An Artificial Intelligence Based Control for Micro Hydro Power Plants

IJEIT Vol. 1 No. 1 Oct 2009

33

An Artificial Intelligence based Control for Micro Hydro Power Plants

Himani Goyal, M.Hanmandlu

Abstract-- Micro hydropower plants are emerging as a major renewable energy resource today as they do not encounter the problems of population displacement and environmental problems associated with the large hydro power plants. However, they require control systems to limit the huge variation in input flows expected in rivulets over which these are established to produce a constant power supply. This paper proposes an electric servomotor as a governor for a micro hydro power plant especially those plants that are operated in isolated mode. An advanced controller is developed combining four control schemes for the control of the governor following the concept that the control action can be split up into linear and non linear parts. The linear part of this controller contains an adaptive Fast Transversal Filter (FTF) algorithm and normalized LMS (nLMS) algorithm. The non-linear part of the controller incorporates Fuzzy PI and a neural network. The concept behind splitting the control action is reasoned out and the conditions for stability of the controller are proved. The new controller has a superior performance compared to other control schemes. Index Terms-- Hydro power plants, ANN, FTF, Fuzzy PI, nLMS, Non-linear systems, PI Controller, Servomotor, Stochastic Load Disturbance

I INTRODUCTION

In an electric power system, consumers require uninterrupted power at rated frequency and voltage. To maintain these parameters within the prescribed limits, controls are required on the system. Voltage is maintained by the control of excitation of the generator and frequency is maintained by eliminating the mismatch between generation and load demand. Since frequency is an indicator of the energy balance in the system, the problem of maintenance of constant frequency is analyzed in this paper. A novel scheme is proposed for the speed control of hydro turbines. This scheme regulates the flow of water being fed to the turbine in accordance with the load perturbations thereby maintaining the frequency of the system at the desired level.

A. Conventional Governors

Conventional Governor Systems can be classified as mechanical-hydraulic governors, electro hydraulic governors or mechanical types. Mechanical hydraulic governors are sophisticated devices which are generally used in large hydro power systems. They require heavy maintenance and are expensive to install, making their usage in micro hydro power plants uneconomical. Electro hydraulic governors are complex devices needing precision design and are expensive. Mechanical governors incorporate a massive fly ball arrangement and usually do not provide flow control. They require an elaborate set of complex guide vanes, inlet valves and jet deflectors. Hence conventional governing systems because of their cost and complexity are not ideally suited for installing at the isolated areas that are not grid

connected. The current trend is therefore to use load side regulation.[ 2,3,5,6]B. Electronic Load Controller for Water Turbines

Electronic load controllers govern the turbine speed by adjusting the electrical load on the alternator. As lights and electrical appliances are turned on and off, the electronic controller varies the amount of power fed into a ‘ballast’ load. The load controller therefore maintains a constant electrical load on a generator in spite of changing user loads. This permits the use of a turbine with no flow regulating devices and the governor control system. Load controllers however waste precious energy that can be used gainfully. Also they do not carry out flow control implying that themineral rich water is made to spill away which could have been diverted at high head for irrigation purposes. Henderson [39, 40, 41] describes development of a microprocessor based electronic load governor for a micro hydroelectric power plants. The governor maintains the speed of the set by adjusting an electrical ballast load connected to the generator terminals, thus balancing the total electrical load torque with the hydraulic input torque from the turbine. [8]

C.Servomotor as a Governor

In the proposed control system an electric servomotor is used as a governor [1]. An electric servo motor is a precision electric motor whose function is to cause motion in the form of rotation or linear motion in proportion to a supplied electrical command signal. Type Zero servomechanism is used in the proposed system. A feedback control system of Type Zero is generally referred to as a regulator system. Such systems are designed primarily to maintain the controlled variable as constant at a certain desired value


34

despite disturbances. Here the controlled variables are the frequency and the turbine power. The electric servo motors are preferable for the control of micro hydro power systems as they have a simple design, require less maintenance and are less expensive than conventional governors.

D. Literature SurveyGlattfelder [30] has advocated use of a compensating element in addition to a speed regulator as a speed governor for low head hydro units in an isolated grid.Hagihara et al. [31] consider the effect of derivative gain and other governor parameters on the stability of a hydraulic turbine supplying an isolated load. Pereira et al. [32] propose the addition of eddy current brake to help governor achieve greater degree of control. Schniter et al. [33] make use of the adjustable blade angles to achieve maximum operating efficiency at a given load. Tano and sannomiya [34] have developed an integrated digital control panel for control, protection and supervisory functions. Malik et al. [35] recommend the use of microprocessor based governor for frequency measurement and control and Thappar et al. [36] present the distributed microprocessor based control for stable frequency and voltage output. Djukanovic et al. [37] propose the non linear multivariable control using adaptive network based fuzzy inference system (ANFIS)

E. Need for a New Governing System

The new Governing System should be relatively inexpensive, simple to operate and easy to maintain by incorporating the flow control. Therefore, we will explore a set of advanced control schemes for better load frequency control.

In this work, we will discuss how the control action can be split up into linear and non linear components as this will allow the selection of appropriate control schemes for the micro hydro power plant. In the light of this concept we will explore different control schemes consisting of combinations of linear and nonlinear parts to come out with a scheme that meets the desired performance in terms of peak overshoot and steady state error. We will also show that the chosen scheme is stable. Thus this work will pave the way for the design of a suitable controller for any type of plant by an appropriate choice of control components.

The organization of this paper is as follows: Section

II gives formulation of the state space model for the hydro plant. Some of the advanced control schemes are discussed and a new controller is proposed based on the concept of splitting up of control action in Section III. Performance of this new controller is compared with other control schemes to illustrate its effectiveness in Section IV. Conclusions are drawn in Section V. The concept and the proof of stability find place in the Appendices. II. FORMULATION OF PLANT MODELS FOR MHP PLANT

The approximate transfer function for the servo motorbased governor is considered for the analysis and is

given by

G(s) = 1 1 (1) (1 +sT1) (1+sT2)where, T1 = mechanical time constant, T2 = electrical time constant. In addition, unity gain is applied as a feedback. A PI controller with the following transfer function is superimposed on the servomotor based governor:G(s) = Kpl + Ki

sWhere Kpl = Proportional constant, Ki = Integral constant

Fig. 1: Model of a Micro hydro power plant using

Servomotor as a Governor

The block diagram of micro hydro power (MHP) plant is shown in Fig.1. This plant can be reduced to a simpler representation as in Fig. 2 by employing partial fractions.


35

Fig. 2: Simplified representation using Partial

Fractions

The differential equations for the governor can be written as:

1E i p ld dX K f K fd t d t

(2)

2 2 3 12 2

1 1 1[ ]E E E Ed X X X f Xdt T T R

(3)

3 3 23 3

1 1E E E

d X X XT Td t

(4)

The change in power generated is given by:

3 1[ ]g E gP C X P (5)

The differential equations for the hydro turbine are as

follows:

1 1 31 1

1 [ ]0.5 0.5

g g Ew w

d DP P Xdt T T

(6)

1 31 [ . ]p

g E Lp p

d Kf f P C X Pdt T T

. In view of the above, Eqn. (2) becomes

1 1 31

[ [ . ]]p

E i pl g E Lp p

d KX K f K f P C X P

dt T T

From Eqns. (3)-(8) , the parameters are determined as C = -2, D = 3. The system dynamics described by the above set of differential equations appears in the state space form as:

[ ] [ ] [ ]X A X B p

(9)

where X, and p are the state, control and disturbance vectors respectively and [A], [B] and

[] are constant matrices of appropriate dimensions. Using Eqns. (2)-(8), Eqn. (9) is rewritten as :

(10)

III. ADVANCED CONTROL

PI controllers provide a good control action for micro hydro power plants. However the control action can be further improved using advanced control methods. In these methods, the representation and adaptation of information are the key issues to reduce complexities and to eliminate the heuristic procedures in process control. Moreover, good transient and steady state responses for different operating points of the processes can be achieved. These advanced techniques include the Fuzzy PI, the nLMS algorithm, the FTF algorithm and a Neural Network (NN). Here NN incorporates an adaptive algorithm, which is a combination of nLMS and gradient descent algorithms. Fuzzy techniques drastically reduce the development time and cost for the synthesis of nonlinear controller for dynamical systems. Triangular membership functions are generally preferred. The nLMS algorithm is used in many applications where the input signals are subject to widely fluctuating power levels causing gradient noise amplification, which in turn affects the stability, convergence and steady-state properties of the LMS algorithm. The advantage of nLMS in micro hydro power plant is that it adapts the gain to its optimal value, resulting in fast, stable convergence. The FTF algorithm, a well-known tool in the field of signal processing, is also applied for control. In FTF algorithm, projection techniques and

(7)

(8)


36

vector space methods are used to derive a fixed order transversal least squares filter. A new controller is now proposed using a combination of the above mentioned techniques with a view to minimize the peak overshoot and achieve the early settling time by tapping the advantages of individual components.The schematic of the proposed controller is shown in Fig. 3.

A.Different control combinations

The new controller incorporates the advanced control techniques to cater to the plant linearities and nonlinearities. The underlying concept is that the non-linear part of the controller operates on non-linear error signals to make them adhere to the set point and the linear part of the controller tries to maintain the linearity between the two points. This concept advocated by Srivastava in her thesis [19] is adapted here to justify the composition of the new controller, and is enumerated in [42]. From this appendix it is possible to choose appropriate linear and nonlinear components of controller such that the desired performance is achieved. [12]. Moreover, it has been noticed that each technique retains its advantage and contributes to the overall performance of the controller. Keeping this in mind, our control scheme shown in Fig. 4 is devised. [38] In this, nLMS and FTF constitute the linear part and Fuzzy PI and NN constitute the non linear of the controller. These four constituents are now discussed in detail followed by the stability analysis of the controller given in Appendix A.

Fig 4: The block diagram of the proposed Scheme of control The combined output of the controller is

1) 1 2 3 4( ) ( ) ( ) ( ) ( )u k u k u k u k u k

(11)

where u1(k) is the output of NN, u2(k) is the output of FTF, u3(k) is the output of Fuzzy *PID and u4(k) is the output of n-LMS.

(a)Scheme of control employing FTF and Neural NetworksA combination of FTF algorithm and a neural network from [19-21] is shown in Fig. 5. The weights of the neural network are adjusted by n-LMS and gradient descent algorithms. [13]

2) The output of the NN, denoted by u1(k) is

11

( ) ψ ( ) ( )M

ni

u k w i e i b

(12)

where M is the number of samples taken at a time, yre is the error, y is the actual output, r is the set

point. The somatic gain denoted by ψ is the advanced

feature that improves the performance of the neural network. The NN used here is composed of only input

Fig. 3: The model of the proposed scheme

Fig. 5: A Scheme of Control employing FTF and Neural Networks


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and output layers. The weights of the NN are adjusted by the following equation [10]:

( 1) ( ) ( )n n nn

Vw k w k w k

w

(13)

)()(')( kekeαkwn

(14)

where 21

2V e and

2'

eα

, with and being

the step sizes used in - LMS and gradient learning

respectively.

Off line parameter optimization using ANN

Fig. 6: Block diagram of MLP feed forward ANN

The training of parameters using Multi Layer Perceptron (MLP) feed forward ANN (See Fig. 6) is now discussed. Inputs to the ANN are different values of regulation parameter R, water starting time

wT and nominal loading. Output of ANN is the

desired proportional gain pK and integral gain, iK .

Prior to conducting training, a set of input–output patterns is first prepared. The network is trained until a good agreement between predicted gain settings and the actual gains is reached. Once the network is adequately trained, the network is again tested to ensure that it can adequately predict the correct gain settings for the inputs that are not included in the training set. The results show that predictions by ANN are in good agreement with the training data. It

is observed that parameter optimization of pK and

iK is independent of the magnitude of the step

disturbance. [9,11,15,17,18]

3) The FTF controller part

4) The output of the FTF, denoted by u2(k) is

2 1 2( ) ( ) ( 1)f fu k w r k w r k

(15)

where 1fw and 2fw are the FTF weights. The

computation of these weights can be found from [16].

(b) Fuzzy PI Control

A schematic diagram of the Fuzzy PI controller is given in Fig. 7.

The output of a product-sum fuzzy controller is of the form [22-26]: u = A + PE where E = ke e = ei , A is the input membership

function, e is the error , u is the output of fuzzy controller, ke is the scaling factor and P is equivalent proportional term [25]. Hence, the control input to the plant can be approximated byu3(k) = α. [A + PE] + β∫ (A+PE).dt

= α.A+ αPE + βA t +βP∫ ke.e.dt = α.A+ αPE + βA t + βP k e ∫.e.dt = α.A+ αP k e.e + βA t + βP k e ∫edt

Where α is the weight on PD type fuzzy controller and β is the weight on PI type fuzzy controller. Here, the fuzzy controller becomes a parameter cum time-varying PI controller with its equivalent proportional control and integral control components being αPke and βPke

respectively. Hence this Fuzzy PI controller behaves as the PI type fuzzy controller. In (15) the derivative of e for the fear of accentuating the stochastic disturbance is not used.(c)Normalised LMS ControlThe weight update in α -LMS rule is given by Wk+1=Wk+α.Єk.Xk/|Xk|

2 (18) The time index or adaptation cycle number is k, Wk+1 is the next value of the weight vector, Wk is the present value of the weight vector and Xk is the present input

Fig. 7 Scheme employing Fuzzy PI control


38

pattern vector. The present linear error Єk is the difference between the desired response sk and the linear output rk = Wk

T.Xk [14]HenceΔЄk=Δ(sk-Wk

T.Xk)=-XkT.ΔWk

(19) Rewriting the α -LMS rule from Eqn. (19), we haveΔWk=Wk+1–Wk= α.Єk.Xk / |Xk|

2 (20) In view of Eqn. (20), Eqn. (19) is written asΔ Єk = - α . Єk .Xk

T.Xk / |Xk|2 = - α . Єk (21)

But in our case Δf = Δek; so the output u4(k)= WkT. ek

.

Stability and speed of convergence depend on the parameter α. For input pattern vectors independent in time, stability is ensured for most practical purposes if 0 < α < 2. Choosing α greater than 1 results in over corrections hence practical range of α is 0.1 < α < 1.0. The analysis of Lyapunov stability of this controller is provided in Appendix-A.IV. COMPARISON OF PERFORMANCE

Exhaustive and comprehensive simulations are carried out on micro hydro power plants using the proposed controller designated as “g” as well as different combinations of the control schemes (a- f) with a view to come up with an efficient combination that can reduce the peak overshoot and ensure quick stabilization of the supply frequency. The flow chart of the controller scheme useful for implementation purpose is shown in Fig. 8. The data model employed is given in Appendix-B. The plots of f vs. t for

different control schemes are shown in Fig. 9 to ascertain their relative performance. The composition of various schemes is as follows:

Fig.8: Flowchart

t (sec)

As shown in Fig. 9, here type ‘a’ controller shows PI type, type ‘b’ shows ‘ n LMS+PI ’ type controller, type ‘c’ shows ‘ FTThe results of simulations demonstrate that in general the application of the advanced control techniques using the linear and non linear parts improves the performance of the micro hydro power plants as compared to a simple PI controller. The proposed controller “g” outperforms over all other controllers by achieving the least peak overshoot and the early settling time as shown in Table 1 where it may be observed that all controllers (i.e., d, f, & g) having both linear and non linear parts have less Squared Error (SE). In Table 1,

we denote the under shoot and over shoot by u and

0 respectively and the settling time by st . As is seen

from this Table 1 here, controller “g” has the minimum squared error whereas controller “a” has the maximum squared error. Therefore we rate the controller as Best in terms of there squared errors.

Type max

{ , }o u st 1st

u

2nd

o

3rd

uJ= (SE)

a 7 7 0.99 0.427 0.353 1.38178

b 4 5 0.834 0.291 0.267 0.90322

c 6 6 1 0.423 0.317 1.34276

5

d 3 4 0.6929 0.2869 0.2545 0.68026

e 5 2 0.993 0.22 0.2449 1.10637

9

f 2 3 0.691 0.28055 0.22439 0.64025

g 1 1 0.69 0.2798 0.1655 0.58978

0

Fig.9 Comparison of different control


39

Table 1: Comparison of Control Combinations (Here

1: Best; 7: Worst)

Table 1 indicates guidelines for the choice of control components. We will first try a linear component one after another and see the performance. Which ever is the best we will select that one. Next we repeat the experiment with one non-linear component at a time. We will analyze the performance. This will be continued with next set of linear components followed by the non-linear components until we get the desired combination of control components.

V.CONCLUSIONS

The maintenance of desired power generation and frequency of micro hydro power plants using flow control is the main theme of this paper. An electric servomotor is suggested as a governor for these plants. A state space model of the plant is derived. A new scheme is proposed for the control of micro hydro power plants. This scheme consists of dividing the controller action into two parts: Linear and Non-linear. The non-linear part of the controller incorporates Fuzzy PI and NN. The linear part is based on the FTF and nLMS algorithms. The concept behind splitting the controller is that any nonlinear error signal is better represented by linear and nonlinear parts. The conditions for the stability of the controller are derived using the Lyapunov criterion. The performance of the new controller and several others with different linear and linear components is compared. The new controller is found to be superior to that of other control techniques in terms of reducing the sum of the squared error. Thus this work makes an important contribution in terms of splitting of control action, stability proof and providing guidelines for the choice of new control schemes. Wehave also implemented the proposed controller on small hydro power plants and the results are found to be equally good as that of MHP.

There are reservations in some circles on the use of sophisticated control schemes for the control of micro hydro power plants. However, we justify this study on the ground that analysis of different schemes and their combinations will lead to better understanding of the control action and will pave the way to a practically viable scheme. For example an alternative to the proposed controller in which all the individual schemes are simultaneously functioning

could be to switch them in a particular sequence of linear and nonlinear parts so as to achieve the similar performance but at the reduced power consumption and utility.

APPENDIX -A

Analysis of the Proposed Scheme using Lyapunov Stability Criterion

A stability analysis of the proposed scheme using Lyapunov’s criterion [19-21] is now discussed here. Let the Lyapunov function be selected as:

21

2V e

Where yre is the error; r is the set point and y is

the plant output. Now,

ye , As 0dr

rdt

eedt

deeV

dt

dV

The plant output y is taken as:

][ 4321 uuuugy

where g is the non-linear function of plant, 1u is the

output of NN and 2u is the output from FTF, u3 is

output of Fuzzy PI and u4 is the output of n-LMS. These are given by:

bieiwkuM

in

11 )()(ψ)( ;

rwku f)(2 ;

u3(k) = α.A+ αPke.e +βA t+ βPke ∫edt ,

u4(k) = WkT.ek

where nw are the weights of NN and fw are the

weights of FTF. Now,

1 2 3 4

31 2 4

1 2 3 4

1 2 3 4u u u u

dudu du dudy g g g gy

dt u dt u dt u dt u dt

g u g u g u g u

(A.6)


40

nn

n

wdt

de

ee

dt

dw

wu

dt

du

ψψ1

1

ψ ψnw n e nw e e w

(A.7)

rdt

dwu

dt

du f

22

fw r

(A.8)

ePkAudt

due

33

(A.9) T T

4k k k4 W . W . e k

duu e

dt

(A.10)

Using Eqns. (A.7)-(A.10), Eqn. (A. 4) is modified as

1 1 2

k k3 4

T T

k

ψ ψ

( ) (W . W .e )

nu w n u e n u f

e ku u

y g w e g ew g w r

g A Pk e g e

(A.11)

From Eqn. (A.4) we get

1 1 2

3 4

T T

k k

ψ ψ

( ) ( W . - W . )

nu w n u e n u f

e ku u

y g w e g y w g w r

g A Pk e g e y

since

ye k and ee k

1 2 3 4

1 4

T

k

T

k

ψ ( ) W .

1 ψ W .

n

eu w n u f u u

u e n u

g w e g w r g A Pk e g ey

g w g

(A.12) In view of Eqn. (A.12), Eqn. (A.3) is changed to

yeeeV

1 2 3 4

1 4

T

k

T

k

ψ ( ) W .e

1 ψ W

n

eu w n u f u u

u e n u

g w e g w r g A Pk e gV e

g w g

1 2 3 4

1 4

T

k

T

k

ψ ( ) W .e

1 ψ W

neu w n u f u u

u e n u

g w e g w r g A Pk e gV e

g w g

(A.13)

Applying the condition for the stability in Eqn.

(A.13), 0

V , we have

1 2 3 4

1 4

T

k

T

k

ψ ( ) W .e 0

1 ψ W

neu w n u f u u

u e n u

g w e g w r g A Pk e ge

g w g

1 2 3 4

1 4

T

k

T

k

ψ ( ) W .e 0

1 ψ W

neu w n u f u u

u e n u

g w e g w r g A Pk e ge

g w g

(Note:Taking xyx

y

and

ydt

dy)

Again as )()()1(

twt

twtww n

nnn

1

2 211

1

( ) ' 'n

n u wn

uyw t e e e ey u

u w

)'()( 11 nwun uyeetw

(From -LMS and gradient descent algorithms)

Similarly, tw

w ff

(

where c is the gain vector (From FTF algorithm).Using Eqns. (A.14)- (A.16) ,we have

1 1 2 3 4

1 4

T

2k

1

T

k

ψ ( ' ) ( ) W .e 0

1 ψ W

n n

eu w u u u uw

u e n u

g e ey u e g cer g A Pk e ge

g w g

1 1 1 2 3 4 3

1 4

T

3 2k)

1

T

k

( ψ ') ( ψ ) ( W 0

1 ψ W

n nn

eu w u u w u u u uw

u e n u

g e y u g e g cr g Pk g e g A

g w g

1 1 1 2 3 4 3

T

3 2k

1[( ψ ') ( ψ ) ( W ) ] 0

n nn

eu w u u w u u u uw

g e y u g e g cr g Pk g e g A

For β << 0, the product βA <<0 as A is a membership function that assumes a value between 0 and 1. Hence for small values of β, Eqn. (A.18) becomes,

1 1 1 2 3 4

T2 1

k 1[( ψ ') ( ψ ) ( W ) ] 0n nn

eu w u u w u u uwg e y u g e g cr g Pk g

Solution of the above equation is given by :

1 1 1 1 1 2 3 4

1

T

2

k 1 1

1 2

( ψ ) ( ψ ) 4( ψ ')( W )

( , )2( ψ ')

n n nn n

n

eu u w u u w u w u u uw w

u w

y u g y u g g g cr g Pk g

eg


41

where ),( 21 are the roots. So the range of error is:

),max(),min( 2121 e . As our motive

is to minimize the error (e), we will discuss two

cases.

Case 1:

It is possible when roots of the above equation tend

to zero, as 0e . Then, we have

1 1 1 1 1 2 3 4

T

2k

1 1( ψ ) ( ψ ) 4( ψ ')( W ) 0

n n nn n

eu w u u w u u w u u uw w

g y u g y u g g cr g Pk g

(A.20)

Hence,

0)W)('ψ( k

T

4321

ueuuwu gPkgcrggn

(A.21)

This gives the solution as

0W,0,00 k

T

Pwc f , which is

true for FTF algorithm , also P 0, means that the

change in proportional part tends to zero and if

0W k

T

, i.e. , change in nLMS weight tends to

zero as change in error tends to zero.

Case 2:

1 1 1 2 3 4

T

2k1( ψ ) 4( ψ ')( W ) 0

n nn

eu w u u w u u uwg y u g g cr g Pk g

1 1 1 2 3 4

T

2k1( ψ ) 4( ψ ')( W )

n nn

eu w u u w u u uwg y u g g cr g Pk g

2 3 4

1

1

T

k2

1

4 '.( W )( )

.ψn

n

eu u u

u wu w

g cr g Pk gy u

g

2 3 4

1

1

T

k

1

'.( W )2

.ψn

n

eu u u

u wu w

g cr g Pk gy u

g

(A.22)

From Case1, we have

0W,0,00,0 k

T

Pwce f , So

that Eqn. (A.22) becomes

011

nwu uy . In other words, we can rewrite the

above for minimizing the error as: 011

nwu uy .

Therefore, we can conclude by using Eqn. (A.15) that

1

T

k

1

0 , 0 0 , 0 , W 0 ,

0 , 0n

f

u nw

e c w P

y u w

It may be noted that all the conditions in Eqn. (A.23)

tend to zero indicating that the convergence of the

system is guaranteed. Thus these conditions are the

necessary conditions for stability. It is now proved that

this control combination assures stability. Next one can

explore its performance in terms of reducing the sum of

the squared error defined by

2J SE e

which in turn reduces the peak overshoot and settling

time. Here the desired trajectory is zero but one can

possibly take it as the second order response with the

specified first overshoot and settling time. The

performance measure in (A.24) is used to compare the

new controller with other control schemes.

APPENDIX –B

Data for the Model

The following data is considered for constructing the model. 1.Total rated capacity : 50 kW

2.Normal operating Load : 25 kW

3.Inertia Constant H: 7.75 seconds (2<H<8)4.Regulation R: 10 Hz / pu kW ( 2<R<10)

Assumption: Load - frequency dependency is linear. Nominal Load = 48 % = 0.48; Pd = 3 % = 0.03.


42

The damping parameter [4,7], D = Pd/ f = 0.48 25 = 0.004 pu kW / Hz 60 50

Generator parameters are:

Kp = 1 = 250 Hz / pu kW D

Tp= 2 H = 64.64 seconds f0 D

The open loop transfer function of a servomotor is given by [27, 28, 29]

G(s)H(s) = Kn KaKg / Ke

(1+TfS)(1+Tm s)where, Ka = net control field amperes per volt actuating error signal,

Kg = No-load amplidyne terminal voltage per net Control field current,

Tf /Rf= Lf = Time constant of quadrature field of amplidyne, seconds,

Tm = JRa = Time constant of motor and KTKe load, seconds,Kc = Motor volts per radian per second of motor,

Kn = Voltage from tachometer per radian per secondof motor.

For our model, we choose the following values:-Kn =1; KaKg / Ke =1 ; Tf =0.001 seconds andTm =0.01 secondsPI Controller parameters: Kpl = 0.056, Ki = -0.002

REFERENCES

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An Artificial Intelligence Based Control for Micro Hydro Power Plants