Simulation of Hydroelectric System Control

8/10/2019 Simulation of Hydroelectric System Control

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Simulation of hydroelectric

system control

Dewi Jones


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Simulation of hydroelectric system control

Dewi Jones

Report GW002

October 2008

GWEFR CyfTechnium CAST

Ffordd Penlan

Parc Menai

Bangor

Gwynedd LL57 4HJ

Wales

Tel: +44 (0) 2921 251768

Email:[email protected]

http://www.gwefr.co.uk

Care has been taken in the preparation of this report but all advice, analysis, calculations, information, forecasts and

recommendations are supplied for the assistance of the relevant client and are not to be relied upon as authoritative or as in

substitution for the exercise of judgement by that client or any other reader. Neither GWEFR Cyf, nor any of its personnel

engaged in the preparation of this Report shall have any liability whatsoever for any direct or consequential loss arising from

the use of this Report or its contents and give no warranty or representation (express or implied) as to the quality or fitness for

the purpose of any process, product or system referred to in the Report.

Copyright in this Report remains the sole property of GWEFR Cyf.
mailto:[email protected]:[email protected]:[email protected]://www.gwefr.co.uk/http://www.gwefr.co.uk/http://www.gwefr.co.uk/mailto:[email protected]


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Contents

1 Introduction ........................ ........................ .................... ..................... ...................... .................... ...................... ..... 1

2 Outline of the simulation ........................ ...................... ..................... ...................... .................... ..................... ... 1

2.1 Physical layout ...................... ..................... ..................... ...................... .................... ..................... ................. 1

2.2 Model summary ..................... ....................... ..................... ..................... ...................... .................... ............. 3

3 Simulation of hydraulic system with fixed rate GV opening ................. ..................... ...................... ..... 4

4 Lumped parameter models ........................ .................... ...................... ...................... .................... .................... 7

4.1 Lumped parameter, inelastic water column model .................... ...................... ..................... ......... 7

4.2 Linearised model ....................... ...................... ..................... ...................... .................... ..................... .......... 9

5 Control system design ....................... ...................... ..................... ...................... .................... ..................... .......... 9

6 Closed loop simulation with Grid connection .................... ..................... ...................... ..................... ...... 126.1 Frequency control mode. ......................... ..................... ...................... ...................... ..................... ......... 13

6.2 Power dialup mode. ....................... ...................... ..................... ...................... ..................... .................... 16

6.3 Fullload rejection. ........................ ..................... ...................... ..................... ..................... ...................... .. 17

7 Conclusion............................................................................................................................................................... 19


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1

1 Introduction

This sample report outlines how the generic simulation package offered by GWEFR Cyfcan

provide valuable information about the dynamic response of a proposed hydroelectric installation,

given just the basic information about the Plants physical layout, its primary parameters and

modes of operation.

The objective is to increase understanding of how the proposed hydraulic and electrical systems

affect the dynamic response of the Plant and hence the quality of power generation an approach

advocated in IEEE Standard 12072004 IEEE Guide for the Application of Turbine Governing

Systems for Hydroelectric Generating Units [1].

The following section presents a simplified version of the hydraulic system, composed of a

reservoir supplying two Gridconnected Francis turbine/generators via a common tunnel, a

manifold and two identical penstocks. This is used as the basis of a travellingwave model that

estimates the pressure and flow variations in the water passages under defined rates of opening or

closing of the turbine guide vanes.

Comparisons are made between the responses produced by three different types of model, as

suggested by an expert IEEE Working Group [2]:

Nonlinear distributed parameter, elastic water column the most accurate model butcomputationally intensive;

Nonlinear lumped parameter, inelastic water column requires less computation but doesnot represent travellingwave effects;

Linearised model suitable for control design.

Standard tuning rules are applied to design a PID controller based on the linearised model.

The resulting governor is integrated with models for the hydraulics, turbine/generator and Grid to

study system performance for 3 scenarios:

Closed loop frequencycontrol mode Dialup power mode with feedforward Full load rejection

The report provides constructive input to the requirements capture stage of the project and

forthcoming design efforts.

2 Outlineofthesimulation

2.1 Physicallayout

Figure 1 shows the general layout of the hydraulic system assumed in the model. The reservoir is

connected by a long supply tunnel to a manifold that separates into two identical penstocks, which

feed identical turbine/generators. The tailrace is not included in the model at this stage. Note that

the layout is not quite symmetrical because the water path to Unit #2 has additional length due to

the manifold. The dimensions are shown in Figure 2.


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2

Figure1Generallayoutofthehydraulicsystem.

Figure2Cross-sectionandplanviewsshowingdimensions(datumtakenatturbineinlet).

513m

880m

10m

9.5

m

130m

3.3m

10m

80m

9.5m

130m

3.3m


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3

2.2 Modelsummary

Hydraulicsystem:

The 4 pipe sections are modelled using the Method of Characteristics [3] which is used to compute

the time variation of piezometric pressure and uniform flow at 100 discrete points in the network.

All head losses except for friction are considered negligible. There are 5 boundary conditions:

The head at the reservoir outlet is considered constant. At the branch between tunnel, manifold and penstock #1 the head is constrained to be

identical for all 3 branches and continuity of flow is applied.

Similar conditions are applied at the junction between the manifold and penstock #2. Both turbines are modelled as idealised lossless control components where the relationship

between head and flow is given by:

2

2u tb

VH A

G

=

(2.1)

where Hu= head across the turbine

V = flow through the turbine

Atb= turbine constant

G = guide vane opening (0 : 1)

For a flow, Q, the mechanical output power of a turbine is given by:

m u

P QH g= (2.2)

Electricalsystem

It is assumed that the generators are Gridconnected and represented by a linearised version of the

classic swing equations as given, for example, by Kundur [4]:

( )

( )0

1

2r m e D r

se r L

P P KHs

KP Ps

=

=

(2.3)

where:

G= Grid frequency

r= Unit (electrical) speed

PL= load change on Grid

Pm= turbine mechanical power

Pe= generator electrical power

0, r= rated and actual Unit speed

Ks= synchronising coefficient

KD= speed damping coefficient

H = inertia constant

s = Laplace variable


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5

Figure 3 shows that the flow velocity increases in penstock #1 as GV #1 opens with a small dip in

the velocity in penstock #2 over the same period. Opening GV #1 causes the pressure at the turbine

inlet to fall and, after a brief delay while the pressure wave travels through the 2 penstocks and the

manifold, hydraulic coupling causes the pressure at turbine #2 to decrease. The response also

exhibits a poorly damped oscillation with a period of 0.7s as the travelling wave traverses the

tunnel. These effects are reflected in the generated power. Turbine #1 is subject to a brief time

delay before the required power increase begins while turbine #2 is perturbed from its set level.

Figure3Variationofpressurehead,penstockflowandmechanicalpowerwithGV#1openingin2.6s.

Figure 4 shows the head and flow profiles in the pipe network shortly after the simulation isinitiated. The pressure head increases, because of elevation, along the length of the tunnel and then

flattens out over the length of the penstock (the red line shows the pressure in penstock #1). The

small notch of lower velocity between 880 and 960m is located at the manifold, which only carries

the flow to penstock #2. An animated version of Figure 4 shows the pressure wave travelling up

and down the tunnel as the simulation proceeds.

This is a very simple model of the hydraulic system (it should be emphasised that it is not a

substitute for a full study for structural engineering purposes) but quite satisfactory for

representing the dynamics within the tolerance required for a control systems study. Clearly, in

this particular example, the pressure variation is within bounds and quite satisfactory in thisrespect.

480

490

500

510

520

pressurehead(m)

2

3

4

5

6

7

penstockvelocity(m/s)

penstock #1

penstock #2

0 5 10 15

100

150

200

250

300

mechanicalpower(MW

)

time (s)

turbine #1

turbine #2

turbine #1

turbine #2

branch


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6

Figure4Pressureandflowprofilesinthetunnelandpenstocks.

Figure5Variationofpressurehead,penstockflowandmechanicalpowerwithGV#1openingin1.0s.

0 200 400 600 800 10000

100

200

300

400

500

pressurehead(m)

0 200 400 600 800 10000

1

2

3

4

5

6

7

flowvelocity(m/s)

0 200 400 600 800 1000

Pressure head variation (normalised to max and min of range)

distance along pipe (m)

440

460

480

500

520

540

pressurehead(m)

2

3

4

5

6

7

penstockvelocity(m/s)

penstock #1

penstock #2

0 5 10 15

100

150

200

250

300

mechanicalpower(MW)

time (s)

turbine #1

turbine #2

turbine #1

turbine #2

branch


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7

The result in Figure 5 was obtained by decreasing the opening time of GV #1 to 1.0s. This leads to a

much larger variation in penstock pressure head, which falls to 11.5% below and rises to +4.5%

above the static head. There is a corresponding variation of the mechanical power produced by the

turbines, with perturbation peaks for turbine #2 of 9.7% and +6.7% of the steadystate value.

4

Lumpedparameter

models

4.1 Lumpedparameter,inelasticwatercolumnmodel

The model presented in this section is derived from the block diagram in Sec. 2.6 of [2]. The water

column is considered rigid so travellingwave effects are omitted. The inertia of the water column

is represented by parameters known as the water starting times. The model is multivariable, so

hydraulic coupling effects are retained. It is also nonlinear and suitable for use when simulating

large excursions of the variables.

The water starting time for a section of pipe of length is defined as:

bW

b

VT

gH

=

(4.1)

For the layout of Figure 1, the relationship between the head and flow rate variation in the two

penstocks is:

1 3 11 1

1 1 2 42 2

1

1

W W W

W W W W

T T Th q

T T T T h q

+ = + +

(4.2)

where:

h1, h2are the turbine heads

q1, q2are the turbine flows

TW1is the water starting time for the tunnel (0.145s)

TW2is the water starting time for the manifold (0.014s)

TW3, TW4are the water starting time for penstock #1 and #2 respectively (both 0.198s).

Inverting this relationship allows it to be embedded in a Simulink block diagram, as shown in

Figure 6, which incorporates the nonlinear turbine characteristics and head losses due to friction.

The simulation was run with GV #2 set to operate at a fixed power of 288MW. GV#1 was set for an

initial output power of 280MW and then opened linearly over 2.6s to produce a steady state power

of 310MW. The distributed parameter model was run for the same conditions and Figure 7 shows

that there is a good match between the power outputs. Because the simulation is run here with Unit

#1 operating at a higher power level than in Figure 5, both models predict an initial decrease of

output power at turbine #1 (the characteristic nonminimumphase response). The obvious

discrepancy of course is the absence of the travelling wave oscillation from the response predicted

by the inelastic water column model. The difference becomes more evident as the GV opening or

closing times become shorter.


12/24

8

Figure6Simulinkblockdiagramfortheinelasticwatercolumnmodel.

Figure7Comparisonofresponsesfordistributedparameterandlumpedparametermodels.

Inelastic water column , multiple penstock model in p .u. representation .

Based on Figure 8 of the IEEE Wkg Group paper .

Pinel

1

no-load

flow

0

inverse water

starting time

matrix

iTmat * uvec

friction

head loss 2

qhf

friction

head loss 1

qhf

damping 1

1

damping

1

Product 5

Product 4

Product 3

Product 2

Product 1

Product

P.U. base

power

Pb

P.U. base

head

1

Integrator 1

1

s

Integrator

1

s

Dw2

0

Dw1

0

Divide 1

Divide

G2

2

G1

1

h2

q1

q2

Pm1

Pm2

h1

0 1 2 3 4 5 6 7 8 9 10275

280

285

290

295

300

305

310

315

time (s)

Mechanicalpower(MW)

Unit #1 inelas

Unit #2 inelas

Unit #1 dist

Unit #2 dist


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9

4.2 Linearisedmodel

It is useful to have a linear model so that classical control system methods can be applied to

designing a basic controller. Using standard techniques, equations (4.2) and (2.1) can be linearised

to give a small signal state space model of the usual form:

x Ax Bu

y Cx Du

= +

= +

(4.3)

In perunit form, changes in output power (Pm) are related to changes in flow (q) and guide vaneposition (G) around a fixed operating point (G0) by:

01 011 11 12 1 11 12 1

02 022 21 22 2 21 22 2

1 1 1

2 2 2

1 / 0 1 / 02 2

0 1 / 0 1 /

3 0 2 0

0 3 0 2

m

m

G Gq a a q a a G

G Gq a a q a a G

P q G

P q G

= +

=

(4.4)

where the terms a11... a22are the elements of the inverse of the water starting time matrix in (4.2).

Equation (4.4) is a linear relationship whose characteristics change with the selected GV openings

of the two turbines which define the operating points G 01and G02.

Finally, following Sec. 3 in reference [2], the generator model of equation (2.3) can be appended to

the hydraulic model of equation (4.4) to relate changes in Unit speed (r) to GV position (G). Thecomposite model is then in a suitable form for designing a closed loop speed control system.

5 Controlsystemdesign

The crosscoupling terms in equation (4.4) reflect the intrinsic hydraulic coupling of the penstocks

in the physical system. It is known that significant coupling leads to loss of stability margin, so

Jones [6] has proposed a multivariable controller which takes this into account. However, the

traditional (and simpler) strategy of treating the penstocks as being separate is adopted here. This

allows tuning rules for a singleinput singleoutput (SISO) system to be applied to the design of a

basic PID governor for speed control when supplying an isolated load a procedure recommended

in Section F.3 of [1].

A Simulink block diagram for the SISO linearised model and governor is shown in Figure 8 (the

power feedback loop is eliminated by setting the droop gain to zero). Tuning the gains K i, Kpand Kd

for satisfactory closed loop response is done by applying the rules proposed by Hagihara et al [7],

[2] as follows:

"transient droop" Rt= 1/Kp= 5TW/ 8H "transient droop washout time constant" TR= Kp/ Ki= 3.333*TW Kd= TWKp/ 3


14/24

10

Figure8Blockdiagramofthelinearsystemarrangedforclosedloopspeedcontrol.

Setting the operating point at 100% and knowing the Units inertia constant (H) and the water

starting time, taken here as TW= (TW1+ Tw3) = 0.343s for the tunnel and penstock #1, allows the

gains to be evaluated as Ki= 16.1, Kp= 18.4 and Kd= 2.1.

It is common to include an additional pole in a PID compensator to limit high frequency noise due

to the derivative term. Placing it at

=100 r/s means that it has only a minor effect on the closed

loop dynamics.

The open loop Bode plot for the Plant, compensator and forward loop is shown in Figure 9, which

conforms to the typical pattern for a hydroelectric Plant see [2] and sections F1.4.1 and F.3 in [1].

The crossover frequency is about 3r/s. The effect of the righthalf plane zero on the Plant frequency

response is evident in the range 1/TWto 2/TW(3 to 6 r/s), where the increasing phase lag is not

accompanied by a corresponding fall in gain. This limits how much phase lead can be contributedby the compensator over this frequency range, because the associated increase in gain could make

the forward loop gain start to increase. As pointed out in [2], this could easily cause a second

crossover and closed loop instability.

The root locus (see sections F.1.5 & F.1.6 in [1]) for this case is shown in Figure 10. It is possible,

using proportional gain alone, to place the dominant closedloop poles at approximately the same

locations as with the PID controller. However, the step response has a 10% steadystate error and

it is necessary to introduce the integral term to counter it.

Figure 11 shows the closed loop step response to a 0.02 p.u. step demand in speed. The very large

initial dip in the generators speed is due to the very large and rapid GV motion. In practice, a ratelimiter would be included to moderate this action.

hydlin 01.mdl

Simple linearised model

speed

ref

power --> speed

sys2

droop

0

Sum 1

Sum Speed , power

and GV

Power

ref

Governor

power

speed_err

GV

GV --> power

sys1P

S

GV

GV

1

proportional

Kp

integral

Ki

s

derivative

wl*Kd.s

s+wl

Sum1Sum

speed_err

2

power

1


15/24

11

Figure9OpenloopBodeplotforthePlant,PIDcontrollerandforwardloop.

Figure10Rootlocusfor(i)thePlantwithproportionalgainonly,(ii)withthePIDcontroller(wherethe

diamondsshowthelocationsofthedominantclosedlooppoles).

-100

-50

0

50

100

Mag

nitude(dB)

10-2

100

102

104

-270

-225

-180

-135

-90

-45

0

45

90

Phase

(deg)

Frequency (rad/sec)

Plant

Compensator

Forward loop

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-5

0

5

10Root locus for Plant

Real Axis

Imag

inary

Ax

is

-10 -8 -6 -4 -2 0 2 4 6 8 10-10

-5

0

5

10Root locus for Plant + Governor

Real Axis

Imag

inary

Ax

is


16/24

12

Figure11StepresponseofthelinearisedmodelwiththegovernortunedusingtheHagihararules.

It is concluded that traditional analysis, using the linearised, SISO inelastic model gives a good

firstcut at a control system, sufficient at least to use in further simulation using the more accuratemodels. This approach is likely to be overly optimistic in estimating how much gain can be

included in the controller. In a multipenstock installation, hydraulic coupling can have a significant

adverse effect on stability. A long penstock has a large water starting time, which encourages the

designer to include as much derivative action as possible, in order to improve closed loop

bandwidth. However, this is precisely the case where travelling wave effects are significant and

controller design becomes more critical. It is at least necessary to test the controller on a model

with elastic water column, which may indicate that the PID gains must be reduced to prevent an

underdamped response or even instability. In such cases, it would desirable to take the travelling

wave effect into account during control system design.

6 ClosedloopsimulationwithGridconnection

In this section, three operational scenarios are considered. The simulations are performed using

the distributed parameter model for the hydraulics and the PID governor designed in the previous

section. In all cases, additional dynamics to represent the GV servo lags are included as the transfer

function:

( ) 2.5 5.26

( ) ( 2.5) ( 5.26)G

G s

u s s s= + + (6.1)

0 1 2 3 4 5 6 7 8-0.04

-0.02

0

0.02

0.04

Speed(pu)

PID gains Ki = 16.1, Kp = 18.4, Kd = 2.11

0 1 2 3 4 5 6 7 8-10

-5

0

5

Power(pu)

0 1 2 3 4 5 6 7 8-2

0

2

4

6

Guidevane(pu)

time (s)


17/24

13

6.1 Frequencycontrolmode.

Control of Grid frequency typically involves several regulators, of varying capacity and speed of

response, simultaneously connected to the power system. The role of a hydroelectric station in

frequencycontrol mode is to provide accurate and timely supply of its target power contribution to

the Grid. Stable sharing of the load between all the regulating sources is achieved by including a

speed regulation or droop characteristic in their governors.

The objective is to test the response of the Plant to a simulated speed (frequency) step see section

9.2.9 in [1]. The block diagram for the governor, based on the design in the previous section, is

shown in Figure 12. The block diagram for the complete simulation is shown in Figure 13.

Figure12

Simulink

block

diagram

for

the

governor.

There are two feedback loops:

The electrical power generated by the individual Units is measured by a sensor and filter,

represented by the transfer function 1( 1)s + . The power error (P) is formed as the

difference between a (fixed) reference power and the measured electrical power. This is

fed through a droop gain () to the PI part of the controller.

The frequency error (f) is formed as the difference between the demanded and measuredGrid frequency and also added as an input to the PI part of the controller. The frequencyerror is also fed forward into the GV control signal (u G), via the derivative part of the

controller, in order to reduce system response time.

The GV control is therefore formed as:

( ) ( )G Pu PI PID f = + (6.2)

The sum of the electrical powers from the two generators is used as an input to the Grid model.

PID Governor

control 1

1

prop gain

Kp

power

transducer

1

s

int gain

Ki

droop

droop

Integrator

1

s

FF gain

Kff

D term

wl*Kd.s

s+wl

Pe1

3

power _ref1

2

freq _err

1


18/24

Figure13Simulinkblockdiagramforthecompletesimulation

Hydroelectric plant with PID control system .

Hydraulics represented using the Method of Characteristics .

This simulation is called from hydraul _p3.m.

zero

0

select

p.u. base

1/Pb

index

indval

Terminator 1

Terminator

Power

set #1

Power

ref #2

Pe_2

Power

ref #1

ramp Plant

hydraulics

S_moc _v1

Governor 2

freq_err

power_ref2

Pe2

control2

Governor 1

freq_err

power_ref1

Pe1

control1

Generator #2

mech_power

Grid_freq

elec_power

Generator #1

mech_power

Grid_freq

elec_power

GV dynamics

GVC1

GVC2

G1

G2

Freqdem #2

0

Freq

dem #1

G1

G2

GVC1

GVC 2

Pm

H

Q


19/24

15

The simulation is initialised with Units #1 and #2 supplying 100MW and 288MW respectively. The

test input is a step frequency change of 0.07Hz (0.14 p.u.). The result is shown in Figure 14.

Figure14Responsetoastepdemandof0.07Hzinfrequency-controlmode;droopof1%.

Raising the Grid frequency by 0.07Hz requires an additional 506MW of power of which 42MW is

picked up by Unit #1.

Figure 14 is known as the systems primary response characteristic. For generators on the England

& Wales Grid, a typical specification requires 70 90% of the target power output to be achieved

within 10s of the occurrence of the event leading to the frequency deviation [8]. This system

achieves 36.5MW (87%) of its target contribution in 10s, which is within the specified range.

Developing a more detailed specification (see [9]) and a more accurate simulation will yield an

improved assessment of the systems capability.

0 5 10 15 20 25100

110

120

130

140

Unit#1power(M

W)

Freq. loop PID gains Ki = 16.1, Kp = 18.4, Kd = 2.11

mechanical

electrical

0 5 10 15 20 25280

285

290

295

Unit#2p

ower(MW)

mechanical

electrical

0 5 10 15 20 250

0.5

1

Guidevane(pu)

Unit #1

Unit #2

0 5 10 15 20 25

1

1.05

1.1x 10

-3

Grid stiffness = 0.083 pu

Gridfreq(pu)

time (s)


20/24

16

6.2 Powerdialupmode.

In this mode, the goal is to change the generated power rapidly in response to a dialledin

operator request see section 9.2.4 in [1]. Instead of applying a step reference change directly to

the PID, it is preferable to generate a ramp power reference (whose slope is essentially determined

by the maximum allowable GV opening rate) and to feed this forward directly to the GV control via

a gain Kffas well as to the PID.

In general, the feedforward and PID gains would be optimised for this specific mode of operation

but in this simulation the PID settings are kept at their previous values, with K ff= 1. Unit #1 is

commanded to increase its output from 100MW to 205MW by ramping the GV control to its new

setting in 2.6s. This case is similar to Figure 3 but not identical because of the intervening GV

dynamics (6.1). The results are presented in Figure 15.

Figure15ResponsetoarampGVinputindial-upmode.

The graph shows that the required power change is achieved in 3s although there is an overshoot

of 28 MW (27%) followed by a long decay to the final value. Experiment shows that both overshootand settling time could be improved by reducing the feedforward gain.

0 5 10 15 20 25100

150

200

250

Unit#1power(MW

)

Power ramp PI gains Ki = 16.1, Kp = 18.4. Feedforward Kff = 1

mechanical

electrical

0 5 10 15 20 25270

280

290

300

Unit#2p

ower(MW)

mechanicalelectrical

0 5 10 15 20 250

0.5

1

Guidevane(pu)

Unit #1

Unit #2

0 5 10 15 20 25

1

1.2

1.4

x 10-3 Grid stiffness = 0.083 pu

Gridfreq(pu)

time (s)


21/24

17

6.3 Fullloadrejection.

The objective here is to assess performance when the system is disconnected suddenly from the

Grid, perhaps because of some fault condition (see section 9.2.3 in [1]). When the Grid breaker

trips, the reaction torque on the turbine vanishes and the excess torque causes it to accelerate, with

a risk of overspeeding, unless prompt action is taken to close the GV. However, the rate at which

the GV can be closed is limited by overpressure transients in the penstock.

The block diagram of Figure 16 includes a logic signal that simulates the Grid breaker by

disconnecting the feedback loops for electrical power and Grid frequency from the

turbine/generator block. It also initiates an open loop rampdown of both GV controls at a rate of

1/12 p.u./s.

Figure16Simulinkblockdiagramforsimulatingloadrejection.

In Figure 17, the electrical power reduces instantaneously to zero when the breaker is tripped and

both GVs begin to close at a fixed rate, causing the mechanical power produced by the turbines to

decrease. During the closure interval, Unit #1 peaks at 5% overspeed and Unit #2 at 20% over

speed; the Grid frequency decreases to its nominal value. Figure 19 shows the predicted volumetric

flow and head at the two turbine inlets. The flows decrease more or less in proportion to the GV

opening, as expected. As the closure begins, there is a sharp increase in turbine head which starts a

travellingwave oscillation of identical amplitude in both penstocks, because they are hydraulically

coupled. Once GV #1 is fully closed, the mean level of the oscillation decreases and a further

reduction occurs once GV #2 closes, leaving a longlived oscillation around the static head. Whetheror not the pressure variation is acceptable depends on the structural strength of the installation.

Hydroelectric plant simulation for total load rejection .

Hydraulics represented using the Method of Characteristics .

This simulation is called from hydraul _p3.m.

select

p.u. base

change

1/100

p.u. base

1/Pb

earth

breaker

Terminator 1

Terminator

Plant

hydraulics

S_moc_v1Grid model

rs

Generator #2

mech_power

Grid_freq

breaker

elec_power

Generator #1

mech_power

Grid_freq

breaker

elec_power

GV ref #2

ramp

GV ref #1

ramp

GV dynamics

GVC1

GVC2

G1

G2

GV

set #2

GV

set #1

Pe2

Pe1G1

G2

GVC2

GVC1 PmPelec grid_freqgrid_freq

H

Q

elec_ power

1

sync

torque

wb*Ks

selectinertia

1/(2*H)

earth

damping

coefficient

KD

Integrator 1

1

s

Integrator

1

s

breaker

3

Grid_freq

2

mech_ power

1

sp1


22/24

18

Figure17Fullloadrejection:GVclosureandpoweratbothUnits.

Figure18Fullloadrejection,showingspeedincreaseforbothUnitsanddropinGridfrequency.

0 5 10 15 200

50

100

150

Unit#1power(MW)

mechanical

electrical

0 5 10 15 200

100

200

300

Unit#2power(MW)

mechanical

electrical

0 5 10 15 200

0.2

0.4

0.6

0.8

1

time (s)

Guidevane(pu)

Unit #1

Unit #2

0 5 10 15 200

0.05

0.1

0.15

0.2

Generatorspeed(pu)

Unit #1

Unit #2

0 5 10 15 20-4

-2

0

2

4

6

8

10x 10

-4 Grid stiffness = 0.083 pu

Gridfreq(pu)

time (s)


23/24

19

Figure19Fullloadrejection:pressureandflowinthetwopenstocks.

7 Conclusion

The generic models used here provide a wealth of predictive information early in the project, based

on a small set of critical parameters. Although model validation, by comparison with the real

installation, would usually not be possible at this stage, the methods adhere to industry standards

and are well tried and tested on other Plant. The main points of the study are:

basic prediction of pressure and flow variation in the conduit, which can be used to enhanceruleofthumb calculations and precede detailed hydraulic analysis;

development of lumped and distributed parameter models to predict system performance; development of a basic PID governor; simulation under different operational scenarios:

o in frequencycontrol mode, the primary response characteristic is shown to comply

with specification;

o in power dialup mode, feedforward allows a very rapid change of power level to

be made;

o

during full load rejection, the Unit overspeed is limited to 20% during GV closure.

0 5 10 15 20510

515

520

525

530

535

540

545

Headatturbine(m)

Unit #1

Unit #2

0 5 10 15 200

10

20

30

40

50

60

time (s)

Flowatturbine(m3/s)

Unit #1

Unit #2


24/24

Clearly, predictions made on the basis of simplified models have a margin of error and need to be

treated with caution. Nevertheless, they provide valuable results that can be used to make better

informed decisions on later stages of the project. The generic package reported here is only the

first stage of simulation based design. There is ample scope for extension and refinement of the

models as more details of the installation become available.

References

1 Std 12072004, 'IEEEGuidefortheApplicationofTurbineGoverningSystemsforHydroelectric

Generating

Units', New York, IEEE 2004.2 IEEE, W. G.: 'Hydraulic turbine and turbine control models for system dynamic studies',

IEEETransPowerSystems, 1992, 7,(1), pp. 167179.

3 Larock, B. E., Jeppson, R. W. and Watters, G. Z.: 'Hydraulics of Pipeline Systems', 1999 (CRCPress).

4 Kundur, P.: 'Power System Stability and Control', 1994 (McGraw Hill).

5 Jones, D. I.: 'Dynamic parameters for the National Grid', Proc

IEE

Gener.

Transm.

Distrib.,2005, 152,(1), pp. 5360.

6 Jones, D. I.: 'Multivariable control analysis of a hydraulic turbine', TransInstMC, 1999, 21,

(2/3), pp. 122136.

7 Hagihara, S., Yokota, H., Goda, K., et al.: 'Stability of a hydraulic generating unit controlled by

PID governor', IEEETransonPowerApparatus&Systems, 1979, PAS-98,(6), pp. 2294

2298.8 Erinmez, I. A., Bickers, D. O., Wood, G. F., et al.: 'NGC experience with frequency control in

England and Wales provision of frequency response by generators'. Proc IEEE Power

Engineering Society Winter Meeting, New York. 1999, pp 590596.9 Jones, D. I., Mansoor, S. P., Aris, F. C., et al.: 'A standard method for specifying the response of

hydroelectric plant in frequencycontrol mode', ElectricPowerSystemsResearch, 2004, 68,

(1), pp. 1932.

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Simulation of Hydroelectric System Control