# US 9,753,096 B2 · System and method for detecting generator incipient failures

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- Number: US 9,753,096 B2
- Document ID: US9753096B2
- Status: Granted
- Kind: B2
- Application number: 14/518,698
- Filed: 2014-10-20
- Published: 2015-02-05
- Granted: 2017-09-05
- Earliest claimed: 2008-01-31
- Assignees: Basler Electric Company
- Applicants: Basler Electric Company
- Inventors: Kiyong Kim
- Web page: https://patentgrep.com/patent/US9753096B2

## CPC

- G01R 31/42: AC power supplies
- H02P 9/006: {Means for protecting the generator by using control (control effected upon generator excitation circuit to reduce harmful effects of overloads or transients H02P9/10)}
- H02P 9/102: {for limiting effects of transients}
- H02P 23/14: Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
- H02P 29/0241: {the fault being an overvoltage}
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- H02P: CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS

## Abstract

A method, system and computer software for detecting an incipient failure of a generator in a power system including the steps of ascertaining one or more generator reference parameter of the generator for use as a baseline reference; measuring one or more operating parameter values of the generator; using the one or more operating parameter values to solve for an estimated present value of the one or more of the generator's current performance parameters using particle swarm optimization technique; and determining whether the estimated present values of the one or more of the generator's current performance parameters are outside of an acceptable limit.

## Claims

### Claim 1

A method of detecting an incipient failure of a generator in a power system comprising the steps of:
ascertaining at least one generator reference parameter of the generator for use as a baseline reference;
measuring at least one operating parameter value of the generator; and
using the at least one operating parameter value to solve for an estimated present value of at least one of the generator's current performance parameters using particle swarm optimization technique.

### Claim 2 (depends on 1)

The method of claim 1 wherein the step of using the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique further comprises the steps of:
treating each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
a. initializing each particle position,
b. determining an initial value for the dynamic direct and quadrature generator voltage;
c. calculating a response of the generator model with a selected particle position using received operating field voltage,
d. determining a fitness evaluation of the particle to find a self best value and a global best value, and
e. updating a position and a velocity for each particle based on the determined self best value and global best value.

### Claim 3 (depends on 1)

The method of claim 1 wherein the step of using the at least one operating parameter value to solve for an estimated present value of at least one of the generator's current performance parameters using particle swarm optimization technique further comprises the steps of:
treating each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
Step 0: initializing iteration indices, NOI=0, J=0
Step 1: initializing each particle position according to the equation:
{circumflex over (X)}=rand( )·Xno min al
Step 2: calculating initial values for the dynamic equations, E′d(0) and E′q(0), for the simulation models using the equations:
E
d
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
d
⁡
(
k
)
+
R
a
⁢
i
d
⁡
(
k
)
-
X
^
q
⁢
i
q
⁡
(
k
)
E
q
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
q
⁡
(
k
)
+
R
a
⁢
i
q
⁡
(
k
)
+
X
^
d
⁢
i
d
⁡
(
k
)
Step 3: calculating the model's response with a selected particle position, ed(k) and eq(k), k=1, . . . , N, by applying the measured field voltages to the equations:
E
d
′
⁡
(
k
+
1
)
=
E
d
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
qo
′
⁢
(
-
E
d
′
⁡
(
k
)
+
i
q
⁡
(
k
)
⁢
(
X
^
q
-
X
^
q
′
)
)
E
q
′
⁡
(
k
+
1
)
=
E
q
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
do
′
⁢
(
-
E
q
′
⁡
(
k
)
-
i
d
⁡
(
k
)
⁢
(
X
^
d
-
X
^
d
′
)
+
K
^
sd
⁢
E
fd
⁡
(
k
)
)
e
d
⁡
(
k
)
=
E
d
′
⁡
(
k
)
-
R
^
a
⁢
i
d
⁡
(
k
)
+
X
^
q
⁢
i
q
⁡
(
k
)
e
q
⁡
(
k
)
=
E
q
′
⁡
(
k
)
-
R
^
a
⁢
i
q
⁡
(
k
)
-
X
^
d
⁢
i
d
⁡
(
k
)
Step 4: calculating the fitness function:
J
=
∑
k
=
1
N
⁢
[
(
e
d
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
d
⁡
(
k
)
)
2
+
(
e
q
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
q
⁡
(
k
)
)
2
]
to check the best particle based on the model's responses obtained in step 3 and the recorded responses and if it is better, update the best particle;
Step 5: until all particles are calculated, incrementing a particle counter and repeating steps 2, 3, and 4 above for each particle;
Step 6: updating new particle position and velocity using equations:
Vk+1=αvk+β1rand1(xkself−xk)+β2rand2(xkglobal−xk)
xk+1=xk+vk
Step 7: determining whether the maximum number of iterations has been reached and if the maximum number of iterations has not been reached incrementing iteration counters (NOI and J) and proceed to step 8 and if reached, stopping further estimation of the parameter value;
Step 8: if the index J is 50, proceeding to step 1, and if index J is less than 50 proceeding to step 0.

### Claim 4 (depends on 1)

The method of claim 1 wherein the generator reference parameters comprise at least one of: generator rated voltage and power output, Ra=armature winding resistance, Rfd=field winding resistance, Xl=leakage reactance, Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant or T′qo=generator open circuit quadrature time constant.

### Claim 5 (depends on 1)

The method of claim 1 wherein the generator operating parameters comprise at least one of: Efd=field voltage, Ifd=field current, Et=terminal voltage, It=terminal current, φ=the load angle, δi=the power angle (internal rotor angle), Vgen=generator voltage, Vr=reference voltage, P=Real power of the generator, or Q=Reactive power of the generator.

### Claim 6 (depends on 1)

The method of claim 1 wherein the generator's current performance parameters comprise at least one of: Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant, or T′qo=generator open circuit quadrature time constant.

### Claim 7

A method of detecting an incipient failure of a generator in a power system comprising the steps of:
ascertaining at least one generator reference parameter of the generator for use as a baseline reference;
measuring at least one operating parameter value of the generator;
using the at least one operating parameter value to solve for an estimated present value of at least one of the generator's current performance parameters using particle swarm optimization technique; and
determining whether the estimated present values of the at least one of the generator's current performance parameters are outside of an acceptable limit by:
a. ascertaining for each generator reference parameter a tolerance value from the corresponding generator reference parameter and determining whether the estimated present values of the generator current performance parameter is within a range between the reference value plus the tolerance value and the reference value minus the tolerance value; and
b. comparing the estimated value of at least one of the generator's current performance parameters to a corresponding one of the generator reference parameters; and if the estimated value is not an acceptable value, providing an alarm that an estimated value of at least one of the generator's current performance parameters is unacceptable.

### Claim 8 (depends on 7)

The method of claim 7 wherein if during the step of determining whether the estimated present values of the at least one of the generator's current performance parameters are outside of an acceptable limit it is determined that the estimated present values of all of the generator's current performance parameters are within an acceptable limit, performing the step waiting a predetermined time and repeating the steps of claim 7.

### Claim 9 (depends on 7)

The method of claim 7 wherein the step of using the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique further comprises the steps of:
treating each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
a. initializing each particle position,
b. determining an initial value for the dynamic direct and quadrature generator voltage;
c. calculating a response of the generator model with a selected particle position using received operating field voltage,
d. determining a fitness evaluation of the particle to find a self best value and a global best value, and
e. updating a position and a velocity for each particle based on the determined self best value and global best value.

### Claim 10 (depends on 7)

The method of claim 7 wherein the step of using the at least one operating parameter value to solve for an estimated present value of at least one of the generator's current performance parameters using particle swarm optimization technique further comprises the steps of:
treating each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
Step 0: initializing iteration indices, NOI=0, J=0
Step 1: initializing each particle position according to the equation:
{circumflex over (X)}=rand( )·Xno min al
Step 2: calculating initial values for the dynamic equations, E′d(0) and E′q(0), for the simulation models using the equations:
E
d
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
d
⁡
(
k
)
+
R
a
⁢
i
d
⁡
(
k
)
-
X
^
q
⁢
i
q
⁡
(
k
)
E
q
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
q
⁡
(
k
)
+
R
a
⁢
i
q
⁡
(
k
)
+
X
^
d
⁢
i
d
⁡
(
k
)
Step 3: calculating the model's response with a selected particle position, ed(k) and eq(k), k=1, . . . , N, by applying the measured field voltages to the equations:
E
d
′
⁡
(
k
+
1
)
=
E
d
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
qo
′
⁢
(
-
E
d
′
⁡
(
k
)
+
i
q
⁡
(
k
)
⁢
(
X
^
q
-
X
^
q
′
)
)
E
q
′
⁡
(
k
+
1
)
=
E
q
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
do
′
⁢
(
-
E
q
′
⁡
(
k
)
-
i
d
⁡
(
k
)
⁢
(
X
^
d
-
X
^
d
′
)
+
K
^
sd
⁢
E
fd
⁡
(
k
)
)
e
d
⁡
(
k
)
=
E
d
′
⁡
(
k
)
-
R
^
a
⁢
i
d
⁡
(
k
)
+
X
^
q
⁢
i
q
⁡
(
k
)
e
q
⁡
(
k
)
=
E
q
′
⁡
(
k
)
-
R
^
a
⁢
i
q
⁡
(
k
)
-
X
^
d
⁢
i
d
⁡
(
k
)
Step 4: calculating the fitness function:
J
=
∑
k
=
1
N
⁢
[
(
e
d
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
d
⁡
(
k
)
)
2
+
(
e
q
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
q
⁡
(
k
)
)
2
]
to check the best particle based on the model's responses obtained in step 3 and the recorded responses and if it is better, update the best particle;
Step 5: until all particles are calculated, incrementing a particle counter and repeating steps 2, 3, and 4 above for each particle;
Step 6: updating new particle position and velocity using equations:
Vk+1=αvk+β1rand1(xkself−xk)+β2rand2(xkglobal−xk)
xk+1=xk+vk
Step 7: determining whether the maximum number of iterations has been reached and if the maximum number of iterations has not been reached incrementing iteration counters (NOI and J) and proceed to step 8 and if reached, stopping further estimation of the parameter value;
Step 8: if the index J is 50, proceeding to step 1, and if index J is less than 50 proceeding to step 0.

### Claim 11 (depends on 7)

The method of claim 7 wherein the generator reference parameters comprise at least one of: generator rated voltage and power output, Ra=armature winding resistance, Rfd=field winding resistance, Xl=leakage reactance, Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant or T′qo=generator open circuit quadrature time constant.

### Claim 12 (depends on 7)

The method of claim 7 wherein the generator operating parameters comprise at least one of: Efd=field voltage, Ifd=field current, Et=terminal voltage, It=terminal current, φ=the load angle, δi=the power angle (internal rotor angle), Vgen=generator voltage, Vr=reference voltage, P=Real power of the generator, or Q=Reactive power of the generator.

### Claim 13 (depends on 7)

The method of claim 7 wherein the generator's current performance parameters comprise at least one of: Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant, or T′qo=generator open circuit quadrature time constant.

### Claim 14

A system for detecting an incipient failure of a generator in a power system comprising:
a processor operatively coupled to memory, an input data interface for receiving operating parameters associated with the generator and a user interface, the processor for executing computer executable instructions, the computer executable instructions structured to:
ascertain at least one generator reference parameter of the generator for use as a baseline reference;
measure at least one operating parameter value of the generator; and
use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique.

### Claim 15 (depends on 14)

The system of claim 14 wherein the computer executable instructions structured to use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameter using particle swarm optimization technique are further structured to:
treat each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters, the computer executable instructions being further structured to:
a. initialize each particle position,
b. determine an initial value for the dynamic direct and quadrature generator voltage;
c. calculate a response of the generator model with a selected particle position using received operating field voltage,
d. determine a fitness evaluation of the particle to find a self best value and a global best value, and
e. update a position and a velocity for each particle based on the determined self best value and global best value.

### Claim 16 (depends on 14)

The system of claim 14 wherein the computer executable instructions structured to use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameter using particle swarm optimization technique is further structured to:
treat each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters, the computer executable instructions being further structured to:
a. initialize iteration indices, NOI=0, J=0
b. initialize each particle position according to the equation:
{circumflex over (X)}=rand( )·Xno min al
c. calculate initial values for the dynamic equations, E′d(0) and E′q(0), for the simulation models using the equations:
E
d
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
d
⁡
(
k
)
+
R
a
⁢
i
d
⁡
(
k
)
-
X
^
q
⁢
i
q
⁡
(
k
)
E
q
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
q
⁡
(
k
)
+
R
a
⁢
i
q
⁡
(
k
)
+
X
^
d
⁢
i
d
⁡
(
k
)
d. calculate model's response with a selected particle position, ed(k) and eq(k), k=1, . . . , N, by applying the measured field voltages to the equations:
E
d
′
⁡
(
k
+
1
)
=
E
d
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
qo
′
⁢
(
-
E
d
′
⁡
(
k
)
+
i
q
⁡
(
k
)
⁢
(
X
^
q
-
X
^
q
′
)
)
E
q
′
⁡
(
k
+
1
)
=
E
q
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
do
′
⁢
(
-
E
q
′
⁡
(
k
)
-
i
d
⁡
(
k
)
⁢
(
X
^
d
-
X
^
d
′
)
+
K
^
sd
⁢
E
fd
⁡
(
k
)
)
e
d
⁡
(
k
)
=
E
d
′
⁡
(
k
)
-
R
^
a
⁢
i
d
⁡
(
k
)
+
X
^
q
⁢
i
q
⁡
(
k
)
e
q
⁡
(
k
)
=
E
q
′
⁡
(
k
)
-
R
^
a
⁢
i
q
⁡
(
k
)
-
X
^
d
⁢
i
d
⁡
(
k
)
e. calculate the fitness function:
J
=
∑
k
=
1
N
⁢
[
(
e
d
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
d
⁡
(
k
)
)
2
+
(
e
q
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
q
⁡
(
k
)
)
2
]
to check the best particle based on the model's responses obtained in (d.) and the recorded responses and if it is better, update the best particle;
f. until all particles are calculated, increment a particle counter and utilize the structure of (c.), (d.) and (e.) above for each particle; and
g. update new particle position and velocity using equations:
vk+1=αvk+β1rand1(xkself−xk)+β2rand2(xkglobal−xk)
xk+1=xk+vk
h. determine whether the maximum number of iterations has been reached and if reached, stop further estimation of the parameter value.

### Claim 17 (depends on 14)

The system of claim 14 wherein the generator reference parameters comprise at least one of: generator rated voltage and power output, Ra=armature winding resistance, Rfd=field winding resistance, Xl=leakage reactance, Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant or T′qo=generator open circuit quadrature time constant.

### Claim 18 (depends on 14)

The system of claim 14 wherein the generator operating parameters comprise at least one of: Efd=field voltage, Ifd=field current, Et=terminal voltage, It=terminal current, φ=the load angle, δi=the power angle (internal rotor angle), Vgen=generator voltage, Vr=reference voltage, P=Real power of the generator, or Q=Reactive power of the generator.

### Claim 19 (depends on 14)

The system of claim 14 wherein the generator's current performance parameters comprise at least one of: Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant, or T′qo=generator open circuit quadrature time constant.

### Claim 20

A system for detecting an incipient failure of a generator in a power system comprising software code having a plurality of computer executable instructions comprising instructions structured to:
ascertain at least one generator reference parameter of the generator for use as a baseline reference;
measure at least one operating parameter value of the generator; and
use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique.

### Claim 21 (depends on 20)

The system of claim 20 wherein the computer executable instructions structured to determine whether the estimated present values of the at least one of the generator's current performance parameters are outside of an acceptable limit are further structured to ascertain for each generator reference parameter a tolerance value from the corresponding generator reference parameter and determining whether the estimated present values of the generator current performance parameter is within a range between the reference value plus the tolerance value and the reference value minus the tolerance value.

### Claim 22 (depends on 20)

The system of claim 20 wherein the computer executable instructions structured to determine whether the estimated present values of the at least one of the generator's current performance parameters are outside of an acceptable limit are further structured to:
compare the estimated value of at least one of the generator's current performance parameters to a corresponding one of the generator reference parameters; and
if the estimated value is not an acceptable value, provide an alarm that an estimated value of at least one of the generator's current performance parameters is unacceptable.

### Claim 23 (depends on 20)

The system of claim 20 wherein the computer executable instructions structured to use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique are further structured to:
treat each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
a. initialize each particle position,
b. determine an initial value for the dynamic direct and quadrature generator voltage;
c. calculate a response of the generator model with a selected particle position using received operating field voltage,
d. determine a fitness evaluation of the particle to find a self best value and a global best value, and
e. update a position and a velocity for each particle based on the determined self best value and global best value.

### Claim 24 (depends on 20)

The system of claim 20 wherein the computer executable instructions structured to use the at least one operating parameter value to solve for an estimated present value of the at least one of the generator's current performance parameters using particle swarm optimization technique are further structured to:
treat each estimated value of the at least one of the generator's current performance parameters set as a particle, wherein each set of estimated values is a different position of the particle; and
for each new set of operating parameters:
a. initialize iteration indices, NOI=0, J=0
b. initialize each particle position according to the equation:
{circumflex over (X)}=rand( )·Xno min al
c. calculate initial values for the dynamic equations, E′d(0) and E′q(0), for the simulation models using the equations:
E
d
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
d
⁡
(
k
)
+
R
a
⁢
i
d
⁡
(
k
)
-
X
^
q
⁢
i
q
⁡
(
k
)
E
q
′
⁡
(
0
)
=
1
N
⁢
∑
k
=
1
N
⁢
e
q
⁡
(
k
)
+
R
a
⁢
i
q
⁡
(
k
)
+
X
^
d
⁢
i
d
⁡
(
k
)
d. calculate model's response with a selected particle position, ed(k) and eq(k), k=1, . . . , N, by applying the measured field voltages to the equations:
E
d
′
⁡
(
k
+
1
)
=
E
d
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
qo
′
⁢
(
-
E
d
′
⁡
(
k
)
+
i
q
⁡
(
k
)
⁢
(
X
^
q
-
X
^
q
′
)
)
E
q
′
⁡
(
k
+
1
)
=
E
q
′
⁡
(
k
)
+
Δ
⁢
⁢
t
T
^
do
′
⁢
(
-
E
q
′
⁡
(
k
)
-
i
d
⁡
(
k
)
⁢
(
X
^
d
-
X
^
d
′
)
+
K
^
sd
⁢
E
fd
⁡
(
k
)
)
e
d
⁡
(
k
)
=
E
d
′
⁡
(
k
)
-
R
^
a
⁢
i
d
⁡
(
k
)
+
X
^
q
⁢
i
q
⁡
(
k
)
e
q
⁡
(
k
)
=
E
q
′
⁡
(
k
)
-
R
^
a
⁢
i
q
⁡
(
k
)
-
X
^
d
⁢
i
d
⁡
(
k
)
e. calculate the fitness function:
J
=
∑
k
=
1
N
⁢
[
(
e
d
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
d
⁡
(
k
)
)
2
+
(
e
q
⁢
⁢
_
⁢
⁢
m
⁡
(
k
)
-
e
q
⁡
(
k
)
)
2
]
to check the best particle based on the model's responses obtained in (d.) and the recorded responses and if it is better, update the best particle;
f. until all particles are calculated, increment a particle counter and utilize the structure of (c.), (d.) and (e.) above for each particle;
g. update new particle position and velocity using equations:
vk+1=αvk+β1rand1(xkself−xk)+β2rand2(xkglobal−xk)
xk+1=xk+vk
h. determine whether the maximum number of iterations has been reached and if reached, stop further estimation of the parameter value.

### Claim 25 (depends on 20)

The system of claim 20 wherein the generator reference parameters comprise at least one of: generator rated voltage and power output, Ra=armature winding resistance, Rfd=field winding resistance, Xl=leakage reactance, Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant or T′qo=generator open circuit quadrature time constant.

### Claim 26 (depends on 20)

The system of claim 20 wherein the generator operating parameters comprise at least one of: Efd=field voltage, Ifd=field current, Et=terminal voltage, It=terminal current, φ=the load angle, δi=the power angle (internal rotor angle), Vgen=generator voltage, Vr=reference voltage, P=Real power of the generator, or Q=Reactive power of the generator.

### Claim 27 (depends on 20)

The system of claim 20 wherein the generator's current performance parameters comprise at least one of: Xd=synchronous steady state direct reactance, Xq=synchronous steady state quadrature reactance, X′d=synchronous dynamic direct reactance, X′q=synchronous dynamic quadrature reactance, T′do=generator open circuit direct time constant, or T′qo=generator open circuit quadrature time constant.