market integration of distributed resources through coordinated frequency and price droop

1556 IEEE TRANSACTIONS ON SMART GRID, VOL. 5, NO. 4, JULY 2014

Market Integration of Distributed Resources ThroughCoordinated Frequency and Price Droop

Chin Yen Tee, Student Member, IEEE, and Judith B. Cardell, Member, IEEE

Abstract—Given the appropriate control strategies and marketrules, distributed energy resources (DER) organized into micro-grids have the potential to be active participants in regionalenergy and ancillary services markets. This paper integrates aprice-based control mechanism into the conventional frequencydroop control mechanism to present an integrated droop-basedcontrol framework that could facilitate greater DER penetrationin the power system and electricity markets. The proposed con-trol framework makes use of the concept of “price droop,” andintroduces the idea of a “system frequency elasticity”. These twoconcepts combine the power system control concept of frequencydroop and the economic concept of own price elasticity. Theframework consists of a centralized agent-based learning processand a decentralized operational response. The applicability of theproposed control mechanism is demonstrated through a series ofcase studies. Results highlight the need to consider the dynamicsof the existing system in the design of new technical and marketstrategies to allow for the integration of DER and microgrids intothe power system.

Index Terms—Distributed energy resources, droop character-istic, electricity markets, frequency control, microgrids.

I. INTRODUCTION

G ROWING environmental concerns, recent technologicaladvances and the restructuring of the electricity industry

have brought increased attention to the need and potential fora more efficient and sustainable electric power system. Dis-tributed energy resources (DER), such as small-scale renewablegeneration, storage technologies, and responsive loads, can po-tentially reduce greenhouse gas emissions and improve the effi-ciency of the power system. Recent projects have explored or-ganizing DER into microgrids to allow for greater integrationof DER into the power system and electricity market opera-tions [1], [2]. These projects have demonstrated the function-ality ofmicrogrids, and also highlighted the need to develop newtechnical standards, operational protocols, and market rules toallow for the actual implementation of microgrids in the futurepower system. This paper contributes to this need by proposinga price-based control mechanisms for the coordination of DERwithin a microgrid.

Manuscript received September 05, 2013; revised January 23, 2014, March09, 2014; accepted March 22, 2014. Date of publication May 09, 2014; date ofcurrent version June 18, 2014. This work was supported in part by the NationalScience Foundation under Grant 084429. Paper no. TSG-00724-2013.C. Y. Tee is with the Department of Engineering and Public Policy, Carnegie

Mellon University, Pittsburgh, PA 15213 USA (e-mail: [email protected]).J. B. Cardell is with the Picker Engineering Program and Department of Com-

puter Science, Smith College, Northampton, MA 01063 USA.Digital Object Identifier 10.1109/TSG.2014.2314027

A microgrid is a subsection of a distribution system that con-sists of multiple DER that can operate both autonomously and inparallel with the main electricity grid. One key challenge in theoperation of microgrids is the maintenance of power supply re-liability and frequency stability when the microgrid is operatingin an islanded mode. Islanded microgrids with DER resourcesthat are mainly interconnected via power electronics are moresensitive to small disturbances in the system due to the lackof synchronous generators with large inertia that provide theconventional frequency droop response. For microgrids to func-tion autonomously, a control mechanism that provides the samefunction as the conventional frequency droop response of syn-chronous generators needs to be applied to the power invertersused to connect DER to the grid.In previous studies, various communication based (e.g., [3],

[4]) and droop-based (e.g., [5]–[7]) inverter control strategieshave been implemented to maintain the frequency stability ofa microgrid. Even though communication-based control strate-gies can improve the power quality and power sharing perfor-mance in a microgrid [4], droop-based control strategies are stillthe most widely used as it avoids the possibility of single pointsof failure in a critical networked infrastructure. Two forms ofdroop-based control strategies have been adopted: 1) strategiesbased on the active power vs. frequency (P/f) droop analogousto the traditional frequency droop [2], [6]–[9], and 2) strate-gies based on the active power vs. voltage (P/v) droop that ac-count for the resistive nature of low voltage grid [10], [11]. Ex-perimental studies have demonstrated that the conventional P/fdroop can be successfully applied to resistive low voltage grid[12], [13] for the purpose of real power and frequency controland appears to be the better choice when compared to the P/vdroop [13].In addition to supply-side frequency control, controllable

loads in microgrids and advances in metering and appliancecontrol technologies allow for greater demand-side participa-tion in frequency response services. The use of these loads forprimary frequency control has been explored [14]–[16]. Forgreater participation of loads in primary frequency responseservices, market rules that facilitate demand-side participationin ancillary services market are needed [16], [17].One drawback of the conventional frequency droop response

and other forms of droop-based controls strategies cited aboveis that these strategies do not account for the relative cost ofgenerators providing the response. The conventional frequencydroop response is designed such that the resulting response isshared in proportion to the relative size of the generators. Thispaper proposes an alternative droop based strategy that accounts

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TEE AND CARDELL: MARKET INTEGRATION OF DISTRIBUTED RESOURCES THROUGH COORDINATED FREQUENCY AND PRICE DROOP 1557

for the relative cost of different generators. The motivation forthis work is to develop a method that increases the overall eco-nomic efficiency of the frequency droop response.This proposed price-based control framework is designed to

maintain the frequency stability and real power balance of a mi-crogrid and to allow for the participation of both supply anddemand-side DER in regional energy and real power ancillaryservices markets. The proposed signal, coined the “price droop”(defined in Section II), is derived from the concepts of own priceelasticity and frequency droop. Preliminary work [18] and [19]has been expanded in this paper to demonstrate how the pricedroop mechanism can be integrated into the conventional fre-quency droop mechanism to provide a control framework thatcan maintain the stability and reliability of a microgrid, whiletaking into account the economic aspects of microgrid opera-tions [20]. This integration is done by introducing the idea of a“system frequency elasticity” (SFE), defined in Section II. Theproposed integrated droop control framework consists of twostages. Stage 1 is a centralized agent-based learning processused to determine the droop values for each DER. Stage 2 isa decentralized implementation phase in which the price-droopvalues are used in the operation of a microgrid. Though costs arenot traditionally included at the timescale of primary frequencycontrol, advances in communications technologies now facili-tate the improved system efficiency offered by the proposed in-tegrated droop mechanism.The next section introduces and defines the price droopmech-

anism. Section III outlines the agent-based learning frameworkdesigned to obtain the price-droop value. Section IV describesthe state-space modeling framework used to simulate a mi-crogrid operating with the price droop mechanism. Section Vpresents the results of the simulation. Section VI highlightssome issues that are relevant to the implementation of theproposed mechanism and Section VII concludes.

II. THE PRICE DROOP MECHANISM

A. Definition of the Price Droop Signal

With the expanding use of DER, there is increasing interest inthemarket aspects of microgrid operation and control [21]–[24].The price droop concept is proposed to increase the economicefficiency of the droop mechanism and to explicitly bring eco-nomic factors into the primary control time scale. This proposedmechanism is not designed to influence the secondary or tertiarycontrol responses.Traditional frequency droop, which does not account for the

economic impact of the response, is defined as:

%%

(1)

where is the system frequency, is the real powergeneration from generator , and the indicates ‘changein.’ Thus, is the percent change in omega %and is the percent change in generation% . The ratio of these two percent change values istraditionally defined to be the frequency droop.

Fig. 1. Energy and Information Flows with the Price Droop Mechanism [19].

Modeled after the concepts of frequency droop and own priceelasticity from economic theory, price droop proposed here isdefined to be the percentage change in price for a one percentchange in power injection.

(2)

where represents the system electricity price and repre-sents either real power generator input or load consumption.

is the change in system price from a given system distur-bance, , the change in real power, is the response of thegenerator or load to the system price, represents the initialsystem price, and represents the maximum load or gener-ation capacity [18], [19]. This price-based signal enables DERto consider the relative economic cost of the response in deter-mining each DER’s contribution to the droop response.As discussed in Section III, each DER learns its own price

droop value for a given base case dispatch through a multi-agentlearning process. The price droop values are then used to de-termine the decentralized response of the DER to subsequentdisturbances until the price droop values are updated through aslower moving control loop. The timescale for this slower con-trol loop would be determined by the microgrid coordinator.The price droop mechanism assumes there is a microgrid co-

ordinator that will communicate system disturbances in the formof price signals to each DER. Fig. 1 illustrates the projectedflow of energy and information among individual DER, micro-grid coordinators, and the centralized system operator under theprice droop framework [19]. Within a single microgrid, basicpower system parameters such as real and reactive power andbus voltages are considered to be public information that areshared among the DERwithin themicrogrid. Themarginal pricedroop values and cost curves of the DER are considered to beproprietary information that are not shared among the DER. Themicrogrid coordinator maintains the reliability and stability ofthe microgrid and communicates with the distribution systemoperator, whose role is to interface between the microgrids andthe bulk power system.


B. Integrated Droop Control Mechanism

As mentioned earlier, a weakness of communication-basedDER control strategies is the potential for single points of failurein the microgrid operating framework. One strategy to reducethe reliance of the price droop mechanism on the communica-tion infrastructure is to incorporate the price droop values intothe conventional frequency droop mechanism.The generator frequency droop value used in the conventional

frequency droop mechanism (see (1)) is defined to be the per-centage change in frequency for a one percent change in gen-erator output [25]. To integrate the proposed price droop signalinto a broader coordinated droop control mechanism, we ob-serve that the generator frequency droop parameter can be de-composed into two components:

%%%%

%% (3)

where , and are as defined earlier. Based on (3), thefrequency droop parameter is seen to be the product of the pricedroop value and the ratio we identify as the system frequencyelasticity, SFE. The SFE is defined to be the percentage changein system frequency for a given percentage change in systemprice. Since the SFE is based on system frequency and price, theSFE is the same for all DER in the microgrid. Thus (3) revealsthat the frequency droop will maintain the relative proportion ofthe price droop values for the different generators.The SFE is a design parameter that is system specific. It is

dependent on the characteristics of the synchronous generatorsin the system and also on the desired frequency range for thesystem. Therefore, for the same microgrid, the appropriate SFEwhen the system is connected to the bulk power system is dif-ferent from the appropriate SFE when the system is islanded.When combinedwith the price droop signal, it allows the systemoperator to adjust the sensitivity of the DER output to changesin system frequency without changing the relative proportion ofthe responses as defined by the price droop values. As demon-strated in Section V (and Fig. 9), the SFE affects the settlingtime for the dynamic response of the microgrid following a dis-turbance, as well as the extent to which synchronous generatorsrespond in the microgrid. The SFE requires infrequent updates,based on the system operator’s analysis of the variability in thechange in system frequency for a change in system electricityprice. It would need to be updated for changes to the generatoror load composition, such as a new power plant.Returning to (3), once the price droop values are learned

(see Section III), the DER within the microgrid calculate theirfrequency droop values based on (3). They then provide pri-mary frequency response services within the microgrid withoutany further communication with the microgrid coordinator. Anypower imbalance in the microgrid will result in a change infrequency in the system, which in turn triggers the frequency

droop response of the DER. The difference between the fre-quency droop response under the proposed integrated droopcontrol framework and the conventional frequency droop re-sponse is that the integrated droop control framework accountsfor the relative cost of providing the frequency response fromthe different DER. This is significant as it integrates market con-siderations into the conventional primary frequency responsemechanism. Subsequent communication among the DER andthe microgrid coordinator is only needed to update the pricedroop values in response to a change in system state, or oper-ating point. How often the price droop values are updated can bedecided by the microgrid coordinator. Sets of price droop valuescan be determined in advance of real time operation if desired,consistent with typical operating points.This integrated droop control mechanism is particularly

useful for DER that are interconnected into the power systemvia power electronics. In previous work using frequency droopcontrol on power inverters, the generator droop parameterswere found by choosing droop values that would allow thefrequency to drop by a specified amount as the generator outputincreases from zero to its maximum generation capacity [2],[6]–[8]. Equation (3) provides a methodology to account for theeconomic aspects of the system in the selection of frequencydroop parameters.Finally, the integrated droop mechanism allows for the

parallel operation of traditional synchronous generators andinverter-interfaced generators under a common control frame-work. This can potentially make it easier for inverter-interfacedgenerators to participate in the market for frequency control.

III. DISTRIBUTED RESOURCE AGENT LEARNING

The potential for increased intelligence in power system op-eration has led to the increased use of multi-agent modelingtechniques in power system research [26]–[28]. In this paper, amulti-agent reinforcement learning algorithm is adopted to de-termine the price droop values of each DER agent [19]. A multi-stage process is implemented where the goal is to maintain thepower balance in the system while maximizing individual DERprofits. A flow chart outlining the learning framework is shownin Fig. 2 and some key features of the agent learning algorithmare highlighted below. Interested readers should refer to [19] fora full discussion of the DER learning framework used here.The Q-learning algorithm is a well known reinforcement

learning algorithm that works by assigning values to state-ac-tion pairs based on previous experiences (refer to [29] forthe theory behind Q-learning). During the learning process,the learning agents explore the search space in order to learnthe state-action value function. Each time an agent selects aspecific action from a given state to move to the next state, thestate action pair is updated using the Q learning function in(4). At the end of the learning cycle, the optimal solution pathis the solution obtained by taking the action with the highestvalue at any given state. In this study, the states of the systemare defined by the magnitude of the power imbalance while theactions are the changes in individual generator supply or powerdemand. The generator and demand agents explore the searchspace in order to determine the best joint actions to return to the


Fig. 2. Agent Learning Flow Chart [19].

state of power balance after a disturbance. The value associatedwith each state-action pair is updated using the following Qlearning function:

(4)

where is the system state, is the agent action, is the timestep, is the value of the state-action pair, is the reward forthe action taken, is the learning rate, and is the discountfactor, which defines the relative value of current versus futurerewards [19]. The discount factor and learning rate used in thisstudy are 0.8 and 0.5 respectively [19]. A relatively high dis-count factor is used because the main objective of this study isto find the long term joint optimal solution rather than to max-imize the short term performance of individual agents. A mod-erate learning rate is selected to strike a balance between theneed to retain old information and the need to ensure that no

Fig. 3. Decision Tree for the Reward Function.

state-action pair is prejudiced against due to an anomalous neg-ative experience early on in the learning cycle.One key implementation question with Q-learning is the se-

lection of an appropriate learning policy. The learning policydetermines how the DER agents select their actions during thelearning process. For the learning of the price droop values, theindividual profit at each time step is less important than theability for the agents to achieve a joint optimal solution andmaintain the system power balance. Therefore, an adaptation ofthe -greedy learning policy is used in this learning framework.The learning policy is defined to be:

(5)

where t is the time step, T is the length of the learning cycleand is the probability that the agent would choose to explore(i.e., pick a random action) rather than to exploit (i.e., select thebest known action). The learning policy defined above is heavilyweighed towards exploration, especially at the beginning of thelearning cycle.A second key implementation question for the Q-learning al-

gorithm is the design of a suitable reward function. The rewardfunction used in this study is designed to encourage maintainingthe system power balance while accounting for the profit or con-sumer surplus of the generator and load agents (see Fig. 3).During the learning process, the state-action pair for an agentis rewarded positively if the power difference in the new stateis lower than the power difference in the previous state. In ad-dition, the state-action pair is also rewarded positively if theprofit or consumer surplus of the agent at the new state is greaterthan the profit or consumer surplus at the previous state. A de-tailed discussion of the implementation of the learning frame-work used in this paper has been presented in [19].At the end of the learning process, each agent picks its

own best strategy by taking the action with the highest valueat each state based on their individual state-action functionuntil the system achieves power balance. The best strategyto the given price disturbance is then used to calculate eachindividual agent’s price droop value. These price droop valuesare the means through which the electricity price, and thuseconomic factors, are brought into the system’s primary controlmechanism.


IV. DYNAMIC STATE-SPACE MICROGRID MODEL

The previous section outlined the learning algorithm usedto determine the set of coordinated price droop values for theDER. This algorithm will be run within a microgrid for eachoperating point identified by the microgrid coordinator. In thissection, the use of these price droop values is explored. A dy-namic state-space microgrid model is developed to demonstratethe implementation of the integrated droop mechanism fromSection II, in a microgrid test system. This model expands uponthe model presented in [30] by allowing for the inclusion of re-sponsive loads and inverter-interfaced DER. One key thing tonote is that the model focuses on the real power and frequencydynamics of the system and is predicated upon the assumptionthat real power can be controlled using frequency alone. The ap-plicability of the conventional frequency droop for real powercontrol in microgrids has been demonstrated in [13].

A. Distributed Generation and Responsive Load Modeling

[30] presents low order, linearized state space models of var-ious distributed generators. The model and model parametersfor the steam generator and combustion generator presented in[30] are used in the simulations in Section V. The models cap-ture the machine dynamics of each generator and are hence suit-able for cases where the DER are connected directly to the dis-tribution system without a power electronics interface. For thepurpose of this paper, the DER are mainly assumed to be con-nected via power inverters.Once there is a power electronics interface between the DER

and the distribution system, the machine dynamics of the DERare essentially isolated from the distribution system. Assumingthat the inverter control is ideal, the internal dynamics of thepower electronics can be ignored. In this case, the inverter con-trol is analogous to the swing dynamics with the governor re-sponse of synchronous generators and hence the inverter-inter-faced DER can be modeled after a governor model. For an in-verter-interfaced DER that is responding based on a frequencydroop, the model includes only one state equation:

(6)

where is the frequency droop parameter that is typicallynegative, is the output of the generator, is the outputfrequency of the generator, and is the time constant rep-resenting the speed of the inverter response. In this paper, theinverter-interfaced distributed generators are modeled using (6)where is defined to be the product of the SFE and the gen-erator’s price droop value.To demonstrate how DER responding based on price signals

can be used alongside DER responding based on frequency sig-nals, the responsive loads are modeled based on the originalprice droop mechanism. The single-state equation representingthe behavior of the inverter-interfaced responsive loads is:

(7)

where is the price droop value that is typically negativefor loads, is the price signal, and is the time constant rep-

resenting the speed of the inverter response. In the case studiespresented below, .For demonstrative purposes, the price signal used in this

paper is the linearized market price assuming that the market isperfectly competitive and that there are no generator or systemconstraints about the operating point. The dynamic equationfor the price signal is:

(8)

where is the competitive market price and is a positiveconstant representing the rate of change in price for a unitchange in total power generation. This price signal is selectedpurely for the ease of computation within the modeling frame-work. In the actual implementation of the price droop controlframework, the real-time market clearing price, typically up-dated every five to ten minutes, obtained from actual electricitymarket operation can be used. As shown in (9) the dynamicinput to the microgrid is assumed to be a load disturbance. Theelectricity prices are used directly in learning the price droopvalues. Subsequently the electricity prices are used via thelearned droop values to respond to a system disturbance.

B. Distribution System Modeling

The next component of the modeling framework involves themodeling of the distribution system. In order to develop thedistribution system model, the operating point of the system isfound using an AC power flow program. The AC power flowequations are then linearized about the operating set point ofthe system using the Jacobian matrix. With some manipulation(see [30] for details), the final form of the distribution systemmodel is:

(9)

where

is a partition of the Jacobian matrix and is defined to be(where is the generator buses (G) or load buses

(L)) and represents a load disturbance in the system. In (9),the matrices and represent the line parameters and net-work connectivity. The equation thus captures the dynamic re-sponse of the real power from each DER, as a function ofthe system frequency, and the input disturbance, . Thedynamic model of each DER is included within (9), making thelinearized system acceptable for small changes in andabout the original operating point. For the purpose of this paper,the term is decomposed into two components:

(10)

where is the rate of change in load due to the response ofresponsive loads and is the rate of change in load due to


an external disturbance. Substituting (7) into (10) gives the finalform of the distribution system equation:

(11)

C. Interconnected System Modeling

The final step of the modeling framework involves the mod-eling of the coupling of the DER via a distribution system.Under this modeling framework, is used as the couplingvariable for the system and hence was included in all theindividual generator models used in this paper. The generatormodels in [30] and the inverter-interfaced generator model in(6) above share the following structure:

(12)

where is the generator’s localized state vector, is thegenerator’s localized system matrix, is the vector consistingof the coupling variable, and is the matrix of model coeffi-cients associated with the coupling variables.By combining (7), (8), (11), and (12), the overall intercon-

nected system model takes the form of:

...

...

...

...

...

...

(13)

where is the full system matrix. In the full system matrixshown in (14), at the bottom of the page,

, and are as defined earlier, is a block diagonal matrixused to transform such that the coefficients in are asso-ciated with the correct state variables, and is the subset of

associated with the responsive loads.

V. CASE STUDIES

In this section, the learning algorithm presented in Section IIIand the state-space distribution system modeling frameworkpresented in Section IV are applied to a test system.

Fig. 4. 37 Bus Distribution System.

TABLE IDISTRIBUTED GENERATOR PARAMETERS

A. Test System

A 37 bus test system (Fig. 4) is used for the case studies pre-sented in this section. The microgrid test system has a base loadof 18.6 MW and a total generation capacity of 24 MW. Whenthe system is operating in grid connected mode, the microgrid isconnected to the bulk power system via a substation connectedto bus 1. The line parameters given in [31] are used in this study.Table I shows the parameters for the distributed generators

used in this study. Distributed generators are located at buses 1,15, 32, 33 and 37 of the test system. The generators are cate-gorized as either Type A or Type B generators. Type A genera-tors are generators with low marginal cost of generation such ashydro generation, wind turbines and solar panels, whereas TypeB generators are generators with high marginal cost of genera-tion such as small combustion turbines and fuel cells. The costcoefficients shown in Table I are not based on actual generatorcost data but are instead created to capture the relative costs ofType A and Type B generators. The case studies below assume

. . .. . .

.... . .

...

. . ....

. . ....

. . ....

.... . .

.... . .

.... . .

...

(14)


Fig. 5. Distributed Generators Response to a Local Load Disturbance based onPrice Droop Values Learned.

Fig. 6. Responsive Loads Response to a Local Load Disturbance (2.5MW loadincrease shown in figure) based on Price Droop Values Learned.

that all the DER are able to ramp up or down in response todisturbances in the system. Non-dispatchable energy sources,such as a wind turbine, are assumed to be connected to a storagesystem that is controllable in the primary response time scale ofthe system.Responsive loads are located at all buses in the system ex-

cept buses 33 to 37. The base load of the loads in the systemranges from 0.225 MW to 2.1 MW. These loads represent largecommercial or industrial loads, clusters of residential loads, orsmaller microgrids that behave like a responsive load from thepoint of view of the larger microgrid. The demand own priceelasticities used in this paper are selected randomly from a dis-tribution of household price elasticity of electricity [32].Figs. 5 and 6 present the coordinated DER agent behavior re-

sulting from the agent learning based on the process outlinedin Section III. These figures show the DER agent responses tosystem disturbances. In response to an increase in load in the test

Fig. 7. Response of DER to load disturbance: (a) Changes in generator fre-quency, (b) Changes in generator supply, and (c) Changes in power demand(Only shown for subset of load).

system, the distributed generators increased their output whilethe responsive loads decreased their consumption in order tomaintain the energy balance within the microgrid. The pricedroop values learned for this base case are used in the followingcase studies.

B. Case Study 1: Islanded Microgrid With OnlyInverter-Interfaced DER

The goal of Case Study 1 is to assess the performance of theintegrated droop framework presented in the earlier sections andto evaluate the significance of the SFE defined in Section II. Themodeling framework presented in Section IV is used to simulatethe response of the system to a 1 MW load disturbance. For anislanded microgrid, bus 1 is modeled as a DER. Fig. 7, showingtypical responses for a subset of buses, demonstrates that thesystem frequency remains stable and the power imbalance iscompensated through an increase in power generation and a re-duction in load. The response of the generators accounted for40% of the total response.The model is simulated using different values of SFE. In this

case, as long as the magnitude of the SFE is not greater than70 (Note that the SFE is negative), the only effect the SFE hason the microgrid is on the magnitude of the frequency excur-sion and the time it takes for the system to reach steady state.The relative magnitude of the responses of the different DER re-mains the same regardless of the value of the SFE. Even thoughthe system becomes unstable when the magnitude of the SFE isgreater than 70, it is irrelevant in this context as a 70% changein frequency for a 1% change in price is likely to be impracticalfor any distribution system. When the SFE is more elastic (i.e.,when the magnitude of the SFE is higher), the magnitude of thefrequency excursion gets larger and the system oscillates for alonger period of time before reaching steady state. Since it is


Fig. 8. Response of DER to load disturbance for Case Study 2: (a) Changes ingenerator frequency (Note: The dash lines in figures (a) and (b) represent theresponse for the synchronous generator), (b) Changes in generator supply, and(c) Changes in power demand (Only shown for subset of load).

preferable to maintain the frequency of the microgrid within atighter limit, a relatively inelastic SFE should be adoptedin the case where only inverter-interfaced DER are present inthe system.

C. Case Study 2: Microgrid With Both Inverter-InterfacedDER and Synchronous Generators

This case study evaluates the performance of the integrateddroop framework in the presence of synchronous generatorswith conventional frequency droop control. In this case study,the generator at bus 1 is replaced with either a steam generatoror combustion generator with fixed governor frequency droopcontrol. This case study is relevant for 1) the islanded operationof microgrids that include one or more synchronous generator,and 2) the grid-connected operation of microgrids.Simulation results show that the dynamics of the synchronous

generator have a significant influence on the overall frequencydynamics of the system. The frequency excursion of the systemis dampened by the mechanical inertia of the synchronous gen-erators. However, the mechanical inertia of the synchronousgenerator also lengthens the time required for the system toreach steady state (Fig. 8). In this case, the microgrid test systemremains stable even when the SFE is highly elastic. Due to thelimits on the frequency excursion imposed by the synchronousgenerators, the SFE in this case has a large effect on the propor-tion of total response that is borne by the synchronous generatorin the system.The combined response of the generators accounted for 40%

of the total response (i.e., load plus generator response) whenbus 1 is replaced with a combustion generator, and 45% ofthe total response in the case where bus 1 is replaced with asteam generator. This proportion is not affected by the SFE.However, the proportion of total generator response accountedfor by the synchronous generator is strongly affected by the

Fig. 9. Semilog Plot of Percentage of Total Generator Response Borne by theSynchronous Generator vs. Magnitude of SFE.

SFE value. Fig. 9 illustrates the relationship between SFE andthe percentage of the total generator response borne by the syn-chronous generator on a semilog scale. The relationship shownin Fig. 9 can be explained as such: When the SFE is highlyinelastic, the frequency is relatively insensitive to changesin price. Since the synchronous generator respond solely tochanges in frequency, the power output of the synchronousgenerator will change by only a small amount due to the smallchange in frequency. On the other hand, the inverter-interfacedgenerators using the integrated droop framework defined in (3)are able to response to the underlying change in price despitethe small change in frequency. Hence, the percentage of totalgenerator response borne by the synchronous generator isnearly negligible at very low magnitude of SFE. The reverseargument can be used to explain the high proportion of gener-ator response accounted for by the synchronous generator atlarge magnitude of SFE.This result is significant as it implies that the appropriate SFE

of a system is highly dependent on the existing synchronousgenerators in the system. The differences between the graph forthe combustion generator with 5% fixed frequency droop andthe graph for the same generator with a 2% fixed frequencydroop in Fig. 9 demonstrate that the existing droop characteristicof the system needs to be taken into consideration in the imple-mentation of the integrated price droop framework presented inthis paper. The successful implementation of the price droopframework described in this paper is predicated upon the abilityto calibrate the SFE to allow for appropriate power sharing be-tween the synchronous generators and inverter-interfaced dis-tributed generators.In order to participate in regional bulk energy and real power

ancillary services market, a microgrid needs to be able to coor-dinate its internal operation in order to present itself as a singlestable and reliable entity to the bulk power system when it isconnected to the bulk power system. The behavior of the micro-grid under grid-connected condition can be simulated by con-necting bus 1 to a large synchronous generator with a high me-chanical inertia. In order to implement the proposed frameworkin grid-connected condition, a very high magnitude SFE needsto be adopted to enable the DER to respond appropriately to


very small changes in frequency. The use of a very high mag-nitude SFE is consistent with the definition of the SFE as thesystem frequency within the microgrid in this case is dependenton the frequency of the bulk electric grid, which is insensitiveto changes to local system price. Based on Fig. 9, when the SFEis highly inelastic, any power disturbances within the microgridwill be compensated for by the DER within the grid, with negli-gible contribution from the synchronous generator (i.e., the bulkpower system in this case). This characteristic implies that themicrogrid is able to reliably provide the agreed upon quantityof electricity to the bulk power system when it participates inregional bulk energy and real power ancillary services market.

D. Case Study 3: Microgrid Dynamics When Some DER Failto Response

As mentioned earlier, one of the key concerns with using acommunication-based microgrid control framework is the po-tential for single points of failure in the system. This final casestudy aims to evaluate the performance of the integrated pricedroop framework in cases where not all the responsive loads re-spond as planned. This could occur if a failure in communicationoccurs between the microgrid controller and the load agents.The results of the simulations show that the system can re-

main stable even if not all the DER respond. The remainingDERwill compensate for the lost of responsive load by increasing themagnitude of their responses in proportion to their relative pricedroop values. Even though the percentage of total response ac-counted for by the generators increases with the lost of respon-sive loads, the proportion of total generator response borne bythe synchronous generator remains the same. In other words, theoptimal SFE value for the system is not affected by the the lostof responsive loads. This result is significant as it shows that thestability of the system is not reliant on the the reliability of thecommunication system.

VI. DISCUSSION

Since the purpose of this proposed mechanism is to enableDER to participate in day-to-day local and regional electricitymarkets, the operation of microgrid during normal operatingconditions is of particular interest. The proposed framework isdesigned to work when the microgrid is connected to the bulkpower system during normal operating conditions and post-is-landing after the microgrid have recovered from the initial largesystem transient. Large system transient subsequent to islandingand the operation of the microgrid under other contingency con-ditions will require additional control mechanisms that is be-yond the framework presented in this paper.In addition, this paper focuses on real power balance and

frequency stability. For the proper implementation of theproposed mechanism, other forms of ancillary services will berequired. Experimental studies have shown that even thoughfrequency can still be used to control active power in this case,voltage cannot be controlled using the conventional droopmechanism [13]. Since the proposed mechanism makes useof the conventional frequency droop response, an alternativevoltage support mechanism will be needed to implement theproposed mechanism. Previous studies that have proposedsolutions to the voltage control issue include [6] and [33].

VII. CONCLUSION

This study addresses the need to develop control strategiesand market rules that allow DER and microgrids to partici-pate effectively in electricity markets. By accounting for therelative costs of providing primary frequency response ser-vices for the different DER, the proposed framework is ableto produce an overall response that is more economically ef-ficient than the traditional frequency droop framework. Theintegrated droop-based control framework presented in thispaper combines the strengths of the price droop mechanismand the conventional frequency droop control framework toproduce a control strategy that is both reliable and marketfriendly.The case studies presented in this paper demonstrate the com-

plementary nature of the pure price droop mechanism, the com-bined price-frequency droop mechanism, and the conventionalfrequency droopmechanism. Simulation results indicate that theproposed control framework can be implemented successfullyto allow DER to maintain the frequency stability and power bal-ance of a microgrid operating in islanded and grid-connectedmode. The results also suggest that the proposed control frame-work will allow DER in a microgrid to participate as a unified,controllable unit in regional energy and ancillary services mar-kets. To further develop the robust implementation of the inte-grated droop mechanism, additional case studies including anal-ysis of the impact of line congestion and varying line parametersare for future work.This study highlights the need to account for the relative

DER costs as well as the dynamics of the existing system inthe design of control strategies for the integration of DER andmicrogrids into the power system. Even though the proposedintegrated control framework can potentially be a useful mech-anism that enables the reliable integration of DER and micro-grids into the future IT-enabled power system, the successfulimplementation of the control framework is predicated uponthe ability to calibrate the droop parameters, such as the SFE,to complement the existing system. One of the key challengesahead for the design of control strategies and market rules forDER and microgrids is the need to ensure that the new controlstrategies and market rules are compatible with existing systemand market dynamics.

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Chin Yen Tee (S’09) received the B.A. degree in engineering and economics atSmith College, Northampton, MA, in May 2011. She is currently pursuing thePh.D. degree in engineering and public policy at Carnegie Mellon University,Pittsburgh, PA, USA, focusing on the electric power industry.

Judith B. Cardell (M’96) received B.S.E.E. and A.B. degrees from CornellUniversity, Ithaca, NY, USA, in 1989 in electrical engineering and government.She received the M.S. and Ph.D. degrees in technology and policy from theElectrical Engineering and Computer Science Department, Massachusetts In-stitute of Technology, Cambridge, MA, USA, in 1994 and 1997.She is currently an Associate Professor at Smith College, Northampton, MA.

USA, in the engineering and computer science departments. Previously sheworked at FERC and as a consultant to the electric power industry with TCA inCambridge, MA, USA.

market integration of distributed resources through coordinated frequency and price droop

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