Degree project in

Improved Governing of Kaplan Turbine

Hydropower Plants Operating Island

Grids

MARTIN GUSTAFSSON

Stockholm, Sweden, June 2013

XR-EE-RT 2013:013

Automatic Control

Master's Thesis

Improved Governing of Kaplan TurbineHydropower Plants Operating Island Grids

A Degree Project in System Control

MARTIN GUSTAFSSON

Master’s Thesis at the Department of Automatic ControlSupervisor: M.Sc. Bengt Johansson

Examiner: Professor Elling W. Jacobsen

XR-EE-RT 2013:013

iii

Abstract

To reduce the consequences of a major fault in the electric power grid,functioning parts of the grid can be divided into smaller grid islands. Thegrid islands are operated isolated from the power network, which places newdemands on a faster frequency regulation.

This thesis investigates a Kaplan turbine hydropower plant operating anisland grid. The Kaplan turbine has two control signals, the wicket gate andthe turbine blade positions, controlling the mechanical power. The inputs arecombined to achieve maximum turbine efficiency at all operating points. Inrelative terms, the wicket gate has a fast dynamic but small effect on themechanical power, while the turbine blade has slow dynamic and large effecton the output, seen around an operating point.

The proposed method to get a faster frequency control uses a differentcombination of the turbine inputs, transferring control effect from the turbineblades to the wicket gates at the cost of loss of turbine efficiency. The methodis investigated with time domain simulations on a model containing all essentialparts of a Kaplan turbine hydropower plant.

v

Acknowledgements

This report is the result of a master’s thesis project at the Department of Auto-matic Control at the Royal Institute of Technology (KTH) in Stockholm, Sweden.The work has been done at Solvina in Västerås under the supervision of M.Sc.Bengt Johansson. Examiner and supervisor at KTH has been Professor Elling W.Jacobsen.

I would like to express my gratitude to the persons that have been supportingme during this project; supervisor Bengt Johansson for his great input and com-mitment, Professor Jacobsen for his advice in the planning process and feedback ofthe linearised analysis, fellow colleges at Solvina for their kindness and helpfulnessand to family and friends for their inspiration and patience.

Contents

Contents vi

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theory of Kaplan Turbine Hydropower Plant 52.1 Kaplan Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Wicket gates and turbine blades . . . . . . . . . . . . . . . . 72.1.2 Servos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Combination Unit . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Penstock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Per Unit - pu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Frequency Control 113.1 PID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 Droop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Anti-windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Regulation criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Control Strategies 174.1 Combination Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2 Inverted Combination Anti-windup . . . . . . . . . . . . . . . . . . . 20

5 Simulation Model 235.1 Governor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.2 Servos and Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . 245.3 Turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.4 Generator and Load . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Analysis Method 276.1 Time Domain Simulation . . . . . . . . . . . . . . . . . . . . . . . . 27

vi

CONTENTS vii

6.1.1 Stationary Behaviour study . . . . . . . . . . . . . . . . . . . 286.1.2 Efficiency Losses . . . . . . . . . . . . . . . . . . . . . . . . . 296.1.3 Load Disturbance Simulations . . . . . . . . . . . . . . . . . . 306.1.4 Inverted Combination Anti-windup . . . . . . . . . . . . . . . 31

6.2 Controllability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 31

7 Results 337.1 Stationary Behaviour Study . . . . . . . . . . . . . . . . . . . . . . . 33

7.1.1 Turbine blade position as a function of wicket gate positionand mechanical power α = f (γ, Pm) . . . . . . . . . . . . . . 33

7.1.2 Mechanical power as a function of wicket gate and turbineblade positions Pm = f (γ, α) . . . . . . . . . . . . . . . . . . 34

7.2 Efficiency Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357.2.1 Efficiency as a function of electric power and combination

offset η = f (Pm, offset) . . . . . . . . . . . . . . . . . . . . . 357.2.2 Efficiency, wicket gate and turbine blade position relationship 36

7.3 Load Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377.3.1 Maximum Load Step Disturbance . . . . . . . . . . . . . . . 377.3.2 Step Responses . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.4 Inverted Combination Anti-windup. . . . . . . . . . . . . . . . . . . 41

8 Conclusions 43

9 Glossary 45

Bibliography 47

Chapter 1

Introduction

This master’s thesis treats frequency regulation of Kaplan turbine hydropowerplants when running an isolated electric island grid. The purpose of the projectis to analyse and propose improvements of the frequency control based on a generalmodel of a Kaplan hydropower plant.

1.1 Background

In today’s modern society, reliability of electric power supply is something taken forgranted. Large and long lasting disturbances on the electric grid pose a threat tothat and may have critical consequences for the functioning of a society. Extremeweather, sabotage, acts of war or technical problems in the operation may result infull or partial breakdown of the electric grid.

Events of this nature can never be completely prevented. Instead, the focuslies on reducing the consequences of a disturbance by isolating the problems whenthey occur. By operating the electric grid in smaller, pre-defined islands, the con-sequences of a large disturbance can be reduced. When running island operation,the island will be isolated from the rest of the grid and therefore self-supporting onpower. In order to obtain stable operation, generated and consumed power withinthe island grid must be in balance. This places new demands of a faster frequencyregulation of the generating power units within the island, since they are no longersupported by a strong electric grid.

In Sweden, 45% of the power is generated in hydropower plants, mostly locatedin the northern part of the country. The great majority are Kaplan turbine plants,which are suitable for operation at lower fall heights. As of this, the Kaplan turbinehydropower plants play a significant part in operation of a number of grid islands.[1]

Simply put, a Kaplan turbine has two control signals, the wicket gate and theturbine blade positions, and the mechanical power as output. In relative terms, thewicket gate has a fast dynamic but small effect on the mechanical power, while theturbine blade has slow dynamic and large effect on the output around the operating

1

2 CHAPTER 1. INTRODUCTION

point. The adjustable wicket gates control the flow of water in to the turbinechamber. After passing the chamber, the water is led onto adjustable turbine bladeswhere the kinetic energy is transformed into rotation of the turbine. A governorcontrols the turbine’s output of mechanical power. To gain maximum efficiency, i.e.to produce the demanded power at the lowest cost of water flow, adjustments ofthe wicket gates and the turbine blades need to be coordinated. Adjustment of thewicket gates are controlled directly by the turbine governor. For each position ofthe wicket gates, the turbine blades are adjusted to the most efficient combinationof the two, by a combinational unit. The properties and the combination of thewicket gates and the turbine blades are central when it comes to improving theability for island operation of the turbine. For older turbines, the wicket gates havefast dynamics and can open and close within 5-15 second whereas the turbine bladesneed 30-60 seconds for full movement. In modern turbines, not considered in thisthesis, the wicket gates and turbine blades can achieve full movement within 5-8seconds. When the turbine is running in island operation, a change of the load willcause the wicket gates to adjust in order to compensate for the change in powerdemand. Since the turbine blades are adjusted slower than the wicket gates, the fulleffect of the change of the power generation will not occur until the turbine bladeshas reached their optimal position. By then, the change in frequency might havegrown large and the wicket gates would need to compensate for that. For a largerchange of the load this might lead to oscillation and slow settling of the frequency.In worst case, the oscillations will lead to instability with collapse of the island gridas a result. [2], [3]

Simulations and measurements of the ability to run in island operation of someSwedish Kaplan hydropower plants have shown need for improvement of the gov-erning in order to satisfy demands of stable island operation.

As of now, there is not much to find in the literature specifically studying gov-erning of Kaplan turbines operating island grids. Most publications describes hy-dropower plants in general, where the use of PID governors are widespread.[4] Re-cent research has considered single-input multiple-output non-linear models, includ-ing the effect of water compressibility. A proposed multi-loop cascaded governorusing polynomial H∞ optimization has shown to be better than the conventionalPID governor.[5]

1.2 Purpose

The Swedish national grid (Svenska Kraftnät) is the authority responsible for thereliability of electric power supply in Sweden. In normal operation, their require-ments state that the frequency should be held within ±0.1 Hz from nominal fre-quency f0 = 50 Hz. When running in island operation, the ability for fast regulationof the frequency is lowered. Hence, the frequency regulation requirements on islandgrids are less strict. The purpose of this master’s thesis is to improve the frequencyregulation of a Kaplan turbine running an island grid. The objective is to achieve

1.3. LIMITATIONS 3

a general method for improving the frequency regulation such that the island gridwill

• keep the frequency within ±2 Hz of nominal at load changes of 10% of ratedpower.

• manage increases of the load by 10% of rated power from operating pointsbetween 0-80% of rated power.

• manage decreases of the load by 10% of rated power from operating pointsbetween 100-20% of rated power.

1.3 LimitationsA master’s thesis project performed at Solvina 2009 [6] did result in a training sim-ulator for a Kaplan turbine hydropower plant. This model, built in the simulationand modulation tool Dymola, includes all the relevant parameters to fit the modelfor various types of operational conditions.

In this thesis, the purpose of proposing improvements are limited to improvingthe frequency control of the training simulator model. The model is fitted to rep-resent a typical Kaplan turbine hydropower plant, based on measurement data ofdifferent plants, with limited or no ability to run island grids.

Chapter 2

Theory of Kaplan Turbine HydropowerPlant

This section will give a brief presentation of the main components of a Kaplanturbine hydropower plant. From the water inlet to resulting generation of power,the plant is divided into the subsystems; penstock, turbine and generator. Anoverview of the system is depicted in Figure 2.1. The theory presented for eachof the subsystems constitutes the base of the simulation model and the purpose isto give a basic understanding of each part’s properties and functions. A detailedpresentation of the simulation model is found in Chapter 5.

Upper water level

Lower water level

Electrical grid

Kaplan

Inlet

Outlet

Reservoir

Turbine passage

Figure 2.1: Kaplan hydropower plant. (Source: www.wikipedia.org/wiki/Hydropower)

5

6 CHAPTER 2. THEORY OF KAPLAN TURBINE HYDROPOWER PLANT

2.1 Kaplan Turbine

The Kaplan turbine is the most commonly used type in hydropower plants in Swe-den. The main reason for this is its flat efficiency curve, which is due to the turbine’sability to operate with high efficiency in a wide range of operating points and atdifferent water heads. The Kaplan turbine is an axial reaction turbine, in which thepressure in the turbine chamber is higher than the atmospheric pressure. Unlikethe impulse turbine, such as a Pelton turbine, the water at the inlet in a reactionturbine possesses both pressure energy and kinetic energy. Shown in Figure 2.2, the

Turbine blades

Turbine axis

Figure 2.2: Kaplan turbine and generator. (Source: www.wikipedia.org/wiki/Water_turbine)

water is led through the inlet onto the wicket gates. The wicket gates are adjustableand control the water flow into the turbine. They are attached around the turbinechamber and shaped for best flow properties. [7] After passing the wicket gates,the water is led onto the adjustable turbine blades. The turbine typically has 4-8slightly curved blades, which shape resembles a boat propeller. As the water passesthrough the runner, the pressure energy gradually changes to kinetic energy. Theshape of the blades enhances the fluid velocity with only a small loss of efficiency.The higher pressure of the water on top of the blades forces the water past theturbine and the pressure energy is transferred to the turbine axis. Ideally, if allkinetic energy in the water was to be transferred to the turbine axis, the velocity

2.1. KAPLAN TURBINE 7

of the water should be zero after passing the turbine. Since the water needs to betransported away some kinetic energy is kept.

2.1.1 Wicket gates and turbine bladesThe Kaplan turbine is characterized by that both the wicket gates and the turbineblades are adjustable. The regulation of the two are coordinated and combined togain maximum efficiency. For every wicket gate position, the turbine blade positionis chosen such that it maximizes the ratio of output power and water volume.

The wicket gates, which regulate the water flow into the turbine chamber, areattached on the wicket gate ring, depicted in Figure 2.3 a) seen from above. Thewicket gate position γ ∈ [0, 1] pu, where γ = 1 pu= 60◦ denote fully open and γ = 0pu= 0◦ closed. The angles used in the simulation model are defined as in Figure2.3 b), with γ = 0◦ being along the side of the wicket gate ring. The turbine bladeposition used in the simulation model α ∈ [0, 1] pu= [2.5◦, 32.5◦] is defined as inFigure 2.3 c), where α = 0◦ lies along the horizontal axis.

α = 2 5. o

α = 32.5o

γ = 0o

γ = 60o

a) b) c)

Figure 2.3: a) Wicket gate ring seen from above. b) Definition of wicket gateposition. c) Definition of turbine blade position.

2.1.2 ServosTo adjust the wicket gate ring and the turbine blades, hydraulic servos are used.The wicket gate position is regulated by rotating the ring upon which they arefixed. The hydraulic servo regulating the turbine blades are positioned inside theturbine axis, which also holds the two pipes transporting the hydraulic oil. Sensorsmeasuring the blade angle are connected via the turbine axis since it is placed ina sealed area. However, the wicket gate ring is in no contact with water and itsadjustments can be seen by the naked eye. One actuator for each hydraulic systemcontrols the oil pressures.

As mentioned earlier, the opening and closing times of the wicket gates and theturbine blades are of interest when studying governing in island operation. Adjust-ing the wicket gates between closed and fully open typically takes 5-15 seconds.

8 CHAPTER 2. THEORY OF KAPLAN TURBINE HYDROPOWER PLANT

Apart from the physical limitations in the servo, the speed limiter is needed to keepthe pressure changes in the penstock within its predefined boundaries when closing.Adjusting the turbine blades between the endpoints typically takes 30-60 seconds.The main reason for the relatively slow control of the turbine blades is problem toget enough oil through the turbine axis to the hydraulic servo in a short period oftime. [2]

To avoid vibrations of the turbine blades, a backlash can sometimes be intro-duced in the turbine blade servo. It allows the blades to be kept static when thedifference between setpoint and actual position is small, which reduces the wear onthe hydraulic system.

2.1.3 Combination Unit

The purpose of the combination unit is to achieve maximum efficiency at all oper-ating points. As shown in Figure 2.4, the turbine blade setpoint position αsetpointis computed by the combination unit, based on the wicket gate setpoint positionγsetpoint or the actual wicket gate position γactual. Both these choices of input sig-nals to the combination unit are used. When running an island grid, it is preferredto use γsetpoint to avoid the time delay of the wicket gate servo. The combination

Combination Unit

Wicket gate

servo

Turbine blade

servo

setpoint

setpointactual

actual

H

Figure 2.4: Block diagram of servos and combination unit

of the two is chosen such that the maximum turbine efficiency is achieved. Thecombination unit data, which is based on measurements from turbine tests, is afunction of the water head H. The turbine tests consist of measuring the efficiencyof the turbine at different combinations of wicket gate and turbine blade positionsat a constant revolution speed. This is performed by fixing the turbine blades andletting the wicket gates go from closed to fully open while registering the turbineefficiency. The test is then repeated for a number of turbine blade positions. Thewater head will affect the mechanical power of the turbine and thus also the optimalcombination curve. In a hydropower plant it is therefore common to have a numberof different combination curves depending on water head.

2.2. PENSTOCK 9

2.2 PenstockThe penstock is the water transport system supplying the turbine. The theoreticallylargest amount of energy available to the turbine is determined by the net head,which is the difference between the upper and lower water levels. However, theenergy is affected by friction losses and the water’s dynamic behaviour.

The penstock usually consists of an inlet, turbine passage and an outlet, alldepicted in Figure 2.1. The construction of the inlet and outlet differs betweenplants depending on the conditions of the surrounding environment. The inlet andoutlet can be low friction metal pipes or tunnels burst in rock causing large friction.There will also be some losses of kinetic energy in the turbine. Ideally the watervelocity is zero after passing the turbine, meaning all kinetic energy is absorbed bythe turbine axis. This is not possible since the water needs to be transported away.

The dynamical behaviour of the penstock is linked to the mass inertia of thewater. While the turbine is operating in a stationary state, the penstock has noaffect on the turbines behaviour. Once changes of the demanded power load occur,leading to opening or closing of the wicket gates, the turbine and the penstock willinteract. If the load increases, the wicket gates are opened to increase the waterflow. This will initially lead to the pressure dropping on the inlet side of the turbinedue to that the water head is used to accelerate the water. As a result of this, theturbine’s mechanical power decreases until the pressure is restored and the powercan increase. The size of this non-minimum phase characteristics of the penstockdepends on the water’s mass inertia. The mass inertia of the penstock is expressedby the water starting time Tw, which is discussed further in 3.4. [2]

2.3 GeneratorIn an electric power grid, the generated electric power is instantly consumed. Sincethe consumption of power is constantly changing, the generation must change ac-cordingly. This relationship of the generator is described by the first swing equation2.1.

∆ω̇ = 12H (Pm − Pe −D∆ω) (2.1)

In Equation 2.1 ω is the angular frequency, Pm and Pe the mechanical andelectrical power, D a positive damping constant and H the inertia. All parametersare expressed in pu. In the case of the damping D = 0, the system will be inequilibrium and hence the frequency constant only if the generated power Pm andconsumed power Pe are equal.

The generator, which is coupled to the turbine by the turbine axis, converts me-chanical power to electrical power. The kinetic energy in the water is transformedto mechanical energy, which accelerates the turbine and generator while the con-sumption of electrical power on the grid decelerates the turbine and generator [8].If the generated power is larger than the consumed power, Pm > Pe, the generator

10 CHAPTER 2. THEORY OF KAPLAN TURBINE HYDROPOWER PLANT

and turbine will accelerate and the frequency thereby increase. If Pm < Pe theturbine and generator will be decelerated and the frequency decrease.

When Pm 6= Pe, the time derivative of the frequency depends on the powerimbalance ∆P = Pm − Pe and the stored kinetic energy in the system’s rotatingmasses. The inertia H is a measure of the system’s stored kinetic energy in theunit seconds. The inertia constant can be explained by assuming the event of themechanical power of the turbine instantly going from Pe to zero. If the generatorwill keep transforming kinetic energy to electric energy at rated power, the time ittakes for the turbine’s and generator’s speed to reach zero is the inertia constantH.

The damping D is a small positive constant describing the contribution of me-chanical friction [9]. The load, Pe in Equation 2.1, can be assumed to be frequencydependent to some extent, i.e. Pe = Pe,0 (1 +DPe ·∆ω). DPe is a positive dampingconstant acting similarly to D in Equation 2.1. The frequency control is improvedby having a large proportion of frequency dependant load, since the load then coun-teracts the frequency change ∆ω in Equation 2.1.

2.4 Per Unit - puPer unit, pu, is a convenient method to normalize all generator, turbine and servoquantities. The quantities are scaled such that rated or nominal value correspondto 1 pu. For example, this means a frequency of f = 50 Hz correspond to f = 1 pu.This nomenclature will be used throughout the report.

Having presented the general theory of a Kaplan turbine hydropower plant, nextchapter will treat the theory of the frequency control.

Chapter 3

Frequency Control

A Kaplan turbine hydropower plant is a complex non-linear, non-minimum phasesystem and the control system that regulates the electrical frequency is called gov-ernor. Theory and design of the governor and regulation criteria will be treatedseparately in this chapter.

The control system, containing the governor, actuators and servos are depictedin Figure 3.1. This system is a two inputs - two outputs system, although thegovernor only has one output. The governor uses the generator frequency f and apower signal feedback as inputs.

The power signal feedback to the governor is either the wicket gate position γor the electrical power Pe. This signal is used to determine a turbine’s participationin the frequency control. This function is referred to as droop and is described in3.2.

The governor’s output is the wicket gate setpoint position γsetpoint, which con-trols the actuators and servos. In the upper branch in Figure 3.1, γsetpoint controlsthe wicket gate actuator and servo. In the lower branch the combination unit com-putes the turbine blade position setpoint, αsetpoint, which controls the turbine bladeactuator and servo.

The most commonly used governors are quite simple and there has been littlechanges of the design over a long period of time. Originally the governors wereentirely mechanical and implementation of digital governors can therefore have no-ticeable resemblance in design structure. [10],[4].

Apart from the inherent non-minimum phase characteristics of the turbine andpenstock, the saturations in the servos present significant effect to the frequencyresponse. The governors used to control frequency and power generation in Kaplanturbines are usually PIDs. An alternative governor approach, where projectivecontrols are used to solve the sub optimal regulator problem, is presented in [5].For a simpler implementation of this thesis’ proposed improvements, the generalstructure of a PID governor is kept.

11

12 CHAPTER 3. FREQUENCY CONTROL

setpoint

D

P

I

Droop

Anti

w-u

reff

f

ref

setpoint

1

openT

1

close aT

1

close bT

1

s

1

actuators

1

1s

delayse

1

sT

d

dt

1

openT

1

close aT

1

close bT

1

s

1

actuators

1

1s

delayse

1

sT

d

dt

setpoint

se

tpo

int

Combination Unit

Turbine blades actuator, servo

Wicket gatesactuator, servo

PID controller

f

Figure 3.1: Block diagram of the control system

3.1 PID

A classical PID controller is the most widely used type of governor, depicted inFigure 3.1. An ideal PID regulator is defined as in Equation 3.1, where e (t) is thecontrol error.

u (t) = KP e (t) +KI

t∫t0

e (τ) dτ +KDde (t)dt

(3.1)

The proportional gain KP treats the current control error, the integration gain KI

the past control error and the differential gain KD the predicted future controlerror. Equation 3.2 shows the transfer function of the PID controller. The standardnomenclature in Swedish hydropower plants are bgp = KP = K, bgi = KI = K

τI,

bgd = KD = KτD.

F (s) = KP + KI

s+KDs = K

(1 + 1

τIs+ τDs

)(3.2)

On the topic of hydropower governors, there is a great deal of research on thePID parameter settings. This thesis does not treat the tuning of the PID parametersin the simulation model. A straightforward method is presented in [15]. The ruleof thumb parameter setting below are developed using the PI governor setting byHovey and Schleif [13],[14]. The governor setting is expanded by an appropriatederivative gain and the parameters are defined by the water starting time Tw and

3.2. DROOP 13

the generator inertia H.

KP = H

0.625 · TwKI = 10 ·KP

3 · TwKD <

KpTw3

The water starting time, Tw, is defined as the time it takes for the current waterhead to accelerate the water in the penstock through gravitation to the currentwater velocity.

The non-minimum phase properties of the turbine and penstock is due to thewater starting time Tw. The effect of the non-minimum phase response increasesas Tw increases. Practically, Tw give rise to a delay in the turbine response. Thismeans that the PID must be set with a small proportional gain KP such that thenon-minimum phase behaviour is limited. The relation of Tw and KP is seen inthe parameter setting above. In the case of island operation, the use of derivativecontrol action is beneficial, particularly for plants with larger water starting timesTw. [5]

D

P

I

Droop

Anti

windup

reff

f

,ref e refP

eP

setpoint

Figure 3.2: Block diagram of the PID controller with droop and anti-windup.

3.2 DroopWhen changes of the load occur in an electrical grid with more than one turbine gov-ernor, the change in generated power must be distributed over these turbines. Therate of each turbine’s static participation in the frequency control is set individuallyin all turbine governors and is termed droop or ep. The droop can be interpreted asthe percentage change in frequency required to change the output power 100% of

14 CHAPTER 3. FREQUENCY CONTROL

rated power. The static droop is derived from the stationary changes in frequencyand generated power in Equation 3.3.[9]

ep = − ∆f∆Pm

(3.3)

The droop is used to tell the governor how to balance the objectives of controllingthe frequency and the power. Setting ep = 0 implies that the governor only regulatesthe frequency. Typical values of the droop are ep ∈ [0.03, 0.06] pu/pu. [12]. Thedroop input is a power feedback signal which is either γ or Pe. The use of Pehas the advantage of easier setting of the droop and the power output reference.However, the use of γ as substitute for a feedback of the power signal is common.If instead Pe feedback is used, the output from the droop block in Figure 3.2 willbe ep (Pref − Pe). For an increase of the load Pe, the governor will react as if theactual frequency is initially increased while the frequency is actually decreasing asa result of the power imbalance. The larger the droop gain ep, the larger will theeffect of this non-minimum phase behaviour be. This could be avoided by using γas a substitute of the power.

3.3 Anti-windupThe integration action of the PID in Equation 3.1 treats the past control error, e (t).As long as the control error e (t) 6= 0, its integral will keep increasing. For largeor long lasting control errors, the integration action may saturate the controlleroutput. This phenomenon is called integrator windup and will lead to a impairedcontrol even after the control error is eliminated.

To avoid this problem, an anti-windup can be implemented. The concepts arepresented in Figure 3.3. Once the controller output is saturated, the anti-windupis activated and the integral action ceases to grow. The gain of the anti-windupfeedback has to be high in order to quickly reach steady state under saturationconditions.

3.4 Regulation criterionIn terms of frequency control, hydropower plants can be divided into three categories

1. No control - the generator is linked to a strong electrical grid which frequencyentirely determines its rotational speed.

2. The plant has a part in controlling the frequency of the grid, decided by thedroop settings (usually 4-6 %)

3. The plant controls the frequency of an island grid.

For category 2 and 3, a complete governor is needed. Results from empiricalstudies of hydropower plant’s small signal stability are used to determine whether

3.4. REGULATION CRITERION 15

Anti

windup

1

s

Figure 3.3: Block diagram of anti windup

or not frequency control is possible at a specific hydro power plant. The small signalstability criteria is given by Tm

Tw, which is the ratio of the turbine axis and water

time constants.The turbine axis time constant Tm is defined as the time it takes for the cur-

rent turbine torque to accelerate the system’s inertia to the synchronous rotationalvelocity. At rated power, Tm = 2H. As mentioned before, the water starting time,Tw, is defined as the time it takes for the current water head to accelerate the waterin the penstock through gravitation to the current water velocity. This means thatthe time constants differs depending on operating point in terms of water velocityand power. However, looking at the ratio of the two time constants, empirical evi-dence suggests that Tm

Tw≥ 2.5 is needed for a hydro power plant of category 2 and

TmTw≥ 3 (value of 4-6 is desirable) for a hydro power plant controlling the frequency

in an island grid. [2]. This criteria is only based on small signal stability, whichis a condition for stability at larger disturbances. The time constants, Tm and Tw,are determined by the hydro power plant’s construction, hence reduced friction inthe penstock and larger turbine inertia would increase Tm

Tw. To determine how large

disturbances are affecting the system, computer simulations must be used.Fulfilling Tm

Tw≥ 3 does not guarantee stable governing of an island grid. As

described in 2.1.2 and also seen in Figure 3.1 there are saturations and backlashesfound in the servos. The effect that these non-linear components have on the fre-quency control will be explained by support of measurement data of a Swedishhydropower plant. Figure 3.4 shows the frequency, active power, wicket gate andturbine blade positions when a step increase occurs in the demand of electricalpower in an island grid.

As the step occurs, the consumed power is larger than the generated power andthe frequency begin to decrease, as described by Equation 2.1. This causes thewicket gates to open in order to accelerate the turbine. The constant slope of theturbine blade position curve indicates that the servo reached its saturation. As

16 CHAPTER 3. FREQUENCY CONTROL

30

40

50

60

70

80P

ositi

onc[w

cofcf

ully

cope

n]

10 20 30 40 50 60 70 80 90 10048

49

50

51

52

Timec[s]

Fre

quen

cyc[H

z]

20

22

24

26

28

Act

ivec

Pow

erc[M

W]

γ bcWicketcgates bcTurbinecblades

Pm

Pe

Frequency

α

Figure 3.4: Measurements data of frequency, power, wicket gate and turbine bladepositions after a step increase of demanded power in a Swedish hydropower plantoperating an island grid.

long as the frequency is lower than nominal, the governor output will continue toopen the wicket gates. The turbine blades, which have a slower servo, try to getto the position of the optimal combination. When the turbine blades reach thepoint where the generated and consumed power are in equilibrium, the wicket gateshave opened too far and the mechanical power continues increasing. In order todecrease the power, the wicket gates are rapidly closed, the turbine blades followat their maximum speed and the system exhibits stable oscillations. The test andmeasurements are then aborted due to risk of tripping the generator. The effect ofthe turbine blade servo backlash can be noticed in the troughs of the turbine bladeposition curve.

The measurements in Figure 3.4 show a common turbine behaviour when run-ning island operation. The unsatisfactory stable oscillations are mainly caused bythe speed limiter of the turbine blade servo. In the next chapter, two proposedcontrol strategies for counteract this behaviour are presented.

Chapter 4

Control Strategies

In 3.4, the effect of a large disturbance on a hydropower plant running an island gridwhere shown. This should only be treated as an example of a Kaplan hydropowerplant without any adaptation tries to run an island grid, as all power plants havedifferent built-in abilities for island operation. However, the behaviour shown inFigure 3.4 is relevant and the problems with the frequency regulation after the loaddisturbance can be divided into two governor requirements:

• Quick response after load changes

The frequency amplitude of the first swing is only depending on how quicklythe turbine responds to changes of demanded power and the inertia of the ro-tating mass. The inertia is not easily changed which leaves trying to improvethe control effect of the governor output.

• Damping of oscillations after load changes

The oscillations may have several reasons but is mainly due to the turbineblades lagging the wicket gates, leading to a large deviation from the opti-mal combination. Improvement of the response time of the turbine will alsobenefit damping of oscillations. However, to get a smoother tune in of thefrequency, the governor’s output must be limited when the difference betweenthe turbine blade setpoint and actual position grow large.

Two control strategies to improve these properties are proposed and evaluated inthis thesis. The strategies are named Combination Offset and Inverted Combina-tion Anti-windup. Design and implementation of these are presented in followingsections. Results of the analysis of these strategies and proposed improvements arepresented in Chapter 7. The methods used for the analysis are found in Chapter 6.

17

18 CHAPTER 4. CONTROL STRATEGIES

4.1 Combination Offset

When trying to improve the response time of the turbine, and thus reducing thefirst frequency swing, the turbine inputs are in focus. The turbine’s two controlsignals have different properties around an optimal operating point. In relativeterms, wicket gates have fast dynamic but a small effect on the output while theturbine blades have slow dynamic and large effect of the output.

Components limiting the control signals, such as speed saturations, time delaysand backlashes in the servos can not be easily affected. The main matter is essen-tially the speed saturation in the turbine blade servo. When the turbine is operatingwith optimal combination, connected to a strong electrical grid, the speed satura-tion does not pose any problem. The optimal combination is constructed such thatfor every wicket gate position, the turbine blade position is chosen to give maximumefficiency. The idea behind the Combination Offset strategy is to depart from theoptimal combination in order to gain a faster response of the turbine’s mechanicaltorque. This implies that control effect is transferred from the turbine blades to thewicket gates. As a result, a more rapid increase of power generation is gained atthe cost of loss of efficiency.

In Figure 4.1, curves of the turbine’s generated power as a function of the wicketgate and turbine blade position are shown. In the same figure, the optimal com-bination curve and the optimal combination curve with an arbitrary offset are alsodepicted. To explain the idea of this strategy, the stationary behaviour is stud-ied. The turbine is assumed to be operating at steady state in the operating pointmarked 1), along the optimal combination curve. An increase of the generatedpower by 0.1 pu, demands some movement of the turbine blades. The wicket gatesalone, with fixed turbine blades, could not increase the power by 0.1 pu, which isalso shown in Figure 4.2. If instead the turbine is operating at the same power onthe offset combination curve in Figure 4.1, marked 2), a 0.1 pu increase of the powerwould need no movement of the turbine blades.

When using the Combination Offset, the limitations of the turbine blade servoare no longer as important for a fast increase of power. At a greater extent, theresponse time of the turbine are depending on the wicket gate servo, with a fasterregulation as a result. Letting the turbine blades be ahead of their optimal com-bination does also improve the response time of decreasing the power since it to alarger extent depends on the change of the wicket gate position, as can be seen inFigure 4.1. This represents the basic idea behind the Combination Offset strategy.The same reasoning is briefly mentioned in [2] but has not been found analysed orimplemented.

Implementation of the combination offset does not entail major intervention.The optimal combination curve is simply shifted upwards with a constant corre-sponding to the combination offset. Seen in Figure 4.3 this means that the turbineblades never reach their lower endpoint. Since the steps between the power levelsare smaller for low wicket gate positions, seen in Figure 4.1, the frequency regu-lation is not improved by having a constant offset in this area. The combination

4.1. COMBINATION OFFSET 19

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Wicket8gate8position8γ

Tur

bine

8bla

de8p

ositi

on8α

data1data2data3data4data5data6data7data8data9data10data11data12data13data14

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

data1data2data3data4data5data6data7data8data9data10data11data12data13data14

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

data1data2data3data4data5data6data7data8data9data10data11data12data13data14

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1

data1data2data3data4data5data6data7data8data9data10data11data12data13data14

Mechanical8powermP

Optimal8combination8curve

Offset8combination8curve

0.48pu0.18pu 0.78pu 1.08pu

1)

2)

Figure 4.1: Mechanical power Pm as a function of the wicket gate position γ andthe turbine blade position α. The wicket gates alone have a greater impact on thepower when operating on the offset combination curve compared to the optimalcombination curve.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Wicket[gate[position[γ

Mec

hani

cal[p

ower

[Pm

[pu]

Figure 4.2: Mechanical power Pm as a function of the wicket gate position γ andfixed turbine blade position α = 0.15 pu. Operation with optimal combination,marked �, can not achieve ∆Pm = 0.1 pu with adjustment of the wicket gatesalone.

curve can instead be allowed to reach the turbine blade position α = 0, which willbe beneficial in terms of efficiency, without loss in frequency control. This is im-plemented by letting the combination curve linearly go from turbine blade positionα = 0 to the point where the constant level of the combination curve ends, withroughly the same slope as in that point. The combination curve is also adapted to

20 CHAPTER 4. CONTROL STRATEGIES

have a maximum turbine blade position of 1 pu. The dotted and dashed lines inFigure 4.3 show the combination curve before and after these implementations.

offset

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

Wicketggategpositiongγ

Tur

bine

gbla

degp

ositi

ongα data1

data2data3data4data5data6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0

data1data2data3data4data5data6

Offsetgcombinationgcurve

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0

data2data3data4data5data6

Optimalgcombinationgcurve

Figure 4.3: Implementation of combination offset curve.

4.2 Inverted Combination Anti-windupAs mentioned, large load disturbances causes the turbine blades to lag the wicketgates, resulting in larger frequency deviation which could lead to power oscillations.This behaviour is further exacerbated when increase of the wicket gate positioncauses the mechanical power to decrease. As shown in Figure 4.2, the mechanicalpower is seen decreasing when the wicket gates lead the optimal combination byapproximately 0.1 pu.

The governor’s internal anti-windup saturates the wicket gate setpoint positionif it exceed its limits. Normally the limiter has a fixed upper and lower levels. Thismeans that the wicket gate setpoint position on the governor’s output will be limitedat the same upper level regardless of the actual operating point. If the turbine isoperating at low power and the wicket gate position is small, this could mean thatthe setpoint signal goes from almost closed wicket gates to fully open before the itis limited.

To counteract the continuous movement of the wicket gates, while the turbineblades are lagging far behind, the inverted combination anti-windup is proposed.The strategy has the same principle used by the internal anti-windup but instead of alimiter with fixed limits, a variable limiter is implemented. The levels of the variablelimiter is controlled by the actual turbine blade angle. Since the anti-windup iscomparing wicket gate positions on the governor’s output, the turbine blade positionmust be transformed into a wicket gate position. The principle is shown in Figure4.4. An inverted optimal combination curve returns the corresponding wicket gateposition γα to a given turbine blade position α. This position is feedbacked to

4.2. INVERTED COMBINATION ANTI-WINDUP 21

control the upper saturation level of the limiter. To give the governor its necessaryworkspace a constant σ is added to the γα.

setpoint

Inverted

combination

f

Actual turbine blade

position

Wicket gate setpoint

position

min1

1

s

AWK

Figure 4.4: Block diagram of Inverted Combination Anti-windup.

The implementation of the Inverted Combination Anti-windup in the modelis made in several steps. First, if a combination offset is used, described in 4.1,it subtracted from α. The optimal combination curve described by a 4th orderpolynomial is inverted. The inverted combination converts α into γα which is feed-backed to the variable limiter. The constant σ is added to γα to give the governorworkspace. Finally, to assure that the governor output never exceeds 1, the condi-tion min (γα + σ, 1) is added on the limiter input.

In next chapter, implenentation of the two proposed strategies and the reset ofthe simulation model used, is presented.

Chapter 5

Simulation Model

The training simulator used for the analysis is built in the modeling and simulationtool Dymola. Dymola uses the object-oriented modeling language Modelica. Thereis a large library of standard components but the user may also create their own.The models consists of differential, algebraic and discrete equations creating anequation system which is solved numerically when running simulations. [16].

Figure 5.1 shows a block diagram of the simulator model used in this thesis. Amore detailed presentation of the blocks are presented in the following sections.

Governorsetpoint

setpoint

HQ

reff

ref

Wicket gate

actuator, servo

Combination

unit

Propeller blades

actuator, servo

Turbine

Penstock

Generator

and grid

eP

Inverse

combination

unit

offset

f

f

mP

M

f

f

Figure 5.1: Block diagram of the simulation model.

The purpose of this project is to achieve a method for improving the abilityfor an arbitrary Kaplan turbine to operate an island grid. This means that thepractice simulator at hand is not fitted to any specific power plant. None the less,the initial work of fitting the simulator model in terms of delays, saturations andother parameters are essential for getting a qualitative model.

For fitting of the model, measurement data from tests on several different hy-dropower plants, where the island operation was not satisfactory, is used. Thesimulation model is fitted with parameters representing a worst case in terms ofability to operate an island grid. The measurements are from power plants with

23

24 CHAPTER 5. SIMULATION MODEL

rated power of 20-50 MW which represents the typical size of a Swedish Kaplanturbine hydropower plant, where the results of this project are intended to be im-plemented.

5.1 GovernorThe turbine governor is a PID-regulator with anti-windup and droop. The blockdiagram of the governor is shown in Figure 5.2. There are three input signals to thegovernor; the frequency error ∆f = fref − f and wicket gate error ∆γ = γref − γ.The last input signal γα, used for the anti-windup, is the inverted combinationof the actual turbine blade position, i.e. the optimal position of the wicket gatescorresponding to the actual turbine blade position. It is added with a constant σ,preventing the governor output to be constantly saturated. The output signal isthe setpoint position of the wicket gate, γsetpoint. The governor model is largely

reff

f

ref

setpoint

1

D

D

K s

Ks

N

PKpe

IK

s

f

min

1

AWK

Figure 5.2: Governor model.

explained by Figure 5.2 and only standard components has been used. The deriva-tive part is equipped with a low-pass filter to avoid rapid changes of the controlerror which gives an infinite derivative action. The filter constant N determines thecut-of frequency.

5.2 Servos and ActuatorsAs mentioned, the servos for the wicket gates and the turbine blades play an im-portant part in controlling the turbine outputs. Typical Kaplan turbines, withoutany requirements on island operation, have an opening time of the turbine bladesof 30-60 seconds and the wicket gates of about 5-15 seconds [2]. The measurementin Figure 3.4 shows an opening time of the turbine blades of about 60 s. This shows

5.3. TURBINE 25

quite a wide range of opening times for servos in different hydropower plants. Forthe purpose of testing a method suitable for improving the frequency regulation inisland operation, the model is adapted for a realistic worst-case scenario.

The servo and actuator model shown in Figure 5.3 have the same structurefor both the wicket gates and turbine blades. The actuator is realised by a first-order function and a time delay only used for the turbine blades. The servo modellooks more complex than it is because of the two switches. Neglecting them tobegin with, the circuit is more intelligible. The servo model basically consists of again 1

Ts, where Ts is the servo time constant, and an integrator. The servo output

is a position, which is feedbacked into the servo. In the turbine blade servo, abacklash is introduced to reduce vibrations. However, the main part of interest is thespeed limiter before the integrator. The limiter has variable saturation levels whichcontrols the time derivative of the servo movement. Hence, the lower saturationlevel controls the maximum closing time and the upper limit the maximum openingtime. For the turbine blades, the opening and closing times are both set to 60seconds and the switches are therefore not being used. Based on measurements andtypical values, the wicket gate opening time is set to 10 seconds. As seen in Figure5.3, there are two different closing times depending on how near the wicket gatesare to being shut. This is because of the need to slow down the wicket gates thelast bit, in order to avoid damaging pressure waves. Controlled by the condition >,the closing time is 10 seconds when the wicket gate position is > 0.25, 20 secondsotherwise. The other switch condition d

dt checks if the wicket gates are opening orclosing.

1

openT

1

close aT

1

close bT

1

s

1

actuators

1

1s

delayse

1

sT

d

dt

positionsetpoint

Figure 5.3: Servo and actuator model.

5.3 TurbineThe core of the simulation model, the turbine model, has four inputs and twooutputs. The turbine is controlled by the outputs from the servos; the wicket gateposition γ and the turbine blade position α. The generator frequency f and thewater head H are the other two input signals. From these, the water flow Q iscomputed, which is feedbacked to the penstock model. This feedback is needed

26 CHAPTER 5. SIMULATION MODEL

because the water head is affected by changes of the water flow. The mechanicaltorque M is the second output signal.

The water flow and the mechanical torque are computed in two steps. From thewicket gate and turbine blade positions, the unit flow Q11 and unit torque M11 arecomputed. The unit values are based on a turbine operating at a water head of 1m and a turbine propeller with a diameter of 1 m. To transform the unit values fora geometrically uniform turbine operating at a different head, the uniformity andaffinity laws are used. The uniformity law is valid for two geometrically uniformturbines operating at the same head. It states that if the turbine size is changed,defined by the turbine propeller diameter, the water speeds at geometrically similarpoints will be unchanged if all other parameters are kept. The affinity law can thenbe used to compute the changes of the water speeds in the a turbine at differentwater heads. [2]. Transforming the unit values to actual values, where the frequency,propeller diameter and head is used, yields the mechanical torque M and the waterflow Q. The turbine model also includes functions to compute the efficiency η andthe mechanical power Pm. The mechanical power is a function of frequency and themechanical torque. The efficiency is a function of the mechanical power, the waterhead and the water flow. The equations are shown in Equations 5.1 and 5.2, ω isthe angular velocity, ρ the water density and g the acceleration of gravity.

Pm = M · ω (5.1)

η = PmρgHQ

(5.2)

5.4 Generator and LoadThe dynamics of the generator is described by the two-axis model. It consists of4 differential equations, the swing equation 2.1 being one of them. Providing ajustifiable explanation of these equations is extensive and lies outside the the scopeof this thesis. For this application, the essential dynamics are captured by the swingequation. The generator model is built for more advanced applications and the otherequations have has no practical significance in these simulations. For the interestedreader any literature on power system stability such as [11] is recommended.

The generator model has two inputs; the turbine torque and the generator fieldvoltage. By the two-axis generator model, the electrical power, current, voltage andfrequency is determined. A built-in limited PI-regulator controls the stator voltageby affecting the field voltage.

The load model is directly connected to the generator model. Wanted powerload levels and step disturbances are entered as well as the percentage of frequencydependent load. As described in 2.3 the electric power demand Pe during simula-tions is an input to the generator model.

In next chapter, the model presented is used for time domain simulation studiesof the two proposed control strategies.

Chapter 6

Analysis Method

In order to meet the frequency requirements in 1.2, the strategies CombinationOffset and Inverted Combination Anti-windup have been proposed to improve thegoverning of a Kaplan turbine hydropower plant operating an island grid.

The objective of the Combination Offset is to gain a control system that cankeep the initial frequency deviation ∆f < 2 Hz for a load disturbance of 0.1 pu.The purpose of the analysis is to study if the method has an improving effect onthe governing and if so, how the Combination Offset should be chosen to fulfill therequirements at lowest loss of efficiency.

The purpose of the Inverted Combination Anti-windup is to reduce the settlingtime of the frequency after a load disturbance of 0.1 pu. The analysis of this strategyis less extensive and is based on step responses of load disturbances.

Mainly the Combination Offset is studied and two analysis methods have beentried; time domain simulation and controllability analysis. Attempts with the latterhave not been successful which is further discussed in the end of this chapter, 6.2.The performing and purpose of the time domain simulations are described in detailin following section.

6.1 Time Domain Simulation

The time domain simulations have been performed on the model presented in Chap-ter 5. The simulation tool used is Dymola, which uses the Modelica language todefine the model. Every component of the model is built up by equations, as well asconnectors and conditional statements. These form an equation system describingthe model, which is solved numerically. The simulation results are then exported toMATLAB for numerical analysis. The model contains a complete island grid andthe possibility to control the load. It also allows to simulate a sub-part of the modelalone or to manipulate certain signals.

Simulations of the Combination Offset will be treated first. These are dividedinto three categories for a more comprehensible presentation. Lastly, the InvertedCombination Anti-windup simulations are treated.

27

28 CHAPTER 6. ANALYSIS METHOD

6.1.1 Stationary Behaviour study

The stationary behaviour study focuses on investigating the turbine behaviour.The purpose is to show how the turbine inputs, the wicket gate and turbine bladepositions, affects the output - the generated power. The data used from thesesimulations are captured after the inputs and output have tuned in and the systemis in steady state. Hence, the response times of the wicket gate and turbine bladepositions has no affect on the generated power.

One set of simulations are performed, presenting the turbine model behaviourfrom two different viewpoints.

Mechanical power as a function of wicket gate and turbine bladepositions a) Pm = f (γ, α)

The simulation set-up is presented in Figure 6.1.

Governorsetpoint

fixed

reff

ref

,e fixedP

f

fmP

M

ff

Actuators

and servos

Turbine and

penstock

Generator

and grid

Figure 6.1: Set-up for simulation of Mechanical power as a function of wicket gateand turbine blade positions α = f (γ, Pm)

The signals marked in red are set with fixed values and the ones marked inblue are used for the simulation results. A set of simulations is started by settinga value on the electrical power, Pe,fixed. The turbine blade position, αfixed is alsogiven a fixed value and the simulation is run. The governor tunes the wicket gateposition γ until the turbine output, the mechanical power Pm, and the electricalpower Pe,fixed are equal. Wicket gate and turbine blade positions, γ and αfixed,and the mechanical power Pm are captured in steady state. Several values of αfixedis simulated for each value on Pe,fixed covering [0, 1] pu.

The result presented in Figure 7.1 show the wicket gate - turbine blade positionrelationship for each value of the mechanical power. This turbine inputs-outputrelationship in steady state shows the difference in control effect of the wicket gateand turbine blades. The optimal combination curve of the unaltered system and afew offset combination curves are depicted in the same plot. This is meant to explainwhy the Combination Offset is likely to give a faster power response, bearing in mindthat the wicket gates move much faster than the turbine blades.

6.1. TIME DOMAIN SIMULATION 29

Mechanical power as a function of wicket gate and turbine bladepositions b) Pm = f (γ, α)

The same simulation data is used as in the previous simulations. The only differenceis the presentation of the results, depicted in Figure 7.2. The results here is plottedas the relationship between the wicket gate position and the mechanical power foreach turbine blade position. This aims to clearly demonstrate the wicket gates’limited control effect of the mechanical power.

6.1.2 Efficiency Losses

The optimal combination curve used in the unaltered system result in the turbineoperating at its maximum efficiency at all operating points. Since the CombinationOffset is based on shifting the optimal combination curve, this implies loss of turbineefficiency.

These simulations study how the efficiency of the turbine is affected by usingCombination Offset. The data is captured when system is in steady state. This isstudied in two different ways.

Efficiency as a function of mechanical power and combination offset

η = f (Pm, offset)The simulation set-up used is seen in Figure 6.2, where the signals marked in

red are fixed and the blue used for the results.

Governor

setpoint

setpoint

HQ

reff

ref

Wicket gate

actuator, servo

Combination

unit

Propeller blades

actuator, servo

Turbine

Penstock

Generator and

grid

.c o m b

o f f s e t

f

fmP

M

,e fixedP

Figure 6.2: Set-up for simulation of efficiency as a function of mechanical powerand combination offset η = f (Pm, offset)

The full simulation model is used with a fixed value on the combination offset.A set of simulations are performed with values on the electrical power Pe,fixed inthe range [0.1, 1] pu, i.e. 10-100% of rated power. This is repeated for several valuesof combination offsets.

The simulation results consists of one curve for each combination offset simu-lated, showing the relationship between the efficiency and the mechanical power.

30 CHAPTER 6. ANALYSIS METHOD

Hence, the affect of the combination offset on the efficiency can be analysed withrespect to the generated power. The results are depicted in Figure 7.3.

Efficiency, wicket gate and turbine blade position relationship

For this simulation, only the turbine model is considered. The set-up is presentedin Figure 6.3.

H

QTurbine

Penstock

M

f

Figure 6.3: Set-up for simulation of efficiency as a function of electric power andcombination offset η = f (Pe, offset)

The frequency must be fixed to its nominal value (50) Hz since the generator isnot connected. For each simulation, the wicket gate and turbine blade positions areset and the resulting efficiency data captured. Several simulations are performedcovering a sufficient amount of combinations of the wicket gate and turbine bladepositions in the range [0, 1] pu.

The simulation data is interpolated and presented with MATLAB functioncontour with respect to the wicket gate and turbine blade positions. Combina-tion curves with different offsets are depicted in same figure to show the effect ofthe combination offset on the efficiency with respect to the wicket gate and turbineblade positions. The result is found in Figure 7.4

6.1.3 Load Disturbance Simulations

To complete the analysis, the effect on the governing with Combination Offsetimplemented is studied. Stated in the governor requirements, load increases anddecreases of 0.1 pu should be managed from initial operating power of 0-80% and100-20% respectively, keeping ∆f < 2 Hz. Repeated load disturbance simulationswith gradually increased combination offset is performed. The objective is to con-clude a suitable range of the combination offset, to fulfill the governing requirementsover the full range of initial operating powers.

6.2. CONTROLLABILITY ANALYSIS 31

Maximum Load Step Disturbance

The maximum load step disturbance ∆Pe is simulated for the case when the fre-quency deviation ∆f = 2 Hz. The entire simulation model is used. The simulationsare performed by increasing or decreasing the load step disturbance until the fre-quency deviation reaches 2 Hz. The procedure is repeated at different initial loadsP 0e and combination offsets.Two different plots are shown simulating load step increases and load step de-

creases, depicted in Figures 7.5 and 7.6 respectively.

Step Responses

A load disturbance of Pe = 0.1 pu is simulated using the entire simulation model.Only increasing load disturbances is considered since those are more critical in termsof keeping ∆f < 2Hz. The combination offset is implemented and set to a suitablevalue concluded from previous simulation results. The result in Figure 7.7 showthe frequency when the system is subjected to the disturbance, at different initialoperating points Pe,0.

6.1.4 Inverted Combination Anti-windup

The analysis of the Inverted Combination Anti-windup is studied with a straight-forward approach. The constant σ, which controls the governor output workspace,is tuned in through testing. This is more thoroughly explained in 3.3. Step dis-turbances of 0.1 pu with and without the method implemented are simulated forcomparison.

The full model is simulated without the Combination Offset active. The resultis depicted in Figure 7.10.

6.2 Controllability Analysis

The purpose of the controllability analysis is to analytically study the system’s con-trollability. By developing a linearised system model around an operating point,the aim is to analytically determine a satisfactory combination offset that will meetthe governing requirements. The linearised model is developed by simulating theturbine with a random binary signal with small perturbations on the wicket gate set-point γsetpoint. Using the system identification toolbox in MATLAB, the linearisedmodels were found sufficiently consistent with the simulation model.

However, the approach of the controllability analysis described falls short whenanalysing island operation. The idea that the linearised model would be validaround the operating point is true to some extent but the span of where the modelis valid is not sufficient for larger changes in γsetpoint. For larger changes of the loadas ∆Pm = 0.1 pu, small signal stability analysis is not sufficient, since effects from

32 CHAPTER 6. ANALYSIS METHOD

non-linearities will be noticeable. A compilation of articles discussing linearisedturbine models for analyse of island operation is presented below.

In [17], the authors conclude that small signal stability studies "adequately canbe modelled linearizing the non-linear turbine model about the appropriate operat-ing point". For transient stability it is concluded that in "studies of small isolatedpower systems the governor speed regulation and the response of the turbine mustbe included in the model".

In [5] a review on hydroplant models is presented. With the same reasoning asin [17] and [10], linear turbine models are described being valid only for small signalperformance study such as governor tuning. "As the hydraulic turbine exhibitshighly nonlinear characteristics that vary significantly with the unpredictable loadon the unit, this requires controller gain scheduling at different gate positions andspeed errors...Nonlinear models are required when speed and power changes arelarge during an islanding condition".

Chapter 7

Results

The results of the time domain simulations are depicted and commented in thesame order as presented in Chapter 6. For easier comparison of the results, allsimulations studying offset combination curves use the same four values. These val-ues [0, 0.05, 0.10, 0.15, 0.20] are considered sufficient for concluding an recommendedcombination offset interval.

7.1 Stationary Behaviour Study

These simulations investigates the turbine inputs-output behaviour. The resultspresented in Figures 7.1 and 7.2 are based the same set of simulations presentedfrom two different viewpoints.

7.1.1 Turbine blade position as a function of wicket gate position andmechanical power α = f (γ, Pm)

Figure 7.1 shows the relationship between turbine blade position α and the thewicket gate position γ at constant levels of mechanical power Pm. These resultscontain the explanation to why larger load disturbances in island operation willtrip the generator. A load increase of 0.1 pu, when operating along the optimalcombination curve, can not be compensated for by the wicket gates alone. Move-ment of only the wicket gates implies moving parallel with the horizontal axis inFigure 7.1. The small output effect of the wicket gates when using optimal com-bination demand simultaneous movement of the turbine blades to manage a largerdisturbance.

When shifting the combination curve upwards with some combination offset, theoutput effect of the wicket gates are seen increasing. Output effect of the slower tur-bine blades are allocated to the faster wicket gates. Even a small combination offsetis seen having an improving effect on the ability to manage large load disturbances.

It should also be noted that at all operating points with optimal combination,a decrease of the power by 0.1 pu can be achieved by the wicket gates alone.

33

34 CHAPTER 7. RESULTS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

Wicketwgatewpositionwww w

Tur

bine

wbla

dewp

ositi

onw α

γ

data1

data2

data3

data4

data5

data6

data7

data8

data9

data10

data11

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data13

data14

data15

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data17

data18

data19

data1data2data3data4data5data6data7data8

data1data2data3data4data5data6data7data8d t 9

data1data2data3data4data5data6data7data8data9data10

data1data2data3data4data5data6data7data8data9data10

data1data2data3data4data5data6data7data8data9data10

Combinationwcurveswwwwwwwwoffset=0offset=0.05offset=0.10offset=0.15offset=0.20

0 4

0.6

0.8

1

bla

de

wpo

sitio

nα

data1

data2

data3

data4

data5

data6

data7

data8

data9

data10

data11

data12

data13

MechanicalwpowerwmP

0.1wpu 0.4wpu 0.7wpu 1.0wpu

Figure 7.1: Mechanical power as a function of wicket gate and turbine blade posi-tions Pm = f (γ, α)

7.1.2 Mechanical power as a function of wicket gate and turbine bladepositions Pm = f (γ, α)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wicketbgatebpositionbγ [pu]

Mec

hani

calbp

ower

bPm

[pu]

α=0.2

α=1.0

α=0.4

α=0

α=0.6

α=0.8

α=0.2

α=1.0

α=0.4

α=0

α=0.6α=0.8

optimalbcombination

Turbine blade position

Figure 7.2: Turbine blade position as a function of wicket gate position and electricpower α = f (γ, Pe)

Figure 7.2 use the same simulation data as previous figure. This presentation allowsmore clearly to study the limited output effect of the wicket gates. The six curvesshow the relationship of the mechanical power Pm and the wicket gate positionγ for a constant turbine blade position α. The curves are seen flatten out as γ

7.2. EFFICIENCY LOSSES 35

increases. Without the coordinated movement of the turbine blades, the wicketgates are shown to have limited effect on the mechanical power.

The simulation for each curve is ended when the maximum mechanical poweris reached. Increasing the wicket gate position past that point result in the powerdecreasing. The squares mark the optimal combination of the wicket gates andturbine blades. Thus, operation with optimal combination does not allow the wicketgates alone to compensate a load disturbance of 0.1 pu.

7.2 Efficiency LossesResults from two different simulation set-ups, studying efficiency losses due to theCombination Offset are presented. The first simulation consider the entire simula-tion model while in the second, only the turbine model is used.

7.2.1 Efficiency as a function of electric power and combination offsetη = f (Pm, offset)

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.150

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0=0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.150

0.1

0.2

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0=0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.150

0.1

0.2

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0=0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.150

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0=0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.150

0.1

0.2

0.3

InputpAmplitudepA

P m[p

u]

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0=0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

Combinationpcurvesoffset=0

offset=0.05offset=0.10offset=0.15offset=0.20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

40

50

60

70

80

90

100

MechanicalppowerpPm

[pu]

Effi

cien

cypη

[E]

Figure 7.3: Efficiency as a function of mechanical power and combination offsetη = f (Pm, offset)

The simulation result of Figure 7.3 show the relationship between the turbine effi-ciency and the generated mechanical power, for different combination offsets. TheKaplan turbine is know for its high and flat efficiency curve which is also confirmedby the results. At lower power generation, the efficiency is drastically lowered. Thisis the reason why Kaplan turbines never for operate longer periods of time at thesepowers during normal circumstances.

Comparing the loss of efficiency with Combination Offset implemented, thesmallest differences are seen at the maximum power generation. This is expected

36 CHAPTER 7. RESULTS

since the combination curves are identical for γ > 0.8 pu. However, such largeloads are not possible when operating an island grid, since the turbine must beallowed room for manoeuvring. A reasonable assumption is that most operationwill be in the range of Pm ∈ [0.1, 0.7] pu. An exact percentage of efficiency lossfor each combination offset is hard to derive from these results, but it provides anestimate of losses to be expected using this method. The largest losses are foundfor Pm ∈ [0.2, 0.4] pu. Maximum loss with offset = 0.15 is approximately 20%.

7.2.2 Efficiency, wicket gate and turbine blade position relationship

WicketTgateTposition γ

Tur

bine

Tbla

deTp

ositi

onα

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1

data1data2data3data4data5data6data7data8data9data10

1

data1data2data3data4data5data6data7data8data9data10

1

data1data2data3data4data5data6data7data8data9data10

1

data1data2data3data4data5data6data7data8data9data10

1

da adata2data3data4data5data6data7data8data9data10

1

data3data4data5data6data7data8data9data10

EfficiencyTη

CombinationTcurvesTTTTTTTToffset=0

offset=0.05

offset=0.10

offset=0.15

offset=0.20

η=0.95 η=0.90

η=0.85 η=0.30

Figure 7.4: Efficiency of different combinations of wicket gate and turbine bladepositions.

In Figure 7.4, the efficiency corresponding to combinations of the wicket gate andturbine blade positions are depicted together with the combination curves. The sixinnermost lines are levels of 1 % while the rest represent steps of 5 % of efficiency.

The simulation results are interpolated around fixed values of the efficiency.This presentation is chosen so that the efficiency can be easily related to the offsetcombination curves. This may be used for optimization of the offset combinationcurves. For instance, at operating points where the load disturbance requirementis met by a wide margin, there is unnecessary loss of efficiency. For segments ofthe combination curves corresponding to these operating points, a downward shiftwould be beneficial for the overall efficiency loss.

Much of the insight gained from Figure 7.3 can also be seen in this figure.Though, this presentation facilitates getting an approximate value of efficiencychanges. The wicket gate positions γ ∈ [0.1, 0.6] represents an approximate range ofoperating points during during island operation (derived from the assumption that

7.3. LOAD DISTURBANCES 37

Pm ∈ [0.1, 0.7] pu, using the combination curves in Figure 7.1). In this segment inFigure 7.4, the maximum loss of efficiency between the combination curves plottedare 5%.

In can be worth noticing that the optimal combination curve, offset=0, almostdivides the plot in the center, demonstrating that it actually represent the maximumefficiency.

7.3 Load Disturbances

The previous simulation results of the optimal combination have shown its limi-tations when running island operation. The effect of the Combination Offset hasalso been studied and the simulation results show how control effect is shifted fromthe turbine blades to the wicket gates. In addition, an approximation of how theefficiency is affected by different combination offsets has been presented.

These final simulations focuses on testing if the method holds up to the require-ment on load disturbance and frequency deviations.

7.3.1 Maximum Load Step Disturbance

Simulation results of maximum load step increase and decrease ∆Pe when frequencydeviation ∆f = 2 Hz are depicted in Figures 7.5 and 7.6 respectively. The result isgiven at different initial operating points and offsets.

Results of Figure 7.5 show that the need of combination offset is coupled with theoperating point. At operating point P 0

e = 0.1, the optimal combination is sufficientto manage a load step disturbance of 0.1 pu keeping ∆f < 2 Hz while at operatingpoint P 0

e = 0.9, a combination offset of 0.2 would be needed.Referring to the reasoning in 7.1.1, the result in Figure 7.6 show that the load

decreases are managed without any use of combination offset.

38 CHAPTER 7. RESULTS

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0

0.7

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

CombinationAcurvesoffset=0

offset=0.05offset=0.10offset=0.15offset=0.20

0.1 0.3 0.5 0.7 0.90.05

0.1

0.15

0.2

Pe0 [pu]

∆P

emax

[pu]

Figure 7.5: Maximum load step increase ∆Pe as a function of initial load P 0e and

combination offset.

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.30

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

0 0.05 0.1 0.15 0.20

0.1

0.2

0.3

γ0

0

InputpAmplitudepA

P m[p

u] data1data2data3data4data5

Combination]curvesoffset=0

offset=0.05offset=0.10offset=0.15offset=0.20

0.4 0.6 0.8 10.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

Pe0 [pu]

∆P

emax

[pu]

Figure 7.6: Maximum load step decrease ∆Pe as a function of initial load P 0e and

combination offset.

7.3.2 Step Responses

Responses of a step disturbance of ∆Pe = 0.1 pu are presented in Figure 7.7. Withthe objective to manage the disturbance at initial operating point Pe,0 = 0.7 pu,combination offset = 0.13 is found sufficient.

7.3. LOAD DISTURBANCES 39

195 200 205 210 215

0.3

0.4

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1.1

Time [s]

f, P

e[p

u]

195 200 205 210 215 220 225

0.7

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Time [s]

f, P

e[p

u]

Pe,0

=0.7

data1data2data3eP

f

0.96pu0.96pu

0.96pu 0.96pu

195 200 205 210 215

0.2

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1

Time [s]

f, P

e[p

u]

195 200 205 210

0.3

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1

1.1

Time [s]

f, P

e[p

u]

195 200 205 210 215

0.5

0.6

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1

1.1

Time [s]

f, P

e[p

u]

Pe,0

=0.5

195 200 205 210 215 220

0.7

0.8

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1

1.1

Time [s]

f, P

e[p

u]

Pe,0

=0.7

data1data2data3eP

f

195 200 205 210 215

0.3

0.4

0.5

0.6

0.7

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1

1.1

Time [s]

f, P

e[p

u]

Pe,0

=0.3

data1data2data3eP

f

195 200 205 210 215

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.1

195 200 205 210

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Time [s]

f, P

e[p

u]

Pe,0

=0.3

data1data2data3eP

f

0 10 20

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.1

0 10 20

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.3

0 10 20

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.5

0 10 20 30

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.7

Figure 7.7: Frequency respons of load step disturbance ∆Pe = 0.1 pu with combi-nation offset = 0.13, at initial load Pe,0.

To better show the effect of the combination offset, step responses, without andwith combination offset implemented are depicted in Figures 7.8 and 7.9 respec-tively. With the Combination Offset disabled, the system needs about 50 secondsto return to stable operation, during which the frequency severely deviates from thenominal value. Under normal operation, any power plant would trip long beforethe frequency deviation reaches these levels. One of the reasons for behaviour seenis the lack of control effect of the wicket gates. Secondly, the wicket gates leadingtheir optimal combination causes the mechanical power to decrease. Hence, thelittle control effect of the wicket gates is weakened further.

Figure 7.9 shows the same load step disturbance with the combination offsetimplemented. The figure shows how the wicket gate movement, with very little helpfrom the turbine blades, manages to restore the system frequency in 10 seconds withthe deviation being within acceptable bounds.

40 CHAPTER 7. RESULTS

0

0.2

0.4

0.6

0.8

1

f,6P

m,6P

e

0 10 20 30 40 50 60 70 800

0.2

0.4

0.6

0.8

1

Time6[s]

γ,6α

Mechanical6powerElectrical6powerFrequency6f

mP

eP

Turbine6blade6position6α6

Wicket6gate6position66Υ

Figure 7.8: Response of frequency, mechanical power, wicket gate and turbine bladepositions when a load step disturbance ∆Pe = 0.85 pu occurs at initial load Pe,0 =0.5 pu, with Combination Offset disabled.

00.20.40.60.8

1

0 10 200

0.20.40.60.8

1

Time [s]

γ, α

Figure 7.9: Response of frequency, mechanical power, wicket gate and turbine bladepositions when a load step disturbance ∆Pe = 0.85 pu occurs at initial load Pe,0 =0.5 pu. Combination offset implemented with offset = 0.13.

7.4. INVERTED COMBINATION ANTI-WINDUP. 41

7.4 Inverted Combination Anti-windup.

The Inverted Combination Anti-windup constant σ = 0.16 used in the simulationis found through testing. The responses of load disturbance steps ∆Pe = 0.1 pu arepresented in Figure 7.10.

The plots simulated show load disturbances at different initial operating pointsPe,0. Plots show two frequency curves, f being without Inverted Combination Anti-windup and fICAw with.

Judging from these results, the method has a positive effect on the governing.By appropriate settings of the variable limiter through σ, the governor output islimited at a point where an increase of the wicket gate position only worsen theturbine control.

The simulation with Pe,0 = 0.1 pu show identical step responses for both cases.At the other plots, the Inverted Combination Anti-windup keeps the generator fromtripping.

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.1 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.3 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.5 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.7 pu

data1data2data3

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.1 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.3 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.5 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

f

ePICAwf

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.1 pu

0 10 20 300

0.2

0.4

0.6

0.8

1

Time [s]

f, P

e[p

u]

Pe,0

=0.5 pu

f

ePICAwf

0.2

0.4

0.6

0.8

1

f, P

e[p

u]

Pe,0

=0.1 pu

0.2

0.4

0.6

0.8

1

f, P

e[p

u]

Pe,0

=0.3 pu

f

ePICAwf

0

0.2

0.4

0.6

0.8

1

f, P

e[p

u]

Pe,0

=0.1 pu

f

ePICAwf

Figure 7.10: Load step disturbance ∆Pe = 0.1 pu at initial load Pe,0 with andwithout Inverted Combination Anti-windup, σ = 0.16.

To draw any conclusions of the results in Figure 7.10, the turbine behaviourneed to be studied more closely. The load step disturbances without and with theInverted Combination Anti-windup are shown in Figures 7.11 and 7.12 respectively.

42 CHAPTER 7. RESULTS

10

0.2

0.4

0.6

0.8

1

f,4P

m,4P

e[p

u]

0 5 10 150

0.2

0.4

0.6

0.8

1

Time4[s]

γ,4α

[pu] data1

data2

data1data2data3

Mechanical4powerElectrical4powerFrequency4f

mP

eP

Turbine4blade4position4α4

Wicket4gate4position44Υ

Figure 7.11: Load step disturbance ∆Pe = 0.1 pu at initial load Pe,0 = 0.5 puwithout Inverted Combination Anti-windup.

Figure 7.11 reveals the answer to why the generator tripped in Figure 7.10. Asthe step occurs the wicket gates are opened with maximum speed in an attemptto increase the mechanical power. As been shown in Figure 4.2, the mechanicalpower will begin to decrease when the wicket gates are too far ahead of the optimalcombination. We see the effect of this here. At the very point where the mechan-ical power has a negative slope, the wicket gates continuous movement causes thefrequency collapse.

0

0.2

0.4

0.6

0.8

1

f,6P

e,6Pm

0 10 20 300

0.2

0.4

0.6

0.8

1

Time6[s]

γ,6α

Mechanical6powerElectrical6powerFrequency6f

mP

eP

Turbine6blade6position6α6

Wicket6gate6position66Υ

Figure 7.12: Load step disturbance ∆Pe = 0.1 pu at initial load Pe,0 = 0.5 pu withInverted Combination Anti-windup, σ = 0.16.

Figure 7.12 show the turbine behaviour when the Inverted Combination Anti-windup is implemented. Once the turbine blades are ramping up at full speed,the wicket gates are limited to move in the same pace. With a slow increase ofmechanical power and rather large overshoot, the system returns to stable operation.

Chapter 8

Conclusions

In this thesis, the governing of a Kaplan turbine hydropower plant operating anisland grid has been studied. Two methods improving the disturbance rejection,Combination Offset and Inverted Combination Anti-windup, has been proposedand evaluated through time domain simulations.

The Combination Offset has been found satisfactory, meeting the frequencyregulation requirements for island operation. Settings of the combination offset isa balance between loss of turbine efficiency and gained turbine control effect. Byassuming that the operation is limited to Pe ∈ [0.1, 0.7] pu, a combination offsetof 0.13 is found sufficient for meeting the requirements of the frequency regulation.With this combination offset setting, the maximum loss of efficiency compared tooptimal combination is approximately 15%.

A great advantage of the Combination Offset is that it is rather easily im-plemented. If measurement on hydropower plants would show similar frequencyresponses as the simulated results, this would create opportunities to build sev-eral smaller island grids. Already larger industries can sometimes be self-supportedthough their island grids. Even though the loss of efficiency is an important fac-tor, the use of island operation in supporting the communities is only seen as anextraordinary action. Under those circumstances one may need to chose the secondworst option.

Further work on this method is needed to optimize the offset combination curve.A first step towards this would be to adapt the combination offset curve for smallwicket gate position, where the need of increased wicket gate control effect is lessneeded.

The ideas to the The Inverted Combination Anti-windup did emerge when de-signing the Combination Offset. The rather small study performed showed promis-ing results for future studies. The method did succeed in limiting the governoroutput at an appropriate point, helping the system to recover from the disturbance.Originally, the Inverted Combination Anti-windup was thought as a method fordamping the under- and overshoots after the first frequency swing. Instead, themethod turned out to improve the first swing in the same way as the Combination

43

44 CHAPTER 8. CONCLUSIONS

Offset. However, instead of transferring control effect to the wicket gates, the con-trol signal are coordinated in a way such that maximum output is gained. A majordrawback of the method is that the manoeuvre room set for the governor output hasbeen fitted to handle a specific disturbance magnitude. For smaller disturbancesthere would be less or no effect at all. An area of improvement lies in automatingthe setting of the constant σ. A solution based on limiting the governor output oncethe turbine blades are moving at their maximum speed could also be considered.

Chapter 9

Glossary

actuator ställdondroop statik

governor frekvensregulatorwater head fallhöjdpenstock vattenväg

turbine blades, runner, propeller löphjulwater starting time vattentidskonstant

wicket gate ledskenawicket gate ring ledkrans

45

Bibliography

[1] Svensk Energi, Vattenkraft, Utgåva 7, September 2001

[2] Evald Holmén, Speciell Kurs i Flödesmekanik och Vattenturbiner, VeteranKraft,Stockholm, Oktober 2001

[3] Evald Holmén, Turbinreglering, Vattenkraftstationers dynamiska egenskaper,STF Ingenjörsutbildning

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