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Title A steady-state voltage stability analysis of power systems with high penetrations of wind
Authors(s) Vittal, Eknath; O'Malley, Mark; Keane, Andrew
Publication date 2010-02
Publication information IEEE Transactions on Power Systems, 25 (1): 433-442
Series Electricity Research Centre (ERC)
Publisher IEEE
Link to online version http://dx.doi.org/10.1109/TPWRS.2009.2031491
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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010 433
A Steady-State Voltage Stability Analysis of Power
Systems With High Penetrations of Wind
Eknath Vittal, Student Member, IEEE, Mark O’Malley, Fellow, IEEE, and Andrew Keane, Member, IEEE
Abstract—As wind generation begins to contribute significantly
to power systems, the need arises to assess the impact of this
new source of variable generation on the stability of the system.
This work provides a detailed methodology to assess the impact
of wind generation on the voltage stability of a power system. It
will also demonstrate the value of using time-series ac power flow
analysis techniques in assessing the behavior of a power system.
Traditional methods are insufficient in describing the nature of
wind for steady-state analyses, and as such, a new methodology is
presented to address this issue. Using this methodology, this paper
will show how the voltage stability margin of the power system
can be increased through the proper implementation of voltage
control strategies in wind turbines.
Index Terms—Power flow analysis, time series, voltage control,
voltage stability, wind power generation.
I. INTRODUCTION
W
IND generation levels are growing in power systems
around the world in response to increased pressure to
reduce
levels and dependence on fossil fuels. Given the
increase in wind generation and the highly variable nature of
the resource, the stability of power systems will be impacted
significantly. Traditional techniques are limited in capturing this
variable behavior and new study techniques and methodologies
will be required to properly quantify the stability of a power
system.
The most common wind turbine technology installed in sys-
tems today is the doubly-fed induction generator (DFIG) ma-
chine. The older fixed speed squirrel cage induction generator
(FSIG) machines are still in service, but it is uncommon for them
to be utilized in new wind farm installations. Both machines
contribute asynchronous power to the system, and as such, a
large penetration of wind generation will impact the stability
of the system, particularly the voltage stability of the system.
Since the DFIG is the predominant technology installed in wind
farms, this paper will focus on the changes in a power system’s
steady-state voltage stability in response to an increase in DFIG
wind generation. The main advantage of the DFIG turbine is the
ability to provide reactive power control without installing ad-
ditional capacitive support. The DFIG can be operated in one
Manuscript received April 02, 2009; revised July 21, 2009. First published
November 17, 2009; current version published January 20, 2010. This work has
been conducted in the Electricity Research Centre, University College Dublin,
which is supported by Airtricity, Bord Gáis, Bord na Móna, Commission for
Energy Regulation, Cylon, EirGrid, Electricity Supply Board (ESB) Networks,
ESB Power Generation, ESB International, Siemens, SWS, and Viridian. The
work of E. Vittal and A. Keane was supported by the Charles Parsons Energy
Research Award. Paper no. TPWRS-00234-2009.
The authors are all with University College Dublin, Dublin, Ireland (e-mail:
eknath.vittal@ucd.ie; mark.omalley@ucd.ie; andrew.keane@ucd.ie).
Digital Object Identifier 10.1109/TPWRS.2009.2031491
of two control modes; firstly, fixed power factor (PF) control,
where the turbine controls reactive power production in order
to achieve a specified power factor; secondly, terminal voltage
control, where the reactive power is controlled to meet a target
voltage. Using these two control schemes, this paper will as-
sess the impact of DFIG reactive power control on the system’s
voltage stability margin.
Various technologies and strategies have been developed in
order to implement terminal voltage control. Work in [1] has
shown the capabilities of reactive power control in DFIGs using
combinations of grid side control and rotor side control. In [2],
a case study on the Danish power system demonstrated the im-
portance of reactive power and voltage control in maintaining
system stability. In [3], PI-based control algorithm is described
and implemented to manage the reactive power out of a DFIG
wind farm. A coordinated voltage control strategy is applied
using a DFIG wind farm in [4]. In [5], a novel algorithm for
direct active and reactive power control was implemented. In
[6], several generalized methods of reactive power control are
provided.
Work in [7] and [8] showed that increased voltage control
will improve the probability that bus voltage will lie within a
specified range and improve voltage performance within the
power system. Voltage performance refers to achieving desired
voltages within a specified operating range, and while the im-
provement in voltage performance indicates increased system
robustness, it is not a true measure of the power system’s sta-
bility. In assessing a system’s stability, a measure such as a
power-voltage (PV) curve is a much better indicator of voltage
stability [9].
In order to properly assess the voltage stability and in partic-
ular the voltage stability margin, a detailed ac power flow anal-
ysis of the transmission system is necessary. However, there are
several issues that arise when completing power flow studies in-
volving wind generation. As power flow studies have tradition-
ally focused on a single operating point in the system, challenges
arise in assessing the true impact of wind generation on a power
system. In particular, the variable nature of wind necessitates
new techniques to assess its impact.
The use of statistical techniques to analyze power systems
is a well-established concept known as probabilistic load flow
(PLF), and has been successfully modified to model wind. The
foundation for PLFs was established in [10] and showed how
transforming the input variables into random variables (RV),
a resulting set of output RV can be achieved. Generally, the
form of both the input and output RV is given as a proba-
bility density function (PDF), and will relay information about
several operational aspects of the power system. In [11]–[13],
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434 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010
the focus was on the traditional operation of power systems,
and required nonlinear optimization methodologies in order to
achieve a solution. As a result, additional techniques must be
implemented in PLFs when incorporating a variable resource
such as wind.
In [14] and [15], PLFs were used to assess system reliability
with large levels of wind generation, while [16] examined the
transmission planning aspect of power systems by incorporating
a sequential time-series along with a PLF in order to maximize
the firm connection of wind generation into the system. In [17]
and [18], the aspects of probabilistic load modeling and the in-
corporation of wind generation in power systems was examined.
Since in PLF analyses, the historical data input is treated as an
RV, it will include only the probability that the worst-case point
will be captured during the simulation and that the system is se-
cure for all contingencies.
In comparison to PLFs, time-series load flow simulations
will deterministically model the power system and will ex-
plicitly capture the system response at the worst-case point.
Studies have previously applied the time-series approach to
model power systems. In [19], it was shown how time-series
power flows can be applied to systems to determine overload
conditions and specify non-firm connection agreements for
new generators on the distribution system. In [20], a time-series
analysis was implemented in modeling variable resources such
as solar photovoltaic and gas-fired micro-CHP (cogeneration) in
low voltage networks. Both studies examined the application of
historical time-series data on the distribution level of the power
system. Using a time-series data set for wind speeds and loads
for multiple years, this paper will analyze the data
a priori,
and build a sequential simulation around the single worst-case
point contained in those years, called a time-series power flow
(TSPF) for a future power system at the transmission level.
By utilizing time-series data as the input, the worst-case point
within the data set will be deterministically modeled. This al-
lows the simulation to maintain the correlation between the wind
speeds and load levels seen throughout the year. Since this is a
sequential simulation that models the variability of wind gener-
ation in a power system, it is necessary to maintain the balance
between the changing generation and the load in the system.
This will be achieved by re-dispatching the conventional units
in the system using a merit-order economic dispatch. It is also
crucial that the correct units are scheduled to be online during
the period of simulation. As such, a unit commitment is required
to determine the online plants during the worst-case point, while
taking into consideration the forced outage rates and availability
of the units.
By incorporating ac power flow along with economic dis-
patch and unit commitment, this paper will produce a realistic
simulation of a transmission system that captures the variable
behavior of the wind energy resource that will provide insight
into the system’s steady-state voltage stability. It will be di-
vided as follows: Section II will describe the overall method-
ology associated with the TSPF analysis. Section III provides
an overview of the test system on which the methodology was
applied. Section IV will present the results and provide a discus-
sion about their implications, and Section V draws conclusions
from the results.
Fig. 1. Flow chart describing the methodology used in the analysis.
II. METHODOLOGY
This section will develop a methodology for completing a
TSPF analysis based on an analysis of time-series wind and
loading data, and is described in the flow chart presented in
Fig. 1. Each element in the flow chart represents a critical as-
pect of the methodology and will be described further in the
following subsections.
The analytical description of the power flow used in these
simulations is given in (1) [21]. The
and values are up-
dated every time-step from
, the starting time of the simu-
lation, to
, the ending time of the simulation time-period.
The values of
and are used to solve for voltage, (2) and
angle,
(3). It should be noted that in (1), the initial voltage and
angle value used to solve the power flow come from the previous
time-step,
. This aids in convergence and simulation time
and is completed for the
buses in the system:
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
(1)
.
.
.
(2)
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VITTAL et al.: STEADY-STATE VOLTAGE STABILITY ANALYSIS OF POWER SYSTEMS 435
.
.
.
(3)
A. Importance of Time-Series Analysis and Historical Data
Traditionally, the worst-case operating point of the system
generally occurs when the transmission system is most stressed
(maximum load) or when generation is at a minimum and
system voltages are much lower. These two scenarios are when
transmission overloads and low voltage collapse are most
probable. Prior to wind becoming a significant proportion of
power system generation portfolios, the worst-case operating
point was easily identified based on traditional weather and
loading patterns.
The methodology established in this paper approaches the
problem from a different perspective in comparison to PLFs.
By analyzing sufficient time-series data pre-simulation, the data
themselves are reduced to capture the single worst-case oper-
ating point and simulated around that point for a shorter period
of time. This reduction of data reduces computation time, and
allows for a robust assessment of the power system’s voltage
stability under high penetrations of wind generation. It is impor-
tant to make sure that the loading and wind power output data
are chronologically synchronized in order to ensure it captures
the complex underlying relationship between wind and load. By
identifying the worst-case point for multiple years of data and
directly inputting that into a TSPF, a more thorough analysis is
possible and a true measure of a system’s stability and robust-
ness can be realized.
In high wind penetration systems, the worst-case operating
point for voltage stability studies occurs when wind genera-
tion serves the largest proportion of the system’s demand, and
system stability support mechanisms are at a minimum. Trans-
mission overload studies would focus on the point where wind
generation and demand were the greatest and the transmission
system is the most stressed. Frequency stability studies would
focus on the period when spinning reserve and inertial support
is at a minimum.
B. Resource Analysis and System Model Setup
The improvement in bus voltage performance due to the ad-
dition of wind generation, in particular when utilizing the ter-
minal voltage control capability on DFIG wind turbines, is a
highly localized phenomena. This is due to the fact that the ter-
minal voltage control will most significantly impact the region
in which the wind generation is located. More significant than
the locality of the control, is the power output dependence on
the wind speeds of a particular region. Using the same average
wind power output across an entire system will not capture the
true variability of the resource as one area of the system will not
see the same wind speeds as another. As a result, the use of re-
gionally specific wind power output data for different areas of
the system is required.
Using an appropriate resource assessment will aid in the
placement of wind farms in the test system and provide the
highest level of accuracy in the results of the simulations. A
thorough assessment will be based on the transmission capacity
of the system as well as the availability of high annual wind
speeds. By utilizing a resource assessment in conjunction with
geographically diverse wind power output data, the most real-
istic simulation can be achieved that captures the correlation
between wind and load for any given time.
The resource analysis will provide wind power outputs and
allow for the calculation of new power output levels from the
farms in the system. In (4), the regional wind power output
data,
, is used with the installed wind capacity, ,
to build wind power matrix,
. This matrix is updated every
time-step and represents the variability of the wind resource:
.
.
.
.
.
.
(4)
C. Balancing Load and Variable Generation
The main difficulty in achieving a realistic simulation that
incorporates significant levels of wind generation is capturing
the variability of the wind resource. Using historical time-series
data captures the variability of the wind; however, it presents
significant challenges in an ac power flow model.
As wind farm power output and system loading changes at
each time-step in the simulation, action must be taken in order
to maintain system-wide load/generation balance. In a TSPF,
the commitment and power output of the conventional genera-
tion units are inter-temporally dependent, i.e., the past state of
the unit will impact any future state. However, there are two
distinct levels of this inter-temporal dependence; the first is be-
tween each individual time-step. As wind generation and system
loading are updated continuously, load/generation balance will
need to be maintained using an economic dispatch algorithm
[21]. This allows the online conventional generation to ramp up
or ramp down output levels in order to achieve a system balance.
The second issue arises in the determination of which conven-
tional units are online and available to ramp their output levels.
This is dealt with by using the wind power output and loading
data in conjunction with a unit commitment algorithm to de-
termine a commitment schedule [22]. This takes into account
the minimum start-up times and up and down times of the gen-
erating units and makes sure that a generator does not start-up
or shut-down outside of its operating limitations. A unit com-
mitment can be completed as often as necessary based on the
make-up of the system’s generation portfolio. Using economic
dispatch and unit commitment together will facilitate load/gen-
eration balance within the system as wind generation varies
across the system.
By using (4), in conjunction with an economic dispatch,
, and unit commitment algorithm, , the power
output from the conventional units in the system is determined
(5). In (5),
represents a function of the , , and .
Next, by combining the power outputs from
and ,
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436 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 25, NO. 1, FEBRUARY 2010
a matrix containing the power generated at all units in the
system is achieved (6):
.
.
.
.
.
.
(5)
.
.
.
.
.
.
.
.
.
(6)
Utilizing (6) and the desired terminal voltage set-points for
the voltage controlled buses in the system,
, the reactive
power levels at all the machines in the system can be determined
(7).
will vary based on the type of voltage control algo-
rithm implemented. If the operator desires to achieve secondary
or tertiary voltage control a broader area-wide or regional con-
trol scheme must be implemented [23], [24]. In (7),
repre-
sents a voltage control algorithm that behaves similar to a simple
excitation system [25] found in conventional synchronous ma-
chines. Voltage is controlled to a specified control level, and im-
plemented locally to achieve a specific target voltage at a partic-
ular bus. Finally, the determination of the active power (6) and
the reactive power (7) allows for the solution of (1), and the de-
termination of the voltage levels (2) and angles (3) for all the
buses in the system:
.
.
.
.
.
.
.
.
.
(7)
D. Data Analysis and PV Curves
Voltage stability is a crucial component of system stability
and will be impacted with the addition of a variable generation
resource such as wind generation. PV curves are an indication of
a system’s voltage stability as active power injection increases
in the system [9].
In the case of this analysis, the active power injection is given
by the wind generation produced at each bus and the voltage
stability is reflected in the bus voltages at the varying voltage
levels. As the control strategy shifts from fixed PF to terminal
voltage control, the bus voltages will vary greatly as the wind
power output changes. The use of the TSPF analysis allows the
PV curves to represent the changes in wind power output and
the resulting voltages that occur due to the variance in the power
generation.
The behavior of PV curves and the relationship to voltage
stability is a well-established concept [9], [26]. The PV curve
is influenced by the PF of the system. More inductive PFs limit
the power transfer capability of the bus, and lower the value at
which the critical voltage is reached. The opposite is true for ca-
pacitive PFs, where the critical voltage or the point of voltage
collapse is extended and allows for increased power transfer in
the system. This extension of the critical voltage point is known
as the voltage stability margin, and is a measure that directly re-
flects an increase in voltage stability in the power system and
indicates that the system is more secure. Since the maximum
power transfer for a particular bus is limited to the size of the
connected wind farm, the voltage value reached at maximum
power will indicate an increase or decrease in the voltage sta-
bility margin of a bus.
III. I
RISH
ELECTRICITY SYSTEM
MODEL
This section will describe the application of the method de-
veloped in Section II to the 2013 all-island Irish power system.
The Irish system serves as an excellent test system for power
systems studies, especially those that involve wind generation.
The small size and islanded nature of the system provide height-
ened responses to both voltage and frequency studies that can
provide valuable insight into the future behavior of larger power
systems.
As wind generation increases, several issues regarding sta-
bility and reserve will come to the forefront of operating the
Irish system with high penetrations of wind. Large penetrations
of wind generation will displace significant portions of dynamic
reactive power support and spinning inertia. This will require
study of not only the voltage stability impacts, but also the need
for increased reserve requirements for secure system operation
[27]; changes in unit commitment schedules to handle the uncer-
tainty of wind and manage its variability [28]; improvements in
the methods of frequency control and regulation [29], [30]; and
increased accuracy in capacity value calculations [31].
The model used in this analysis is the full island model,
meaning that the system includes both the Northern Ireland
(NI) power system along with the Republic of Ireland (ROI)
power system. It is important to note that these two synchronous
systems interconnect wind generation at two different voltage
levels; the NI system interconnects wind generation at the
33-kV level while the ROI system interconnects at the 20-kV.
In the all-island model, the transmission system is considered
to be at voltages greater than and including 110-kV, while the
distribution system lies at all voltages below the 110-kV level.
Wind generation was added to the system based on the resource
analysis compiled in the All-Island Grid Study [32]. Overall,
2188 MW of wind generation was installed across the island.
Of this, 1930 MW was DFIG generation, while 258 MW were
existing FSIG machines.
A. Identification of Worst-Case Scenarios
In the ROI and NI system, the two loading scenarios that
are traditionally incorporated into power flow studies are the
Summer Night Valley (SNV) and the Winter Peak (WP). The
SNV represents the minimum loading and generation operating
point. Traditionally this is where the system is most susceptible
to low voltage collapse and occurs during the warm summer
night generally between July and August. The WP is the max-
imum loading and generation operating point and is when the
transmission system is most severely stressed. The WP occurs
during the colder winter evenings from December to January.
Studies around these two operating points were sufficient in
determining the Irish system’s steady-state stability. However,
as wind penetration increases, the worst-case operating point
shifts. Often, it will not coincide with the traditional loading sce-
narios and an analysis of the time-series data needs to be com-
pleted to determine the new worst-case point.
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