Download II. H∞ output feedback controller design

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Reducing the Short-Circuit Current of MontazerQaem Bus Using a
Proposed H∞ Controller for the Corresponding Generator
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Abstract—In Iran power network especially in
Tehran Regional Electric Company like other
power systems, Short-circuit current increases
by extension of the electrical power system
because of rising demand of electrical power.
This fault current magnitude is more than the
circuit breaker interrupting ratings especially in
MontazerQaem power plant. Fault currents have
a great influence on power system. For reducing
these risks, some expensive or complicated
solutions are proposed based on increasing the
impedance of power network like FCLs or series
reactors or split bus. The approach of this paper
is controlling the sources of the faults. It
proposes a new solution for reduction of the fault
current by a controller. The controller is
designed by H∞ mixed-sensitivity minimization
method to control the fault current through
controlling the field current of the generator.
This method is simulated on a generator unit
which its exciter system is considered for
modeling and control design. The results show
that this economical solution is efficient enough.
Index Terms—Short circuit current, Power
system faults, Field current, H∞ method.
NOMENCLATURE
vdp, vqp SG terminal voltages in dq frame.
idp, iqp SG stator currents in dq frame.
vf , if voltage and current of the main field winding.
Ld, Lq SG direct and transverse stator inductances.
LD, LQ SG direct and transverse dampers
inductances.
Lf SG main field inductance.
Msf SG mutual inductance between the direct stator
winding and the main field one.
MfD SG mutual inductance between the main field
winding and the direct damper one.
MsD,MsQ SG mutual inductance between the direct
stator
winding and the direct/transverse damper
windings.
Rs,Rf SG stator resistance and SG main field
resistance.
RD,RQ SG direct and transverse damper resistances.
ωep SG electrical angular speed.
vde, vqe Exciter machine (EM) armature voltages.
ide, iqe EM armature currents.
vexc, vexc Voltage and current of the EM main field
winding.
Lde, Lqe EM direct and transverse armature
inductances.
Le EM main field winding inductance.
Mse EM mutual inductance between direct armature
winding and main field one.
Rse,Re EM armature resistance and main field
resistance.
ωee EM electrical angular speed.
I. INTRODUCTION
Fault currents have a great influence on power
system planning and operation. Short-circuit current
increases in the whole power system by permanent
extension of the electrical power system and rising
demand of electrical power. These currents can
cause mechanical and thermal stresses and they may
damage the equipment. Also at some points, the
available short-circuit current may exceed the
maximum short circuit ratings of the switchgear.
Consequently, the reduction and control of short
circuit currents is a must.
One solution to reduce the risk of increasing short
circuit levels in the power system is to upgrade the
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protection equipment so that the estimated fault
currents are kept within the equipment capacity.
This usually involves complete rebuilding of the
substation. Nevertheless, this solution does not
represent a high cost ratio benefit. It is an expensive
solution, especially if primary and secondary
breakers with their associated equipment are
numerous. In addition to the cost, upgrading of the
existing substations can be a complicated process
because of the number of equipment to be
substituted, redesigned or tested [1].
Devices and techniques such as circuit breakers,
fuses, air-core reactors, employing high-impedance
transformers, bus-splitting (system reconfiguration)
and fault current limiters (FCLs) have been used to
limit the available short circuit currents, so that the
underrated switchgear can be operated safely[2].
There are some components in power systems that
cause the fault current. The four basic sources of
short circuit current are:
1. Generators
2. Synchronous Motors
3. Induction Motors
4. Electric Utility Systems
All these sources can feed the short-circuit current
into a short circuit [3].
The approach of designing "fault current limiters"
is based on limiting the current by increasing the
impedance in the path of current from the sources to
the fault location but the approach of this paper is
reduction of fault current by controlling the sources.
This approach can be applied on synchronous
machines. The chosen method for designing the
controller is H∞ and the simulations approve the
efficiency of the controller whilst the cost of this
method for reduction of fault current is very less.
II. H∞ OUTPUT FEEDBACK CONTROLLER DESIGN
The standard H∞ mixed sensitivity formulation for
output disturbance rejection and control effort is
shown in Figure 1, and its equivalent standard form
for tracking is shown in Figure 2. In these figures,
G(s) is the open loop system model; K(s) is the
controller to be designed W1(s) and W2(s) are
weighting functions for shaping characteristics of
the open-loop plant. Normally, in the mixed
sensitivity design, bounds (weights) are applied on
S(s)/K(s)S(s). The sensitivity function S(s) denotes
the transfer function from disturbance input d(s) to
measured output y(s). K(s)S(s) is the transfer
function from disturbance input d(s) to control input
u(s). The complete details of the mixed sensitivity
control design can be found in [4]. The design
objective of control design is to minimize the
sensitivity functions S(s) and K(s)S(s).
Fig 1. H∞ Mixed Sensitivity in standard form (disturbance
rejection).
Fig 2. H∞ mixed-sensitivity minimization in standard form
(tracking).
For tracking, the partitioning of corresponding
generalized plant P is such:
u  K (s )v
z   P11  P12 K ( I  P22 K ) 1 P21 w
(1)
The state space description of the augmented plant
P(s) is:
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where x is the plant state vector, u represents the
control input, w is a state vector of exogenous input
which include disturbances d, measured noise n (not
considered here), reference signals r, etc., y is the
measured output, and z is a vector of output signals.
The system is assumed to be stabilizable and
detectable. This assumption ensures the existence of
an internally stabilizing output feedback control law
u = K(s) y. Without loss of generality, it is assumed
that D11 =D22 = 0. This assumption makes the
closed-loop state space matrices linear in the control
matrices. In addition, the following assumptions are
typically made in H∞ problems:
(A1) (A;B2; C2) is stabilizable and detectable.
(A2) D12 and D21 have full rank.
(A3)
has full column rank for allω.
(A4)
has full row rank for all ω.
Let Twz(s) denotes the closed-loop transfer function
from w to z for a dynamical output-feedback law
u=K(s)y.
The sensitivity function S(s) = [I+G(s)K(s)]-1 is
that ensures disturbance attenuation and good
tracking performance. K(s)S(s) = K(s)[I+G(s)K(s)]-1
handles the issues of robustness and constrains the
effort of the controller.
The goal of this work is to obtain a dynamical
output-feedback controller law u = K(s)y, with the
following state-space description
where xk is state variable of the controller. The plant
and controller K(s) are defined above.
The constraint Twz (s )    can be interpreted as a
disturbance rejection problem. This constraint is
also useful to enforce robust stability [5].
III. THE PROBLEM DESCRIPTION
Reducing the short circuit current of a power system
is the main purpose of this paper; therefore, we try
to define the problem to design a controller.
A. Power System Short Circuit
Safe and reliable application of over-current
protective devices based on some requirements
mandate that a short circuit study and a selective
coordination
study
be
conducted.
These
requirements include, among others:
 Interrupting Rating
 Component Protection
 Conductor Protection
 Equipment Grounding Conductor Protection
 Marked Short-Circuit Current Rating;
Compliance with these code sections can best be
accomplished by conducting a short circuit study as
a start to the analysis. The protection for an
electrical system should not only be safe under all
service conditions but, to insure continuity of
service, it should be selectively coordinated as well.
A coordinated system is one where only the faulted
circuit is isolated without disturbing any other part
of the system. Once the short circuit levels are
determined, the engineer can specify proper
interrupting rating requirements, selectively
coordinate the system and provide component
protection.
To determine the fault current at any point in the
system, first draw a one-line diagram showing all of
the sources of short-circuit current feeding into the
fault, as well as the impedances of the circuit
components. To begin the study, the system
components, including those of the utility system,
are represented as impedances in the diagram. It
must be understood that short circuit calculations
are performed without current-limiting devices in
the system. Calculations are done as though these
devices are replaced with copper bars, to determine
the maximum “available” short-circuit current. This
is necessary to project how the system and the
current limiting devices will perform.
Low voltage molded case circuit breakers also
have their interrupting rating expressed in terms of
RMS symmetrical amps at a specific power factor.
However, it is necessary to determine a molded case
circuit breaker’s interrupting capacity in order to
safely apply it [6].
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B. Modeling of a synchronous generator (SG)
with Short Circuit Condition
Models of complex interconnected network
systems, such as an electric power grid, must
capture both the natural response of its components
to various disturbances, but also the effects of the
interactions between individual components and/or
aggregated groups of components. These
interactions are often the result of distributed
sensing, estimation, actuation, and decision making
based on these internalized models of the
environment[7].
The approach of this paper is using the voltage
control to reduce the fault current then the controller
synthesis takes into consideration a fixed impedance
connected to the SG (see Fig. 3). This method is
used in [8] for voltage control.
Fig. 3. Modeling of the SG with Short Circuit Condition.
(3)
The system model given by (3) can be written as:
During short circuit fault, the field current is
changed with the field winding time constant, called
the d-axis transient short circuit time constant[10].
A typical field current responses following a stator
short-circuit is shown in Fig. 4 [11]. Therefore, field
current as a state variable is useful to be observed
for controller designing. The observation matrix is
chosen as:
c
(2)
Where idl and iql are the Park transformation of the
currents in the three-phase inductance Ln. Rn and
Ln can be chosen as the fault impedance or other
equipments impedance. According to [9] we have
these equations:
f
  0 0 0 0 0 1 0 0
Fig. 4. A typical field current response following a stator
short-circuit
This choice shows that the current of the main field
winding is chosen as the output of the SG. Fig. 5
shows a representation of the global system. Bf1 is
the first column of the matrix Bf.
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Fig. 5. State space representation of SG.
C. Approach to Solution
The DC excitation (or field) current, required to
produce the magnetic field inside the generator, is
provided by the exciter. The excitation current, and
consequently the generator’s terminal voltage is
controlled by an automatic voltage regulator (AVR).
According to the model and output observation,
H∞ mixed-sensitivity minimization in standard form
(tracking) is used to reduce the short circuit current.
The field current as an output variable (feedback
signal) is compared with its normal value and the
error signal is used to control the plant (SM). A
Simplified diagram of proposed control strategy is
shown in Fig 6. In this approach, the control signal
u is added to output of exciter vexc and the result is
the voltage of the field winding Vf.
estimated fault currents are kept within the
equipment capacity. This resulted in complete
rebuilding of the substation but this solution is
expensive because the breakers with their associated
equipment are numerous.
In this paper, we try to reach the risk reduction
through a very low cost solution i.e. designing a
feedback controller for the power plant to reduce the
short circuit current.
B. Controller Design
To design a controller for the generator, it is
necessary to follow these stages:
1. Determining the input and output variables (in
this paper input variable is the field voltage
and the output variable is the field current).
2. Creating the state-space model of the system
(according to physical equations that
described before): it is a 12 state-system for
the case of this paper.
3. Defining W1(s) and W2(s) as the weighting
functions: for the case of this paper we
choose:
150
(s+1)2
1100
W2 
(4)
(s+2)2
4. Calculating and obtaining the controller K(s):
Using H∞ mixed-sensitivity minimization in
standard form (tracking) for the case of this
paper, results in a state-space model of a SISO
controller with 1 outputs, 1 inputs, and 12
states. The resulted constraint for the total
system is Twz (s )   23.18
5. Reducing the order of the controller: The
reduced order controller can be achieved by an
approximation method [14] and the 4-order
controller K(s) can be given by:
W1 
Fig.6. Simplified diagram of proposed control strategy.
IV. MONTAZERQAEM POWER PLANT STUDY
A. Case Representation
MontazerQaem power plant is in Tehran Regional
Electric Company and its fault current magnitude is
more than its circuit breaker ratings [12]. The
corresponding data is obtained from Iran Grid
Management Company (IGMC) [13]. The rated
parameters of the steam generator are 14.4kV,
176MVA, 50Hz. The excitation system is also
considered in the modeling and calculations.
Engineering Studies on the problem resulted in
some solutions but because of operation limits
especially reliability issues; these solutions could
not be used. Therefore the selected solution is
upgrading the protection equipment so that the
K r (s ) 
1.92 s4 + 1.02  105s3 +2.17  106s2 + 1.3 107s +3.74 106
s4 +1336s3 + 1.1  106s2 -3.52 105s+2.76  107
(5)
Bode magnitude diagram of full order and
reduced order controller is shown in Fig. 7. it is
clear that the reduced order controller can be
used for simulation.
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performance and it is less than the interrupting
rating of the breakers. The short circuit current is
about 25kA without control performance in the base
case therefore the reduction of the fault current is
36% then it is desirable.
40
20
full order
reduced order
10
40
0
35
-10
30
-20 -2
10
10
-1
10
0
1
10
10
Frequency (rad/s)
2
10
3
10
4
Fig. 7. The bode magnitude diagram of full and reduced
order controller.
C. Simulation Results
To show the effects of the controller on the power
plant performance in the fault condition, a 3-phase
short circuit fault is studied on the terminal of the
generator at t=50ms. Fig.8 shows the field current
during the short circuit with and without control.
The performance of the controller resulted in
reduction of the field current.
12
with control
without control
Field Current(pu)
10
8
RMS Fault Current(kA)
Magnitude (dB)
30
with control
without control
25
20
15
10
5
0
0
50
100
150
200
Time(ms)
250
300
350
400
Fig. 9. The fault current with and without control.
D. Economical Points
It is important to know that the reduction of the
fault current by an efficient controller has a very
negligible cost in comparison with upgrading the
equipments or other solutions which need new
power element like FCLs. It can cancel or delay the
huge investment for upgrading the substation
interrupting rating.
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V. CONCLUSION
4
2
0
0
50
100
150
200
250
300
350
400
Time(ms)
Fig. 8. The field current with and without control.
Fig.9 shows the R.M.S short-circuit current with
and without control. The peak of the current is
reduced by 8% and the breaking current is reduced
from 30kA to 25kA at the t=150 ms i.e. after 5
cycles since fault occurring.
According to engineering studies on transient
stability of Iran power grid [15], the critical clearing
time (CCT) of MontazerQaem power plant
generators is more than 200 ms then the breaking
action can be done safely at t=250 ms when the
short circuit current is about 16kA with control
There are some solutions based on increasing the
impedance of power network for reducing the risks
of high fault level of power systems. These
solutions are not used in some power systems like
substation of MontazerQaem power plant because
of the constraints of operation or needing huge
investment or complicated conditions.
A new method for reduction of short circuit
current based on controller design Using H∞ mixedsensitivity minimization is proposed in this paper.
The control system uses the field current of the
generator as a feedback signal and changes the
exciter output to reduce the terminal voltage of the
generator and consequently reduces the fault
current. This method results in cancelling or
delaying the extra investment on upgrading the
interrupting rating of therefore substation
equipments therefore it is very economical solution.
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