P +

∫ 0

−2τ

R(θ) dθ < 0 (23)[pP −R(θ) PA(θ)

AT (θ)P −P

]< 0 for 0 ≤ θ ≤ 2τ (24)

Theorem 1 implies that the time-delay system in (21) isstable provided the time delay τ is such that M satisfies theLMI in (22) [9]. The use of an LMI package (ex. SeDuMidescribed in [12]) enables the determination of an optimalupper bound on τ . In particular, the upper bound can becalculated by increasing τ until the positive definiteness ofP is violated while (21) is satisfied.

V. CONCLUSIONS

The introduction and availability of Advanced MeteringInfrastructure technologies have introduced a paradigm shiftin the analysis of power markets. In this paper, we study theeffect of a smart meter that may be typically deployed ina smart grid at a customer service location. We consideran elastic power market model introduced previously in[4], introduce into it a smart meter that provides access tothe power generated and consumed, but with a time-delay.The resulting model is then used to illustrate the impact ofsmart meter, on two important properties of a power grid,congestion and stability.

The proposed model is only possible in the presence ofa distributed and integrated metering system. Reaching thisgoal requires two changes according to the proposed method.First, the cost of energy for the energy to the end-user shouldmatch the load. This in turn motivate the consumers toshift their consumption to the off-peak intervals. The secondchange is the cost of energy at any point in time shouldbe visible to the end-user. This regulates the consumersconsumption. Simulations proposed in this paper illustratealleviation of congestion effect and spreading consumersdemand over time as well as increase of social Welfare.

While the introduction of a smart meter has an obviousadvantage described above, the inherent time delay presentin obtaining information from the smart meter can also affectthe stability of the overall system. In this paper, we have alsoanalyzed the resulting time-delay model and established itsstability for a range of time-delays. In particular, we derivean upper bound on τ , using an LMI approach, for whichstability can be guaranteed.

VI. ACKNOWLEDGMENTS

The authors gratefully acknowledge Harald Voit and C.-C. Chen from Technische Universitat Munchen for theirvaluable discussion and talks.

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