IEEE TRANSACTIONS ON POWER SYSTEMS 1

Power System Enterprise Control with InertialResponse Procurement

Aramazd Muzhikyan, Student Member, IEEE, Toufic Mezher, and Amro M. Farid, Senior Member, IEEE

Abstract—As the power system evolves to better addressenvironmental and reliability concerns, its overall dynamicschanges and consequently challenges the adequacy of establishedoperating procedures. This evolution brings a significant increasein the number of integrated renewable energy sources (RES)and HVDC connections. RES are normally connected to thegrid through power electronic converters, which reduces orcompletely eliminates their electrical coupling to the power grid.As a result, such units are unable to contribute to the inertiaof the system, posing a potential threat to the grid’s physicalsecurity. More specifically, post-fault frequency characteristics,such as rate of change of frequency (RoCoF), frequency nadirand quasi-steady-state frequency, depend on the system inertiaand their respective limits may potentially be violated. One wayto address this problem is adding constraints to the unit com-mitment formulation so that operations maintain their frequencycharacteristics within acceptable limits. This paper studies howsuch changes affect the system frequency deviation from its ratedvalue. The power system is modeled as an enterprise controlthat combines multiple layers of control operations into onepackage. Such integration allows capturing how the effects ofwind integration and the addition of unit commitment inertiaconstraints propagate through control layers to impact the systemfrequency.

Index Terms—Power system enterprise control, power systeminertia, power system dynamics

NOMENCLATURE

f0 system rated frequencyω0 system rated angular frequencyM angular momentum at the rated frequencyD damping parameter1/R net gain of the governorK automatic generation control (AGC) gainTCH prime mover time constant (charging time)TG governor time constantJi moment of inertia of generator iEi kinetic energy of generator iEsys kinetic energy of the whole system

Manuscript received December 25, 2016.Copyright c© 2017 IEEE. Personal use of this material is permitted.

However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org

A. Muzhikyan is with Thayer School of Engineering, DartmouthCollege, 14 Engineering Drive, Hanover, NH 03755, USA.aramazd.muzhikyan.th@Dartmouth.edu

T. Mezher is with Faculty of Department of Industrial and Sys-tems Engineering, Khalifa University, PO Box 54224, Abu Dhabi, UAE.tmezher@masdar.ac.ae

A. M. Farid is with Faculty of Thayer School of Engineering, Dart-mouth College, 14 Engineering Drive, Hanover, NH 03755, USA. am-farid@dartmouth.edu; and a research affiliate at Massachusetts Institute ofTechnology, 77 Massachusetts Avenue Cambridge, MA, 02139, USA. am-farid@mit.edu

Hi inertia constant of generator iHsys inertia constant of the whole system∆ f (t) system frequency deviation∆Pm(t) system mechanical power deviation∆Pe(t) system electrical power deviation∆PV (t) valve position deviation∆Pre f (t) reference powerPDA day-ahead demand forecastPST short-term demand forecast∆PST short-term demand increment forecastPLF load following reserve requirementRRP ramping reserve requirementPRG regulation reserve requirementP(t) real-time actual demand∆PDA(t) power imbalances at the SCUC output∆RDA(t) ramping imbalances at the SCUC output∆PST (t) power imbalances at the SCED output∆PRT (t) power imbalances in the real-timeI(t), It residual system imbalancesCU

i shutdown cost of generator iCD

i startup cost of generator iCF

i fixed cost of generator iCL

i linear cost of generator iCQ

i quadratic cost of generator iPmax

i maximum power output of generator iPmax

sys maximum power output of the whole systemPmin

i minimum power output of generator iRmax

i maximum ramping rate of generator iFmax

l maximum flow limit of line lPit power output of generator i∆Pit power increment of generator iGt amount of regulation in useFlt power flow level of line lwit ON/OFF state of the generator iwu

it startup indicator of the generator iwd

it shutdown indicator of the generator iNB number of busesNG number of generatorsB ji correspondence matrix of generator i to bus jγ jt incremental transmission loss factor (ITLF) of bus jal jt bus j generation shift distribution factor (GSDF) to

line lTh scheduling time step (normally, 1 hour)Tm real-time market time step (normally, 5 minutes)

I. INTRODUCTION

As the power system evolves to better address environmen-tal and reliability concerns, its overall dynamics changes and

IEEE TRANSACTIONS ON POWER SYSTEMS 2

consequently challenges the adequacy of established operatingprocedures [1]. This evolution brings a significant increasein the number of integrated renewable energy sources (RES)and HVDC connections. The variable nature of the REScreates additional challenges for the power system balancingoperations and leads to increased requirements for operatingreserves [2]–[4].

Besides the variability, the RES and the traditional gen-eration units have differences from the perspective of systeminertia. RES are normally connected to the grid through powerelectronic converters, which reduces or completely eliminatestheir electrical coupling to the power grid. As a result, suchunits are unable to contribute to the inertia of the system,posing a potential threat to the grid’s physical security. Also,increasing penetration of RES into the power grid drivesinstallation of more HVDC connections to accommodate thetransmission of remotely generated renewable energy to theconsumers. However, HVDC connections electrically decouplethe parts of the system they connect, which results in a systemwith electrically decoupled areas with smaller inertia. Reducedsystem inertia alters the post-fault frequency dynamics and canhave a negative impact on the frequency stability of the powergrid [5].

Many studies have addressed this issue by integrating post-fault frequency requirements into different levels of powersystem operations, such as economic dispatch and unit com-mitment. A multi-period unit commitment problem with in-tegrated primary frequency regulation constraints is proposedin [6]. The primary frequency regulation provision from eachgeneration unit is modeled as a linear function of system fre-quency deviation, which refers to the steady-state value of thepost-fault frequency deviation. In [7], [8], frequency controlconstraints are incorporated into the market dispatch model.Rate of change of frequency (RoCoF) and minimum frequencyconstraints are derived in terms of dispatch decision variables,which ensures that the generation dispatch meets the frequencycontrol requirements. The authors of [9] have developed aset of constraints for the dispatch model to ensure adequateprimary frequency response. These constraints are expressedas functions of the system inertia and governor response ramprates. However, the load damping is ignored and the system in-ertia is assumed to be a known constant. A two-stage stochasticeconomic dispatch model with added frequency constraints isdeveloped in [10]. Simplified dynamic models are used to de-rive the post-fault maximum frequency deviation constraints.In [11], a mixed-integer linear programming formulation forthe stochastic unit commitment is proposed. A set of frequencyconstraints are introduced to ensure the post-fault frequencydynamics meets the RoCoF, frequency nadir and quasi-steady-state frequency requirements. Reference [12] derives a mod-ified system frequency response model which is used to findan analytical representation of the system frequency nadir.The derived analytical expressions are later linearized by apiecewise linearization technique and integrated into the unitcommitment problem. In contrast, the authors of [13] studyhow fast-response battery units can be used to maintain thefrequency nadir and RoCoF within the desired limits. Theoutputs of battery units are adjusted immediately after loss of

a generation to minimize the system imbalances. This controltechnique is integrated into the linearized unit commitmentproblem.

This paper studies how incorporating RoCoF and frequencynadir requirements into the unit commitment affects the systemfrequency variations in the real-time. This paper achieves thisby making the following two contributions. First, expressionsfor inertial response requirements are derived that keep thesystem within the given RoCoF and frequency nadir limits.While such expressions have been derived in the literaturebefore, the existing methods mainly use simplified modelsfor generation control, usually consisting of the rotating massand the frequency damping only. This reduces the systemdynamics to a first order differential equation and significantlysimplifies the derivations. However, this leaves out other majorcomponents of the generation control, such as the governorand the prime mover. This paper develops more generalizedderivations that take the governor with primary control intoaccount. The system dynamics is described by a second orderdifferential equation in this case. The dynamics introducedby the prime mover are omitted in this paper to avoid over-complication of the derivations and will be addressed in thefuture work. Next, after the expressions for inertial responserequirements are derived, the second step is to study how theserequirements, that are designed to constrain certain aspects offrequency variations, affect the real-time frequency profile. Tothis end, the inertial response requirements are incorporatedinto the unit commitment problem. This gives an insight intohow the presence of these constraints changes the commitmentof the generation units for different scenarios of the RESintegration. However, in order to obtain the real-time frequencyprofile, the dynamics of the physical power grid should bemodeled and simulated for the generators scheduled by the unitcommitment. Additionally, the dynamic model should receivegeneration setpoints from the real-time market, that dispatchesthe generation units to new levels every 5-15 minutes. Thus,to achieve the goal of this paper, different layers of the powersystem operations should be modeled and simulated together.

As shown in Fig. 1, the power system operations are mod-eled as a multi-layer hierarchical control on top of the physicalpower grid called enterprise control [1]. It has been used tosystematically study the integration of renewable energy [14],[15], energy storage [16], and demand side resources [17]. Theprimary advantage of enterprise control is that it demonstrateshow changes in one control layer will propagate through theother control layers to impact the grid’s physical behavior. Forthe purposes of this study, two modifications are made to theenterprise control simulator. First, new constraints are added tothe unit commitment problem that ensure the RoCoF and thefrequency nadir are always within the acceptable limits duringthe system operations. Second, the steady-state model of thephysical power grid and the regulation service are replacedwith their corresponding dynamic models. This gives access tothe notion of system frequency otherwise absent in the steady-state model.

The paper is organized as follows. Section II presentsthe background information on the power system generationcontrol and inertia. Section III derives the RoCoF and the

IEEE TRANSACTIONS ON POWER SYSTEMS 3

Regulation Service

Physical Power Grid

)(tP

)(tI

Resource Scheduling

Balancing Actions

SCEDManual

Operator Actions

SCUCReserve

SchedulingIm

bal

ance

Me

asu

rem

ent

Reg

ula

tion

Le

vel

)(tPDA

)(tPST

)(tPRT

RGP

LFP RPR)(tRDA

][ˆ kPDA

][ˆ kPST

LFPRPR

RGP

Fig. 1. Power system enterprise control simulator model [14], [15]

Rotating mass & load

Prime moverGovernor

Regulation

Fig. 2. Power system generation control [18], [19]

frequency nadir as functions of the generator’s dynamic char-acteristics. Section IV briefly describes the enterprise controlsimulator used for this study and the introduced modificationsto facilitate the needs of this study. Section V describes thesystem configurations and the simulation scenarios used inthis paper. Section VI discusses the results and Section VIIpresents the conclusions.

II. BACKGROUND

This section provides background information on the powersystem generation control and inertia.

A. Power System Generation Control

The general form of the generation dynamic control blockdiagram is presented in Fig. 2 [18], [19]. It consists of fourmain components, namely rotating mass & load, prime mover,governor and regulation. The mathematical formulation ofeach block is described in this subsection.

First, the rotating mass & load block is described by thefollowing first order equation [18]:

Md∆ f (t)

dt+D ·∆ f (t) = ∆Pm(t)−∆Pe(t) (1)

where M is the angular momentum of the machine at therated frequency. D is the damping parameter that indicates thesensitivity of the frequency-dependent load on the system fre-quency. ∆Pm(t) and ∆Pe(t) are the changes of the mechanicaland electrical powers of the system respectively.

The prime mover, be it a steam or hydro turbine, drives thegenerator. The simplest nonreheat turbine is described by afirst order equation and relates the mechanical power output∆Pm to the position of the valve ∆PV [18]:

TCHd∆Pm(t)

dt+∆Pm(t) = ∆PV (t) (2)

where TCH is a time constant called charging time.The governor controls the input valve to maintain the

system frequency at the rated value. The simplest governoris described by a first order equation and relates the valveposition ∆PV to the system frequency deviation ∆ f (t) [18]:

TGd∆PV (t)

dt+∆PV (t) = ∆Pre f (t)−

1R

∆ f (t) (3)

where 1/R is the net gain of the governor and TG is a timeconstant. 1/R feedback loop is also called primary control.However, the governor is unable to wholly restore the systemfrequency after a change of the load ∆PL occurs.

The regulation service, implemented as an automatic gener-ation control (AGC), restores the frequency to the rated valueby measuring the system frequency deviation ∆ f and adjustingthe reference power ∆Pre f [19]:

∆Pre f (t) =−K ·∫

∆ f (t)dt (4)

Regulation service is also called secondary control.

B. Inertia from Synchronous GenerationThe power system inertia is the resistance of the syn-

chronous generators and turbines to the rotational speedchange. The kinetic energy of the generator i rotating at ω0rated angular frequency can be written as [5]:

Ei =Jiω

20

2(5)

where Ji is the moment of inertia of the generator i. Itis important to mention the relation between the angularmomentum M and the kinetic energy E:

E =f0 ·M

2(6)

The kinetic energy in (5) is often normalized to the max-imum power output Pmax

i and is called the inertia constantHi [5]. Inertia constant defines the duration the generator isable to provide maximum power only using the stored kineticenergy (5):

Hi =Ei

Pmaxi

(7)

Since the system frequency is the same for all throughout thenetwork, all generators can be combined into one. Thus, thetotal energy stored in the system is:

Esys =N

∑i=1

Ei =N

∑i=1

Hi ·Pmaxi (8)

IEEE TRANSACTIONS ON POWER SYSTEMS 4

Thus, the combined inertia constant of all synchronous gener-ators can be written as [5]:

Hsys =Esys

Pmaxsys

=

N∑

i=1Hi ·Pmax

i

N∑

i=1Pmax

i

(9)

III. RATE OF CHANGE OF FREQUENCY (ROCOF) ANDFREQUENCY NADIR DETERMINATION

Rate of change of frequency (RoCoF) and frequency nadirare two important characteristics of the port-fault systemfrequency dynamics [5]. The RoCoF is the initial rate atwhich the frequency changes immediately after a contingencyhappens and is critical to reliable power system operation.Frequency nadir, on the other hand, is the minimum levelthe frequency drops following the event, before recovering toits steady-state value. If the RoCoF or the frequency nadirexceed their allowed limits, the generator protection maytrigger disconnecting it from the grid.

A. Frequency Deviation Profile

Expressions for the RoCoF and the frequency nadir canbe derived from the frequency deviation profile ∆ f (t), thesolution of the power system dynamic equations (1)-(4). Asstated above, this paper ignores the dynamics introduced bythe prime mover, ∆PV (t) = ∆Pm(t). Also, the calculations ofthese frequency characteristics are carried out in the absenceof the regulation service, ∆Pre f (t) = 0. Thus, the system boilsdown to the following couple of differential equations:

Md∆ f (t)

dt+D ·∆ f (t) = ∆Pm(t)−∆Pe(t) (10)

TGd∆Pm(t)

dt+∆Pm(t) =−

1R

∆ f (t) (11)

For the rest of the calculations the subscript in TG will beskipped for simplicity of equations, i.e., T ≡ TG assignmentis used. Also, ∆Pe(t) is assumed to be a step function with amagnitude ∆P. Thus, (10) and (11) can be combined into thefollowing second order differential equation:

MTd2∆ f (t)

dt2+(DT +M)

d∆ f (t)dt

+

(D+

1R

)∆ f (t) =−∆P

(12)

The roots of the characteristic equation for (12) are:

x =−(DT +M)±

√(DT −M)2− 4MT

R2MT

(13)

Thus, the solution of (12) can be represented as:

∆ f (t) =C1ex1t +C2ex2t (14)

where x1 and x2 are the roots of the characteristic equation(13), and C1 and C2 are constants defined by the initial con-ditions of (12). Thus, when both x1 and x2 are real numbers,according to (14), the system frequency decreases exponen-tially towards the quasi-steady-state value, without having afrequency nadir. This goes against the purpose of this paper to

study the impact of the system inertia on frequency nadir andRoCoF. In contrast, when x1 and x2 are both complex numbers,the solution (14) becomes a sine profile with exponentiallydecreasing magnitude. This guarantees presence of frequencynadir, which is at the core of this paper’s interest. Thus, inorder for x1 and x2 to be complex, the expression under thesquare root in (13) should be negative:

(DT −M)2 <4MT

R(15)

When the assumption (15) holds, the solution of (12) can bewritten as:

∆ f (t) =(− 1

D+1/R+(

Acosβ t +Bsinβ t)

e−αt)

∆P (16)

where α and β are real and imaginary parts of (13) respec-tively:

α =DT +M

2MT, β =

√4MT

R− (DT −M)2

2MT(17)

To calculate A and B, the following initial conditions aretaken into account. First, the frequency deviation is still smallimmediately after the loss of a generation unit, ∆ f (0)≈ 0. Asa result, the governor response is also negligible, ∆Pm(0)≈ 0[11]. These initial conditions yield A and B as:

A =1

D+1/R, B =

1β

(α

D+1/R− 1

M

)(18)

Equations (16)-(18) are used in the following subsections toderive the RoCoF and the frequency nadir.

B. Rate of Change of Frequency (RoCoF)

Once the frequency deviation profile in (16)-(18) is ob-tained, the next step is to calculate the derivative of thefrequency deviation in (16):

d∆ f (t)dt

=((Bβ −Aα)cosβ t− (Bα +Aβ )sinβ t

)e−αt

∆P

(19)

Thus, using (17) and (18), the RoCoF is calculated from (19):

RoCoF =d∆ f (0)

dt= (Bβ −Aα)∆P =−∆P

M(20)

Using (6) and (8), RoCoF takes the following final form:

RoCoF =− f0 ·∆P2Esys

=−f0 ·Pmax

k

2 ·N∑

i=1i6=k

Hi ·Pmaxi

(21)

C. Frequency Nadir

First, the time tn when the system reaches its nadir isdetermined. Since the frequency derivative should be zero atnadir, tn is determined by equating the right-hand-side of (19)to zero. Thus, using (17) and (18):

tanβ tn =Bβ −Aα

Bα +Aβ=

α

D+1/R− 1

M− α

D+1/R1β

(α2 +β 2

D+1/R− α

M

) (22)

IEEE TRANSACTIONS ON POWER SYSTEMS 5

The expression α2 +β 2 is calculated separately using (17):

α2 +β

2 =(DT +M)2 +4MT/R− (DT −M)2

4M2T 2 =D+1/R

MT(23)

Substituting (23) into (22), we get:

tanβ tn =2MT β

DT −M(24)

The arctangent function is used to extract tn from (24). How-ever, since the range of the arctangent output is [−π/2;π/2],tn can have a negative value when DT −M < 0. To avoid this,the range is shifted to [0;π] by adding π to the arctangentoutput when DT −M < 0:

tn =

1β

arctan(

2MT β

DT −M

), if DT −M ≥ 0

1β

(arctan

(2MT β

DT −M

)+π

), if DT −M < 0

(25)

Now, once tn is obtained, it can be substituted into (16) tocalculate the frequency nadir. The calculations for differentsigns of DT −M are slightly different, but yield the sameresults. Therefore, in the following derivations DT −M > 0 isassumed. First, the trigonometric part of (16) is calculated:

Acosβ tn +Bsinβ tn = cosβ tn (A+B · tanβ tn) =

=A+B · tanβ tn√

1+ tan2 β tn=

1D+1/R

+

(α

D+1/R− 1

M

)· 2MT

DT −M√1+4M2T 2β 2/(DT −M)2

=

=

DT −MD+1/R

+

(DT +M

2MT (D+1/R)− 1

M

)·2MT√

(DT −M)2 +4M2T 2β 2=

=

DT −MD+1/R

+

(DT +M−2T (D+1/R)

2MT (D+1/R)

)·2MT√

(DT −M)2 +4MT/R− (DT −M)2=

=DT −M+DT +M−2T (D+1/R)

(D+1/R)√

4MT/R=−

√RT/M

DR+1(26)

Substituting (26) into (16) gives the frequency nadir:

∆ fnadir =−R+

√RT/M

DR+1e−αtn∆P (27)

where tn is given by (25). Thus, if ∆ fmax is the maximumof the frequency nadir absolute value, the following conditionshould hold:

R+√

RT/MDR+1

e−αtnPmaxk ≤ ∆ fmax (28)

However, the left-hand-side of (28) is a nonlinear function ofM and cannot be directly integrated into the unit commitmentproblem as a constraint.

On the other hand, it can be shown that αtn is a monotoni-cally increasing function of M while condition (15) holds. As a

result, the left-hand-side of (28) is a monotonically decreasingfunction of M. Thus, if M∗k is the solution of:

R+√

RT/MDR+1

e−αtnPmaxk = ∆ fmax (29)

the condition (28) holds as long as Mk ≥M∗k or, using (6):

N

∑i=1i 6=k

Hi ·Pmaxi ≥

f0M∗k2

(30)

It is important to notice that in (29), tn depends on M too.As a result, it has no analytical solution and M∗k is found bynumerical solution.

IV. POWER SYSTEM ENTERPRISE CONTROL WITH INERTIAPROCUREMENT

As mentioned in the introduction and depicted in Fig. 1,the power system operation is modeled as a multi-layerhierarchical control on top of the physical power grid. Thecontrol layers are resource scheduling, balancing operationsand regulation service and the interested reader is referred to[14], [15] for a detailed description.

The original enterprise control formulation is modified tofacilitate the needs of this study and are summarize as follows.First, new constraints are added to the unit commitmentformulation that make sure the RoCoF and the frequency nadirlimits are respected. Next, the original steady-state formulationof the physical power grid and the regulation service arereplaced with a dynamic model described by the differentialequations presented in Section II-A. Utilization of the dynamicmodel is necessary to introduce the concept of the systemfrequency into the simulations. A brief description of eachcontrol layer is presented in the following subsections.

A. Resource Scheduling

The resource scheduling layer is implemented as a security-constrained unit commitment problem (SCUC). The goal ofthe SCUC problem is to choose the right set of generationunits, that are able to meet the real-time demand with mini-mum cost. In the original formulation, the SCUC problem isa nonlinear optimization problem with integrated power flowequations and system security requirements [20]. However,the constraints are often linearized to avoid convergenceissues. The SCUC formulation in [14], [15] is amended hereto include inertia constraints that keep the RoCoF and thefrequency nadir within allowed limits:

min24

∑t=1

NG

∑i=1

(witCF

i +CLi Pit +CQ

i P2it +wu

itCUi +wd

itCDi

)(31)

s.t.NG

∑i=1

Pit = PDAt (32)

−Rmaxi Th ≤ Pit −Pi,t−1 ≤ Rmax

i Th (33)

witPmini ≤ Pit ≤ witPmax

i (34)

wit = wi,t−1 +wuit −wd

it (35)

IEEE TRANSACTIONS ON POWER SYSTEMS 6

NG

∑k=1k 6=i

wktHkPmaxk ≥

f0 ·witPmaxi

2 ·RoCoFmax (36)

NG

∑k=1k 6=i

wktHkPmaxk ≥ f0 ·witM∗i

2(37)

NG

∑i=1

witPmaxi −

NG

∑i=1

Pit ≥ PLF (38)

NG

∑i=1

Pit −NG

∑i=1

witPmini ≥ PLF (39)

NG

∑i=1

witRmaxi −

NG

∑i=1

(Pit −Pi,t−1

Th

)≥ RRP (40)

NG

∑i=1

(Pit −Pi,t−1

Th

)−

NG

∑i=1

witRmini ≥ RRP (41)

where i and t are generator and time indices respectively. Theinertia constraints (36) and (37) are derived from (21) and (30)respectively, and include {wit} binary variables on both sidesto allow generators to be switched on and off.

B. Balancing ActionsThe real-time market moves available generator outputs to

new setpoints (re-dispatch) in the most cost-efficient way. Inits original formulation, generation re-dispatch is implementedas a non-linear optimization model, called AC optimal powerflow (ACOPF) [21]. Due to problems with convergence andcomputational complexity [20], most of the U.S. indepen-dent system operators (ISO) moved from ACOPF to linearoptimization models. The most commonly used model iscalled security-constrained economic dispatch (SCED) and isformulated as an incremental linear optimization problem [22]:

minNG

∑i=1

(CLi ∆Pit +2CQ

i Pit∆Pit) (42)

s.t.NB

∑j=1

(1− γ jt)

(NG

∑i=1

B ji∆Pit −∆PSTjt

)= It +Gt (43)

NB

∑j=1

al jt

(NG

∑i=1

B ji∆Pit −∆PSTjt

)≤ Fmax

l −Flt (44)

−Rmaxi Tm ≤ ∆Pit ≤ Rmax

i Tm (45)

Pit −Pmini ≤ ∆Pit ≤ Pmax

i −Pit (46)

where i, j, l and t are generator, bus, line and time indicesrespectively. Use of incremental values for generation andload allows incorporation of sensitivity factors and problemlinearization. Sensitivity factors establish linear connectionsbetween changes of power injections on the buses and state-related parameters of the system [18]. Two sensitivity factorsare used in the SCED. The incremental transmission loss factor(ITLF) for bus i shows how much the total system losseschange, when power injection on bus i increases by a unit[23].

C. Regulation Service and Generation ControlThe enterprise control simulator described in [14], [15] uses

steady-state models for the regulation service and the physical

power grid. In contrast, this paper uses generation controland regulation dynamic models described in Section II-A tostudy the impact of wind integration on the system frequencydeviation. As mentioned above, for the simplicity of the model,this paper ignores the dynamics introduced by the primemover, ∆PV (t) = ∆Pm(t), which yields to the following systemof three linear differential equations:

Md∆ f (t)

dt+D ·∆ f (t) = ∆Pm(t)−∆Pe(t) (47)

TGd∆Pm(t)

dt+∆Pm(t) = ∆Pre f (t)−

1R

∆ f (t) (48)

d∆Pre f (t)dt

=−K ·∆ f (t) (49)

where ∆Pe(t) is the solution of the SCED problem (42)–(46).The resulting ∆ f (t) frequency deviation profile is the subjectof interest of this paper.

V. CASE STUDY

The main objective of this paper is to study the impactof wind integration on the power system inertia and itsconsequent impact on the system frequency deviation from therated value. This section describes the simulation scenariosnecessary to achieve this objective and the simulation setupused in this paper.

It is important to notice, that test systems, in general,are defined by their topology and the generation base. Thedegree to which these two sets of data is important dependsupon how a model depends on these input parameters. Asthe issues related to the system topology are not central tochanges in the system’s inertial response, they detract fromthe central message of the paper regarding the interactionsbetween the SCUC program, the balancing behavior, and theinertial response. It is for this reason, that the paper hasspecifically focused on the generation base. This paper studiesfour different scenarios, described in Section V-A, that modeldifferent case of wind power integration and the enforcementof inertial response procurement constraints in the SCUCproblem.

A. Simulation Scenarios

To allow comparison of the simulation results, four differentpower system configurations are considered here:• Traditional system. The power system consists of only

thermal generation units. The inertia constraints (36)–(37)are ignored.

• Traditional system with inertia constraints. Similarto the previous configuration, the power system consistsof only thermal generation units. The inertia constraints(36)–(37) are enforced.

• Wind integrated system. In addition to the thermalgeneration units, the system contains wind generationcapacity equivalent to 30% of the system peak load. Theinertia constraints (36)–(37) are ignored.

• Wind integrated system with inertia constraints. Simi-lar to the previous configuration, the system contains wind

IEEE TRANSACTIONS ON POWER SYSTEMS 7

generation capacity equivalent to 30% of the system peakload. The inertia constraints (36)–(37) are enforced.

In order to gain insight into the impact of wind integrationand the enforcement of inertia constraints, the system behaviorof these four configurations are studied within the context ofenterprise control assessment. Three behaviors are specificallydiscussed:• Unit commitment. The unit commitment results for each

system configuration are obtained. Integration of the windalters the number of committed units and consequentlythe system inertia. Meanwhile, the enforcement of inertiaconstraints restores the inertia but changes the dispatchlevels and their associated costs.

• Step function response. The response of the systemfrequency to a 50MW jump of the load is studied for dif-ferent combinations of the generation commitment. Thisserves to understand how different generation commit-ments alter the dynamics of the system, which eventuallydefines the system frequency deviation behavior duringthe operations.

• Frequency deviation. The power system operations aresimulated for one day period using the enterprise controlsimulator described above so as to study the systemfrequency deviations. The results are compared for allfour system configurations.

B. Simulation Setup

In order to simulate power system operations, the enterprisecontrol simulator described in Section IV is used. The SCUCformulation in (31)–(41) with inertia procurement constraintsis used for commitment of generation units. The real-timedispatch of the committed generators is performed by theSCED formulations in (42)–(46). The physical power grid isrepresented by the dynamic model of the the IEEE New Eng-land test system, consisting of 39 buses and 10 generators [24],where the generators are modeled by the differential equationsin Section II-A. Because the New England test system data isoriginally meant for steady-state power flow analysis, it lacksinformation about the dynamic properties of the generators.These properties are chosen within reasonable ranges and areaggregated in Table I along with the generation capacities. Forsimplicity, identical values are assigned to each generator forall the dynamic properties. The daily load and wind profilesare taken from the Bonneville Power Administration (BPA)repositories [25] and the system peak load is 8000MW. Thispaper also assumes that the wind turbines do not contributeto the inertia of the system. The RoCoF and the frequencynadir limits are taken 0.5Hz/s [11], [26] and 0.8Hz [9], [11]respectively.

The simulations are performed in the following order. First,the SCUC problem is run to produce the generation commit-ment schedules for each hour that meet the forecasted demandand maintain the desired RoCoF and frequency nadir. Next,the committed units are dispatched in the real-time balancingoperations by the SCED program, and the dispatched valuesare sent to the dynamic model of the physical power gridas generation setpoints. Finally, the dynamic model of the

TABLE ITHE PHYSICAL PROPERTIES OF THE GENERATORS

Pmax Pmin H D T R K(MW) (MW) (s) (MW/Hz) (s) (Hz/MW) (MW)

Gen 1 1040 312 15 100 10 0.01 5

Gen 2 646 193.8 15 100 10 0.01 5

Gen 3 725 217.5 15 100 10 0.01 5

Gen 4 652 195.6 15 100 10 0.01 5

Gen 5 508 152.4 15 100 10 0.01 5

Gen 6 687 206.1 15 100 10 0.01 5

Gen 7 580 174 15 100 10 0.01 5

Gen 8 564 169.2 15 100 10 0.01 5

Gen 9 865 259.5 15 100 10 0.01 5

Gen 10 1100 330 15 100 10 0.01 5

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

2

3

4

5

6

7

8

9

10

Num

ber

of C

omm

itted

Gen

erat

ors

Traditional System | Cost = $56415Traditional System with Inertia Constraints | Cost = $56415Wind Integrated System | Cost = $43392Wind Integrated System with Inertia Constraints | Cost = $45762

Fig. 3. The number of committed generators for each power systemconfiguration

physical power grid solves the differential equations (47)–(49)to obtain the frequency deviation profiles. The simulations arerun for each scenario in Section V-A.

VI. RESULTS AND DISCUSSION

This section reports and discusses the results of the en-terprise control simulation. Each of the four power systemconfigurations are simulated and discussed in terms of thethree behaviors mentioned above.

A. Unit Commitment

The unit commitment results are obtained for each of fourpower system configurations. As shown in Table I, althoughthe generators have different capacities and ramping rates,the dynamic characteristics have been set to identical values.Because this paper is focused on the system-wide inertiaand dynamic behavior, the relative allocation of inertia toeach generator is not of concern. Therefore, the number ofcommitted generators for each operating hour is shown inFig. 3 as a proxy for the total system-wide inertia.

According to the results in Fig. 3, the commitment of thetraditional system is indifferent towards the enforcement of the

IEEE TRANSACTIONS ON POWER SYSTEMS 8

Time (s)0 20 40 60 80 100 120

Fre

quen

cy D

evia

tion

(Hz)

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

05 generators | E = 66255 MWs | RoCoF = 0.0226 Hz/s6 generators | E = 76035 MWs | RoCoF = 0.0197 Hz/s7 generators | E = 85725 MWs | RoCoF = 0.0175 Hz/s8 generators | E = 93195 MWs | RoCoF = 0.0161 Hz/s9 generators | E = 100725 MWs | RoCoF = 0.0149 Hz/s

Fig. 4. The response of the system to a loss of 500MW generation unit.

inertia constraints. This is explained by the fact the generationrequired to meet the daily demand already carries enoughinertia to satisfy these constraints. They are not binding. Theminimum number of generators is seven. On the other hand,when wind energy is integrated into the power system, thenet load drops and the system is able to meet the demandwith less generators. During the night, for instance, onlyfive generators is needed to meet the demand. However,when the inertia constraints are enforced, the commitmentof the generators changes. Now, there are seven units onlineduring the night. This indicates that the system with only fivegenerators violates the inertia requirement. In this case, theadditionally committed units do not generate power. They areonline only for maintaining the inertia of the system.

The total operation cost is also affected. As expected, theoperation cost drops when wind is integrated into the system asless generation is required to meet the demand. On the otherhand, enforcement of the inertia constraints in the presenceof wind increases the cost only slightly. This additional costcorresponds to the fixed cost of the generators that don’tgenerate power but are still required to stay online.

B. Inertial Response

Next, the inertial response of the system is simulated fora different number of online generators. This will help tounderstand how the dynamics of the system change with thereduction of inertia and provide more insight into the results ofthe frequency deviation presented in the following subsection.As shown in Fig. 3, the number of simultaneously onlinegenerators varies from five to nine. Therefore, the inertialresponse of the system to a 50MW step load increase att = 0 is simulated for 5, 6, 7, 8 and 9 online generation. Thecorresponding frequency profiles are presented in Fig. 4.

The results in Fig. 4 show that there are two importantfactors that affect the frequency deviation of the actual system.First, the frequency nadir is lower for the system with lessinertia. This shows that for the same load jump, the frequencyof the system with lower inertia is more volatile and is morelikely to violate the frequency nadir limit. On the other hand,the system with higher inertia has more delay when respondingto a load jump. This can also have a negative impact on theability of the system to fix the frequency deviation after amajor jump of the load or a loss of a generator occurs. Thus,

Frequency Deviation (Hz)-0.1 -0.05 0 0.05 0.1

Dur

atio

n (s

)

100

101

102

103

104

Traditional System | STD = 0.0179 HzTraditional System with Inertia Constraints | STD = 0.0179 HzWind Integrated System | STD = 0.0194 HzWind integrated System with Inertia Constraints | STD = 0.0196 Hz

Fig. 5. The distribution of the frequency deviation of different power systemconfigurations

there is no definite answer whether higher inertia is morebeneficial for maintaining the system frequency, and it dependson how much role each of these two factors will play. The nextsubsection studies the impact of these factors on the frequencydeviation of the system.

C. Frequency DeviationAs mentioned in the previous section, the frequency devi-

ation depends on how much contribution the differences infrequency nadirs and response delays for the given systeminertia will have. To answer that question, the power systemoperations are simulated for the four configurations describedabove using the enterprise control simulator. The distributionsof the frequency deviations for each configuration are pre-sented in Fig. 5.

Fig. 5 shows the similarity of all four curves relative toeach other. As expected, the traditional system has the samefrequency deviation for both configurations. The blue curveis hidden behind the red one because they have identical unitcommitment as shown above. The distribution for the windintegrated systems is slightly wider, which is not necessarily aresult of reduced inertia and can be due to high intermittencyof the wind power. The latter is more likely to be true accord-ing to Fig. 5 because when the inertia constraints are enforced,the standard deviation increases slightly. However, the impactof inertia on the system frequency is relatively negligible incompared to the impact of the net load intermittency.

Another interesting aspect of Fig. 5 is, that on the loga-rithmic scale, the trends of the distributions resemble straightlines. Linear least squares regressions are run for each branchof the curves and the results are presented in Fig. 5 by dashedlines. These lines also indicate that while the gap betweenthe traditional and wind integrated system configurations isnoticeable, the lines for the configurations with and withoutinertia constraints are almost indistinguishable.

This work was demonstrated on the IEEE 39-Bus system.The choice of a test case with a relatively small number of

IEEE TRANSACTIONS ON POWER SYSTEMS 9

generators demonstrates how small changes in the commitmentof generators can have noticeable impacts on the system’sRoCoF. Such effects would also appear for much largersystems but only when the penetration of variable energyresources increases accordingly. Because the mathematicalmodel is presented for systems of arbitrary size, the impactsdemonstrated here can be expected in other systems of varioussizes.

VII. CONCLUSION

This paper studies the impact of wind integration andenforcement of inertia constraints on the power system fre-quency deviations. This is achieved by utilizing the two maincontributions of this paper. First, generalized expressions forinertial response requirements are derived that keep the systemwithin the given RoCoF and frequency nadir limits. Thisapproach models the dynamics of the system by a second orderdifferential equation, taking the governor with primary controlinto account. Second, the inertial response requirements areincorporated into the unit commitment problem to study howthe presence of these constraints changes the commitment ofthe generation units for different scenarios of the renewableenergy integration. Additionally, different layers of the powersystem operations are modeled and simulated together so thatthe generation setpoints from the real-time market are fed intothe dynamic model.

The results show that enforcing the inertia constraints has noimpact on the unit commitment of the traditional system, whileit forces the system to schedule idle generators in the case ofthe wind integrated system. The results also show that theinertial response is characterized by both its frequency nadirand response delay. A system with greater inertia has a longersettling time and a smaller frequency nadir. Consequently, thedistribution of frequency deviations at such small timescalesis relatively similar. More importantly, the impact of thesystem inertia on the frequency deviation is relatively smallin comparison to the impact of the net load profile and itsintermittency.

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[1] A. M. Farid, B. Jiang, A. Muzhikyan, and K. Youcef-Toumi, “Theneed for holistic enterprise control assessment methods for the futureelectricity grid,” Renewable and Sustainable Energy Reviews, vol. 56,pp. 669–685, 2016.

[2] A. Muzhikyan, A. M. Farid, and K. Youcef-Toumi, “An EnhancedMethod for the Determination of Load Following Reserves,” in AmericanControl Conference 2014 (ACC2014), Portland, OR, 2014, pp. 926–933.

[3] A. Muzhikyan, A. M. Farid, and K. Youcef-Toumi, “An EnhancedMethod for the Determination of the Ramping Reserves,” in AmericanControl Conference 2015 (ACC2015), Chicago, Ill., 2015, pp. 994 –1001.

[4] A. Muzhikyan, A. M. Farid, and K. Youcef-Toumi, “An EnhancedMethod for the Determination of the Regulation Reserves,” in AmericanControl Conference 2015 (ACC2015), Chicago, Ill., 2015, pp. 1016 –1022.

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[6] J. F. Restrepo and F. D. Galiana, “Unit commitment with primaryfrequency regulation constraints,” IEEE Transactions on Power Systems,vol. 20, no. 4, pp. 1836–1842, 2005.

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[12] H. Ahmadi and H. Ghasemi, “Security-Constrained Unit CommitmentWith Linearized System Frequency Limit Constraints,” IEEE Transac-tions on Power Systems, vol. 29, no. 4, pp. 1536–1545, 2014.

[13] Y. Wen, W. Li, G. Huang, and X. Liu, “Frequency dynamics constrainedunit commitment with battery energy storage,” IEEE Transactions onPower Systems, vol. 31, no. 6, pp. 5115–5125, 2016.

[14] A. Muzhikyan, A. M. Farid, and K. Youcef-Toumi, “An EnterpriseControl Assessment Method for Variable Energy Resource InducedPower System Imbalances. Part I: Methodology,” Industrial Electronics,IEEE Transactions on, vol. 62, no. 4, pp. 2448–2458, 2015.

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[16] A. Muzhikyan, A. M. Farid, and K. Youcef-Toumi, “Relative merits ofload following reserves & energy storage market integration towardspower system imbalances,” International Journal of Electrical Power &Energy Systems, vol. 74, pp. 222–229, 2016.

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Aramazd Muzhikyan received his Sc.B and Sc.Mdegrees from Yerevan State University, Yerevan,Armenia, in 2008. He completed his second Sc.Mdegree at Masdar Institute of Science and Technol-ogy, Abu Dhabi, U.A.E, in 2013. He is currentlya PhD student at Thayer School of Engineering atDartmouth College. His research interests includesignal processing, power system optimization, powersystem operations and renewable energy integration.

IEEE TRANSACTIONS ON POWER SYSTEMS 10

Toufic Mezher is a Professor of Industrial and Sys-tems Engineering at Khalifa University since 2008.He is currently affiliated with the Institute Centerfor Smart and Sustainable Systems (iSmart). BeforeJoining Khalifa University, he was a Professor ofEngineering Management at the American Univer-sity in Beirut from 1992 to 2007. He earned a BS inCivil Engineering from University of Florida, and aMaster and ScD in Engineering Management fromGeorge Washington University in 1988 and 1992 re-spectively. His research interests include Renewable

Energy Management and Policy, Sustainable Development, and TechnologyStrategy and Innovation Systems.

Amro M. Farid received his Sc.B and Sc.M de-grees from MIT and went on to complete his Ph.D.degree at the Institute for Manufacturing within theUniversity of Cambridge Engineering Departmentin 2007. He is currently an associate professor ofEngineering and leads the Laboratory for Intelli-gent Integrated Networks of Engineering Systems(LI2NES) at Thayer School of Engineering, Dart-mouth College. He is also a research affiliate at theMassachusetts Institute of Technology – Technologyand Development Program. He maintains active con-

tributions in the MIT Future of the Electricity Grid study, the IEEE ControlSystems Society, and the MIT-MI initiative on the large-scale penetration ofrenewable energy and electric vehicles. His research interests generally includethe system architecture, dynamics and control of power, water, transportationand manufacturing systems.