International Renewable Energy CongressNovember 5-7, 2009 - Sousse Tunisia

Fuzzy controller for frequency regulation and water energy save on micro-hydro electrical power plants

Issam Salhi1, Said Doubabi1

1 Electrical systems and Telecommunications LaboratoryFSTG - Marrakesh Morocco

e-mail: isalhi@yahoo.fr , doubabi@fstg-marrakech.ac.ma

ABSTRACT

Micro-hydro power is one of the most importantrenewable energy in the world. It does not encounterthe problem of population displacement and is not asexpensive as solar or wind energy. However, micro-hydro electrical generating units are usually isolatedfrom the grid network; thus, they require control tomaintain of constant the frequency, the scheduledpower and the voltage for any working conditions. Inthis study, a new controller based on TS fuzzyinferences has been designed for applying to micro-hydro electrical power plant. The controller is able tomaintain the generated electrical power's characteristicsas constant in spite of changing user loads (even forlarge variations on consumption) at any operating point.Further, the controller manages the available water (inorder to save it) depending on the users demand byusing only the needed quantity of water for electricitygeneration. Results obtained by simulation show therapidity and the robustness of the controller and itsability to save water. The used model for simulationwas constructed based on the mathematical equationsthat summarize the behavior of the plant and wasvalidated based on a micro-hydro electrical power plantprototype

Index Terms— Renewable energy, micro-hydropower plants, modeling, fuzzy control, ruralelectrification

1. INTRODUCTION

Micro-hydro power was one of the earliest small scalerenewable energy technologies to be developed, and isstill an important source of energy today. It has thepotential to produce an important share of power, with alow price, more than solar or wind power. Micro-hydroelectrical power plants (MHPP) are usually built inremote communities, as they use the river’s flow in themountains.User loads require a uniform and an uninterruptedsupply of input energy. In addition, MHPP are oftenisolated from grid networks. Therefore, their technicalcharacteristics require control to maintain an

uninterrupted power at rated frequency and voltage, fordirectly powering loads. Mainly, voltage is maintained bycontrolling the excitation of the generator (if it's accessible)and frequency is maintained by eliminating the mismatchbetween generation and load demand. In case of apermanent magnet generator, no way to directly controlvoltage, and control of frequency is sufficient.So, MHPP control consists in maintaining fixed thefrequency of the voltage waveform, this may be done byaction on the injector position (by adjusting the water flowvia a servomotor) to produce just the necessary poweraccording to the load connected on the electrical network[1-4]. These controllers become insufficient in case ofimportant variations on the electrical power consumption,and the stability of the system could be completely lost [5-6]. In addition, the use of such controller cannot satisfy agood control and should not be used (especially in case ofpermanent magnet generator) as the stabilizing time extendsup to 70 sec [1]. It takes that time because of theservomotor which must be relatively slow to minimize thewater hammer effect.Further, electronic load controllers (ELC) are used in orderto simplify the MHPP control and to limit damages causedby the motorized injector [7]. They govern the turbine speedby adjusting the electrical load on the alternator, thus bybalancing the total electrical load torque with the hydraulicinput torque from the turbine. Therefore, they maintain aconstant electrical load on the generator in spite of changinguser loads. The turbine gate opening is kept at its maximumin order to use a constant and the maximum water flow andhence guarantee the maximal mechanical power at thegenerator shaft. This permits to use of a turbine with noflow regulating devices. The stabilizing time is very shorteven for large variations. Development of a microprocessorbased ELC for a MHPP has been described in [8] and thestabilizing time is less than 2 sec.The ELC however waste precious energy that can be usedgainfully. Also they do not carry out flow control implyingthat the mineral rich water is made to spill away whichcould have been diverted at high head for irrigationpurposes [2].Therefore, output errors of the plant have to be determinedand reduced to minimum value in short time. For thesereasons, advanced control techniques usage must beinevitable in such systems.

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Recently, micro-hydro electrical power plant frequencycontrol has received great attention by the researchersand many control strategies has been realized in theliterature. In this latter, some linear models are writtenby linearizing the differential equations describing thedynamic performance of the power system around anoperating point [1-2], [9-14]. Additionally, several newcontrollers such as intelligent controllers and adaptivecontrollers have been applied for load frequency controlof hydro electrical power plant [15-20]. However, thefuzzy logic is an important technology and a successfulbranch of automation and control theory, which providesgood results in control of power systems.MHPP is a complex non-linear system. Fixed controlstructure is not suitable for such a system [19] [21]. Incase of the use of a PI controller, its parameters shouldvary with the operating points. TS fuzzy controllersmust be designed based on this principle, thus PIcontroller parameters are modified with fuzzy logicrules.In this paper, the main idea is to combine the roles ofboth controllers: ELC and servomotor, in only onecontroller able to:

First, maintain as constant the frequency (and byconsequence the voltage) with a short stabilizing timefor any operating conditions, even for large stepchanges in the power consumption. When we talkabout any operating conditions, it means any variationsat the user consumption and any position of theturbine's gate opening.

Second, save the precious water by managing theopening gate according to the electrical power requiredby the users. When there is less demand, the controllerclose the gate until there will be an equality betweenthe generated and the required power. If the usersrequire more electrical power, the controller open thegate to satisfy the demand. In this case, the frequencymay fall down under the desired value and remains inthat, as the servomotor is relatively slow and may notopen the gate quickly. This is why we keep 20% of thegenerated electricity on the ballast load. That way,when there will be a brusque and random demand ofelectricity, the controller will be able to satisfy thedemand by balancing the dissipated power from theballast load to the mini-grid network, and then thecontroller will start opening the gate.

TS fuzzy controller is proposed to both regulate theoutput of MHPP for all operating conditions and managethe available water. Suitable for non-linear and timevariant systems, this technique is used to adjust the gainsof PI controller according to each operating point.As we will report our practice on a MHPP prototype. Avalidation of a proposed mathematical nonlinear modelwas done based on that prototype features. The usedmathematical model for simulation study is based on themathematical equations resuming the operating ofMHPP. It incorporates nonlinear equations of themechanical power; the electrical consumed power and

the relationship between the turbine flow, the turbine headand the frequency of the voltage waveform. A previousstudy to valid that model behavior was done in [22].The used micro-hydro generating unit prototype (200 W)consists of a Pelton turbine and a synchronous machinegenerator (single phase, Permanent-Magnet, two poles)which directly feeds a load formed by lamps.The organization of the paper is as follows. Thenomenclature explains the quantities that appear in thesection II. Section III describes mathematical model ofMHPP. Section IV describes the designed fuzzy controller.Simulation results with a discussion on the results areprovided in Section V. The conclusion and future workfollow lastly.

2. NOMENCLATURE

tP : turbine power [W],

tQ : water flow [m3/s],

g : gravity acceleration [m/s2],

= 1000kg/m3: water's density,

eH : effective high [m],

tV : drive speed of the turbine,

1V : water's speed in the contact of the jet with the buckets,

2V : the water's speed at the exit of the buckets,

m : report of1V and

2V ,

: angle between1V and

2V ,

tR : ray of the turbine (m),

tq : turbine flow (pu),

1v : jet speed (pu),

tn : turbine speed (pu),

tnQ : nominal flow of the turbine (m3/s),

nV1 : nominal speed of the jet (m/s),

tn : nominal speed of the turbine (rad/s).

tnP : nominal turbine power (W)

tc : the turbine torque (pu),

tH is the effective fall (m),

tnH : nominal fall (m),

th : effective fall in (pu),

tC : the mechanical torque (N.m),

t : angular velocity of the generator (rad/s),

eC : the resistant torque (N.m),

nS : nominal power (VA)

J : combines moment of inertia of the generator and

turbine.

rF : frequency of the generated e.m.f (Hz).

rf : frequency of the generated e.m.f (pu).

eP : load consumption.

dP : electrical power dissipated on the ballast load.

3. MATHEMATICAL NONLINEAR

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MODEL

Huimin Gao in [14] presents four detailed hydroturbine models for Francis hydro turbine. In this paper,the proposed mathematical model is for MHPP usingPelton hydro turbine. The Pelton turbine is used forthe high falls and small flows. It consists of a set ofspecially shaped buckets mounted on the periphery ofa circular disc. It is turned by jets of water dischargedfrom one to six nozzles that strike the buckets. By amobile needle inside the nozzle the water flow can beadjusted.

3.1. Mathematical nonlinear MHPP model

The main components of a hydroelectric system maybe classified into two groups. First, the hydraulicsystem components that includes the turbine, theassociated conduits – like penstocks, tunnel and surgetank. Secondly, the electric system componentsformed by the synchronous generator and its controlsystem.

3.1.1. Hydraulic part

The turbine model is based on equations for steadystate operation, relating the output power to water flowand head [23]:

ett HgQP (1)

In case of Pelton turbine, it becomes: [3])cos1)((.. 1 mVVVQP tttt (2)

and using per units, it becomes:

)....(....

).cos1.( 11 ttntntn

tntttntt nRVv

P

nRQqmp

(3)

The water's velocity in the output of the penstock isgiven by:

tgHV 21 (4)

and the expression of the jet speed is as follow:

thv 1 (5)

We note:

n

tntt V

Rk

1

. (6)

Thus, the turbine power is given by:

2

1

.

1

.t

t

ttt

t

ttt n

k

kqn

k

hqp

(7)

3.1.2. Electrical part

Well known, synchronous generator model has beenwidely used in many power systems dynamic studies[15]. The differential equation linkage the mechanicaltorque and the resistant torque above the shaft is givenby:

ett CC

dt

dJ

. (8)

which can be write as follow :

dt

dJ

PP t

t

et

. (9)

this expression becomes using per units:

etat ppT

dt

dn .2

2(10)

with:

2. tn

na

J

ST

(11)

The frequency of the voltage waveform and the turbine'srotate speed are related by a linear equation, thus, theexpression of the frequency in (pu) is as follow:

tr nf (12)

So, the two equations that summary the MHPP's behaviorare given by:

* 2

1

.

1

.r

t

ttr

t

ttt f

k

kqf

k

hqp

(13)

* etar ppT

dt

df .2

2(14)

In [22], from the two expressions (13) and (14), aMatlab/Simulink model was obtained and its behaviorwas validated by analyzing a MHPP prototype'sperformances.

3.2. Identification of the model parameters based onprototype characteristics:

Micro-hydro electrical generation system is a complicatednon-linear system. The used model for simulation studiesmust, therefore, be reliable and suitable for representingthe MHPP prototype performances for large, severedisturbances as well as for small perturbations. Thisexplain the interest in parameter ( tk , aT ) identification.

Using the measured data from an open loop online test,the two parameters were identified using the environmentMatlab/Simulink and the obtained values are: 632.0tk

and 52.0aT . As an example, we show on the figure 1

the frequency response of the studied plant with variationin the user load of 25% (discharge at 3.2sec and anoverload at 13.5sec). The shown results were obtainedexperimentally (solid line) and by simulation (dashedline). It is clearly seen from the figure that the simulationand experimental results are comparable; thus, theproposed model represents perfectly the MHPP prototype.It is also confirmed by the figure 2 which shows theabsolute value of the calculate error between theexperimental and simulation output. The error is verysmall even for the transient regime where it does notexceed as a maximum value: 2.5 10-2 pu.

3.3. Model of other control scheme components

The proposed control strategy of the power plant ispresented in the figure 3. It shows the MHPP model, thecontroller, an injector, a servomotor and an actuator. Inthe used experimental setup, we do not have yet a

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servomotor. An Analogue Power Controller (APC)connected to a ballast load (BL) was chosen as anactuator. The APC in the proposed control schemeshould compensate the disconnected load’sconsumption to maintain a constant load on thegenerator in spite of changing load demands.

0 4 8 12 16 20

1

1.1

1.2

1.3

Time (s)

Freq

uenc

y (p

u)

MeasurementSimulation

Figure 1. Validation of the proposed model. (solid line)experimental results, (dashed line) simulation results.

The APC excited by the control signal, dissipatessome electrical power in the BL according to thecontrol signal. The transfer function representing theAPC connected to the used BL was identifiedindependently from the generating unit, and is givenby the following expression:

41.629.7

03.83)(

2

pppG (15)

The approximate transfer functions for the servomotorand the injector are considered for the analysis and weretaken from [2] and [6] respectively.

4. CONTROL METHOD

Since the calculated gain values of a conventional PIcontroller are constant throughout the operation, thecontroller suffers from some difficulties to adapt tononlinear system (or to changing system parameters). Forthis reason, some advanced controllers that vary their gainparameters throughout the operation must be preferred.Therefore, the system can be controlled much better.Using the scheme of the figure 3, we first tested therobustness of conventional PI controller. We used onlyone conventional PI controller to control the plant indifferent operating points. It gives good result around oneoperating point, and becomes insufficient around others.In the mean time, in each of those operating points, otherPI controllers give good results. Thus, TS fuzzy controllershould be used in the study.Nowadays, fuzzy logic has attracted the interest ofresearchers and engineers in various scientific andindustrial areas where most of the real systems aregenerally complex and difficult to be controlled, one ofthem is power plant control. Therefore, fuzzy logicsystem has been used successfully in virtually all thetechnical fields, including control, modeling, image/signalprocessing, and expert systems [24-28]. The practicalbenefits of the fuzzy controllers are [29]:

1) Can handle with good results the variation of theplant parameters by load disturbance or thermalvariations.2) Offer satisfactory results for an unknown non-linear

system by maintaining the operating point in the stableregion compared with classical linear control that showshigh performance only for one unique point.3)Offer convenient ways to incorporate heuristic laws

into an easy human understanding form.4)They are appropriate for rapid applications.

In this paper, the presented controller in figure 4 isproposed to both: regulate the frequency output of MHPPfor all operating conditions and to manage the availablewater on the forebay tank. Since it is a suitable techniquefor non-linear plant, it’s used to adjust the gains of PIcontroller according to the value of the turbine's gateopening (which define the nominal power of the plant andhence the operating point).The used TS fuzzy controller consists of two membershipfunctions (MFs) for two-input (x: gate position; Pd:electrical power dissipated on the ballast load). The MFswere chosen triangular to obtain fast response from thesystem (see figures 5 and 6).

Figure 3. Control strategy of a MHPP using theproposed TS fuzzy controller.

Figure 2. Absolute value of the error used for modelvalidation.

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5. SIMULATION RESULTS ANDDISCUSSION

As it was mention from the beginning, the purpose ofthis present work is to create such a controller that hasto be robust enough to control the MHPP in unknownconditions. More than that, it has to limit the waste ofwater energy if there is not enough consumption of theelectrical energy. In this chapter, some simulationresults obtained using our controller are presented.In order to test the robustness, stability and accuracyof the proposed fuzzy logic controller, differentoperating cases were taken into account, for large,severe load rejections as well as for small rejections.First, we show in figure 7 the control result in case of

important discharge on users load (40% step loadrejection, at the instant: 2sec). As it can be seen from thefigure, the controller guaranties the stability of the plantas the frequency return to its steady state in a very shorttime. To compensate the lost electrical consumption thecontroller had to dissipate the necessary power on theballast load (Pd), immediately after establishing thefrequency regulation, the controller order to close theservomotor in order to produce less energy (Pn) and bythe way reduce the dissipated power to its acceptablevalue that has been chosen to be 20% of the nominalpower.

0 2 6 10 14 18 22 26 300.9

1

1.1

1.2

1.3

Time (s)

Freq

uenc

y (p

u)

Discharge of 40%

0 2 6 10 14 18 22 26 300

0.2

0.4

0.6

0.8

1

Time (s)

Powe

r (p

u)

PnPePd

Discharge of 40%

Figure 7. Control result after an important discharge (40%)on the mini-grid network.

Second, we show in figure 8 the control result in case ofimportant overload on the users load (20% at the instant:2sec) and in the figure 9 the result obtained with anoverload of 10%. As it can be seen, the controllerguaranties the stability of the plant as the frequency returnto its steady state in a very short time. To satisfy thedemand, the dissipated power was injected into the mini-grid network. Immediately after establishing thefrequency regulation, the controller order to open theservomotor to produce more energy (Pn) and by the wayincrease the dissipated power to its acceptable value (20%of the nominal power).Other cases were tested. Even for random and large load,the controller keeps satisfactory dynamics. It guaranteesclosed loop stability at all operating conditions. We couldsee that the proposed TS fuzzy controller causes lessfrequency drop and damps out frequency oscillationsrapidly with save of water energy.

Figure 4. Control strategy of a MHPP using theproposed TS fuzzy controller.

Figure 5. Generated membership functions for wicketgate position.

Figure 6. Generated membership functions for thedissipated electrical power.

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0 2 6 10 14 18 22 26 300.7

0.8

0.9

1

1.1

Time (s)

Freq

uenc

y (p

u)

Overload of 20%

0 2 6 10 14 18 22 26 300

0.2

0.4

0.6

0.8

1

Time (s)

Powe

r (p

u)

PnPePd

Overload of 20%

Figure 8. Control result after an important overload(20%) on the mini-grid network.

0 2 6 10 14 18 22 26 300.9

0.95

1

1.05

1.1

Time (s)

Freq

uenc

y (p

u)

Time (s)Time (s)Time (s)

Overload of 10%

0 2 6 10 14 18 22 26 300

0.2

0.4

0.6

0.8

1

Time (s)

Pow

er (

pu)

PnPePd

Overload of 10%

Figure 9. Control result after an overload of 10% on themini-grid network.

6. CONCLUSION

Since morocco has plenty of hydrological resources, itwas aimed to contribute to the economical way to usewater energy via improving MHPP. This paper includesbetter solution in term of efficiency and a modernapproach is presented, based on the construction of amathematical model of the plant and on its numericalsimulation. That model was validated based on a MHPPprototype. A TS fuzzy controller was proposed. It is ableto maintain the frequency as constant in spite of changinguser loads at any operating point. Further, the controllermanages the available water depending on the usersdemand by using only the needed quantity of water forelectricity generation.The simulation results prove that the TS fuzzy controllerhas good performances. Moreover, good transient andsteady state responses for different operating points of theprocesses can be achieved.Thanks to using modern control methods, the productivityof the power system can be augmented; the machines andpower plants are to be longer lived. Also, the economicallife of their equipments can be increased. Environmentalpollution and CO2 emissions values can also be reduced.In conclusion, because of all the reasons abovementioned, the proposed TS fuzzy controller can berecommended as an advanced controller to guaranteecontrol of micro-hydro electrical power plants. Finally,the efficiency of the novel controller will be checked onan experimental test bench as soon as possible.

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