n Polyak Sami Ammari Lamine Mili

IRD Corp
George Mason University
Virginia Tech, ARI
P.O. Box 34901
4400 University Drive
206 N. Washington Street, Suite 400
Bethesda, MA 20827 Fairfax, VA 22030-4444

Alexandria, VA 22314



Abstract: The remote blackstart operation is a
significant industry problem because a considerable
portion of the electricity is supplied by base-loaded
steam electric units. These units are located remote
from the load centers supplying power over high -and
extra-high voltage lines, they generally have no
blackstart capability and need considerable off-site
power for startup operations. On the other-hand,
combustion turbine units are installed close to the load
centers, they are used as cycling units to meet the daily
peak demands, and need no off-site power for startups.
Although they have not been designed, nor intended as
the blackstart source, they can be an economical and a
very attractive option for the remote blackstart of steam
electric units, provided they meet the reactive power
requirements.
This paper reports on application of a modified
barrier-augmented Lagrangian (MBAL)-based
nonlinear optimal power flow (OPF) method for
maximizing reactive power capability of a twin
combustion turbine for the blackstart of a remote steam
electric unit. The feasibility of the blackstart operation
is demonstrated in the 12-Bus Test System that is in
operation in a Mid-western utility.

Keywords: Remote Blackstart, Ancillary Service,
Optimization, Reactive Power, Generator Excitation

1. INTRODUCTION

The objective in this study was to address the
remote blackstart problem, applying the Optimal Power
Flow (OPF) based on the modified barrier -augmented
Lagrangian (MBAL) method.
In the course of a blackstart operation, two
limiting conditions place severe demands on the
reactive power capability of the blackstart source. One
extreme operating condition occurs during the initial
energization of the transmission path when the
combustion turbine station (CTS) is called upon to
absorb the charging currents of the high- and extra-high
voltage connecting lines. The other extreme operating
condition, is when the combustion turbine generators
supply the large amount of reactive power required
during startup of the largest auxiliary motor in the
steam electric station (SES). These under-and over-
excitation demands can be met by optimum selections
of the CTS step -up transformer and step -down auxiliary
transformer tap positions, and by control of the
generator voltage set points.
The blackstart operation is complicated by the fact
that the generator step up and auxiliary transformers are
typically equipped with no-load (fixed) taps. Therefore,
in the planning phase and prior to the blackstart
operation, the optimum tap positions for these
transformers and the correct terminal voltage set
point(s) for the generator need to be determined to
satisfy the two conditions [1,2].
This paper describes blackstart of a coal-fired
drum -type SES, from a remote CTS. The MBAL-based
OPF is used to determine the feasibility of the
blackstart, and to determine:

The CTS generators over-and under-excitations
required by the blackstart operation,

The tap positions for the CTS generator step-up
transformer and for the auxiliary step-down
transformer to provide adequate lead and lag
reactive powers, and

The allowable voltages for the generator terminal at
the CTS, and the allowable high and low voltage
levels at the auxiliary bus in the SES.
The 12-Bus Test System being a typical blackstart
system was obtained from a Midwestern utility for
testing and verifying the MBAL-based OPF method and
results.
The paper is organized as follows. Section 2
reviews linear and nonlinear optimization methods.
Section 3 outlines the MBAL-based OPF method.
Section 4 describes the 12 -bus test system while
Section 5 provides some simulation results of the
MBAL-based OPF. The latter are checked against the
Generator Reactive Capability (GRC) [3,4] and an
interactive power flow programs in Section 6.

2 STATE-O F-THE ART IN OPTIMIZATION
Since late 70s the work of Scott and Hobson [5]
on Linear Programming (LP) has been widely used for
power system optimization problems. Since mid 80s,
the Interior Point Methods (IPMs) has become the most
popular tool for solving constrained optimization
problems with inequality constraints. The IPMs in
general and the Primal-Dual IPMs in particular used for
LP calculations have been a great success [13]. Not
only the IPMs have become the mainstream in the
14th PSCC, Sevilla, 24-28 June 2002
Session 25, Paper 6, Page 1
2
modern optimization theory, but they also have been
successfully applied to OPF problems [6]-[12]. The
success of the IPM in LP stimulated applications of the
basic Primal-Dual IPM ideas for NLP [16]. Although
the Primal-Dual approach produced for a number of
NLP problems reasonable results [16], still there is
substantial gap in terms of numerical efficiency
between LP and NLP calculations.
In LP calculations, it is possible to avoid ill-
conditioning phenomena thanks to the special structure
of the Log-barrier function Hessian coupled with
substantial advances in numerical linear algebra [14].
In NLP, the structure of the corresponding Hessian is
fundamentally different. It has an extra term that is the
Hessian of the classical Lagrangian for the original
problem (in LP calculations, the corresponding term is
just the zero matrix). The extra term makes the ill
conditioning in NLP fundamentally different from the
corresponding effect in LP calculation. Therefore, there
is a substantial gap between the efficiency of the IPM
for LP and NLP calculations.
The OPF problems faced by the electric power
industry are inherently nonlinear and of large dimension
[15], [17]. Moreover, along with inequality constraints,
they have nonlinear equations. To control the
feasibility for the equations one has to introduce a
penalty term. It can only increase the ill-conditioning
effect. Therefore, in the following section we present
an alternative to the classical barrier/penalty function
approach for NLP. The approach is based on the
Modified Barrier Function (MBF) [18] and Augmented
Lagrangian (AL) [19] theories. It allows to eliminate
the basic drawbacks of the classical barrier and penalty
methods and at the same time to keep their best
features.

3 - THE MBAL-BASED OPF METHOD

Maximizing the reactive power requirement of the
12-Bus Test System can be formulated as static
Nonlinear Optimization (NLP) problems subject to both
inequality and equality constraints. This is typically an
Optimal Power Flow (OPF) problem where the equality
constraints are the conventional power flow equations.

The inequality constraints include the upper and lower
bounds on the voltages across the system, the
limitations on the generator reactive power capabilities,
and the limits imposed on the apparent power flows
through the transmission lines and transformers.
The Modified B arrier Function (MBF) [18]
approach allows overcoming the difficulties of the
classical Log-Barrier functions for inequality
constraints whereas the Augmented Lagrangian (AL)
[19] eliminates the basic problems associated with the
penalty type functions for equality constraints. Before
describing the MBAL method, the basic features that
distinguish MBAL from the other approaches for large-
scale NLP should be mentioned.
Let
f ,

c
i
and
d
j
be smooth enough functions.
We consider the following problem:

x
X
Arg
f x c x
i
p
d x
j
q
i
j
*
*
min{ ( ) | ( )
,
,..., ;
( )
,
,..., }. = =
=
=
0
1
0
1
(1)
We apply the MBF methodology [18] for inequality
constraints and the Augmented Lagrangian for the
equations [19]. The MBAL function
L
:
× × ×
+
+
n
p
q
, was introduced in
[20], as follows:

L
( , , , )
( )
ln(
( )
)
( )
.
( )
x
v k
f x
k
kc x
v d x
k
d x
i
i
i
p
i i
i
i
q
i
q
= +
+ =
=
= 1
1
2
1
1
1
05
(2)
The first two terms represent the Lagrangian function
for the equivalent problems in the absence of the
equality constraints, because for any fixed
k
>
0
, the
system
ln(
( )
)
,
,...,
kc x
i
p
i
+
=
1
0
1
is equivalent to
c x
i
p
i
( )
,
,..., =
0
1
. The last two terms represent
the Augmented Lagrangian for equality constraints
[19]. Along with the classical Lagrangian term, = v d x
i i
i
q
( )
1
, there is a penalty term,
0 5
2
1
.
( )
k
d x
i
i
q
= ,
which is designed to penalize the violation of the
equality constraints. Keeping in mind that the MBF
function given by

F x
k
f x
k
kc x
i
i
i
p
( , , )
( )
ln(
( )
)
= + = 1
1
1
(3)

has all the characteristics of the Interior Augmented
Lagrangian (see [18]), one can view the MBAL
L
( , , , )
x
v k as Interior-Exterior Augmented
Lagrangian.
Before describing the MBAL-multipliers method,
a few important characteristics of the MBAL function at
the primal-dual solution should be emphasized. In
contrast to the Classical Barrier Function, the MBF
exists at the solution together with its derivatives of any
order. Moreover for any
k
>
0
, the MBAL possesses
the following important properties at the primal-dual
solution:
1
0
.
L
( , , , )
( ).
*
*
*
*
x
v k
f x =