Degree project in
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 Turbine Hydropower Plants Operating Island Grids
A Degree Project in System Control
MARTIN GUSTAFSSON
Master’s Thesis at the Department of Automatic Control Supervisor: 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. The grid islands are operated isolated from the power network, which places new demands on a faster frequency regulation.
This thesis investigates a Kaplan turbine hydropower plant operating an island grid. The Kaplan turbine has two control signals, the wicket gate and the turbine blade positions, controlling the mechanical power. The inputs are combined to achieve maximum turbine efficiency at all operating points. In relative terms, the wicket gate has a fast dynamic but small effect on the mechanical power, while the turbine blade has slow dynamic and large effect on the output, seen around an operating point.
The proposed method to get a faster frequency control uses a different combination of the turbine inputs, transferring control effect from the turbine blades to the wicket gates at the cost of loss of turbine efficiency. The method is investigated with time domain simulations on a model containing all essential parts 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 supporting me during this project; supervisor Bengt Johansson for his great input and com- mitment, Professor Jacobsen for his advice in the planning process and feedback of the linearised analysis, fellow colleges at Solvina for their kindness and helpfulness and to family and friends for their inspiration and patience.
Contents vi
1 Introduction 1
1.1 Background . . . 1
1.2 Purpose . . . 2
1.3 Limitations . . . 3
2 Theory of Kaplan Turbine Hydropower Plant 5 2.1 Kaplan Turbine . . . 6
2.1.1 Wicket gates and turbine blades . . . 7
2.1.2 Servos . . . 7
2.1.3 Combination Unit . . . 8
2.2 Penstock . . . 9
2.3 Generator . . . 9
2.4 Per Unit - pu . . . 10
3 Frequency Control 11 3.1 PID . . . 12
3.2 Droop . . . 13
3.3 Anti-windup . . . 14
3.4 Regulation criterion . . . 14
4 Control Strategies 17 4.1 Combination Offset . . . 18
4.2 Inverted Combination Anti-windup . . . 20
5 Simulation Model 23 5.1 Governor . . . 24
5.2 Servos and Actuators . . . 24
5.3 Turbine . . . 25
5.4 Generator and Load . . . 26
6 Analysis Method 27 6.1 Time Domain Simulation . . . 27
vi
CONTENTS vii
6.1.1 Stationary Behaviour study . . . 28
6.1.2 Efficiency Losses . . . 29
6.1.3 Load Disturbance Simulations . . . 30
6.1.4 Inverted Combination Anti-windup . . . 31
6.2 Controllability Analysis . . . 31
7 Results 33 7.1 Stationary Behaviour Study . . . 33
7.1.1 Turbine blade position as a function of wicket gate position and mechanical power α = f (γ, Pm) . . . 33
7.1.2 Mechanical power as a function of wicket gate and turbine blade positions Pm = f (γ, α) . . . 34
7.2 Efficiency Losses . . . 35
7.2.1 Efficiency as a function of electric power and combination offset η = f (Pm, of f set) . . . 35
7.2.2 Efficiency, wicket gate and turbine blade position relationship 36 7.3 Load Disturbances . . . 37
7.3.1 Maximum Load Step Disturbance . . . 37
7.3.2 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 hydropower plants when running an isolated electric island grid. The purpose of the project is to analyse and propose improvements of the frequency control based on a general model of a Kaplan hydropower plant.
1.1 Background
In today’s modern society, reliability of electric power supply is something taken for granted. Large and long lasting disturbances on the electric grid pose a threat to that and may have critical consequences for the functioning of a society. Extreme weather, sabotage, acts of war or technical problems in the operation may result in full or partial breakdown of the electric grid.
Events of this nature can never be completely prevented. Instead, the focus lies on reducing the consequences of a disturbance by isolating the problems when they 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 on power. In order to obtain stable operation, generated and consumed power within the island grid must be in balance. This places new demands of a faster frequency regulation of the generating power units within the island, since they are no longer supported by a strong electric grid.
In Sweden, 45% of the power is generated in hydropower plants, mostly located in 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 turbine hydropower 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 the turbine blade positions, and the mechanical power as output. In relative terms, the wicket gate has a fast dynamic but small effect on the mechanical power, while the turbine blade has slow dynamic and large effect on the output around the operating
1
point. The adjustable wicket gates control the flow of water in to the turbine chamber. After passing the chamber, the water is led onto adjustable turbine blades where the kinetic energy is transformed into rotation of the turbine. A governor controls 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 of the wicket gates and the turbine blades need to be coordinated. Adjustment of the wicket gates are controlled directly by the turbine governor. For each position of the wicket gates, the turbine blades are adjusted to the most efficient combination of the two, by a combinational unit. The properties and the combination of the wicket gates and the turbine blades are central when it comes to improving the ability for island operation of the turbine. For older turbines, the wicket gates have fast dynamics and can open and close within 5-15 second whereas the turbine blades need 30-60 seconds for full movement. In modern turbines, not considered in this thesis, the wicket gates and turbine blades can achieve full movement within 5-8 seconds. When the turbine is running in island operation, a change of the load will cause the wicket gates to adjust in order to compensate for the change in power demand. Since the turbine blades are adjusted slower than the wicket gates, the full effect of the change of the power generation will not occur until the turbine blades has reached their optimal position. By then, the change in frequency might have grown large and the wicket gates would need to compensate for that. For a larger change 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 grid as a result. [2], [3]
Simulations and measurements of the ability to run in island operation of some Swedish 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 governor using polynomial H∞ optimization has shown to be better than the conventional PID governor.[5]
1.2 Purpose
The Swedish national grid (Svenska Kraftnät) is the authority responsible for the reliability 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 regulation of the frequency is lowered. Hence, the frequency regulation requirements on island grids are less strict. The purpose of this master’s thesis is to improve the frequency regulation 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 grid will
• keep the frequency within ±2 Hz of nominal at load changes of 10% of rated power.
• manage increases of the load by 10% of rated power from operating points between 0-80% of rated power.
• manage decreases of the load by 10% of rated power from operating points between 100-20% of rated power.
1.3 Limitations
A 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 simulation and modulation tool Dymola, includes all the relevant parameters to fit the model for various types of operational conditions.
In this thesis, the purpose of proposing improvements are limited to improving the frequency control of the training simulator model. The model is fitted to rep- resent a typical Kaplan turbine hydropower plant, based on measurement data of different plants, with limited or no ability to run island grids.
Chapter 2
Theory of Kaplan Turbine Hydropower Plant
This section will give a brief presentation of the main components of a Kaplan turbine hydropower plant. From the water inlet to resulting generation of power, the plant is divided into the subsystems; penstock, turbine and generator. An overview of the system is depicted in Figure 2.1. The theory presented for each of the subsystems constitutes the base of the simulation model and the purpose is to give a basic understanding of each part’s properties and functions. A detailed presentation 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
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’s ability to operate with high efficiency in a wide range of operating points and at different water heads. The Kaplan turbine is an axial reaction turbine, in which the pressure in the turbine chamber is higher than the atmospheric pressure. Unlike the impulse turbine, such as a Pelton turbine, the water at the inlet in a reaction turbine 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 adjustable and control the water flow into the turbine. They are attached around the turbine chamber 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 4-8 slightly curved blades, which shape resembles a boat propeller. As the water passes through the runner, the pressure energy gradually changes to kinetic energy. The shape 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 the turbine and the pressure energy is transferred to the turbine axis. Ideally, if all kinetic 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 be transported away some kinetic energy is kept.
2.1.1 Wicket gates and turbine blades
The Kaplan turbine is characterized by that both the wicket gates and the turbine blades are adjustable. The regulation of the two are coordinated and combined to gain maximum efficiency. For every wicket gate position, the turbine blade position is 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, are attached on the wicket gate ring, depicted in Figure 2.3 a) seen from above. The wicket gate position γ ∈ [0, 1] pu, where γ = 1 pu= 60◦ denote fully open and γ = 0 pu= 0◦ closed. The angles used in the simulation model are defined as in Figure 2.3 b), with γ = 0◦ being along the side of the wicket gate ring. The turbine blade position used in the simulation model α ∈ [0, 1] pu= [2.5◦,32.5◦] is defined as in Figure 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 gate position. c) Definition of turbine blade position.
2.1.2 Servos
To 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 are fixed. The hydraulic servo regulating the turbine blades are positioned inside the turbine axis, which also holds the two pipes transporting the hydraulic oil. Sensors measuring the blade angle are connected via the turbine axis since it is placed in a sealed area. However, the wicket gate ring is in no contact with water and its adjustments can be seen by the naked eye. One actuator for each hydraulic system controls the oil pressures.
As mentioned earlier, the opening and closing times of the wicket gates and the turbine 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.
Apart from the physical limitations in the servo, the speed limiter is needed to keep the 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 to get enough oil through the turbine axis to the hydraulic servo in a short period of time. [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 the difference between setpoint and actual position is small, which reduces the wear on the 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 αsetpoint
is computed by the combination unit, based on the wicket gate setpoint position γsetpoint 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 preferred to use γsetpoint to avoid the time delay of the wicket gate servo. The combination
Combination Unit
Wicket gate servo
Turbine blade servo setpoint
setpoint
actual
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. The combination unit data, which is based on measurements from turbine tests, is a function of the water head H. The turbine tests consist of measuring the efficiency of the turbine at different combinations of wicket gate and turbine blade positions at a constant revolution speed. This is performed by fixing the turbine blades and letting the wicket gates go from closed to fully open while registering the turbine efficiency. The test is then repeated for a number of turbine blade positions. The water head will affect the mechanical power of the turbine and thus also the optimal combination curve. In a hydropower plant it is therefore common to have a number of different combination curves depending on water head.
2.2. PENSTOCK 9
2.2 Penstock
The penstock is the water transport system supplying the turbine. The theoretically largest 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, the energy is affected by friction losses and the water’s dynamic behaviour.
The penstock usually consists of an inlet, turbine passage and an outlet, all depicted in Figure 2.1. The construction of the inlet and outlet differs between plants depending on the conditions of the surrounding environment. The inlet and outlet 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 water velocity is zero after passing the turbine, meaning all kinetic energy is absorbed by the 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 the water. While the turbine is operating in a stationary state, the penstock has no affect 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 will interact. If the load increases, the wicket gates are opened to increase the water flow. This will initially lead to the pressure dropping on the inlet side of the turbine due to that the water head is used to accelerate the water. As a result of this, the turbine’s mechanical power decreases until the pressure is restored and the power can increase. The size of this non-minimum phase characteristics of the penstock depends on the water’s mass inertia. The mass inertia of the penstock is expressed by the water starting time Tw, which is discussed further in 3.4. [2]
2.3 Generator
In an electric power grid, the generated electric power is instantly consumed. Since the consumption of power is constantly changing, the generation must change ac- cordingly. This relationship of the generator is described by the first swing equation 2.1.
∆ ˙ω = 1
2H(Pm− Pe− D∆ω) (2.1)
In Equation 2.1 ω is the angular frequency, Pm and Pe the mechanical and electrical power, D a positive damping constant and H the inertia. All parameters are expressed in pu. In the case of the damping D = 0, the system will be in equilibrium and hence the frequency constant only if the generated power Pm and consumed 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 transformed to 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
and turbine will accelerate and the frequency thereby increase. If Pm < Pe the turbine and generator will be decelerated and the frequency decrease.
When Pm 6= Pe, the time derivative of the frequency depends on the power imbalance ∆P = Pm − Pe and the stored kinetic energy in the system’s rotating masses. The inertia H is a measure of the system’s stored kinetic energy in the unit seconds. The inertia constant can be explained by assuming the event of the mechanical power of the turbine instantly going from Pe to zero. If the generator will keep transforming kinetic energy to electric energy at rated power, the time it takes for the turbine’s and generator’s speed to reach zero is the inertia constant H.
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 frequency dependent to some extent, i.e. Pe= Pe,0(1 + DPe·∆ω). DPe is a positive damping constant acting similarly to D in Equation 2.1. The frequency control is improved by 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 - pu
Per unit, pu, is a convenient method to normalize all generator, turbine and servo quantities. The quantities are scaled such that rated or nominal value correspond to 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, next chapter will treat the theory of the frequency control.
Chapter 3
Frequency Control
A Kaplan turbine hydropower plant is a complex non-linear, non-minimum phase system and the control system that regulates the electrical frequency is called gov- ernor. Theory and design of the governor and regulation criteria will be treated separately in this chapter.
The control system, containing the governor, actuators and servos are depicted in Figure 3.1. This system is a two inputs - two outputs system, although the governor only has one output. The governor uses the generator frequency f and a power signal feedback as inputs.
The power signal feedback to the governor is either the wicket gate position γ or the electrical power Pe. This signal is used to determine a turbine’s participation in the frequency control. This function is referred to as droop and is described in 3.2.
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 controls the wicket gate actuator and servo. In the lower branch the combination unit com- putes the turbine blade position setpoint, αsetpoint, which controls the turbine blade actuator and servo.
The most commonly used governors are quite simple and there has been little changes of the design over a long period of time. Originally the governors were entirely 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 and penstock, the saturations in the servos present significant effect to the frequency response. The governors used to control frequency and power generation in Kaplan turbines are usually PIDs. An alternative governor approach, where projective controls are used to solve the sub optimal regulator problem, is presented in [5].
For a simpler implementation of this thesis’ proposed improvements, the general structure of a PID governor is kept.
11
setpoint
D P
I Droop
Anti w-u
f
reff
ref
setpoint
1 Topen
1
close a
T 1
close b
T
1
s
1
actuator
s
1 1 s
delays
e
1 Ts d dt
1 Topen
1
close a
T 1
close b
T
1
s
1
actuator
s
1 s1
delays
e
1 Ts d dt
setpoint
setpoint
Combination
Unit Turbine blades
actuator, servo Wicket gates actuator, 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 in Figure 3.1. An ideal PID regulator is defined as in Equation 3.1, where e (t) is the control error.
u(t) = KPe(t) + KI
Zt
t0
e(τ) dτ + KD
de(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 control error. Equation 3.2 shows the transfer function of the PID controller. The standard nomenclature in Swedish hydropower plants are bgp = KP = K, bgi = KI = τKI, bgd= KD = KτD.
F(s) = KP +KI
s + KDs= K1 + 1
τIs+ τDs
(3.2)
On the topic of hydropower governors, there is a great deal of research on the PID parameter settings. This thesis does not treat the tuning of the PID parameters in the simulation model. A straightforward method is presented in [15]. The rule of thumb parameter setting below are developed using the PI governor setting by Hovey and Schleif [13],[14]. The governor setting is expanded by an appropriate derivative 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 · Tw
KI = 10 · KP
3 · Tw
KD < KpTw
3
The water starting time, Tw, is defined as the time it takes for the current water head to accelerate the water in the penstock through gravitation to the current water velocity.
The non-minimum phase properties of the turbine and penstock is due to the water starting time Tw. The effect of the non-minimum phase response increases as Tw increases. Practically, Tw give rise to a delay in the turbine response. This means that the PID must be set with a small proportional gain KP such that the non-minimum phase behaviour is limited. The relation of Tw and KP is seen in the parameter setting above. In the case of island operation, the use of derivative control action is beneficial, particularly for plants with larger water starting times Tw. [5]
D
P
I Droop
Anti windup
fref
f
, ref
P
e ref
P
e
setpoint
Figure 3.2: Block diagram of the PID controller with droop and anti-windup.
3.2 Droop
When 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. The rate of each turbine’s static participation in the frequency control is set individually in all turbine governors and is termed droop or ep. The droop can be interpreted as the percentage change in frequency required to change the output power 100% of
rated power. The static droop is derived from the stationary changes in frequency and 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 controlling the frequency and the power. Setting ep = 0 implies that the governor only regulates the frequency. Typical values of the droop are ep ∈ [0.03, 0.06] pu/pu. [12]. The droop input is a power feedback signal which is either γ or Pe. The use of Pe
has 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 will be ep(Pref − Pe). For an increase of the load Pe, the governor will react as if the actual frequency is initially increased while the frequency is actually decreasing as a result of the power imbalance. The larger the droop gain ep, the larger will the effect of this non-minimum phase behaviour be. This could be avoided by using γ as a substitute of the power.
3.3 Anti-windup
The 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 large or long lasting control errors, the integration action may saturate the controller output. This phenomenon is called integrator windup and will lead to a impaired control even after the control error is eliminated.
To avoid this problem, an anti-windup can be implemented. The concepts are presented in Figure 3.3. Once the controller output is saturated, the anti-windup is activated and the integral action ceases to grow. The gain of the anti-windup feedback has to be high in order to quickly reach steady state under saturation conditions.
3.4 Regulation criterion
In 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 frequency
entirely determines its rotational speed.
2. The plant has a part in controlling the frequency of the grid, decided by the droop 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 empirical studies 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 signal stability criteria is given by TTmw, 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 rotational velocity. 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 water in the penstock through gravitation to the current water velocity. This means that the time constants differs depending on operating point in terms of water velocity and power. However, looking at the ratio of the two time constants, empirical evi- dence suggests that TTmw ≥2.5 is needed for a hydro power plant of category 2 and
Tm
Tw ≥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, which is 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 in the penstock and larger turbine inertia would increase TTmw. To determine how large disturbances are affecting the system, computer simulations must be used.
Fulfilling TTmw ≥ 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 backlashes found 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 Swedish hydropower plant. Figure 3.4 shows the frequency, active power, wicket gate and turbine blade positions when a step increase occurs in the demand of electrical power in an island grid.
As the step occurs, the consumed power is larger than the generated power and the frequency begin to decrease, as described by Equation 2.1. This causes the wicket gates to open in order to accelerate the turbine. The constant slope of the turbine blade position curve indicates that the servo reached its saturation. As
30 40 50 60 70 80
Positionc[wcofcfullycopen]
10 20 30 40 50 60 70 80 90 100
48 49 50 51 52
Timec[s]
Frequencyc[Hz]
20 22 24 26 28
ActivecPowerc[MW]
γbcWicketcgates bcTurbinecblades
Pm Pe
Frequency α
Figure 3.4: Measurements data of frequency, power, wicket gate and turbine blade positions after a step increase of demanded power in a Swedish hydropower plant operating an island grid.
long as the frequency is lower than nominal, the governor output will continue to open the wicket gates. The turbine blades, which have a slower servo, try to get to the position of the optimal combination. When the turbine blades reach the point where the generated and consumed power are in equilibrium, the wicket gates have opened too far and the mechanical power continues increasing. In order to decrease the power, the wicket gates are rapidly closed, the turbine blades follow at their maximum speed and the system exhibits stable oscillations. The test and measurements are then aborted due to risk of tripping the generator. The effect of the turbine blade servo backlash can be noticed in the troughs of the turbine blade position curve.
The measurements in Figure 3.4 show a common turbine behaviour when run- ning island operation. The unsatisfactory stable oscillations are mainly caused by the speed limiter of the turbine blade servo. In the next chapter, two proposed control 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 grid where shown. This should only be treated as an example of a Kaplan hydropower plant without any adaptation tries to run an island grid, as all power plants have different built-in abilities for island operation. However, the behaviour shown in Figure 3.4 is relevant and the problems with the frequency regulation after the load disturbance can be divided into two governor requirements:
• Quick response after load changes
The frequency amplitude of the first swing is only depending on how quickly the 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 improve the control effect of the governor output.
• Damping of oscillations after load changes
The oscillations may have several reasons but is mainly due to the turbine blades lagging the wicket gates, leading to a large deviation from the opti- mal combination. Improvement of the response time of the turbine will also benefit damping of oscillations. However, to get a smoother tune in of the frequency, the governor’s output must be limited when the difference between the turbine blade setpoint and actual position grow large.
Two control strategies to improve these properties are proposed and evaluated in this thesis. The strategies are named Combination Offset and Inverted Combina- tion Anti-windup. Design and implementation of these are presented in following sections. Results of the analysis of these strategies and proposed improvements are presented in Chapter 7. The methods used for the analysis are found in Chapter 6.
17
4.1 Combination Offset
When trying to improve the response time of the turbine, and thus reducing the first frequency swing, the turbine inputs are in focus. The turbine’s two control signals have different properties around an optimal operating point. In relative terms, wicket gates have fast dynamic but a small effect on the output while the turbine blades have slow dynamic and large effect of the output.
Components limiting the control signals, such as speed saturations, time delays and 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 operating with optimal combination, connected to a strong electrical grid, the speed satura- tion does not pose any problem. The optimal combination is constructed such that for every wicket gate position, the turbine blade position is chosen to give maximum efficiency. The idea behind the Combination Offset strategy is to depart from the optimal combination in order to gain a faster response of the turbine’s mechanical torque. This implies that control effect is transferred from the turbine blades to the wicket gates. As a result, a more rapid increase of power generation is gained at the cost of loss of efficiency.
In Figure 4.1, curves of the turbine’s generated power as a function of the wicket gate 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 also depicted. 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 point marked 1), along the optimal combination curve. An increase of the generated power by 0.1 pu, demands some movement of the turbine blades. The wicket gates alone, with fixed turbine blades, could not increase the power by 0.1 pu, which is also shown in Figure 4.2. If instead the turbine is operating at the same power on the offset combination curve in Figure 4.1, marked 2), a 0.1 pu increase of the power would need no movement of the turbine blades.
When using the Combination Offset, the limitations of the turbine blade servo are no longer as important for a fast increase of power. At a greater extent, the response time of the turbine are depending on the wicket gate servo, with a faster regulation 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 a larger extent depends on the change of the wicket gate position, as can be seen in Figure 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 or implemented.
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 turbine blades never reach their lower endpoint. Since the steps between the power levels are 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 1
0 0.2 0.4 0.6 0.8 1
Wicket8gate8position8γ
Turbine8blade8position8α
data1 data2 data3 data4 data5 data6 data7 data8 data9 data10 data11 data12 data13 data14
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1
data1 data2 data3 data4 data5 data6 data7 data8 data9 data10 data11 data12 data13 data14
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1
data1 data2 data3 data4 data5 data6 data7 data8 data9 data10 data11 data12 data13 data14
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1
data1 data2 data3 data4 data5 data6 data7 data8 data9 data10 data11 data12 data13 data14
Mechanical8powerPm
Optimal8combination8curve Offset8combination8curve 0.48pu
0.18pu 0.78pu 1.08pu
1) 2)
Figure 4.1: Mechanical power Pm as a function of the wicket gate position γ and the turbine blade position α. The wicket gates alone have a greater impact on the power when operating on the offset combination curve compared to the optimal combination curve.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Wicket[gate[position[γ Mechanical[power[P m[pu]
Figure 4.2: Mechanical power Pm as a function of the wicket gate position γ and fixed turbine blade position α = 0.15 pu. Operation with optimal combination, marked , can not achieve ∆Pm = 0.1 pu with adjustment of the wicket gates alone.
curve can instead be allowed to reach the turbine blade position α = 0, which will be beneficial in terms of efficiency, without loss in frequency control. This is im- plemented by letting the combination curve linearly go from turbine blade position α = 0 to the point where the constant level of the combination curve ends, with roughly the same slope as in that point. The combination curve is also adapted to
have a maximum turbine blade position of 1 pu. The dotted and dashed lines in Figure 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
Turbinegbladegpositiongα data1
data2 data3 data4 data5 data6
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0
data1 data2 data3 data4 data5 data6
Offsetgcombinationgcurve
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0
data2 data3 data4 data5 data6
Optimalgcombinationgcurve
Figure 4.3: Implementation of combination offset curve.
4.2 Inverted Combination Anti-windup
As mentioned, large load disturbances causes the turbine blades to lag the wicket gates, resulting in larger frequency deviation which could lead to power oscillations.
This behaviour is further exacerbated when increase of the wicket gate position causes the mechanical power to decrease. As shown in Figure 4.2, the mechanical power is seen decreasing when the wicket gates lead the optimal combination by approximately 0.1 pu.
The governor’s internal anti-windup saturates the wicket gate setpoint position if it exceed its limits. Normally the limiter has a fixed upper and lower levels. This means that the wicket gate setpoint position on the governor’s output will be limited at the same upper level regardless of the actual operating point. If the turbine is operating at low power and the wicket gate position is small, this could mean that the setpoint signal goes from almost closed wicket gates to fully open before the it is limited.
To counteract the continuous movement of the wicket gates, while the turbine blades 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 a limiter with fixed limits, a variable limiter is implemented. The levels of the variable limiter is controlled by the actual turbine blade angle. Since the anti-windup is comparing wicket gate positions on the governor’s output, the turbine blade position must be transformed into a wicket gate position. The principle is shown in Figure 4.4. An inverted optimal combination curve returns the corresponding wicket gate position 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 necessary workspace a constant σ is added to the γα.
setpoint
combinationInverted
f
Actual turbine blade position
Wicket gate setpoint position
1 min
1 s
KAW
Figure 4.4: Block diagram of Inverted Combination Anti-windup.
The implementation of the Inverted Combination Anti-windup in the model is 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 order polynomial 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 governor workspace. 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 of the simulation model used, is presented.
Chapter 5
Simulation Model
The training simulator used for the analysis is built in the modeling and simulation tool Dymola. Dymola uses the object-oriented modeling language Modelica. There is a large library of standard components but the user may also create their own.
The models consists of differential, algebraic and discrete equations creating an equation system which is solved numerically when running simulations. [16].
Figure 5.1 shows a block diagram of the simulator model used in this thesis. A more detailed presentation of the blocks are presented in the following sections.
Governor
setpoint
setpoint
H
Q
fref
ref
Wicket gate actuator, servo
Combination unit
Propeller blades
actuator, servo
Turbine
Penstock
Generator and grid
Pe
Inverse combination
unit
offset
f
f Pm
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 ability for an arbitrary Kaplan turbine to operate an island grid. This means that the practice 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 and other 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. The simulation model is fitted with parameters representing a worst case in terms of ability to operate an island grid. The measurements are from power plants with
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rated power of 20-50 MW which represents the typical size of a Swedish Kaplan turbine hydropower plant, where the results of this project are intended to be im- plemented.
5.1 Governor
The turbine governor is a PID-regulator with anti-windup and droop. The block diagram of the governor is shown in Figure 5.2. There are three input signals to the governor; 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 combination of the actual turbine blade position, i.e. the optimal position of the wicket gates corresponding to the actual turbine blade position. It is added with a constant σ, preventing the governor output to be constantly saturated. The output signal is the setpoint position of the wicket gate, γsetpoint. The governor model is largely
fref
f
ref
setpoint
1
D D
K s K s
N
KP
ep
KI
s
f
min 1
KAW
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 control error which gives an infinite derivative action. The filter constant N determines the cut-of frequency.
5.2 Servos and Actuators
As mentioned, the servos for the wicket gates and the turbine blades play an im- portant part in controlling the turbine outputs. Typical Kaplan turbines, without any requirements on island operation, have an opening time of the turbine blades of 30-60 seconds and the wicket gates of about 5-15 seconds [2]. The measurement in 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. For the purpose of testing a method suitable for improving the frequency regulation in island operation, the model is adapted for a realistic worst-case scenario.
The servo and actuator model shown in Figure 5.3 have the same structure for 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 model looks more complex than it is because of the two switches. Neglecting them to begin with, the circuit is more intelligible. The servo model basically consists of a gain T1s, 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, a backlash is introduced to reduce vibrations. However, the main part of interest is the speed limiter before the integrator. The limiter has variable saturation levels which controls the time derivative of the servo movement. Hence, the lower saturation level controls the maximum closing time and the upper limit the maximum opening time. For the turbine blades, the opening and closing times are both set to 60 seconds and the switches are therefore not being used. Based on measurements and typical values, the wicket gate opening time is set to 10 seconds. As seen in Figure 5.3, there are two different closing times depending on how near the wicket gates are to being shut. This is because of the need to slow down the wicket gates the last 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 seconds otherwise. The other switch condition dtd checks if the wicket gates are opening or closing.
1 Topen
1
close a
T 1
close b
T
1
s
1
actuator
s
1 1 s
delays
e
1 Ts
d dt
position setpoint
Figure 5.3: Servo and actuator model.
5.3 Turbine
The core of the simulation model, the turbine model, has four inputs and two outputs. The turbine is controlled by the outputs from the servos; the wicket gate position γ and the turbine blade position α. The generator frequency f and the water head H are the other two input signals. From these, the water flow Q is computed, which is feedbacked to the penstock model. This feedback is needed
because the water head is affected by changes of the water flow. The mechanical torque M is the second output signal.
The water flow and the mechanical torque are computed in two steps. From the wicket gate and turbine blade positions, the unit flow Q11and unit torque M11 are computed. The unit values are based on a turbine operating at a water head of 1 m and a turbine propeller with a diameter of 1 m. To transform the unit values for a geometrically uniform turbine operating at a different head, the uniformity and affinity laws are used. The uniformity law is valid for two geometrically uniform turbines 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 similar points will be unchanged if all other parameters are kept. The affinity law can then be used to compute the changes of the water speeds in the a turbine at different water 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 water flow Q. The turbine model also includes functions to compute the efficiency η and the mechanical power Pm. The mechanical power is a function of frequency and the mechanical torque. The efficiency is a function of the mechanical power, the water head and the water flow. The equations are shown in Equations 5.1 and 5.2, ω is the angular velocity, ρ the water density and g the acceleration of gravity.
Pm= M · ω (5.1)
η = Pm
ρgHQ (5.2)
5.4 Generator and Load
The dynamics of the generator is described by the two-axis model. It consists of 4 differential equations, the swing equation 2.1 being one of them. Providing a justifiable explanation of these equations is extensive and lies outside the the scope of this thesis. For this application, the essential dynamics are captured by the swing equation. The generator model is built for more advanced applications and the other equations have has no practical significance in these simulations. For the interested reader any literature on power system stability such as [11] is recommended.
The generator model has two inputs; the turbine torque and the generator field voltage. By the two-axis generator model, the electrical power, current, voltage and frequency is determined. A built-in limited PI-regulator controls the stator voltage by affecting the field voltage.
The load model is directly connected to the generator model. Wanted power load levels and step disturbances are entered as well as the percentage of frequency dependent 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 studies of the two proposed control strategies.
Chapter 6
Analysis Method
In order to meet the frequency requirements in 1.2, the strategies Combination Offset and Inverted Combination Anti-windup have been proposed to improve the governing of a Kaplan turbine hydropower plant operating an island grid.
The objective of the Combination Offset is to gain a control system that can keep 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 on the governing and if so, how the Combination Offset should be chosen to fulfill the requirements at lowest loss of efficiency.
The purpose of the Inverted Combination Anti-windup is to reduce the settling time of the frequency after a load disturbance of 0.1 pu. The analysis of this strategy is less extensive and is based on step responses of load disturbances.
Mainly the Combination Offset is studied and two analysis methods have been tried; time domain simulation and controllability analysis. Attempts with the latter have 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 detail in 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 to define the model. Every component of the model is built up by equations, as well as connectors and conditional statements. These form an equation system describing the model, which is solved numerically. The simulation results are then exported to MATLAB for numerical analysis. The model contains a complete island grid and the possibility to control the load. It also allows to simulate a sub-part of the model alone or to manipulate certain signals.
Simulations of the Combination Offset will be treated first. These are divided into three categories for a more comprehensible presentation. Lastly, the Inverted Combination Anti-windup simulations are treated.
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