Design Method for Hydraulic Turbine Governors via Disturbance Attenuation Approach

Copyright @ IFAC Power Plants and Power Systems Control, Brussels. Belgium, 2000

DESIGN METHOD FOR HYDRAULIC TURBINE GOVERNORS VIA DISTURBANCE ATTENUATION APPROACH

LIU Yongqian*, TONG Songlin**, YE Luqing*··

.: PhD student, Huazhong Univ. o/Sc. & Tech, China; Univ. OfNancy 1, France. Dept. 0/ Hydropower & Automation Engineering, Huazhong Univ. o/Sc. & Tech, Wuhan 430074, China. E-mail: /iuyq@pub/ic2.zz.ha.cn ••: Dept. Of Mathematics, Northwest University, China •••: Huazhong Univ. o/Sc. & Tech., Wuhan, 430074 China;

Abstract: Based on the Disturbance Attenuation Approach of H.o theory, a new method to design hydraulic turbine governors is proposed. The designed system is robustly stable and the disturbance acting on the system can be effectively attenuated. This method can be applied to both linear and nonlinear systems. Copyright ~ 2000 IFAC Keywords: Hydraulic turbines, regulators, H-infinity control, disturbance attenuation approach, algorithms, nonlinear systems, hydrogenerators.

stability and dynamic performance of the turbine governing system become more and more difficult to manage. So it is still a useful topic to study the algorithm with robust stability, and good dynamic performance for hydraulic turbine governors.

1. INTRODUCTION In an electric power system, large hydraulic turbine generating sets usually run as the main sources for regulating the active power generation and controlling the system frequency, because of their fast and economical load regulation characteristics. The hydraulic turbine governors are the kernel devices to realise these functions.

In the past decade, H.o theory has gained much development (Doyle, et al., 1989; Francis, 1987), but there are very few practical design applications based on this theory. In this paper, based on the Disturbance Attenuation Approach (DAA) of H.o theory (Isidori and Astolfi, 1992), we propose a new way to design hydraulic turbine governors. This method has the following advantages:

As the rapid development of electronics and computer technology, microcomputer-based hydraulic turbine governors are widely used(Li, et al.,1992; Ye and Maurin, 1983; Ye, 1984; Ye, et al., 1990). Generally, they are composed of two parts: the microcomputer-based controller and the hydraulic servomechanism. Comparing with the traditional governors, the modern hydraulic governors can have much more functions because the microcomputerbased controller can realise various control algorithms. Many new algorithms, such as Adaptive Algorithm(Li, et al.,1992; Ye and Maurin, 1983; Ye, 1984; Ye, et al., 1990), Neural Network, Genetic Algorithm, Fuzzy Logic(Jin et al.,1998), have been introduced in this field in recent years, but the most popular algorithms actually being used today are still the PID and PID-based algorithms. Nowadays the capacity of the power systems and the unit output of the turbine grow larger and larger, consequently the

It can be used as a standard approach for a hydraulic turbine governor system design and is suitable for both linear and nonlinear hydraulic turbine models.

The designed systems are robustly stable. The disturbances on effectively attenuated.

the

systems

can

be

However, the price paid for this strong robustness of the designed governor is the conservativeness on the performance of the system. Fortunately, this shortcoming is minor and can be practically neglected when "small disturbance" occurs; in hydroelectric engineering a load disturbance is called "small" ifit is less than 5% of the rated load, which is the usual case for discussing the performance of the turbine governing system. 297

Xc

+... /"\ ... \... • ./

r

~ MicrocomputerBased Controller

U .../"\ \, ,./

+

...

..

......

y

Hydraulic Servo11echanism

-

......

Water system, Generating Sets, Power Network

X

r-+

Fig. 1. The schematic diagram of the turbme govemmg system

rn g

+ u

1

X

Tas

+

h

y

e

k Fig. 2. The structural diagram of the controlled system To apply this method, we establish a practical model of a hydraulic turbine governing system in Section 2. In Section 3, we transfonn the model into the standard fonn of DAA and propose a DAA-Based design method for hydraulic turbine governor. In order to test the effectiveness of this method, a practical hydraulic turbine governor is designed by this method and simulation result is presented in Section 5 is our conclusions and Section 4. prospective.

Ta: the inertia time constant of the hydraulic generation sets, Ty : the inertia time constant of the hydraulic servo, Tw : the inertia time constant of the water flow in the hydraulic power system, y: the relative value of the displacement of the hydraulic servo, h: the relative value of the change of water level, x: the relative value of the change of turbine running speed, and eql> eqy, eqx , ey, eh: the transfonnation factors of water turbine.

2. MODEL OF HYDRAULIC TURBINE GOVERNING SYSTE11S

By selecting y, h, and x as the state variables, Le., XI f, we can express the sate variable equations of the system as

The modem hydraulic turbine governing system can be divided into three parts: microcomputer-based controller, hydraulic servomechanism, and the process to be controlled (including water system, hydraulic turbine generating sets, and power network). Fig. 1 shows the schematic diagram of the system.

= [y h x

XI

= AIX1 + B1u + Crng

(I)

where the control input u and the disturbance input mg are scalars. The elements of matrix A I and vectors Eh Care

For the computer-based controller, the other two parts can be regarded as the system to be controlled. Fig. 2 depicts the structural diagram of this controlled system with an auxiliary hydraulic servo. In this model we further assume that the time constants of the guiding valve and the auxiliary servo can be neglected, and the water hammer in the system is rigid. The physical meaning of the parameters used in Fig. 2 are defmed in the following: b;.: the local feedback factor of the auxiliary servo, en: the comprehensive self-balance factor of the hydraulic generation sets, 298

b =_1_ b =_ I bT' 2 J. Y

e qy b 0 bT' 3= eqh J. y

3.2. DAA-Based Control A19orithmjor Hydraulic Turbine Governors

1 T

c =-3

In the real world, to minimise both the control energy

a

consumption and the state errors we have to chose the controlled output Z (in another word, penalty) as a vector Z(X, v) = [X v( Therefore, the Hamilton Functional of the system described in equation (6) can have the fonn H(X,P, v, w) = pT (AzX + B2v+Cw)

In general, the load disturbance mg involves two

parts, Le., m g

= m gO + w. The tenn

mgO

represents

the step change part of the load disturbance and

WE

L] (Francis 1987) is the oscillation part.

(7)

+x T X +v 2 3

where PE R (Doyle, et al., 1989;Isidori and Astolfi, 1992). According to the well-developed DAA, the saddle of Hamilton Functional should be at

3. DAA-BASED DESIGN METHOD FOR THE HYDRAULIC TURBINE GOVERNORS

A design method for the hydraulic turbine governors via DAA (Isidori and Astolfi, 1992) is presented in this section. The attention will be concentrated on the procedures of applying DAA to the design of a hydraulic turbine governor.

W

u=--y+-v bl bl

(X,P)

where P

2 -

a 21

_\a

ll

bl

an a32

a31

a:1

= xTWX

= Vx =-dV = 2WX dX v = -BJWX

(3)

(9)

then (10)

a1_1 y+-v 1 u =__ bl

=

b2

bl

-~Y b -

or in a more concise fonn

0

u =U·(X1,W)

I

=-[(~ b

and Co = Cm go '

(11)

![BTW(X - X 10 )] b 2 I

B, = b l

a33

(8)

Using equations (2) and (5), the DAA control algorithm for the system described in equation (1) is given by

1 A _[

P

H(X,P, v·, w·)(y) ~ 0

where

0

T

2y

VeX)

(2)

= A 2 X I + B 2 v+CO +Cw

1

= - 2 B2

where W is a symmetrically positive defmed matrix. If we select matrix W to satisfy

After substituting equation (2) into equation (1), we have

XI

•

As usual, the Lyapunov functional should be chosen as

Before applying the DAA to a system, we have to transfonn a given system model into the standard fonn defined in DAA. By doing so, we introduce a new input v and express u in tenns of it,

1

= _~BT 2 2P

v·(X , P)

3.1. Model Developmentjor a Hydraulic Turbine Governing System

all

_y2 w 2

I

(12)

0

l

In order to control the frequency of the electricity at a

1 bl

high precision, the relative value of the nmning speed deviation x should be zero when the system reaches its steady states. That is to say, the steady states of the system should satisfy

A2 X I0

=-Co

The above developed control law has the following properties: (1) The closed loop system for system (1) becomes

(4)

To remove the steady state values from the state vector we define

X = XI -X IO '

XI

(5)

= [AI

-BI(~ bl

then the perturbed model of equation (3) can be represented by

X = A2 X + B2 v+Cw

T

+-B2 WXIO

0

oJ

- -1 B)B2T W]X)I +- T B I B 2 X IO + Cm g

b1

(6)

b]

This system is asymptotically stable at X IO •

which is the standard fonn to be used in DAA. 299

(13)

o.05 nr----~-.....___-...,........-~---, ,

(2) The impact of disturbance w on the controlled output Z can be attenuated,

[ ZT (Xl' v)Z(X l ,v)dt

~ y2 [ w

2

dt

0.04

(14)

Where to is the initial time and T ~ to'

0.03

To illustrate the effectiveness of the DAA control algorithm in equation (12), we simulate the performance of a practical hydraulic turbine governing system which structure is shown in Fig. 4 with the following parameter values

= 0.2

o

= 1.0 eh = 1.46 ey = 0.74 eqh = 0.491 eq;x; = 0 eqy = 0.789 Ta = 6.67 Ty = 0.1 Tw = 1.62

-0.02

is

simulated

in

the

= 0.5,

= 5.

a

I I I I

I I I I

t I 1 I

I I I I

:,

:Mg=0.03+w , ,

I

I

I

I

I I I I

I f I I

I I I I

I I I I

I I I

I I I

I I I

I I I

form:

For the convenience

, I

I

x:

i,

i,

I

I

I

I

I I

I I

I I

I I

\j~~ __ ,~

0.1

l, _

r------,----r---r----.--~-__,

, I

I

I

I

I

----~----T----T----T----~----

~h

,......---~-_r__-...,........-___r_-.....,

,

I

I

I

I

I

I

I I I

I I I

I I I

I I I

:

:Mg=0.03

,

I

I I

, I

'y

I

I

I

I I

I I

I I

I I

o

I

I

I

I

I I

I I

I I

L~-'---'

1":--1 I

I.

: I

X:

I

I

:

:

,

,

,

I I I

I

I

I I I

I

I

I

I

t

-0.1

~

- - - -

I I

~

~

- - - -

I I

- - - -

I I

~

- - - -

----~~~---r-.-_r--

, ----r---- ---- ---- ----

Mg=-~.1

t-r-,----'-~-~-___7_-__7_-__i \

\y

I

I

--~-~----}----}----}----~---..,

o

.0.03 L.....-._..l.....-_...1.-_--'---_--'--_--' o 5 10 15 20 Time(Sec) Fig. 3. The case of 3% step change of load disturbance and m g

- -

I I

I

~;C~--~-----i-----i-----i----I I I

I

I

·0.05

- i-----j-----j-----.----I

I

I

I

I

---'-_.

I

,

I

I

I

I

0.01 -----j-----,-----,-----.----I 1

I

I

I

I

, I

I

I

i

,

- -\- r

o

0.02 I-----r-----r-----r-----l----, , , , I

I

-,--~----T----T----T----~---:X : :

.025

/ 0.03 I---....,'r----....,'r----..,'---..,'-----l

I

)

0.05

---~~:. --=_:. ~ --:.:=- ~-:. _-:'"_":.}:-.: ~--.=-

0.04

-0.02

I

-----j-----j-----i'-----

I

-0.01

I

Fig. 4. The case of 3% step change plus weakening oscillation of load disturbance

=

of solving the Riccati equation, chose y 2 . Four different cases are carried out by using the software package Simulink in Matlab$, and their results are shown in Fig.3-6.

o.05

-----,-:" :

I

-0.03 ' - - - _ " - - - - _ . . . 1 . - _ - - ' - - - _ - - ' - - _ - - ' o 5 10 15 20 Time(Sec.)

m g = m gO + w, where w = a e- pt sin(at) with

a = 0.03, f3

I

1

-0.01

disturbance

:

-----~~-:----' /

en

The

I

0.01 -----r-----r-----'-----I-----

= 0.04

k

I

----r-----r-----r-----l-----

0.02

4. SIMULATION AND RESULTS

b A.

Y - ~ ~ :-: ---".:~;. -- =-= -~ =-= --- - ~ --- -=-=-= .

= 0.03

30G

_

~

I

I

5

10

__I I

-' -

.

~

--

-

1 - ' - _.

I

15 20 25 Time(Sec.)

30

Fig. 5. The case of 10% step change of load disturbance and m g

= -0.10

control is only one functional requirement for the hydraulic turbine governor. In order to achieve high reliability, availability and efficiency, a new concept and methodology of automation, Integrated Control Maintenance and technical Management System (CMMS), has been proposed (Petin, et al. 1998). In our future study, the control algorithm will be integrated into the CMMS system.

0.1 .....----.---.---...---.-'-~-....,

,

I

I

I

I

I

!'\----r----T----T----T----~---I I I I I :J \ h II I I I I I I I I

0.05 - - - - .. - - - - T -

:x:

- - - T - - - - T - - - - T - - --

I

:

:

:

I I

I I

I I

I

I

I

--r----r----r----T---I I

o ----,

I ,,

~~-_;._-_r_--r

,,

, ,

,

I

,

,

,

----j---- ----j---- ----7---I

0.05

,

----~----

----t----

----f----

, ,

, ,

I I

L

1

I

I

___ L

r:

:Mg=-~.1 +w:

,l-I\Ai'_--L----.Jl-..::::-~--7,

-0.1

~

\ IL ____

LI

Y ':- - T "

o

I

I

5

10

LI I

~

REFERENCES

I

LI

Doyle J. C., K. Glover, and P. P. Khargonekar(1989) , B. A Francis, "State-space solution to standard H2 and JL, control problems," IEEE Trans. on Automatic Control, Vo1.34, No.S. Francis B. A, A course in JL, control theory(1987), Spinger-Verlag, New York. Isidori A and A Astolfi(1992), "Disturbance attenuation and JL,-control via Measurement feedback in nonlinear systems," IEEE Trans. on Automatic Control, Vo1.37, No.9. JING Lei, YE Luqing and O. P. Malik (1998), "An Intelligent Discontinuous Control Strategy for Hydroelectric Generating Unit," IEEE Trans. on Energy Conversion, Vo1.13, No.1. LI Zhaohui, YE Luqing, WEI Shouping and O. P. Malik (1992). Fault tolerance aspects of a high reliable microprocessor-based water turbine governor. IEEE Trans. on Energy Conversion,

_

-----1

, lI

_

.. _.~ -- .:._ .... I

I

15 20 25 Time(Sec.)

30

Fig. 6. The case of 10% step change plus weakening oscillation of load disturbance Compare Fig. 3 and Fig. 4, we can see that the dynamic response is almost the same when a weakening oscillation disturbance pt w a e- sin(at) with a 0.03, f3 0.5,

= a = 5 is

=

=

Vol. 7, No. 1.

added a small step change 0.03 to the system. In both cases the disturbance is effectively attenuated and the surge time short. From Fig. 5 and Fig. 6 we can see the disturbances is also been effectively attenuated, but the surge time is a bit longer when the step change is large. Many other forms of disturbances have been simulated, the results are similar.

Petin Jean-Francois, Benoit lung, and Gerard Morel(1998), Distributed intelligent actuation and measurement (lAM) system with an integrated shop-floor organisation, Computer in Industry, Vol. 37.

Van der Schafter A J.(1992),"L r gain analysis of nonlinear systems and nonlinear state feedback control," IEEE Trans. on Automatic Control, AC37. YE Luqing and Serge Maurin (1983). Multivariable adaptive control and how to achieve it with microprocessor. In:Proceedings ofACI83 Applied Control and Identification, Copenhagen. YE Luqing (1984). Model reference multivariable optimal control and its realisation with microprocessor. In: Proceedings of Mini and Microcomputers and their Applications, Bari, Italy. YE Luqing, WEI Shouping and LI Zhaohui (1990). An intelligent self-improving control strategy and its microprocessor-based implementation for application to hydro-turbine governing system. Can. J Elect. & Comp. Eng., Vol. 15, No.4.

These simulations suggest that the designed system has a strong robustness. When the disturbance is small, the system also has good dynamic response. However, the surge time is a bit long when the disturbance is large.

5. CONCLUSION In this paper the DAA method has been applied to the design of the control law of a practical linear hydraulic turbine governing system. The designed controller is strongly robust and can effectively attenuate all kinds of disturbances w which belong to L 2 (0, T). However, the penalty for the robustness is the conservativeness of the control effect. The simulation results show that the system achieved satisfactory control effect if the scale of disturbance is small; otherwise, the system does not act fast enough and behaves conservatively. In fact, the hydraulic governing system is a sub system of the whole hydraulic power plant, and the 301