little goose turbine governor model · pdf filecontents 1 general 4 2 turbine governor...

Little Goose Turbine Governor Model

John Undrill

30 January 2016

1

Contents

1 General 4

2 Turbine governor parameters 4

3 List of tests 4

4 Turbine Model - Power-versus-gate characteristic 4

4.1 Move gates with fixed blade - Test 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4.2 Move blades with gate fixed - Test 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.3 Turbine model curves - Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.4 Gate setpoint steps, normal blade movement - Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.5 Water inertia time constant - Test 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.6 Overall gate characteristic - Test 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 Governor Model 6

5.1 Governor parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5.2 Load control mode - Tests 6 and 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5.3 Speed control mode - Tests 7 and 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

6 Load Rejection, rotor inertia constant - Test 5 7

7 Parameter values for h6e dynamic model 7

JMU 2 March 6, 2016

List of Figures

1 Power response - move gates with blades fixed Magenta - power Red - gate set point - playedin Green - gate servo stroke Blue - blade servo setpoint - played in Black - blade servo stroke . . 9

2 Power response - move blades with gate fixed Magenta - power Red - gate set point Green -gate servo stroke Blue - blade servo setpoint - played in Black - blade servo stroke . . . . . . . . 10

3 Measured turbine gate-power and gate-blade curves Red - measured at head of 1.023 per unitBlue - measured and corrected to head of 1.0 per unit Black - data points for h6e model . . . . . 11

4 Step and ramp changes of gate setpoint - varied maxim gate travel rate . . . . . . . . . . . . . . . 12

5 Response of gate servo to step of gate setpoint bvlm=0.075 Tg=0.05 Kg=3.0 black - gate setpoint- played in red - gate servo stroke - simulated magenta - gate servo stroke - test . . . . . . . . . . 13

6 Response of power to steps of gate setpoint - per figure 4 Black - played in power Red - simu-lated power, bgvmin=0.4 Green - simulated power, bgvmin=0.5 Blue - simulated power, bgvmin=0.6 14

7 Response of power to steps of gate setpoint - per figure 4 - expanded time scale Black - playedin power Red - simulated power, bgvmin=0.4 Green - simulated power, bgvmin=0.5 Blue -simulated power, bgvmin=0.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

8 Response of power to steps of gate setpoint - per figure 4 - expanded time scale Black - playedin power Red - simulated power, Tw =0.75 Green - simulated power, Tw=1.00 Blue - simulatedpower, Tw=1.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

9 Response of power to steps of gate setpoint - per figure 4 - expanded time scale Black - playedin power Red - simulated power, Tw =0.75 Green - simulated power, Tw=1.00 Blue - simulatedpower, Tw=1.25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

10 Ramp gates full range in 100 sec Black - Gate power 10-point curve Red = bgvmin=0.4 Green =bgvmin=0.5 Blue - bgvmin=0.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

11 Ramp gates full range in 500 sec Black - Gate power 10-point curve Red = bgvmin=0.4 Green =bgvmin=0.5 Blue - bgvmin=0.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

12 Governor gain settings as shown on governor HMI console . . . . . . . . . . . . . . . . . . . . . . 20

13 Response to injected speed step - load control mode Blue - test Red - Simulation . . . . . . . . . . 21

14 Response to injected speed step - load control mode Blue - test Red - Simulation . . . . . . . . . . 22

15 Response to played in large frequency dip event - load control mode Blue - test Red - Simulation 23

16 Response to played in large frequency dip event - load control mode Blue - test Red - Simulation 24

17 Response to injected speed step - speed control mode Blue - test Red - Simulation . . . . . . . . . 25

18 Response to injected speed step - speed control mode Blue - test Red - Simulation . . . . . . . . . 26

19 Response to played in large frequency dip event - speed control mode Blue - test Red - Simulation 27

20 Response to played in large frequency dip event - Speed control mode Blue - test Red - Simulation 28

21 Load Rejection from 119MW - Test recording Red - gate servo stoke Blue - power Black - speed . 29

22 Load Rejection from 119MW - Test recording - expanded time scale Red - gate servo stoke Blue- power Black - speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

JMU 3 March 6, 2016

1 General

This memorandum describes tests made on Little Goose unit 2 on 12 January 2016. Two sets of tests aredescribed here:

a. Tests in which the gate setpoint was changed directly so that the resulting response of gate servostroke, blade servostroke, and electrical power were completely independent of governor action.

b. Tests in which step changes were added to the speed input of the governor so that the resultingresponse of the gates, blades, and power were the result of governor action without the influence ofchanges in the speed/load reference or feedforward action associated with such changes.

The test recordings are used in this memo as the basis for calibration of the h6e turbine governor model. Themodel is described in the h6e manual page that is attached to this memorandum. The parameter valuesarrived at by the comparisons shown here are listed in section 7.

2 Turbine governor parameters

Turbine base power 94 feetGenerator base power 163 MW

3 List of tests

Test Description File

1 Ramp power from zero to max test1.csv

2 Move gates with blades fixed WECC_1_Gate_Cycle_Fixed_Blades.1.CSV

3 Move blades with gates fixed WECC_1_Blade_Cycle_Fixed_Gates.1.CSV

4 Move gate and blades WECC_1_Gate_Step_120MW.1.CSV

5 Load rejection WECC_1_Load_Reject_120MW.CSV

6 Inject speed steps, load mode WECC_1_Speed_Step_120MW_Load_Mode.1.CSV

7 Inject speed steps, speed mode WECC_1_Speed_Step_120MW_Speed_Mode.1.CSV

8 Play in system event A, load mode WECC_1_Real_Event_Response_Small_Load.CSV

9 Play in system event A, speed mode WECC_1_Real_Event_Response_Small_Speed.CSV

10 Play in system event B, load mode WECC_1_Real_Event_Response_Large_2_Load.CSV

11 Play in system event B, speed mode WECC_1_Real_Event_Response_Large_2_Speed.CSV

4 Turbine Model - Power-versus-gate characteristic

4.1 Move gates with fixed blade - Test 2

Figure 1 shows the variation of turbine power when the gate setpoint was changed at a rate that is slow inrelation to the water inertia time constant. This test does not give a ’clean’ indication of the gain relatingpower to gate servo stroke but is approximately consistent with a gain of unity.

JMU 4 March 6, 2016

4.2 Move blades with gate fixed - Test 3

Figure 2 shows the variation of turbine power when the blades are moved slowly while the gates are held infixed position. The figure indicates that the gain relating power to blade servo stroke is approximately

δPδb

=(121 − 109)

(163 ∗ (.55 − .34))= 0.65

4.3 Turbine model curves - Test 1

The top part of figure 3 shows measured power versus gate servo stroke. The measurement was made withthe plant head at 96.2ft, which is 96.2/94 = 1.023 per unit. The power measured at this head is corrected tonominal head by a multiplying a factor of 1/(1.023**1.5) = 0.966. The corrected power curve is shown in thesecond part of figure 3. The measured curve of blade angle versus gate servo stroke is shown in the bottompart of figure 3.

The black marks in the middle part of figure 3 show the data points to be used in the h6e model to describethe turbine. These points were placed, ’by eye’ on the measured power curve and then corrected by the samefactor as applied to the measured curve. The data points are:

gv = 0.2 0.32 0.45 0.553 0.60 0.70 0.88 0.93 0.96 1.0

pv = 0 0.2015 0.3674 0.4504 0.4741 0.6222 0.8889 0.9600 0.9837 1.0

bv = 0 0 0 0 0 0.30 0.91 0.99 1.0 1.0

4.4 Gate setpoint steps, normal blade movement - Test 4

To reveal the characteristics of the turbine, independently of the action of the governor, a series of quickchanges was applied to the gate position setpoint. Figure 4 shows the behavior of the turbine in response tothese changes. The gate position setpoint was changed at varying rates. The first upward and downwardchanges were steps; subsequent changes were made with a progressively smaller limit on the rate of changeof the setpoint.

Figure 4 shows the overall response of the turbine. The blades were not settled when the first upward stepwas made. Nevertheless there is good correspondence between the test and simulated response. The cyanand blue curves show the test and simulated response of the turbine blades.

Figure 5 shows the response of the gate servo to the initial pure step change of gate position setpoint. Thegood fit of simulation and test is achieved with a the blade servo velocity limit set to 0.075 pu/sec and withthe gate servo parameters set to Tg=0.05 and Kg=3.0. and blade servo time constant set to 3.0 second.

Figures 6 and 7 show the response of electrical power. The red, green, and blue curves in these figures weremade with bgvmin set to 0.4, 0.5, and 0.5. The best fit of power response is with bgvmin=0.4.

The fair fit, shown in figure 7, of power at the start of the two downward changes was achieved with thewater inertia time constant set to Tw=1.0 second.

4.5 Water inertia time constant - Test 4

Because the Little Goose water column includes no substantial penstock, only a very approximate estimate ofits water inertia constant can be made from drawings. Estimation based on drawings puts the value of the

JMU 5 March 6, 2016

water inertia time constant between 0.9 and 1.3 seconds. The initial two quick changes of gate openingdescribed above provide an alternative basis for estimation of the water inertia time constant.

Figures 8 and 9 compare the measured and simulated power response in the initial two step changes of gatesetpoint. The red, green, and blue simulation results were obtained with the water inertia time constantestimated as 0.75, 1.00, and 1.25 seconds. Fair correspondence between the green and black traces supportsan estimate of the time constant as Tw=1.0.

4.6 Overall gate characteristic - Test 1

Figures 10 and 11 confirm that the dynamic model of the turbine reproduces the measuredpower-versus-gate characteristic. Figure 10 shows the simulated response when the gates are run over the fullload range at a rate that is fast enough for the dynamics of blade adjustment to affect the result. The powerlags the gate quite significantly. Figure 11 shows the simulated response when the gates are ramped slowly sothat the effect of the lag in the blade response is minimized; in this simulation the dynamic model matchesthe specified turbine power-gate curve very closely.

5 Governor Model

5.1 Governor parameters

Simulations were made with the governor gains, Kp, Ki, and Kd assigned values taken directly from theoperators display of the American Governor installation, see figure 12. The ’On-Line’ values were used:Kp = 3.3, Ki = 0.5, and Kd = 0.05.

5.2 Load control mode - Tests 6 and 10

Figures 13 and 14 show the response of the machine to injected steps of measured speed. The stepsamplitude was 0.5 percent. The injected signal is an addition to the measured speed; the speed/loadreference is not changed and, accordingly, the feedforward features of the governor have no effect. (Note thatplot of speed is the actual speed of the turbine ; the speed signal that was ’seen’ by the governor was theplotted speed plus the applied steps.)

Figure 15 and 16 show the response of the machine to a played-in profile of frequency. This frequency profilewas obtained from a PMU recording of frequency in a major transmission system disturbance. (The speedplot in these figures shows the speed signal that was ’seen’ by the governor; the act

5.3 Speed control mode - Tests 7 and 11

Figure 17 and 18 show the response of the machine to injected steps of measured speed. The injected signal isan addition to the measured speed; the speed/load reference is not changed and, accordingly, thefeedforward features of the governor have no effect.

Figure 19 and 20 show the response of the machine to a played-in profile of frequency. This frequency profilewas obtained from a PMU recording of frequency in a major transmission system disturbance.

JMU 6 March 6, 2016

6 Load Rejection, rotor inertia constant - Test 5

Figures 21 and 22 show the turbine speed and wicket gate position following opening of the main circuitbreaker to reject 119MW. The magenta line supports an estimate of the generator inertia constant as

H =Pinitial

2 δnδt

H =119/163

2 ∗ (90 − 60)/(60 ∗ (280 − 275.22))= 3.49

Figure 21 shows the maximum gate closing rate to be velm = 0.105 pu/sec and the gate buffering parametersto be buf = 0.1 and buv = 0.008.

7 Parameter values for h6e dynamic model

h6e 61 t

163 tbase

.05 re

.05 rg

.2 tpe

.025 tsp

1 fd

3.3 kp

0.5 ki

0.05 kd

0.05 td

.075 velm

1. gmax

0. gmin

0.1 buf

0.008 buv

3. kg

.05 tg

0. blg

0.0 dbbd

0.5 tbd

0. blb

0. dbbs

3.0 tbs

0.4 bgvmin

0.015 blv

0.5 dturb

0.2 pgc

0. deff

1.023 hdam

.2 gv0

.32 gv1

JMU 7 March 6, 2016

.45 gv2

.553 gv3

.6 gv4

.7 gv5

.88 gv6

.93 gv7

.95 gv8

1. gv9

.0 agv0

0.2015 agv1

0.3674 agv2

0.4504 agv3

0.4741 agv4

0.6222 agv5

0.8889 agv6

0.9600 agv7

0.9837 agv8

1.0000 agv9

0 bgv0

0 bgv1

0 bgv2

0 bgv3

0 bgv4

.3 bgv5

.91 bgv6

.99 bgv7

1. bgv8

1. bgv9

1. tw

0.01 sprate

JMU 8 March 6, 2016

0 100 200 300 400 500 600Time, sec

40

50

60

70

80

90

100

110

120

130

Figure 1: Power response - move gates with blades fixedMagenta - power

Red - gate set point - played inGreen - gate servo stroke

Blue - blade servo setpoint - played inBlack - blade servo stroke

JMU 9 March 6, 2016

550 600 650 700 750Time, sec

30

40

50

60

70

80

90

100

110

120

130

Figure 2: Power response - move blades with gate fixedMagenta - power

Red - gate set pointGreen - gate servo stroke

Blue - blade servo setpoint - played inBlack - blade servo stroke

JMU 10 March 6, 2016

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2U

ncor

rect

ed p

ower

, pu

Little Goose #2, Turbine base = 163 MW

gv .20 .32 .45 .553 .60 .70 .88 .93 .96 1.0pv 0 .2086 .3804 .4663 .4908 .6442 .9202 .9939 1.0184 1.0362bv 0 0 0 0 0 .30 .91 . 99 1.00 1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

Cor

rect

ed p

ower

, pu

gv .20 .32 .45 .553 .60 .70 .88 .93 .96 1.0pv 0 .2015 .3674 .4505 .4741 .6222 .8889 .9600 .9837 1.0bv 0 0 0 0 0 .30 .91 . 99 1.00 1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1gate servo stroke, pu

0

0.2

0.4

0.6

0.8

1

blad

e se

rvo

stro

ke, p

u

Figure 3: Measured turbine gate-power and gate-blade curvesRed - measured at head of 1.023 per unit

Blue - measured and corrected to head of 1.0 per unitBlack - data points for h6e model


0 50 100 150 200 2500.3

0.4

0.5

0.6

0.7

0.8

0.9

1

gate

ser

vo s

troke

, pu

played in gate setptplayed in gatesimulated gateplayed in bladesimulated blade

0 50 100 150 200 250Time, sec

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1played in powersimulated powersimulated powersimulated powerplayed in bladesimulated blade

LGAgsteps

Figure 4: Step and ramp changes of gate setpoint - varied maxim gate travel rate


0 1 2 3 4 5 6 7 8 9 10Time, sec

0.74

0.76

0.78

0.8

0.82

0.84

0.86

stro

ke, p

er u

nit

Figure 5: Response of gate servo to step of gate setpointbvlm=0.075

Tg=0.05Kg=3.0

black - gate setpoint - played inred - gate servo stroke - simulatedmagenta - gate servo stroke - test


0 50 100 150 200 250Time, sec

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

LGAgsteps

Figure 6: Response of power to steps of gate setpoint - per figure 4Black - played in power

Red - simulated power, bgvmin=0.4Green - simulated power, bgvmin=0.5Blue - simulated power, bgvmin=0.6


10 20 30 40 50 60 70 80 90Time, sec

0.65

0.7

0.75

0.8

0.85

0.9

0.95

LGAgsteps

Figure 7: Response of power to steps of gate setpoint - per figure 4 - expanded time scaleBlack - played in power

Red - simulated power, bgvmin=0.4Green - simulated power, bgvmin=0.5Blue - simulated power, bgvmin=0.6


20 22 24 26 28 30 32 34 36 38 40Time, sec

0.65

0.7

0.75

0.8

0.85

0.9

0.95

LGAgstepsTw


Red - simulated power, Tw =0.75Green - simulated power, Tw=1.00Blue - simulated power, Tw=1.25


0 2 4 6 8 10 12 14 16 18 20Time, sec

0.65

0.7

0.75

0.8

0.85

0.9

0.95

LGAgstepsTw


Red - simulated power, Tw =0.75Green - simulated power, Tw=1.00Blue - simulated power, Tw=1.25


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Gate servo stroke, pu

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pow

er, p

er u

nit

ramp

Figure 10: Ramp gates full range in 100 secBlack - Gate power 10-point curve

Red = bgvmin=0.4Green = bgvmin=0.5Blue - bgvmin=0.6


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Gate servo stroke, pu

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pow

er, p

er u

nit

ramp

Figure 11: Ramp gates full range in 500 secBlack - Gate power 10-point curve

Red = bgvmin=0.4Green = bgvmin=0.5Blue - bgvmin=0.6


Figure 12: Governor gain settings as shown on governor HMI console


0 200 400 600 800 1000 1200100

110

120

130

140

150

Act

ive

Pow

er (

MW

)

0 200 400 600 800 1000 12000.99

0.995

1

1.005

1.01

Spe

ed (

pu)

0 200 400 600 800 1000 12000.65

0.7

0.75

0.8

0.85

Gat

e (p

u)

0 200 400 600 800 1000 1200Time, sec.

0.3

0.4

0.5

0.6

0.7

0.8

Bla

de (

pu)

Figure 13: Response to injected speed step - load control modeBlue - test

Red - Simulation


0 200 400 600 800 1000 1200Time, sec.

95

100

105

110

115

120

125

130

135

140

145

Figure 14: Response to injected speed step - load control modeBlue - test

Red - Simulation


0 100 200 300 400 500 600110

115

120

125

130

135

Act

ive

Pow

er (

MW

)

0 100 200 300 400 500 6000.99

0.995

1

1.005

1.01

Spe

ed (

pu)

0 100 200 300 400 500 6000.74

0.76

0.78

0.8

0.82

0.84

Gat

e (p

u)

0 100 200 300 400 500 600Time, sec.

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Bla

de (

pu)

Figure 15: Response to played in large frequency dip event - load control modeBlue - test

Red - Simulation


0 100 200 300 400 500 600Time, sec.

90

95

100

105

110

115

120

125

130

135

Figure 16: Response to played in large frequency dip event - load control modeBlue - test

Red - Simulation


0 200 400 600 800 1000 120090

100

110

120

130

140

150

Act

ive

Pow

er (

MW

)

0 200 400 600 800 1000 12000.99

0.995

1

1.005

1.01

Spe

ed (

pu)

0 200 400 600 800 1000 12000.65

0.7

0.75

0.8

0.85

0.9

Gat

e (p

u)

0 200 400 600 800 1000 1200Time, sec.

0.2

0.4

0.6

0.8

1

Bla

de (

pu)

Figure 17: Response to injected speed step - speed control modeBlue - test

Red - Simulation


0 200 400 600 800 1000 1200Time, sec.

95

100

105

110

115

120

125

130

135

140

145

Figure 18: Response to injected speed step - speed control modeBlue - test

Red - Simulation


0 100 200 300 400 500 600110

115

120

125

130

135

140

Act

ive

Pow

er (

MW

)

0 100 200 300 400 500 6000.99

0.995

1

1.005

1.01

Spe

ed (

pu)

0 100 200 300 400 500 6000.74

0.76

0.78

0.8

0.82

0.84

0.86

Gat

e (p

u)

0 100 200 300 400 500 600Time, sec.

0.4

0.5

0.6

0.7

0.8

Bla

de (

pu)

Figure 19: Response to played in large frequency dip event - speed control modeBlue - test

Red - Simulation


0 50 100 150 200 250 300Time, sec.

90

95

100

105

110

115

120

125

130

135

140

Figure 20: Response to played in large frequency dip event - Speed control modeBlue - test

Red - Simulation


270 272 274 276 278 280 282 284 286 288 290Time, sec

0

20

40

60

80

100

120

Figure 21: Load Rejection from 119MW - Test recordingRed - gate servo stoke

Blue - powerBlack - speed


Figure 22: Load Rejection from 119MW - Test recording - expanded time scaleRed - gate servo stoke

Blue - powerBlack - speed


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