MONITORING AND CONTROL OF HYDRO POWER PLANT

8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT

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MONITORING AND CONTROL OF HYDRO POWER PLANT

Matei Vinatoru

University of Craiova, Faculty of Automation, Computers and Electronics

Str. A. I. Cuza Nr. 13, Craiova, RO 200396

Abstract: In hydro power plants from Romania, there is a major interest for theimplementation of digital systems for monitoring and control replacing the conventional

control systems for power, frequency and voltage. Therefore is necessary to develop

mathematical models capable to accurately describe both dynamic and stationarybehaviour of the hydro units, in order to be able to implement digital control algorithms.

Moreover, it is necessary to implement systems for monitoring and control of hydro

power plants in a cascade system along a river, in order to optimize the use of the river

resources. This paper presents the possibilities of modelling and simulation of the hydro

power plants and performs an analysis of different control structures and algorithms.

Keywords: Hydro power plant, Control system, Digital Control Algorithms.

1. INTRODUCTION

This paper discusses the aspects of modelling and

design of hydro power plants and control of hydro

power groups. There are presented computing

methods for pressure losses on the water intake pipesfrom the reservoir to the turbine, aspects regarding

the energy transformations for different turbine types

(Pelton, Francis, and Kaplan) in order to determinethe net hydraulic power of the plant and to determine

the control options for the turbines.

Also, are presented different control structures for

the power groups and hydro power plants. In this

case, are analyzed different SCADA monitoring and

control systems, for an assemble of hydro power

plants on the same water stream as well as SCADAsystem for high-energy power plants with Kaplan

turbines, and the case studies for the modelling,

design and study of the power groups, with andwithout water towers.

This paper will present several possibilities for the

modelling of the hydraulic systems and the design of

the control system.

2. THE DESIGN OF CONTROL SYSTEMS FORKAPLAN HYDRAULIC TURBINES

2.1.Introduction

Different construction of hydropower systems and

different operating principles of hydraulic turbines

make difficult to develop mathematical models fordynamic regime, in order to design the automatic

control systems. Also, there are major differences in

the structure of these models. Moreover, there aremajor differences due to the storage capacity of the

reservoir and the water supply system from the

reservoir to the turbine (with or without surgechamber). The dynamic model of the plants with

penstock and surge chamber is more complicated

than the run-of-the-river plants, since the water feed

system is a distributed parameters system.

2.2. Modelling of the hydraulic system for run-of-the-river hydropower plants

These types of hydropower plants have a low water

storage capacity in the reservoir; therefore the plant

operation requires a permanent balance between thewater flow through turbines and the river flow in

IFAC Workshop ICPS'07

2007, July 09-11

Cluj-Napoca, Romania

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order to maximize the water level in the reservoir for

a maximum efficiency of water use. Next, we willdetermine the mathematical model for each

component of the hydropower system.

A. Hydraulic turbine. The hydraulic turbine can be

considered as an element without memory since thetime constants of the turbine are less smaller than the

time constants of the reservoir, penstock, and surge

chamber, if exists, which are series connectedelements in the system.

As parameters describing the mass transfer andenergy transfer in the turbine we will consider the

water flow through the turbine Q and the moment M

generated by the turbine and that is transmitted to the

electrical generator. These variables can be

expressed as non-linear functions of the turbinerotational speed N, the turbine gate position Z, and

the net head H of the hydro system.

Q = Q(H, N, Z) (1)

M = M(H, N, Z) (2)

Through linearization of the equations (1) and (2)around the steady state values, we obtain:

zanahaq

ZZ

QN

N

QH

H

QQ

... 131211 ++=

+

+

= (3)

zanaham

ZZ

MN

N

MH

H

MM

... 232221 ++=

+

+

= (4)

where the following notations were used:0Q

Q=q ,

0N

N=n ,

0M

M=m ,

0H

H=h ,

0Z

Z=z which

represent the non-dimensional variations of the

parameters around the steady state values.

B. The hydraulic feed system. The hydraulic feedsystem has a complex geometrical configuration,

consisting of pipes or canals with different shapesand cross-sections. Therefore, the feed system will

be considered as a pipe with a constant cross-section

and the length equal with real length of the studied

system. In order to consider this, it is necessary thatthe real system and the equivalent system to contain

the same water mass. Let consider m1, m2... mn thewater masses in the pipe zones having the lengths l1,

l2,...,lnand cross-sectionsA1, A2,...,Anof the real feed

system. The equivalent system will have the lengthL=l1+l2+...+ln and cross-section A, convenientlychosen. In this case, the mass conservation law in

both systems will lead to the equation:

==

=n

iii

n

ii AllA

11

. (5)

Since the water can be considered incompressible,

the flow Qi through each pipe segment with cross-

section Ai is identical and equal with the flow Qthrough the equivalent pipe

Q=v.A=Qi=vi.Ai for i=1, 2,...,n (6)

Where v is the water speed in the equivalent pipe,

and viis the speed in each segment of the real pipe.From the mass conservation law it results:

QAl

l

Al

lQ

A

Qv

ii

i

ii

ii ...

=== (7)

The dynamic pressure loss can be computedconsidering the inertia force of the water exerted on

the cross-section of the pipe:

dt

dv

g

LAaALamFi .

..... ===

(8)

Where L is the length of the penstock or the feed

canal, A is the cross-section of the penstock, is thespecific gravity of water (1000Kgf/m

3), a is the water

acceleration in the equivalent pipe, and g=9,81 m/s2

is the gravitational acceleration.

The dynamic pressure loss can be expressed as:

dt

dQ

Al

l

g

L

dt

dv

g

L

A

FH

ii

iid

===.

.. (9)

Using non-dimensional variations, from (9) it results:

dt

Q

Qd

Al

lL

H

Q

H

H

ii

i

dd

d

=

0

0

0

0

(10)

Or in non-dimensional form:

dt

dqTh wd = (11)

Where TW is the integration constant of the

hydropower system and the variables have the

following meaning:

===ii

i

d

w

d

dd

Al

lL

H

QT

Q

Qq

H

Hh

0

0

00

,, (12)

It must be noted that this is a simplified method to

compute the hydraulic pressure loss, which can be

used for run-of-the-river hydropower plants, withsmall water head. If an exact value of the dynamic

pressure is required, then the formulas presented in

[8], sub-chapter 8.4 The calculation of hydro energypotential shall be used.

Using the Laplace transform in relation (11), it

results:

hd(s) = - sTw.q(s), and, )(1

)( shsT

sq dw

= (13)

Replacing (13) in (3) and (4) and doing some simple

calculations, we obtain:

)(1

)(1

)(11

13

11

12 szsTa

asn

sTa

asq

ww ++

+= (14)

)(1

)(1

)(11

13

11

12 szsTa

sTasn

sTa

sTash

w

w

w

wd +

+

=

(15)

)(1

)(1

)(11

1323

11

1221 sz

sTa

sTaasn

sTa

sTaasm

w

w

w

w

++

+=

(16)

The mechanical power generated by the turbine can

be calculated with the relation P=..Q.H (see [8]sub-chapter 8.5 Hydraulic turbines), which can be

used to obtain the linearized relations for variations

of these values around the steady state values:

p = .g.Qo.h + .g.Ho.q (17)

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Where is the turbine efficiency, and , Q, and Hwere defined previously.

On the other hand, the mechanical power can be

determined using the relation P=M.=2.M.N,which can be used to obtain the linearized relationsfor variations of these values around the steady state

values:

( )m

P

Np

P

Nn

o

o

o

o222

= (18)

Where P0=M0.0is the steady state power generatedby the turbine for a given steady state flow Q0and a

steady state head H0, and N0 is the steady state

rotational speed.Using these relations, the block diagram of the

hydraulic turbine, for small variation operation

around the steady state point, can be determined andis presented in figure 1, where the transfer functions

for different modules are given by the following

relation:

+=

+=

+=

+=

+=

+=

sTa

sTaasH

sTa

sTaasH

sTa

sTaH

sTa

sTasH

sTa

asH

sTa

asH

w

wmz

w

wmn

w

whz

w

whn

wqz

wqn

11

1323

11

1221

11

13

11

12

11

13

11

12

1)(,

1)(,

1

,1

)(,1

)(,1

)(

(19)

For an ideal turbine, without losses, the coefficients

aij resulted from the partial derivatives in equations(12 - 16) have the following values: a11=0,5;

a12=a13=1; a21=1,5; a23=1. In this case, the transfer

functions in the block diagram are given by thefollowing relation:

sT.,

sTH,

sT.,HH

w

whn

wqzqn

501501

1

+=

+== (20)

+=

+=

sT.,

sT,H,

sT.,

sTH

w

wmn

w

whz

50151

501(21)

sT.,

sT..

sT.,

sT)s(H

w

w

w

wmz

501

501

5011

+

=

+= (46)

2.3. Simulation results

Example. Let consider a hydroelectric power systemwith the following parameters:

-Water flow (turbines): Q(5001000) m3/s, QN=725m3/s;

-Water level in the reservoir: H(1738) m, HN=30m;

-The equivalent cross-section of the penstockA=60m2;

-Nominal power of the turbine

PN=178MW=178.000kW;

-Turbine efficiency =0,94;-Nominal rotational speed of the turbine N=71,43

rot/min;

-The length of the penstock l=li=20m;

It shall be determined the variation of the timeconstant TWfor the hydro power system.

For the nominal regime, using relation (12), where

li=20m, the time constant of the system is:sTw 82,0

6081,9

20

30

725=

= (47)

Next we will study the variation of the time constant

due to the variation of the water flow through theturbine for a constant water level in the reservoir,

H=30m, as well as the variation due to the variable

water level in the reservoir for a constant flowQ=725 m

3/s.

In table I, column 3 and figure 2 a) are presented the

values and the graphical variation of the timeconstant TW for the variation of the water flow

between 500 m3/s and 110 m

3/s, for a constant water

level in the reservoir, H=30m. In table 8.12 column 4

and figure 2 b) are presented the values and thegraphical variation of the time constant TW for the

variation of the water level in the reservoir, for aconstant water flow, Q=725m3/s.

It can be seen from the table or from the graphs that

the time constant changes more than 50% for the

entire operational range of the water flow through theturbine or if the water level in the reservoir varies.

These variations will create huge problems during

the design of the control system for the turbine, androbust control algorithms are recommended.

gQo

gHo

Hqn(s)

Hqz(s)

Hhn(s)

Hhz(s)

Hmn(s)

Hmz(s)

2No/Po

(2No)2/Po

p

np

n

n

n

z

z

z

z

m

h

q

+

Fig. 1. The block diagram of the hydraulic turbine.

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Table I. Variations of the time constant of the hydro

system

H Q Tw(H=30m) Tw(Q=725mc/s

17 1135,46 1,286065 1,449101

20 965,14 1,093155 1,23173623 839,25 0,950569 1,071075

26 742,42 0,8408882 0,947489

29 665,62 0,7538998 0,849473

32 603,21 0,6832217 0,769835

35 551,51 0,6246598 0,703849

38 507,97 0,5753446 0,648282

In figure 3 is presented the block diagram of theturbines power control system, using a secondary

feedback from the rotational speed of the turbine. Itcan be seen from this figure that a dead-zone element

was inserted in series with the rotational speed sensor

in order to eliminate the feedback for 0,5%variation of the rotational speed around thesynchronous value.

The constants of the transfer functions had been

computed for a nominal regime TW=0,8s. Theoptimal parameters for a PI controller are: KR=10,

TI=0,02s. The results of the turbine simulation fordifferent operational regimes are presented in figure

4, for a control system using feedbacks from theturbine power and rotational speed, with a dead-zone

on the rotational speed channel for 0,5% variation

of the rotational speed around the synchronous value(a) Power variation with 10% around nominal value,

b) Rotational speed variation for power control).

Figure 3. Block Diagram of the control system for hydraulic turbines

np

0.0389

0.0016

s4,01

1

+

0.0025

1.1305

p

n

n

n

z

z

z

z

m

h

q

+

s4,01

1

+

s

s

4,01

8,0

+

s

s

4,01

2,05,1

+

s

s

4,01

8,01

+

s

s

4,01

8,0

+

+

sTK

IR

11

--

+

P*

0,6

0,7

0,8

0,9

1

1,1

1,2

1,3

1,4

1,5

15 20 25 30 35 40

[s]

[m]

H

Tw

b)

0,5

0,6

0,7

0,8

0,9

1

1,1

1,2

1,3

1,4

500 600 700 800 900 1000 1100 1200

Tw

Q

[s]

[mc/s]a)

Figure 2 Variation of the integral time constant TW: a) by the flow Q, b) by the water level H

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Fig. 4. Turbine Control simulations with feedbacksfrom turbine power and rotational speed

Fig. 5 Control structure with only power feedback,

a) Power variation with 10% around nominal value,

b) Rotational speed variation for power control

In figure 5 are presented the variations of the turbine

power (graph a) and rotational speed (graph b) forthe control system using a feedback from the turbine

power but no feedback from the rotational speed .

This oscillation has no significant influence on the

performance of the system but would have lead topermanent perturbation of the command sent to theturbine gate.

2.4. Conclusions

The possibility of implementation of digital systems

for monitoring and control for power, frequency andvoltage in the cascade hydro power plant was

discussed. The simplified mathematical models,

capable to accurately describe dynamic andstationary behaviour of the hydro units have been

developed and simulated. These aspects are

compared with experimental results. Finally, a

practical example was used to illustrate the design ofcontroller and to study the system stability.

3. IMPLEMENTATION OF DIGITAL SYSTEMS

FOR MONITORING AND CONTROL IN

CASCADE POWER PLANTS

3.1. Introduction

A series of hydro power plant systems in Romania

are capturing the river water in a geographical area

and store it in reservoirs connected through transport

pipes. Every lake has its own hydro power plant and

the water used through the turbines of one plant issent to the next reservoir, thus using the entire

hydraulic potential offered by the geographical area.A similar hydro power system is built in the north-

west part of Oltenia region, in the south-west part of

Romania. The hydraulic profile of this cascadesystem is presented in figure 6.

As it can be seen in this figure, there are two hydropower plants, CH1 and CH2, with reservoirs and

surge tanks and one run-of-the-river power plant, CH

3, with a reservoir providing only a net head.

In this type of hydropower systems, provided with

small power units connected to the grid, the dynamicof the hydraulic system has a great importance in thestability of the system. The dynamics of the turbine

and electric generator have a very small influence

since the power grid has a great influence and willmaintain the generator rotational speed at a value

synchronized with the electrical frequency of the grid

and the generated power is dependent of the existingunbalance. Therefore, this paper will try to study the

stability of the hydraulic system of the hydropower

system and the achievement of a maximum

efficiency of the water usage in the system.

0 0.5 1 1.5 2 2.5 3-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5 3-2

-1

0

1

2

3

4

5

P[%]

a)

b)

t [s]

t [s]

0 0.5 1 1.5 2 2.5 3-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

P[%]

0 0.5 1 1.5 2 2.5 3-4

-2

0

2

4

6

8

10

12

t [s]

t [s]

a)

b)

n[%]

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3.2. The design of control systems for hydro power

plants with reservoir and surge tank.

Different construction of hydropower systems and

different operating principles of hydraulic turbinesmake difficult to develop mathematical models for

dynamic regime, in order to design the automaticcontrol systems [1,2,5,6]. Also, there are major

differences in the structure of these models.

Moreover, there are major differences due to thestorage capacity of the reservoir and the water supply

system from the reservoir to the turbine (with orwithout surge tank). The dynamic model of the

plants with penstock and surge tank is more

complicated than the run-of-the-river plants, sincethe water feed system is a distributed parameters

system. This paper presents a solution for the

modelling of the hydraulic systems and the design ofthe control system.

As it is know, the hydraulic power available at theturbine is a function of the water flow trough the

turbine Qtand the net head Hn.

Ph= QtHn (25)

In the long run operation of the hydro power plants

with reservoir and surge tank, it results from the

relation (25) that the power generated by the turbine

is maximum when the head Hn is maintained at

maximum value, for variations of the river flow dueto meteorological conditions. In this case, the power

generated by the turbine will be only a function of

the water flow trough the turbine. In this case, thecontroller is controlling the flow Qt in order to

maintain constant the water level in the reservoir,

thus the main feedback will be from the reservoirswater level sensors.

There are cases when the hydro power plants with

high capacity reservoirs are used as peak load plants.In these cases, the power dispatcher will impose the

plant generating power and the plant dispatcher or

the automatic control system will distribute therequired load over the operational power units and

the water level in the reservoir can vary between the

admissible maximum and minimum limits with anadmissible rate of variation. The set-point for the

water level controller is generated by the monitoring

system, has a certain variation profile and is a

function of the required power:

t

nn

Q

PH

** = (26)

In figure 7 is presented the simplified hydraulicdiagram of a hydropower plant with reservoir and

surge tank. Using this structure, a case study is

presented, regarding the modelling, simulation and

the stability of the of the control structure.

3.2.1 Mathematical modelling of the control system

This control system is opening and closing thecontrol gates for the turbines in order to assure an

optimal operation and in the same time to maintain a

constant water level in the reservoir. In a similarmode, a control system may be used for two plants in

a cascade system to maintain the water flows

between the plants.

In order to design the control system, there is

necessary to obtain a mathematical model of theplant, which contains the water tunnel between the

reservoir and the surge tank, the surge tank itself, the

penstock and the hydraulic turbine[4,5,6]. We willanalyze every component of the plant in order to

determine the model, using the energy balance

equations and the continuity equations for the waterflows, in dynamic regime.

For the hydropower plant we will consider the

simplified diagram in figure 7.

a) The continuity equation for the water in thereservoir

wtrB

L QQQdt

dHA = (27)

Where: -ALis the area of the horizontal surface of theequivalent reservoir considered as having a constant

depth HL. HL.AL=Vreal, Qris the water flow entering

the reservoir, QW is the discharging water flow(through the emptying channel or overspill).

b) The energy balance equation for the water tunnelbetween the reservoir and the surge tank:

Surge Tank

Penstok Generator

Water tunnel

Overspill

Figure 7. Simplified model of the hydropower plant

Turbine

ControllerHn

*

Level

transducer

t

Echivalent

reservoir

HBHC

Qcf

QB

Lt

Qe

Qr

c

TurbineGate

HL

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cHBHcQcQCctQtQtCdt

tdQ

gA

L

t

t =++ (28)

Where: -Lt is the length of the tunnel between thereservoir and the surge tank, At is the cross-section

of the tunnel, Qtis the water flow in the tunnel, Qcisthe water flow entering the surge tank, HB is the

water height in the reservoir, HCis the water heightin the surge tank,

dt

dv

g

L

dt

AQd

g

L

dt

dQ

gA

L tttttt

t

t ==)/(

is the

inertial force of the water mass in the tunnelexpressed in hydrostatic units (meters of water

column), Ct/Qt/Qt is the hydraulic pressure loss due

to friction with the tunnel walls; the flow Qt is

considered positive if the water flows from the

reservoir to the surge tank and the loss coefficient Ctwill be positive in this case, Ct/Qc/Qcis the hydraulic

pressure loss due to the cross-section reduction at the

entrance in the surge tank installed to avoid thepressure shocks, -HB-HC is the driving force that

moves the water in the tunnel and the surge tank.

c) The continuity equation for the surge tank

cftcc QQQdt

dHcA == (29)

Where: ACis the cross-section of the surge tank, QC

is the water flow at the entrance of the surge tank

(we assume that there is no water flow through thetop of the surge tank), Qcfis the water flow through

the penstock.

d) The energy balance equation for the penstock and

the turbine

Considering the low water volume existing in thesetwo elements we can neglect the water mass

accumulation (water is considered incompressible).

Therefore, from the energy balance equation, thebehaviour of the penstock and the turbine can be

described by the water flow computed from the

following relation:

o

ccccov

H

QQCHQxQ

+= , (30)

Where: H0is the water level in the surge tank when

the gate is completely open, Q0is the water flow for

a completely open gate and -0 x 1 is the openingfactor for the gate.

We choose this form of the expression in order to usenon-dimensional values for the gate opening and to

avoid some very complex equations describing the

water flow through the gate. Therefore are necessarysome experiments to measure the values of H0 and

Q0. The gate is open completely and the flow Q0 in

steady conditions is measured. After the flow

stabilizes, the water height in the surge tank, H0, ismeasured. It must be mentioned that in steady state

conditions (HL=constant, HC=constant,

Qcf=constant), the water flow into the surge tank

QC=0.

e) The equation of the controller

The control system structure for the water level in thereservoir is presented in figure 7. It is recommended

to use a PI controller if the gate servomotor is a

system with its own position controller (proportionalactuator) or a PD controller if the actuator is of the

integrating type (without its own position controller).In our case we will use a PI controller.

In this control system, the water level in the reservoiris compared with a set-point determined by the

operational conditions. If the level is different than

the set-point, the error is processed by the turbine

controller which will open or close the gates in orderto maintain the water level at the prescribed value.

The equation of the PI controller can be written in

differential form:

dt

HHdKHH

T

K

dt

dx reffRreff

i

R)(

)(

+= (31)

Where: Hrefis the set-point level, Hfis the water level

in the reservoir, KR, T iare the proportional constantand the integral constant of the PI controller.

This equation is not considering some factors suchas: delays due to the servomotor and the controller,

and minimum and maximum variation rates for the

gates.

3.2.2 Stability analysis

The equations (27)-(31), which describe the dynamic

behaviour of the control system for the hydropower

unit, are strongly non-linear. Moreover, some

parameters such as loss coefficients Ct and Cc canchange due to different flow regimes and due to

building parameters of the feeding system. Thereforeis necessary to study the system stability in theoperation point (small stability in Lyapunov way)

and to determine the stability domain in the

operational parameters plane.

a) Small stability of the control system

Equations (27)-(31) will be linearized around the

operation point. For simplicity, it is preferable to usenon-dimensional variables as follows: qt is the

relative variation of the flow through the penstock, hB

is the relative variation of the water level in thereservoir, hcis the relative variation of the water level

in the surge tank, is the relative variation of thecontroller output and qris the relative variation of theriver flow around the steady state value for constant

water level (Qr0=Qt0).

0

0

0

0

0

0

0

0

0

0

r

rrr

c

ccc

B

BBB

t

ttt

Q

QQq;

x

xx;

H

HHh

;H

HHh;

Q

QQq

=

=

=

=

=

(32)

We will introduce the following supplementary

reference parameters,0

200 ;

c

tt

ref

i

H

QCp

H

Tx== ,

where characterize the statism of the integral

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controller (the slope of the controller output for a

step variation of the error) and p characterize the

ratio between the losses on the feeding pipes and thehydraulic pressure at the base of the surge tank.

In steady state regime, HB=const., Hc=const.,

Qt0=Qcf=const. and from equations (27)-(31) itresults that:

02000 )1( cttcrefB HpCHHH Q +=+==

0

0

0

00

c

t

H

H

Q

Qx = .

According with the previous relations and

considering that the spillover flow is zero (QB=0),following linearization of equations (27)-(31), the

linear state equations, expressed with non-

dimensional variables defined in (32), can be writtenas:

-from (27) it results:

rtB

t

refLqq

dt

dh

Q

HA+=

0 (33)

-from (28) it results:

cBc

refc

c

cc

tc

ttt

ct

tt

hhH

Hq

H

C

qH

C

dt

dq

HgA

LQ

Q

Q

=+

++

00

20

0

20

0

0

2

2

(34)

It can be considered that the level control system

works with a zero steady state error, HB0=Href and

Qc0=0 and from equation (28), written for steadystate, it results:

110

20

0

00020

+=+=

==

pH

C

H

Hor

HHHHC

c

tt

c

ref

crefcBtt

Q

Q

In this case, equation (34) becomes:

cBtt

ct

tt hhpqpdt

dq

HgA

LQ++= )1(2

0

0 (35)

From the linearization of equation (29) it results:

00

0

t

cft

c

t

cc

Q

Qq

dt

dh

Q

HA = (36)

Where the variation of the water flow through the

penstock Qcfcan be obtain from the linearization ofthe equation (30) around the steady state values:

ct

t

ccc

cf

hQ

Q

hH

HQx

H

HQxQ

+=

=+=

2

2

00

0

000

0

000

In this case, equation (29) becomes:

= ctc

t

cc

hqdt

dh

Q

HA

2

1

0

0

(37)

The equation system (33 -37) can be expressed in

canonical matrix-vectorial form:

BuAxdt

dx+= or BuAxx +=

Where the following notations were used:

00

0

0

0 ,,t

LrefL

t

ccc

ts

ttt

Q

AHT

Q

AHT

AHg

QLT

=

=

=

.

And

=

c

B

t

h

h

q

x ;

=

1

10

LTB ;

+

=

cc

f

www

TT

T

TT

p

T

p

2

10

1

001

112

A ; [ ]rq0=u .

(39)

The block diagram of the installation is presented in

figure 8.

For the controller, from (7) and noting:

HH

HHh

ref

refrefr

0

0= ,

0

0

xT

HKK

i

refRI= , (integral

constant of the controller

rationalized),0

0

x

HKK

refRP= , the proportional

constant (rationalized) and e(t)=(hr-hBT), we obtain:

dt

tdeKteK

dt

dPI

)()( +=

(40)

Adding equations (33), (35), and (37) and using thenotations from (14), we obtain the complete equation

system for the controller in figure 7:

HR(s) HIT(s)

Hp(s)

hB* hB(s)(s)e(s)

qr(s)

qt(s)

-

+

+-

Figure 8. The block diagram of level controller

Notes: HR(s)-controller transfer function;

HIT(s)-the transfer function on the direct channel

HP(s)-transfer function on the perturbation channel

-51-


9/12

rL

tL

B qT

qTdt

dh+=

11 (41)

ct

Bt

tt

t hT

hT

pq

T

p

dt

dq

++=

112 (42)

=c

cc

tc

c

Th

Tq

Tdt

dh 1

2

11 (43)

Using Laplace transform, for zero initial conditions,from equations (40) to (43) it results:

)s(hsT

)s(hsT

p)s(q

sT

p)s(q

);s(qsT

)s(qsT

)s(h

ct

Bt

tt

t

rL

tL

B

++=

+=

112

11

(44)

)s(eK)s(es

K)s(

)s(sT

)s(hsT

)s(qsT

)s(h

PI

cc

ct

cc

+=

=1

2

11

(46)

These equations can be processed to obtain the

transfer functions on the direct channel and on the

perturbation channel. From (45), the flow qt can beexpressed as:

)(2

1)(

2

)1()( sh

psTsh

psT

psq c

tB

tt +

++

= (48)

This will be used in equation (46):

)s()s(h)s(h

psT

)s(hpsT

)p()s(hsT

cc

t

Bt

cc

+

+

+=

2

1

2

1

2

1

(49)

And the variation of the water level in the surge tank

can be determined as:

)s()p(s)TpT(sTT

psT

)s(h)p(s)TpT(sTT

)p()s(h

tctc

t

B

tctc

c

++++

+

++++

+=

1242

2

1242

1

2

2

(50)

Let note Hn(s)=2TcTts+(4pTc+Tt)s+2(p+1) to

simplify the calculations and let use (50) in (48) todetermine the water flow through the penstock,

which is equal with the flow through turbine.

1242:where

1

2

1

2 ++++=

++

+=

ps)TpT(sTT)s(H

),s()s(H

)s(h)s(H

)s(H

psT

)p()s(q

tctcm

nB

n

m

tt

(51)

And after simple processing from (51) and (44) it

results:

( ))(

)(

)(2)(

)(

2)( sq

sP

sHpsTs

sP

psTsh r

nttB

++

+=

(52)Where the characteristic polynomial of the open-loop

system is:

( )

[ ][ ] )pp(sT)p()TT)(p(p

sTT)p(TT)p(TTp

sTpTTTsTT)s(P

tcL

tctLLc

tctLtcL T

132114

121228

82

2

22

342

++++++++

+++++

+++=

(53)

From (52), the two transfer functions in the block

diagram of the control system presented in figure 2can be calculated:

)(

2)(

sP

psTsH tIT

+= and

( ))(

)(2)(

sP

sHpsTsH ntP

+=

(54)

From (47), using the Laplace transform, we get:

)()()( shs

sKK

shs

sKK

s BTRI

rRI

+

+

= (55)

Replacing (55) in (52), after several simpletransforms, it results:

)s(q)sKK)(psT()s(Ps

)s(H)psT(s

)s(h)sKK)(psT()s(Ps

)sKK)(psT()s(h

rRIt

nt

rRIt

RItB

+++

++

++++

++=

2

2

2

2

(56)

Where the characteristic polynomial of the closed-

loop system is:

( )

[ ][ ]

IRIt

RttcL

tctLLc

tctL

tcLRIt

pKs)pppKKT(

sKTT)p()TT)(p(p

sTT)p(TT)p(TTp

sTpTTT

sTT)sKK)(psT()s(Ps)s(L T

21322

114

121228

8

22

2

2

32

4

52

++++++

+++++++

++++++

+++

+=+++=

For an exact analysis of the hydropower unit

dynamic behaviour it can be considered the exampleof a hydropower plant with reservoir and surge tank

having a low installed power but a high storage

capacity in the reservoir.

Experiment. It is considered a hydropower systemwith the following parameters:

The water volume in the reservoir VL=4,8.106m3;

-The equivalent depth of the reservoir (considered

constant) HL=60m; The equivalent reservoir surface

area is AL4,8.106/60=8.10

4m

2; The length of the pipe

between the reservoir and the surge tank Lt=9650m,

the diameter of the pipe Dt=3,6m and the cross-

section At=10m2; The surge tank has a diameter

Dc=5,4m with a cross-section Ac=23m2; The gross

nominal head HB=260m, HBmax=266m, HBmin=245m;

The gross nominal head at the surge tank Hc0=230m;

The nominal flow through the penstock Qt0=36m3

/s;The length of the penstock Lcf=205m.

-52-


10/12

Using the previous data, the time constants andequations coefficients can be determined using

relation (14):

s..

T

;.

T;,

T

L

ct

5106

36

80000260

15036

2323415

10230819

369560

==

===

=

02303636

230130

130230

230260

20

0

0

0

0

2

,.

.,pHC

;,H

HH

H

Cp

Q

Q

t

ct

c

cref

c

tt

==

=

=

==

(56)

342230

36

0

0

0

00

0

00000 ,

cH

tQ

H

Qx;

H

cHQxtQvQ =====

The steady state value for the controller output x0is

determined using the maximum flow through the

penstock Qvmax=56m3/s and is obtained for x0=1:

73640

3742iar640

56

36

0

00 ,

,

,;,x

H

Q====

Replacing these values in equations (48) and (50),we obtain the operational expressions for the flow q t

and the level in the surge tank:

)s(h

s

,)s(h

s

.)s(q

)s(qs

.,)s(q

s

.,)s(h

cBt

rtB

158

921

158

354

10166010166055

+

+

=

+=

(57)

)s(ss

)s(,

)s(hss

,)s(h Bc

++

+

++

=

1411991

158260

1411991

50

2

2 (58)

( )

[ ][ ]

IRIt

RttcL

tctLLc

tctLtcL

RIt

pKs)pppKKT(

sKTT)p()TT)(p(p

sTT)p(TT)p(TTp

sTpTTTsTT

)sKK)(psT()s(Ps)s(L

T

21322

114

121228

82

2

2

2

32

452

++++++

+++++++

++++++

+++=

=+++=

L(s) = 405.108. s

5 + 153.10

7.s

4 + 348,53.10

5.s

3 +

(35,27.104 +15.KR).s

2 + (15.KI+0,26.KR+4238).s +

0,26.KI (59)

Using the stability criteria Routh-Hurwitz for the

characteristic polynomial (59) we obtain a series of

inequalities for the tuning parameters Ki and KR asfollows:

-from the block diagram of the control system

presented in figure 8, it can be seen that the transfercoefficient on the direct channel is negative,

therefore the controller shall have inverse output and

therefore KR0 it results that the

integral parameter shall be positive;-from the Hurwitz determinant of second order

results:

a0. a

1 = 0,26 K

I .( 15 K

I + 0,26 K

R + 4238) > 0

1630069,57 +


11/12

This diagram was preferred for simulation since itallows highlighting the variation of some specific

parameters of the system, such as the level in the

surge tank and the flow variation in the penstock Q t.

The simulation results are represented in the figures10 and 11.

In figure 10 is presented the system output for a 10%

variation of the set-point for the reservoir waterlevel, with no limitation on the flow control channel.

Oscillations of the flow can be observed, due to the

big differences between the time constants in thesimulation scheme.

To avoid these flow oscillations, the variation of theflow control output is limited in order to avoid big

differences between the subsequent commands sent

to the gate. The simulation results are presented in

figure 11.

3.3. Conclusions

Specifically, a hydropower plant may be composed

of several turbine-generator units, referred to in this

paper as groups. Each hydropower plant must becontrolled by a local SCADA system that will be

connected at the Central SCADA system, which

performs the control of the plants from the hydro-

valley, for optimal generation scheduling and controlfor the reservoir stream-flows.

4. MONITORING SYSTEM FOR CASCADEHYDRO POWER PLANTS.

The optimal generation scheduling is an important

daily activity for hydroelectric power generationcompanies. The goals are to determine which

hydropower groups are to be used in order to

generate enough power to satisfy demand

requirements, with various technological constraintsand with minimum operating cost. In the same time

hydropower systems must consider the stream-flow

equations for reservoirs that couple all reservoirsalong a hydro-valley, because the amount of outflow

water released by one of hydropower plant affects

water volumes in all the plants downstream.Furthermore, other conditions must be imposed as:

water travel times, alternative uses (irrigation, flood

control, navigation). To solve the optimal scheduling

of hydropower plants, a highly sophisticatedmodelling for the operation is required.

In the figure 12 is presented the SCADA systemarchitecture for monitoring and control of hydro

power plants in a cascade system along a river,

implemented in order to optimize the use of the riverresources [7]. This structure is implemented at the

central dispatcher. At the level of hydro power plant

there is a local monitoring and control system,

interconnected with central dispatcher via modemsand radio communication buses.

0 2000 4000 6000 8000 10000-2.5

-2

-1.5

-1

-0.5

0

0. 5

1

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0- 0 . 0 2

0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8

0 .1

0 . 1 2

0 . 1 4

t [s]

hB[%]

Figure 10. The response of the control system for a 10% variation of the set-point

t [s]

qt [%]

0 2000 4000 6000 8000 10000-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Figure 11. The response of the control system with flow limitation

0 2000 4000 6000 8000 10000

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

tt

hB[%] qt

-54-


12/12

The monitoring system presented above is

performing the following functions:

-Data acquisition from the local monitoring systemsinstalled in each power plant, using routers

connected to telephone lines or radio

communications; the data is sent tot the SCADA

server for processing, monitoring and optimization;

-The optimal load distribution between theoperational units in the power plants, depending of

the available water flow, in order to ensure an

efficient usage of the water for the required systempower;

-Monitoring of the water levels in the reservoirs and

water flow control in order to maintain the maximumwater level in the reservoirs;

-In the case of extreme rain conditions, control the

water flows in order to avoid flooding of the areasneighbouring the plants.

5. CONCLUSIONS

The possibility of implementation of digital systemsfor monitoring and control for power, frequency and

voltage in the cascade hydro power plant was

discussed. The simplified mathematical models,

capable to accurately describe dynamic and

stationary behaviour of the hydro units weredeveloped and simulated and these results were

compared with the experimental results. Finally, a

practical example was used to illustrate the design ofcontroller and to study the system stability.

REFERENCES

[1] G., D Ferrari-Trecate, Mignone, D. Castagnoli, M.Morari, Hybrid Modeling and Control of a

Hydroelectric Power Plant, CH 0802, Institut furAutomatik, ETH- Zurich, (2003).

[2] C. Henderson, Yue Yang Power Station TheImplementation of the Distributed Control System,GEC Alsthom Technical Review, Nr. 10, 1992.

[3] G. I. Krivchenko, Hydraulic machines: Turbine andPumps,2nd ed. ISBN 1-56670-001-9, CRC Press,London (1994).

[4] M. Vntoru, E. Iancu, C. Vntoru, Control,Monitoring and Protection of the Turbine andGenerator System, International Symposium on SystemTheory, Robotics, Computers and Process Informatics,

SINTES 9, Craiova , (1998).

[5] O. F. Jimenez, M. H. Chaudhry Water level Control in

Hydropower Plants, Journal of Energy Engineering,Vol118, No. 3 Dec. 1992.

[6] H. Weber, V. Fustik, F. Prillwitz, A. Iliev, Practically

oriented simulation model for the Hydro Power Plant

Vrutok in Macedonia, Balkan Power Conference, 19.

21.06.2002, Belgrade

[7] I.C.E Felix -Bucharest S.A, Arhitectura sistemului decontrol supervizor i achiziie de date (SCADA) alcascadei de hidrocentrale de pe Oltul Mijlociu, http://www.felix.ro/apl.html.

[8] M. Vinatoru, Conducerea automata a proceselor

industriale, vol. II, Editura Universitaria Craiova, 2005.

To CHE

System

ER

RadioEngineering

Pules Message NMEA

Sincron

mGPS

Local Sincron

Server

Ethernet Switch

Pulse Message NMEA

Operator 1 Operator 2

EngineeringServer

SCADA 1

Server

SCADA 2

Hist. Date

Server

Ethernet Bus

Ethernet Switch

Simulator CHE

Router

Asyncron 2

Router

Asyncron 1

- - - - - -Modem 10 Modem 1

Ethernet Bus

Sever Radio

comunication

Fig. 12. SCADA system architecture - Dispatcher

Hydro power plants

Wall Display (4 modules)

-55-

Documents

MONITORING AND CONTROL OF HYDRO POWER PLANT