Content uploaded by Damian Flynn
Author content
All content in this area was uploaded by Damian Flynn on May 05, 2017
Content may be subject to copyright.
Provided by the author(s) and University College Dublin Library in accordance with publisher policies. Please
cite the published version when available.
Downloaded 2017-05-05T17:26:03Z
The UCD community has made this article openly available. Please share how this access benefits you. Your
story matters! (@ucd_oa)
Some rights reserved. For more information, please see the item record link above.
Title Inertia considerations within unit commitment and economic
dispatch for systems with high non-synchronous penetrations
Author(s) Daly, Pádraig; Flynn, Damian; Cunniffe, Noel
Publication
date 2015-07-02
Conference
details 2015 IEEE PowerTech, Eindhoven, Netherlands, 29 June - 2
July 2015
Publisher IEEE
Item
record/more
information http://hdl.handle.net/10197/8090
Publisher's
statement
© 2015 IEEE. Personal use of this material is permitted.
Permission from IEEE must be obtained for all other uses, in
any current or future media, including reprinting/republishing
this material for advertising or promotional purposes, creating
new collective works, for resale or redistribution to servers or
lists, or reuse of any copyrighted component of this work in
other works.
Publisher's
version (DOI) http://dx.doi.org/10.1109/ptc.2015.7232567
Inertia Considerations within Unit Commitment and
Economic Dispatch for Systems with High
Non-Synchronous Penetrations
P´
adraig Daly, Damian Flynn
Electricity Research Centre, University College Dublin
Dublin, Ireland
padraig.daly@ucdconnect.ie, damian.flynn@ucd.ie
Noel Cunniffe
EirGrid Plc
Dublin, Ireland
noel.cunniffe@eirgrid.com
Abstract—The priority dispatch status of non-synchronous
renewable generation (wind, wave, solar), and increasing levels of
installed high voltage direct current interconnection between syn-
chronous systems, is fundamentally changing unit commitment
and economic dispatch (UCED) schedules. Conventional syn-
chronous plant, the traditional provider of services which ensure
frequency stability - synchronising torque, synchronous inertia
and governor response - are being displaced by marginally zero
cost non-synchronous renewables. Such a trend has operational
security implications, as systems - particularly synchronously
isolated systems - may be subject to higher rates of change of
frequency and more extreme frequency nadirs/zeniths following a
system disturbance. This paper proposes UCED-based strategies
to address potential shortfalls in synchronous inertia associated
with high non-synchronous penetrations. The effectiveness of
the day-ahead strategies is assessed by weighing the cost of the
schedules against the risk level incurred (the initial rate of change
of frequency following a generation-load imbalance), and the level
of wind curtailment engendered.
Index Terms—economic dispatch, inertia, unit commitment,
wind generation.
I. INTRODUCTION
As countries attempt to reduce fossil fuel dependency and
greenhouse gas emissions, penetration levels of renewable gen-
eration - most notably variable-speed wind turbines (VSWT)
and solar photovoltaics (PV) - continue to rise. A fundamen-
tal difference with VSWT/PV generators, in comparison to
conventional generation, is their non-synchronous connection
to the power system, i.e. through partial/full-scale frequency
converters. This decoupling of the VSWT rotor angular speed
from the grid frequency results in there being no inherent
change in stored rotational energy, and thus no inherent
provision of an inertial response, to redress a falling/rising
system frequency. The growth of high voltage direct current
(HVDC) interconnection between synchronous systems has
This work was conducted in the Electricity Research Centre, University
College Dublin, Ireland, in collaboration with EirGrid Plc. The Electricity
Research Centre is supported by the Commission for Energy Regulation,
Bord G´
ais Energy, Bord na M´
ona Energy, Cylon Controls, EirGrid, Electric
Ireland, Energia, EPRI, ESB International, ESB Networks, Gaelectric, Intel,
SSE Renewables, and UTRC. The work of P´
adraig Daly was supported by
the Irish Research Council’s Embark Initiative.
also accentuated the level of non-synchronous infeeds. Further-
more, the current electricity market environment - whereby the
emphasis of conventional plant manufacturing is now focused
on machine efficiency/flexibility [1] - is resulting in machines
with lower inertial constants. Such trends are resulting in lower
levels of synchronous inertia online, with a potential twofold
impact on the system short-term frequency response: (i) the
rate of change of frequency (ROCOF) following a generation-
load imbalance is faster, which can result in (ii) more extreme
nadirs/zeniths within a shorter time frame.
Traditionally, low levels of synchronous inertia were only of
concern to smaller, synchronously isolated systems. However,
the transition towards ‘lighter’ systems has been recognised
in larger jurisdictions, such as in the U.S. [2], [3], continental
Europe [4] and Great Britain [5]. Some system operators
are already taking mitigating action: ERCOT [6] and EirGrid
[7] are designing ancillary services to remunerate providers
of synchronous inertia, and, along with Transpower [8], fast
frequency response (≤2s full deployment). In contrast,
Hydro-Qu´
ebec have mandated an emulated inertial response
capability from wind farms via grid code enforcement [9].
Conventional synchronous plant have been the cornerstone
of power system frequency control, and consequently, op-
erational policies have been based on the ubiquitous pres-
ence of such technology. Many of the challenges in man-
aging a synchronous system with high installed capacities
of non-synchronous renewable generation relate to the maxi-
mum allowable real-time penetration level of non-synchronous
sources [10]. Limiting the instantaneous non-synchronous
penetration to enhance system security has implications for
renewable energy targets/economic system operation as it may
result in wind curtailment [11], and may also incur start-up
and production costs associated with committing and running
out-of-merit synchronous plant [12]. Both consequences imply
inefficient system operation. Thus, there is a pressing need
to develop new operational policies, focused on the evolving
plant portfolio - rather than those based on the unequivocal
presence of conventional synchronous generation.
This work proposes unit commitment and economic dis-
patch (UCED)-based strategies to mitigate potential shortfalls
in system inertia levels. A range of constraint and operational
metric formulations are analysed, with focus placed on the
initial ROCOF following a major event, system production
costs, and wind curtailment.
II. IN ERT IA L CONSTRAINT FORMULATION
A. Short-Term Frequency Stability Time Frame
Short-term frequency control refers to the time frame imme-
diately following a generation-load imbalance. There are three
consecutive and distinct response stages [13]: (i) the proximity
effect, (ii) the inertial response, and (iii) the governor response.
Due to rotor inertia, synchronous machine rotor angles will not
instantly change following a disturbance. The energy stored
in the rotating masses cannot be immediately applied, and
at the instant of an active power imbalance (t= 0+), the
energy supplied by the online generators comes from the
energy stored in their magnetic field. The proximity effect is a
purely electrical response [14], and is exclusive to synchronous
generation, regardless of apparent power rating.
The inertial time frame follows the proximity effect. Its initi-
ation will vary with system size, but is typically of the order of
1 or 2 s. The inertial time frame corresponds to when all online
machines experience the same mean deceleration/acceleration
following the loss of generation/load, i.e. synchronising swings
have occurred. During the inertial time frame, the energy
supplied by synchronously-connected machines comes from
the energy stored due to their rotational motion.
When a frequency deviation exceeds a certain limit (the gov-
ernor deadband), turbine-governor control will be activated.
The governor response ensures rotor accelerations eventually
become zero, and a new steady-state is reached. Unlike the
inherent proximity effect and inertial response, the governor
response requires control action.
B. Inertial Constraint Implementation within UCED
The dynamic motion of a conventional unit’s rotor is
determined by the swing equation - a nonlinear second-
order differential equation, with the ‘complete’ set of system
equations including N(the number of online units) swing
equations coupled via the algebraic network equations. How-
ever, frequency stability is determined by overall response
of the system as evidenced by its mean frequency, rather
than the relative motion of machines [15]. Thus, frequency
stability analysis concentrates on the overall system stability
for sudden changes in generation-load balance, as opposed to
machine stability. The ‘complete’ model can be simplified to
a single linear first-order differential equation, Eq. (1) [16],
and if used appropriately, this single bus frequency model
can estimate the essential characteristics of a synchronously
isolated system’s frequency response [17], [18]. In the context
of day-ahead optimisation of operational cost and security,
the single bus frequency representation was deemed adequate,
particularly considering transmission system operator require-
ments for computationally efficient UCED simulations, due to
time constraints of control room operation.
Applied to the inertial time frame, i.e. well before initiation
of the governor response, tgov, the single bus frequency model
is a system-level representation of how an active power imbal-
ance is absorbed by the system. Should a system disturbance
occur, e.g. loss of a system infeed/outfeed1,Pk, the resultant
system active power imbalance, ∆P, is corrected by a change
in the stored rotational energy of the online synchronously-
connected masses in the system, Wkin,sys , and a change in
load consumption, Dsys, due to the frequency deviation, ∆f:
∆P=d
dt Wkin,sys +Dsys ∆f(1)
where
d
dt Wkin,sys ≈2W0
kin,sys
f0
d
dt ∆f(2)
and
W0
kin,sys =W0
kin,gen +W0
kin,load =
N
X
i=1
i6=k
HiSi.(3)
W0
kin,sys is the total system rotational energy at nomi-
nal frequency, f0, and is the sum of the contributions
from synchronously-connected generation, Wkin,gen , and load,
Wkin,load. A machine’s inertial constant, Hi, and apparent
power rating, Sican be used to compute its stored rotational
energy. The initial ROCOF, i.e. just after the instance of
imbalance, (0+< t tgov ), when Dsys∆f≈0, theoretically
corresponds to the maximum system ROCOF [16]:
d∆f
dt
t>0+=f0Pk
2PN
i=1
i6=k
HiSi
.(4)
Two forms of inertial constraint, both with the purpose of
mitigating ‘insecure’ initial ROCOF magnitudes, i.e. ensuring
d∆f
dt
t>0+
<
d∆f
dt
max
, are devised:
1) A static (time-invariant) constraint that ensures the
online system stored rotational energy is always above
a constant minimum level, defined by the absolute
largest infeed/outfeed to the system, Pmax:
W0
kin,sys ≥f0Pmax
2
d∆f
dt
max
(5)
2) A dynamic constraint that sets the minimum system
rotational energy requirement as a function of the
largest infeed/outfeed at each UCED time-step, Pk:
W0
kin,sys ≥f0Pk
2
d∆f
dt
max
(6)
1An infeed is defined as an online generator active power output or HVDC
import to the system. An outfeed is defined as an HVDC export from the
system.
The dynamic inertial formulation considers the loss of each
active power infeed/outfeed, and the post-contingency system
inertia following that loss, e.g. if the largest active power
output from an online generator is 400 MW, and the largest
HVDC import is 500 MW (zero inertial contribution), the
constraint determines which contingency will result in the
greatest initial ROCOF - which may not necessarily be the loss
of the largest infeed. In this example, the loss of the generator
may result in a greater post-contingency ROCOF than the loss
of the HVDC interconnector, as the system would lose the
generator’s inertial contribution.
A system’s post-disturbance initial ROCOF limit will vary
with system size and portfolio capability. In the context of
the test system used in this research, the Ireland and Northern
Ireland system, a ‘secure’ initial ROCOF currently equates to
|ROCOF| ≤ 0.5Hz/s [11]. This ensures that (i) the ROCOF
thresholds of loss of mains protection are not exceeded -
mitigating a potentially greater imbalance due to the tripping
of distributed generation [19], and (ii) there is sufficient time
for a governor response to be fully deployed, so that the fre-
quency nadir/zenith is formed before load/generation shedding
thresholds are reached. However, if new ancillary services
[6], [7] incentivise investment in emulated inertia or other
fast frequency responses, the above ‘secure’ definition could
be redefined, and the inertial constraint reformulated. Due to
the difficulty of accurately estimating both the magnitude and
temporal nature of Wkin,load, and to introduce a safety factor
into the inertia-constrained UCED, the contribution of load
stored rotational energy is not considered here.
C. Modelling and Test System
The PLEXOS modelling tool [20] and Xpress-MP [21]
mixed integer linear programming solver are used to produce
daily UCED schedules of the Ireland and Northern Ireland
power system [22] at an hourly resolution. Two study years,
2012 and 2020, are considered, due to significantly contrasting
levels of installed wind power capacity and HVDC inter-
connection. The annual energy supplied by wind generation
increases from 17% to 37%, and HVDC interconnection
between Ireland and Great Britain increases from 500 to 1000
MW. The instantaneous non-synchronous penetration limit,
Eq. (7) [10], is 50% and 75% for 2012 and 2020 respectively,
as per operational policy forecast [11]. An aggregated (by
fuel type) representation of the Great Britain system is used
[23]. The model co-optimises the expected costs of system
operation and reserve (Table I). The expected costs include
variable operation and maintenance, carbon and fuel [24], and
start-up cost. In the 2012 model, conventional plant must-run
constraints for voltage control in particular network locations
are included, as per current operational practice [25]. It is
forecasted that such constraints will be relaxed in 2020 due to
network reinforcement.
Non-Synchronous Penetration =Pw ind +PHV DC import
Pload +PHV DC export (7)
TABLE I
RES ERVE CATEGORIES
Category Response Target Min. Spinning
Time (% Max. Requirement
Infeed/Outfeed) (MW)
Loss of Infeed
Primary 5 to 15 s 75 160/125†
Secondary 15 to 90 s 75 160/125
Tertiary 1 90 s to 5 min 100 160/125
Tertiary 2 5 to 20 min 100 160/125
Loss of Outfeed§
Primary 5 to 15 s 100 100
Regulation Reserve
Negative*n/a n/a 150
†Lower spinning requirement applies from 00:00-07:00
§Currently not carried by the system operator
*Sum of the active power headroom above conventional units’ min. load
III. RESULTS
A. Transition to ‘Lighter’ AC Synchronous Systems
Hourly UCED schedules were determined for the 2012
and 2020 base case test systems, i.e. no inertial constraint
implemented. Fig. 1 is a frequency distribution of the online
system stored rotational energy (inertia) in 2012 and 2020.
The average wind penetration during the respective periods
of online inertia in 2012 and 2020, is also shown. Fig. 1
illustrates that there may be a significant erosion of system
inertia due to the displacement of synchronous generation with
non-synchronous renewables. For 70% of 2020, the system
inertia is below 26.5 GWs - the level required to ensure that
the initial ROCOF following the loss of the absolute largest
infeed/outfeed, Pmax, does not exceed ±0.5 Hz/s.
Fig. 1. Frequency distribution of system stored rotational energy (inertia) in
2012 and 2020, with corresponding average wind penetration (% demand)
The implication of ‘lighter’ synchronous systems is demon-
strated in Fig. 2, which shows the initial ROCOF2following
2All ROCOF plots show the magnitude of the initial ROCOF following
the loss of the largest single infeed/outfeed, calculated as per Eq. (4). Thus,
the |ROCOF|plotted for each time-step is the greater value that arises from
loss of either the largest infeed or the largest outfeed, i.e. the ROCOF plots
consider both low (loss of infeed) and high (loss of outfeed) frequency events.
Fig. 2. Heat map showing the initial ROCOF following the loss of the largest single infeed/outfeed online for each hour of 2020 (base case UCED schedule)
loss of the largest single active power infeed/outfeed for each
hour of the base case UCED schedule in 2020. While it can
be seen that the largest proportion of ‘insecure’/high ROCOF
(>0.5 Hz/s) periods occur during the weekend (inherently
low load periods), there are seasonal variations to the high
ROCOF events that occur during the week. Loss of infeed
events are the binding contingency for 89.5% of the year,
whereas loss of outfeed events account for 10.5%. Fig. 3, a
frequency distribution of high initial ROCOF as a function
of time of day, shows that, while most extreme ROCOF
events (>1 Hz/s) occur during night-time (i.e. 00:00-07:00),
there is also a significant variation in the hourly distribution
of high ROCOF periods (>0.5 Hz/s) in 2020. Hours which
traditionally would not have been associated with frequency
instability (e.g. periods of high load), may be prone to high
ROCOF; the variable nature of wind generation can result in
the decommitment of synchronous plant at any hour in the day.
Figs. 2 and 3 highlight that, as wind penetration increases, so
too may the operational complexity involved in mitigating high
ROCOFs. Furthermore, while Fig. 1 demonstrates that times
of high wind generation correspond with those of low online
system inertia, this does not necessarily translate to times of
‘insecure’ ROCOF, as during times of high wind penetration,
the largest single infeed may be a conventional unit at its
minimum load.
B. Operational Security Metrics
Operational security metrics reflect operational values show-
ing a strong relationship with relevant system variables. Two
such metrics traditionally associated with short-term frequency
stability have been (i) the instantaneous wind/non-synchronous
penetration level, and (ii) the number of conventional syn-
chronous units online. Fig. 4 shows the relationship between
the penetration level of wind generation and the initial RO-
COF. Fig. 4 illustrates the relatively uncorrelated nature of
wind penetration and initial ROCOF, e.g. with a wind penetra-
Fig. 3. Frequency distribution of high initial ROCOF as a function of time
of day, 2020
tion level of 40%, the initial ROCOF can vary from ∼0.2-0.9
Hz/s. This is due to the vast array of operational scenarios
experienced for a given wind penetration level. Fig. 5 shows
the relationship between the number of ‘large’ (>1 GWs
of stored rotational energy) conventional synchronous units
online and the initial ROCOF. Fig. 5 demonstrates that there
can be a significant variation in ROCOF for a given number
of large plant online, e.g. with 8 units, the ROCOF can vary
from ∼0.25-0.7 Hz/s. Thus, established metrics for frequency
stability, such as wind penetration, Fig. 4, and the number of
conventional units online, Fig. 5, may not be adequate metrics
to predict the initial ROCOF following a generation-load
imbalance as non-synchronous penetrations rise. A dedicated
inertial policy may be prudent. Such a policy should be based
on the level of post-disturbance system inertia and the largest
single infeed/outfeed, given the inherent correlation between
these variables and the initial ROCOF, Eq. (4).
Fig. 4. Initial ROCOF as a function of wind peneration, 2020 base case
Fig. 5. Initial ROCOF as a function of the number of large conventional units
(>1 GWs stored rotational energy) online, 2020 base case
C. Inertial Constraint Implementation within UCED
Two forms of inertial constraint (see Section II-B) are
incorporated (separately) within UCED, with hourly schedules
for 2020 determined. In both cases (static and dynamic),
the same initial ROCOF limit of 0.5 Hz/s is maintained, as
illustrated by Fig. 6 - a duration curve showing the cumulative
probability of the initial ROCOF following loss of the largest
single infeed/outfeed for each time-step. As a comparative,
a case where a constraint requiring a minimum number of 8
‘large’ synchronous units online is implemented within UCED,
and the 2012 base case, are also shown in Fig. 6. Fig. 6
illustrates that there is little need for an inertial constraint
in 2012, due to wind penetrations being significantly lower.
Fig. 6 also highlights how a minimum number of units online
constraint can be insufficient in mitigating extreme ROCOF.
The highest ROCOF magnitudes shown in the base case for
2020 tend to be for loss of the HVDC interconnector at export,
during high wind penetrations.
While both static and dynamic inertial constraints attain
frequency security (|ROCOF|<0.5 Hz/s), they do so in a
contrasting manner. Fig. 7, presented as a duration curve,
Fig. 6. Duration curve of the initial ROCOF, 2020
shows the difference in (a) the largest single infeed/outfeed,
and (b) the number of ‘large’ synchronous units online, for the
base, static and dynamic cases. Fig. 7(a) shows that, with the
dynamic constraint implemented, the UCED’s optimal solution
tends to dispatch down the largest single infeed/outfeed, Pk,
and increase the output of higher cost plant online, rather
than increase the system inertia level, W0
kin,sys , and incur
the start-up and production costs associated with committing
and running out-of-merit synchronous units. The static inertial
constraint requires a constant minimum level of inertia -
designed to cover the loss of the absolute (time-invariant)
largest single infeed/outfeed, Pmax. Consequently, there is
a greater number of conventional plant carried online for
∼80% of the year with the static target, Fig. 7(b). Fig. 8
contrasts how the static and dynamic constraints alter the
UCED schedule for a particular day, showing the difference in
(i) the number of large conventional plant online, (ii) the active
power output/flow of the largest single infeed and outfeed, and
(iii) the level of wind penetration and curtailment, which only
occurs in the static case.
Fig. 7. Duration curve of (a) the largest single infeed/outfeed, and (b) the
number of large conventional units online, 2020
Fig. 8. Comparison of how the dynamic and static inertial constraints alter
the UCED schedule: 8 illustrative time-steps, 2020
D. Total Production Costs and Wind Curtailment
The difference in total production costs and wind cur-
tailment of the UCED schedules are shown in Table II.
Comparing the inertial constraint cases, the primary driver
of the increase in the total production cost of the static
case is the fuel cost associated with the additional number
of conventional generators online to meet the time-invariant
inertial requirement, Fig. 7(b). Table II highlights that keeping
a minimum level of synchronous plant online at all times
(for operational security reasons) may have implications for
wind curtailment, particularly during low demand/high HVDC
import or wind penetration periods. Table II also demonstrates
that implementation of a dynamic inertial constraint is a more
cost-effective solution for the test system under study, with a
total production cost saving of Me10.3 over the static case.
With the dynamic constraint committing less synchronous
units online, Fig. 7(b), wind curtailment is less than that with
the static formulation.
TABLE II
DYNAMIC AND STATIC INE RTIA L CONSTRAINT COMPARISON
Case (2020) Total Production Wind Curtailment
Costs (Me) (% Energy Available)
Base 11,647.99 0.5
Dynamic 11,648.93 0.9
Static 11,659.19 2.7
IV. CONCLUSION
As wind, solar and/or HVDC interconnection penetrations
grow, the initial ROCOF following large generation-load im-
balances may increase significantly - particularly for syn-
chronously isolated systems. Traditional operational metrics,
such as the non-synchronous penetration level, and the number
of ‘large’ conventional synchronous units online, may no
longer be appropriate proxies for ROCOF, and thus short-term
frequency stability as the non-synchronous penetration rises.
There may be a need to formulate a specific inertial policy.
Two forms of inertial constraint, implemented within UCED,
are presented here. It is shown that an inertial constraint that is
a function of relevant system variables, such as active power
infeeds and outfeeds, and the respective post-disturbance sys-
tem stored rotational energy level, as opposed to a time-
invariant inertial constraint, can reduce both operational costs
and wind curtailment.
REFERENCES
[1] J. Glover, M. Sarma, and T. Overbye, Power System Analysis and
Design. Cengage Learning, 2011.
[2] S. Sharma, S.-H. Huang, and N. Sarma, “System inertial frequency
response estimation and impact of renewable resources in ERCOT
interconnection,” in IEEE Power and Energy Society General Meeting,
Detroit, MI, USA, 2011.
[3] D. Gautam, L. Goel, R. Ayyanar, V. Vittal, and T. Harbour, “Control
strategy to mitigate the impact of reduced inertia due to doubly fed
induction generators on large power systems,” IEEE Trans. Power Syst.,
vol. 26, no. 1, pp. 214–224, Feb 2011.
[4] Y. Wang, V. Silva, and A. Winckels, “Impact of high penetration of wind
and PV generation on frequency dynamics in the continental Europe
interconnected system,” in 13th Wind Integration Workshop, Berlin,
Germany, 2014.
[5] IEA-RETD, “Integration of Variable Renewable Energy. Volume II: Case
Studies,” Jan. 2015.
[6] ERCOT, “Future Ancillary Services in ERCOT,” Sept. 2013.
[7] EirGrid and SONI, “DS3: System Services Review TSO Recommenda-
tions,” May 2013.
[8] Transpower, “Ancillary Services Procurement Plan,” Dec. 2013.
[9] J. Brisebois and N. Aubut, “Wind farm inertia emulation to fulfill Hydro-
Qu´
ebec’s specific need,” in IEEE Power and Energy Society General
Meeting, Detroit, MI, USA, 2011.
[10] J. O’Sullivan, A. Rogers, D. Flynn, P. Smith, A. Mullane, and
M. O’Malley, “Studying the maximum instantaneous non-synchronous
generation in an island system-frequency stability challenges in Ireland,”
IEEE Trans. Power Syst., vol. 29, no. 6, pp. 2943–2951, Nov 2014.
[11] EirGrid and SONI, “All Island TSO Facilitation of Renewables Studies,”
June 2010.
[12] P. Cuffe, E. Lannoye, A. Tuohy, and A. Keane, “Unit commitment
considering regional synchronous reactive power requirements: costs and
effects,” in 11th Wind Integration Workshop, Lisbon, Portugal, 2012.
[13] P. Anderson and A. Fouad, Power System Control and Stability. Wiley-
Interscience, 2003.
[14] E. Vittal, A. Keane, J. Slootweg, and W. Kling, “Impacts of wind
power on power system stability,” in Wind Power in Power Systems,
T. Ackermannn, Ed. Wiley, 2012.
[15] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares,
N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsem,
and V. Vittal, “Definition and classification of power system stability
IEEE/CIGRE joint task force on stability terms and definitions,” IEEE
Trans. Power Syst., vol. 19, no. 3, pp. 1387–1401, Aug 2004.
[16] M. Chan, R. Dunlop, and F. Scheweppe, “Dynamic equivalents for
average system frequency behavior following major disturbances,” IEEE
Trans. Power App. Syst., vol. PAS-91, no. 4, pp. 1637–1642, July 1972.
[17] G. Lalor, A. Mullane, and M. O’Malley, “Frequency control and wind
turbine technologies,” IEEE Trans. Power Syst., vol. 20, no. 4, pp. 1905–
1913, Nov 2005.
[18] L. Ruttledge, N. Miller, J. O’Sullivan, and D. Flynn, “Frequency
response of power systems with variable speed wind turbines,” IEEE
Trans. Sustain. Energy, vol. 3, no. 4, pp. 683–691, Oct. 2012.
[19] R. Walling and N. Miller, “Distributed generation islanding-implications
on power system dynamic performance,” in IEEE Power and Energy
Society Summer Meeting, Chicago, IL, USA, 2002.
[20] PLEXOS. [Online]. Available: www.energyexemplar.com
[21] FICO Xpress Opimization Suite. [Online]. Available: www.fico.com
[22] EirGrid and SONI, “All-Island Generation Capacity Statement 2014-
2023,” Feb. 2014.
[23] National Grid, “Electricity Ten Year Statement,” Nov. 2012.
[24] IEA, “World Energy Outlook 2013,” Nov. 2013.
[25] EirGrid and SONI, “Operational Constraints.” [Online]. Available:
http://www.eirgrid.com/aboutus/publications
