MONITORING AND CONTROL OF HYDRO POWER PLANT
-
Upload
joao-pedro-reis-lopes -
Category
Documents
-
view
220 -
download
1
Transcript of MONITORING AND CONTROL OF HYDRO POWER PLANT
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
1/12
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
-44-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
2/12
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)
-45-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
3/12
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.
-46-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
4/12
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
-47-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
5/12
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[%]
-48-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
6/12
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
-49-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
7/12
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
-50-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
8/12
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-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
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-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
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 +
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
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-
-
8/11/2019 MONITORING AND CONTROL OF HYDRO POWER PLANT
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-