Fast-response rotating brushless exciters for improved stability of synchronous generators

Transcription

1 Fast-response rotating brushless exciters for improved stability of synchronous generators JONAS KRISTIANSEN NØLAND UURIE L ISSN Division of Electricity Department of Engineering Sciences Licentiate Thesis Uppsala, 2016

2 Abstract The Norwegian Network Code FIKS from the Norwegian Transmission System Operator (TSO) Statnett, states that synchronous generators 25 MVA must have a static excitation system. It also includes requirements on the step time response and the available field winding ceiling voltage of the excitation system. An improved brushless excitation system is in operation in some pilot power plants. A rotating thyristor bridge is controlled via Bluetooth. The step time response is as fast as conventional static excitation systems. However, a ceiling voltage factor of 2 requires the thyristor bridge to operate at firing angles about 60 degrees. High torque pulsations, low power factor and low utilization of the exciter is the end result. New power electronic interfaces on the shaft results in a betterutilization of the designed exciter and improves the mechanical performance as well as the controllability of the generator field winding. Permanent magnet rotating exciters increase the field forcing strength of the synchronous generator, yielding improved transient stability (Fault Ride-Through req.). Brushless exciters also reduces regular maintenance of the generator. The thesis includes experiments on a state of the art synchronous generator test setup including constructed PM exciter and different power electronic solutions. Some investigations has been done on industrial power plants as well. Keywords: synchronous generators, permanent magnet machines, excitation systems, power electronic interfaces Jonas Kristiansen Nøland 2016

3 To my mother

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5 List of papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I II III IV Nøland, J. K., Hjelmervik, K. B., Lundin, U., "Comparison of Thyristor-Controlled Rectification Topologies for a Six-Phase Rotating Brushless Permanent Magnet Exciter", IEEE Transactions on Energy Conversion, vol. 31, no. 1., March Nøland, J. K., Lundin, U., "Step time response evaluation of different synchronous generator excitation systems", 4 th IEEE International Energy Conference (ENERGYCON 2016) in Leuven, Belgium, in April Nøland, J. K., Evestedt, F., Perez-Loya, J. J., Abrahamsson, J., Lundin, U., "Design and characterization of a rotating brushless PM exciter for a synchronous generator test setup", XXII th International Conference on Electrical Machines (ICEM 2016) in Lausanne, Switzerland, in September Nøland, J. K., Evestedt, F., Perez-Loya, J. J., Abrahamsson, J., Lundin, U., "Evaluation of different power electronic interfaces for control of a rotating brushless PM exciter", 42 nd Annual Conference of the IEEE Industrial Electronics Society (IECON 2016) in Firenze, Italy, in October Reprints were made with permission from the publishers.

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7 Contents 1 Introduction Project background Outline of the thesis Excitation systems Excitation control system Open circuit characteristics Ceiling voltage High initial response excitation system Different excitation systems Static excitation systems Rotating brushless excitation systems Standards and technical requirements Implementation of modern power electronics Analytical solutions of open-circuit dynamics Terminal voltage buildup De-excitation Positive step response Negative step response Electromechanical modelling of synchronous generators Equivalent circuit Grid dynamics Mechanical dynamics Park transformation Steady state operation Parameter exctraction Synchronous generator parameters Field-wound exciter parameters Results Conclusion Future work Exciter armature winding design Power electronic interfaces

8 8.3 Bang-bang excitation control Synchronous generator modelling Summary of papers Svensk sammanfattning Acknowledgements References

9 List of symbols Symbol Unit Description f Hz Fundamental electrical frequnecy TÛf s Field voltage time constant α Firing delay angle of thyristor bridge γ Ceiling voltage factor L f H Field winding self inductance M f H Field winding mutual inductance to the stator R f Ω Field winding resistance (hot) U f V Rated steady state field voltage I f A Rated steady state field current u f V Instantaneous field voltage i f A Instantaneous field current T do s Field winding open circuit time constant T d s Field winding short circuit time constant T f s Field winding voltage buildup time constant T 37% s Field winding de-excitiation time constant T +5% s Field winding positive step response time T +5% s Field winding negative step response time T d s Subtransient short circuit time constant, d-axis T do s Subtransient open circuit time constant, d-axis T q s Subtransient short circuit time constant, q-axis T qo s Subtransient open circuit time constant, q-axis X du Ω Unsaturated synchronous reactance, d-axis X qu Ω Unsaturated synchronous reactance, q-axis X d Ω Saturated synchronous reactance, d-axis X q Ω Saturated synchronous reactance, q-axis X d Ω Transient reactance, d-axis X d Ω Subtransient reactance, d-axis X q Ω Subtransient reactance, q-axis X l Ω Stator leakage reactance 9

10 Symbol Unit Description u f d V Instantaneous field voltage in the equivalent circuit i f d A Instantaneous field current in the equivalent circuit u d V d-axis voltage of the grid seen from the generator (line-to-line rms) u q V q-axis voltage of the grid seen from the generator (line-to-line rms) A 3/2 times the d-axis phase current amplitude the generator i d i q A 3/2 times the q-axis phase current amplitude the generator e d V d-axis terminal voltage of the generator (line-to-line rms) e q V q-axis terminal voltage of the generator (line-to-line rms) L f d H Field winding leakage inductance in the equivalent circuit L 1d H Damper winding d-axis leakage inductance in the equivalent circuit L 1q H Damper winding q-axis leakage inductance in the equivalent circuit L l H Stator winding leakage inductance of the generator L e H Equivalent leakage inductance of the grid (step-up transformer leakage) L ad H Main d-axis inductance of the generator L aq H Main q-axis inductance of the generator R f d Ω Field winding resistance in the equivalent circuit R 1d Ω Damper winding d-axis resistance in the equivalent circuit R 1q Ω Damper winding q-axis resistance in the equivalent circuit R a Ω Phase armature resistance of generator R e Ω Equivalent grid resistance T e Nm Electrical torque from the generator T m Nm Mechanical torque from the turbine P e W Electrical power produced by the generator P m W Mechanical power input from the turbine Q e VA Reactive power produced by the generator p Number of poles of generator ω r rad/s Electrical frequency of the rotor ω s rad/s Electrical frequency of the grid δ Rotor angle ϕ Load angle (power factor angle) 10

11 1. Introduction Hydropower still maintains its position as the most important source of renewable power generation in the world. In these days, most European countries go through a phase of intense refurbishment and upgrading of their existing plants. This leads to new challenges and the engineers need to regain back the knowledge that went lost twenty years ago. The trend in the hydropower industry today is more use of computerized tools and this has really revolutionized the whole design process. The generator is one of the key components of a hydropower plant, since it is responsible for converting the mechanical energy from the turbine to magnetic energy through rotor excitation and finally to electric power absorbed by the stator windings, distributing the energy into the power grid. The generators used in hydro power plants are mainly synchronous generators. Those generators need to be fed with direct current into their rotating field winding. This is the role of the excitation system. This thesis investigates the benefits of a fast-response brushless rotating exciter, intended to feed the synchronous generator with controllable field current. 1.1 Project background The project initially started with a master thesis in 2011 by Peter Butros, in cooperation with industry. Johan Bladh (former PhD student) supervised the work. A brushless field-wound rotating exciter was studied, intended for use in a fast-response brushless excitation system, with Bluetooth communication for control of a thyristor bridge attached to the rotor. The work continued and an exciter rotor was constructed at the Ångstöm Laboratory during the following year. Jonas Kristiansen Nøland (also author of this thesis) did his thesis on design and simulation of a permanent magnet stator, intended to be fitted into to the constructed rotor of the brushless exciter. Six phase topologies was investigated since it seemed to be relevant for the hydro power industry. The whole system was planned to be fitted into a complete state of the art synchronous generator test rig at the Ångstöm Laboratory. The master thesis was presented both at Chalmers University of Technology and Uppsala University, in the end of Mai Representatives from Statkraft was invited to the master thesis presentation at Uppsala University. The meeting with Statkraft opened 11

12 up for a PhD-position at the Ångstöm Laboratory with further work on the fast-response brushless rotating exciter technology. Jonas Kristiansen Nøland started as a PhD-student part-time from the autumn 2013 and full-time (80%) from spring Outline of the thesis Chapter 2 presents an overview of excitation systems. The chapter includes different important terms, standards and types of systems. Chapter 3 derives the analytical solutions of the response times of the excitation system when the synchronous generator is open-circuited. The obtained solutions are closely linked to Paper II, where experimental data from a hydro power plant is investigated. Paper II studies the open circuit step response with a conventional field-wound rotating exciter and compares it with the performance of a shaftdriven PM rotating exciter investigated in Paper I, III and IV. In Chapter 4, a complete dq-equivalent circuit model of the synchronous generator is presented including both mechanical dynamics and grid dynamics. The model parameters are extracted from manufacturer data in Chapter 5. Chapter 6 extends the generator open-circuit step response given in Paper II with a field current step response during loaded operation for the same power plant. The step response is acting against a voltage dip in the connection point of the generator to the grid. In Chapter 7, the conclusions of the thesis are summarized and discussed, and Chapter 8 outlines the work of the PhD thesis to come. 12

13 2. Excitation systems Fig. 2.1 shows a block diagram of the components included in an excitation control system. The exciter generates the direct current for the field winding of the synchronous generator. The excitation system includes the synchronous machine regulator with different control schemes and protective functions. Interactions exists between the power system and the excitation control system, including the feedback dynamics of the synchronous generator. Figure 2.1. Block diagram of the components of an excitation control system. c IEEE2014 [1] 2.1 Excitation control system A complete excitation control system is given in Fig. 2.2, including the most important subsystems. Figure 2.2. General block diagram for synchronous machine excitation control system. c IEEE2005 [2] 13

14 In the terminal voltage transducer, the terminal voltage is sensed and reduced to a dc quantity. The load compensator measures the current from the generator terminals in order to account for the voltage drop in the stepup transformer connecting the generator to the grid. If multiple generators are connected in parallel, the load compensator acts as a artificial coupling impedance for load sharing purposes. The excitation control system also includes a power system stabilizer (PSS), over- and under-excitation limiters and an automatic voltage regulator (AVR). The PSS is an additional function to the voltage regulator to improve the damping of power system oscillations. The dynamic response to a step input is one of the most important features of an excitation system, giving the generator the ability to act against disturbances in the grid. Fig. 2.4 shows some of the most important qualities characterizing such a response, including rise time, overshoot, peak time, and settling time as indicated. Figure 2.3. Typical dynamic step response of a feedback control system to a step change in input. c IEEE2014 [1] 2.2 Open circuit characteristics Fig. 2.4 plots the relation between the terminal voltage of the generator and the field current. The correlation is linear up to a certain point. The fully 14

15 loaded generator would need extra field current to account for the armature reaction with the load currents. Figure 2.4. Determination of no-load field current and air-gap field current. Line 1 plots the linearized air-gap line, whereas line 2 includes the saturation effect. c IEC2011 [3] 2.3 Ceiling voltage The ceiling voltage is the maximum field voltage available for the excitation system. The difference between the positive ceiling voltage and the rated field voltage indicates the field forcing capability and tends to improve power system transient stability [1]. With a voltage-bidirectional excitation system, a negative ceiling voltage is possible. This is helpful for a rapid demagnetizing of the synchronous generator and for control of the generator during overvoltage conditions. A high ceiling voltage can force rapid change in field current. The firing angle margins causes the magnitude of the negative ceiling voltage to be lower than the positive ceiling voltage for thyristor-controlled excitation systems. Bus-fed or transformer-fed potential-source exciters loose some advantage by the fact that the available ceiling voltage is reduced during the actual fault period [4]. During the fault period, the terminal voltage is greatly reduced, directly influencing the bus-fed excitation system. Exciters with ceiling voltage less than 150% of rated field voltage are classified as low ceiling voltage exciters according to IEEE [5]. 15

16 2.4 High initial response excitation system The literature tend to distinguish between high-speed response and normal response excitation systems [6]. Excitation systems with a fast dynamic performance are classified as a high initial response excitation system. Those systems are able to reach 95 percent of the difference between the available ceiling voltage and the rated field voltage in less then 0.1 seconds. A 6- pulse thyristor bridge rectifier directly connected to the field winding is able to change the voltage over the whole range in less than 10 milliseconds with a 50Hz ac input [7]. With six firing pulses per electrical period, the maximum time delay in the voltage response is [8] TÛf = 1 6 f. (2.1) Fig. 2.5 shows the voltage response delay for a step change in the applied field voltage for a thyristor bridge rectifier. The thyristor bridge firing angle is changed from 75 to 0 and the voltage response delay is less than 3ms. Theoretically the thyristor bridge ceiling voltage is obtained with a 0 firing angle, but normally the minimum firing angle is in the range 7-10 to ensure positive forward voltage when the thyristors are triggered. Figure 2.5. DC voltage waveform applied over the field winding due to a step change in the firing angle. Effects of commutation is neglected. c IEEE1968 [8] Fig. 2.6 shows how the nominal voltage response of an excitation system is characterized. This evaluation is mostly used for slow response brushless excitation systems with an uncontrollable rotating diode bridge in the rotor. 16

17 Figure 2.6. Excitation system nominal response. c IEEE2014 [1] 2.5 Different excitation systems Static excitation systems Potential source bus-fed excitation system Fig. 2.7 shows a block diagram of the static exication system. All components in these systems are stationary. They feed the direct current to the field winding through slip rings. The most common type is the potentialsource controlled-rectifier excitation system. The excitation power is bus-fed or transformer-fed, generated from the synchronous generator terminals and fed to a controlled rectifier through a shunt-connected step-down power potential transformer. The system has a fast inherent response, it is easy maintainable and inexpensive. However, the available ceiling voltage is dependent on the input ac voltage to the controlled rectifier. During system-fault conditions, the depressed terminal voltage reduces the available ceiling voltage. Nowdays, the potential-source excitation system is usually designed with higher ceiling voltage levels to ensure satisfactory fault-on field-forcing capability. The ceiling voltage requirement is typically 2 times the rated field voltage. As an example; With a 30 percent drop in terminal voltage, a ceiling voltage of 1.4 times the rated field voltage is available for field forcing. For high power synchronous generator excitation systems, the potential-source thyristor rectifier exciter is the dominant topology [9]. Recent studies has shown that the implementation of modern power electronic interfaces in static excitation systems can improve the field-forcing capability during reduced terminal voltages [10 12]. 17

18 Grid Transformer Stationary Rectifier Synchronous Generator Load Controller - + Voltage Sensors Reference Figure 2.7. Diagram of the conventional static excitation system. Compound-cource excitation system Compound excitation systems were very popular in the early 1970s and before, since prior to that time, fault current could not be provided by other sources [13]. The cost of a compound system is approximately 2 times the cost of a potential source bus-fed system. Where excitation support is needed, a power current transformer is included, yielding a compund-source static excitation system. When the generator produces an output current, some of the excitation power is provided by series connected power current transformers, yielding an equivalent to the field forcing capability in a shaft driven excitation system. All field excitation power is supplied by the power potential transformer when the generator operates at no-load Rotating brushless excitation systems Brushless synchronous machines became reality with the introduction of compact high-power silicon diodes during the 1950s [14]. In the beginning they were introduced for aircraft applications, where special flameproofing in hazardous atmospheres were needed [15]. In rotating brushless excitation systems, the excitation power for the generator field winding is generated physically close to the utilization point. With an armature core carrying alternating current, the rotor core should be laminated to reduce core loss. Solid steel rotors offers better mechanical stability, but laminated cores has been proven successful for large induction motors. Another challenge arises with wireless measurement and control system of field voltage and field current. However, the signals could also be delivered through brushes to attain better redundancy. Conventional bus-fed brushless excitation system One of the main problems associated with the conventional brushless excitation system (Fig. 2.8) was the slow step response of the generator field current. Because of a rotating uncontrolled diode bridge, the generator field voltage is not directly controlled. It takes time to change the field voltage to attain the ceiling voltage. It was proven that this problem could be solved by minimizing the inductances of the exciter in the initial design [16]. The ac-exciter could be designed to be capable of extremely fast changes of flux [17]. However, the 18

19 diode bridge could still not attain negative voltage for de-excitation purposes. This problem could be solved by a de-excitation resistor on the shaft [18]. Maintenance is a very important aspect for the operation of synchronous generators, since it can reduce the cost of the power production. The use of slip-rings and carbon-brushes is one of the key contributors to the required maintenance [19, 20]. The brushes needs to be replaced regularly as they get worn down during use. The use of a rotating brushless exciter can handle this problem and thereby reduce the maintenance cost. However, several problems related to the conventional brushless excitation system in the past, made a market driver for the static excitation instead [21]. Grid Transformer Stationary Rectifier Rotating Exciter Rotating Rectifier Synchronous Generator Load Controller - + Reference Voltage Sensors Figure 2.8. Diagram of the conventional bus-fed brushless excitation system. Improved bus-fed brushless excitation system The improved bus-fed brushless excitation system shown in Fig. 2.9 is in operation on some pilot power plants. They are still not operated with the same dynamic performance as the static excitation system. This is due to the dual control scheme, where the stationary thyristor bridge reduces the ceiling voltage available for the rotating thyristor bridge. Operators tend to not let the rotating thyristor bridge operate at higher firing angles during steady state conditions. Keeping the firing angle low, reduces the steady state torque pulsations caused by the rotating rectifier as well as keeping the power factor of the rotating armature currrents high. Grid Transformer Stationary Rectifier Rotating Exciter Rotating Rectifier Synchronous Generator Load Controller Controller Voltage Sensors Reference Figure 2.9. Diagram of the dual control bus-fed brushless excitation system. 3-stage shaft-driven brushless excitation system With a permanent-magnet generator (PMG) overhung from the ac-exciter, the total excitation power requirements is obtained directly from the generator 19

20 shaft [15]. Since all excitation power is derived directly from shaft rotation, this system is classified as a [?] or [?] exciter. The independence of power system disturbances provides improved reliability. Fig shows the schematic diagram of the conventional PMG excitation system. Because of the uncontrolled rotating diode bridge connected to the field-wound exciter, this excitation system lacks a fast dynamic response. Pre-exciter Stationary Rectifier Stationary Chopper Rotating Exciter Rotating Rectifier Synchronous Generator Load N S Controller - + Reference Voltage Sensors Figure Diagram of the conventional shaft-driven brushless excitation system. 2-stage shaft-driven brushless excitation system The 2-stage shaft-driven excitation system utilizes the permanent magnet generator as the main exciter in an outer pole PM topology. A wirelessly controlled power electronic interface is needed on the shaft. Fig and 2.12 proposes two different power electronic interfaces suitable for the 2-stage shaft-driven brushless excitation system. The thyristor-based interface is investigated in Paper I of this thesis. It includes even multiphase topologies. Paper III presents the complete design characterization of a designed outer pole PM exciter for a 2-stage configuration. Paper IV investigates modern power electronic interfaces as shown in Fig Rotating Exciter N S Rotating Synchronous Rectifier Generator Load Voltage Sensors Reference Controller + - Figure Diagram of the 2-stage shaft-driven brushless excitation system with rotating thyristor-based power electronic interface. Rotating Exciter N S Rotating Rectifier Rotating Synchronous Chopper Generator Load Voltage Sensors Reference Controller + - Figure Schematic diagram of the 2-stage shaft-driven brushless excitation system with rotating PWM chopper-based power electronic interface. 20

21 2.6 Standards and technical requirements Different transmission system operators (TSO s) operates their grids with different standards related to the excitation system of synchronous generators. Table 2.1 compares standards for the step response and the field winding ceiling voltage from different standards. Table 2.1. Performance of the different interfaces Standard Owner OC step response test Requirement Ceiling voltage FIKS Statnett 0.95pu 1.00pu 0.5s 2.00pu SvKFS Svenska Krafnat 1.00pu 1.10pu 0.8s NA NGTR Statkraft/Vattenfall 0.95pu 1.05pu 0.5s 2.00pu IEEE IEEE Std pu 1.03pu NA 1.50pu IEEE standard defines no step response time requirement for the excitation system but prefers to require a high initial response type exciter for larger generators. This is because a fast field voltage response is directly linked to the response of the field current. The TSO s specifies requirements on the fault ride-through capability of the grid connected generators. Fault ride-through means the capability of electrical devices to be able to remain connected to the network and operate through periods of low voltage at the connection point caused by secured faults. FIKS states that synchronous generators should be able to withstand a fault in the grid if the actual time-dependent voltage profile lies within a certain minimum requirement ("worst case"). The generator should also be able to support the grid during the whole low voltage ride-through. After the fault clearing, the generator should be able to operate with a lower voltage level as a result of a weaker grid. The time it takes to clear the fault will determine the real voltage profile of the grid. Fig shows the time-dependent voltage profile required for generators connected to a grid with 220kV operating voltage or higher. U[pu] t[ms] Figure Time-dependent fault ride-though voltage profile for generators connected to a grid with operating voltage above or equal to 220kV [22]. 21

22 2.7 Implementation of modern power electronics The thyristor bridge rectifier was introduced by General Electric in 1957 [23]. From then, a revolution in the control of power was initiated. It marks the beginning of modern power electronics as we know it. The semi-controlled thyristor devices was able to rectify a controlled dc voltage by adjusting the delay firing angle. However, the expense of the delayed firing angle causes a larger phase shift between voltage and current fed from the ac input. Especially in the hydropower industry, where a high firing angle is required for an available ceiling voltage, a high firing angle causes low power factor for the excitation power. In Fig. 2.14, a step change in the dc output voltage is compared with a thyristor bridge rectifier and a dc-dc step-down converter. The dc-dc converter changes the voltage reference by adjusting the duty cycle. The dc input could be fed from an uncontrolled diode bridge rectifier with no delay angle, yielding a higher power factor. For a shaft-driven exciter, less torque ripple is also the end result (Paper IV). With modern power electronics, the voltage response is instead related to the switching frequency of the pulse-width modulation, yielding TÛf = 1, (2.2) f sw which causes a faster response of the field voltage compared to thyristorcontrolled rectifiers. The voltage time response becomes independent of the fundamental electrical frequency in the exciter armature. The switching frequency tends to be much higher than the fundamental frequency. Figure Comparison of different voltage control techniques. (a) Step-down dc-dc converter. (b) Three-phase thyristor rectifier. c IEEE2015 [24] 22

23 3. Analytical solutions of open-circuit dynamics An unloaded synchronous generator excitation system can be simplified as a classical RL-circuit. The relation between the instantaneous field voltage (u f ) and instantaneous field current (i f ), is given by u f = L f di f dt + R f i f, (3.1) or written in circuit form shown in Fig L f R f + u f i f Figure 3.1. Simple equivalent circuit of the excitation system with unloaded generator. At rated steady state conditions, the voltage-current relationship is given by ohms law, yielding U f = R f I f, (3.2) where U f is the rated mean steady state field voltage and I f is the rated field current. If u f = γu f, the general solution for Eq. 3.1 yields where T do = L f R f. i f = γi f + Ke t T do, (3.3) 3.1 Terminal voltage buildup If the excitation system initially starts with zero excitation current, i f (0) = 0, then K = γi f in Eq. 3.3, yielding ( ) i f = γi f 1 e t T do, (3.4) 23

24 with u f = γu f as the applied field voltage. The time it takes to reach the nominal field current becomes [ ] γ T f = T do ln. (3.5) γ 1 Fig. 3.2 shows how the terminal voltage buildup of a generic unloaded synchronous generator depends on the applied field voltage. With γ = 2, the generator reaches the terminal voltage in T f T do = ln(2) The voltage buildup time T f will then become smaller than the generator d-axis transient time constant. The positive ceiling factor (γ) improves the dynamic response Current [pu] γ = 3.0 γ = 2.8 γ = 2.6 γ = 2.4 γ = 2.2 γ = 2.0 γ = 1.8 γ = 1.6 γ = 1.4 γ = 1.2 γ = Time [pu] Figure 3.2. No-load terminal voltage buildup: Field current, i f I f, as a function of time, t T do, with different applied field voltages, u f = γu f. 3.2 De-excitation De-excitation starting with rated excitation current, i f (0) = I f, leads to K = (1 γi f ) in Eq. 3.3, yielding i f = γi f + (1 γ)i f e t T do, (3.6) with u f = γu f as the applied field voltage. The time it takes to reach 37 percent of the nominal terminal voltage yields [ ] T 37% = T do 1 γ (3.7) 1 e γ at no-load operation. There exists certain requirements in the NGTR of how fast the system should be demagnetized. If the generator time constant T do =7.5s, 24

25 the requierement is T 37% T do 1 5 = 0.2. The requirement should be met from nominal load. Fig. 3.3 shows the benefit of applying a negative field voltage during de-excitation of the generator. Notice that it takes T do to reach 1 e I f if the applied field voltage is zero during de-excitaiton. During balanced short circuit of the synchronous generator terminals, the subtransient short-circuit time constant, T d, should be used for calculation of T 37%. Current [pu] γ = -3.0 γ = -2.8 γ = -2.6 γ = -2.4 γ = -2.2 γ = -2.0 γ = -1.8 γ = -1.6 γ = -1.4 γ = -1.2 γ = -1.0 γ = -0.8 γ = -0.6 γ = -0.4 γ = -0.2 γ = Time [pu] Figure 3.3. No-load de-excitation response: Field current, i f I f, as a function of time, t T do, with different applied field voltages, u f = γu f. 3.3 Positive step response Given that i f (0) = 0.95I f initially, leads to K = (0.95 γ)i f in Eq. 3.3, yielding i f = γi f + (0.95 γ)i f e t T do. (3.8) With a field current step change from 0.95pu to 1.00pu, 90% is reached when i f (t) = 0.995I f, yielding [ ] 0.95 γ T +5% = T do ln. (3.9) γ According to FIKS, T +5% 0.5s. If the generator time constant T do =7.5s, then T +5% T do A positive ceiling factor (γ) is needed for fast postive step response. FIKS requirement is gamma equal to 2. 25

26 3.4 Negative step response Given that i f (0) = I f initially, leads to K = (1 γ)i f in Eq. 3.3, yielding i f = γi f + (1 γ)i f e t T do. (3.10) With a field current step change from 1.00pu to 0.95pu, 90% is reached when i f (t) = 0.955I f, yielding [ ] 1 γ T 5% = T do ln (3.11) γ With a six pulse thyristor bridge, a negative value of γ is possible. With the positive ceiling factor (γ) of 2 at a firing angle of 10 degrees, a negative ceiling factor (γ) of about is obtainable at 150 degrees firing angle during unloaded operation. A large difference applies between the nominal field voltage and the actual negative ceiling voltage during a negative step response. In comparison to the positive step response, the negative step response is usually faster for fully controlled thyristor rectifiers. 26

27 + 4. Electromechanical modelling of synchronous generators During transient simulation of the synchronous generator, the rotor speed will no longer be constant as in the steady state model. The rotor speed dependent voltage terms in the equivalent circuit model leads to a non-linear set of differential equations to be solved. If one assumes that the synchronous generator feeds a balanced set of source voltages through an equivalent inductance L e and an equivalent resistance R e, those components needs to be included in the equivalent circuit equations [25]. 4.1 Equivalent circuit The final equivalent circuit model is given in Fig. 4.1 and Fig The circuits are magnetically cross-coupled. The generator terminal voltages are denoted e d and e q, whereas the grid voltages are denoted u d and u q. R a L l i f d + R f d R 1d R e L f d L 1d L ad e d L e + u f d i 1d i d + u d ω r ψ q Figure 4.1. Synchronous machine d-axis equivalent circuit 27

28 R a L l R 1q + R e L 1q L aq e q L e i 1q ω r ψ d i q + u q + Figure 4.2. Synchronous machine q-axis equivalent circuit The d- and q-axis flux linkages are calculated from the d- and q-axis currents, yielding ψ d = L ad ( i d + i 1d + i f d ) (L l + L e )i d (4.1) ψ q = L aq ( i q + i 1q ) (L l + L e )i q, (4.2) where the equivalent inductance (L e ) is added to the stator leakage inductance (L l ) of the synchronous generator. With the modified d- and q-axis flux linkages, the grid-side d- and q-axis voltages equals u d = (R a + R e )i d ω r ψ q + dψ d dt (4.3) u q = (R a + R e )i q + ω r ψ d + dψ q, (4.4) dt where the equivalent resistance (R e ) is added to the stator armature resistance (R a ) of the synchronous generator. 4.2 Grid dynamics Since all electrical components between the generator and the infinite bus is now included in the equivalent circuit, the d- and q-axis voltages can be obtained from the instantaneous rotor angle (δ), yielding 28 u d = U sinδ (4.5)

29 u q = U cosδ. (4.6) For modelling of static exciation systems, the available field voltage is proportional to the voltage on the generator terminals. The generator terminal voltage can be calculated from the infinite bus voltages, yielding e d = u d + R e i d ω r L e i q + L e di d dt (4.7) e q = u d + R e i d + ω r L e i d + L e di q dt. (4.8) Note that the mutual coupling between the d-axis circuit and the q-axis circuit is a function of the instantaneous rotor electrical angular speed (ω r ) and not the synchronous electrical angular speed of the grid (ω s ). In steady state operation, ω r = ω s. 4.3 Mechanical dynamics The deviations in the rotor speed is found from T m T e = 2J p dω r dt, (4.9) where T m is the applied mechanical torque and the electrical torque is calculated from T e = p 2 [ψ di q ψ q i d ]. (4.10) The assumption of a constant mechanical torque is not fully valid in reality. To account for the turbine effect on the torque as a result of speed deviations, another model [26] equals the turbine torque T m = p 2 P m ω r, (4.11) where the turbine power, P m, is assumed to be constant instead. With an increase in the rotor speed, the turbine will react with a slightly lower torque, causing a damping effect. The oscillations in the rotor angle (δ) are obtained by integrating the difference between rotor speed and synchronous speed, yielding ω r ω s = dδ dt. (4.12) The instantaneous power factor angle seen from the connection point to the grid, could be calculated from the instantaneous rotor angle, yielding ( ) ϕ = tan 1 id δ. (4.13) i q 29

30 4.4 Park transformation The real time-dependent phase voltages are found from power-invariant transformation, yielding u a cos(θ) sin(θ) 1 u b 2 = cos(θ 2π 3 3 ) sin(θ 2π 3 ) 1 u d u q, (4.14) cos(θ + 2π 3 ) sin(θ + 2π 3 ) 1 u c similarly for the phase currents i a cos(θ) sin(θ) 1 i b 2 = cos(θ 2π 3 3 ) sin(θ 2π 3 ) 1 i d i q. (4.15) cos(θ + 2π 3 ) sin(θ + 2π 3 ) 1 i c As a result of the power-invariant transformation, u d and u q displays a vector with magnitude equal to the line-to-line rms voltage. The magnitude of the current vector composed of i d and i q is equal to 3/2 times the rms phase current. The power delivered to the grid equals and the reactive power production equals P e = u d i d + u q i q, (4.16) Q e = u q i d u d i q. (4.17) u 0 i Steady state operation By applying KVL rule on the d- and q-axis equivalent circuits, steady state operation yields R a I d U sin(δ) + ω s L q I q = 0 (4.18) R a I q U cos(δ) + ω s L ad I f d ω s L d I d = 0. (4.19) Equation 4.18 could be expressed as R a I sin(δ + ϕ) +U sin(δ) = X q I cos(δ + ϕ). (4.20) The solution with respect to the rotor angle yields tan(δ) = X qi cos(ϕ) R a I sin(ϕ) U + R a I cos(φ) + X q I sin(ϕ). (4.21) The rotor angle at rated apparent power, power factor and terminal voltage can be obtained with R a and X q in per unit quantities, yielding 30 tan(δ) = X q,pu cos(ϕ) R a,pu sin(ϕ) 1 + R a,pu cos(φ) + X q,pu sin(ϕ). (4.22)

31 Also, the required steady state field current given from 4.19, yielding I f d = U cos(δ) + X di sin(δ + ϕ) + R a I cos(δ + ϕ) X ad. (4.23) The field current in real quantities is equal to I f = U cos(δ) + X di sin(δ + ϕ) + R a I cos(δ + ϕ), (4.24) 3 2 ω sm f where the factor 3/2 comes from the fact that the mutual inductance in the equivalent circuit model is scaled up as a result of power invariant transformation. The field winding reduction factor k f is equal to 2L ad/ 3M f. 31

32 5. Parameter exctraction 5.1 Synchronous generator parameters Table 5.1 compares the re-specification of the Svante generator with the original specification (generator in the lab). The major change is the increased length of the air gap from 4mm to 8.3mm. Studies of the generator has already been made in [26 28]. Table 5.2 compares the rating of four different larger generators. Generator G4 has already been investigated extensively in [29, 30]. The collection of generators show the variations in terminal voltage, mechanical speed and apparent power. G2 and G3 are installed with a brushless rotating exciter with rotating thyristor bridge and wireless triggering. Table 5.1. Specification of the test generator in the lab Description Symbol G1 G1* Unit Apparent power S kva Power factor cos(ϕ) Rotor angle, rated load δ Terminal voltage U V Rated current I A Field voltage, rated load U f V Field current, rated load I f A Field current, ceiling limit Î F A Field current, rated no load I FNL A Field current, rated short circuit I FSC A Field current, air gap line I FAG A Frequency f Hz Number of poles p Air gap length g mm Mechanical speed n rpm Moment of inertia J kgm 2 Inertia constant H s 32

33 Table 5.2. Specification comparing four different synchronous generators in operation in nordic countries Symbol G2 G3 G4 G5 Unit S MVA cos(ϕ) δ U kv I ka U F V I F A I FNL A I FSC A I FAG A f Hz p n rpm J tm 2 H s Additionally to the generator rating, also a proper design specification lies behind. Table 5.3 shows the design chosen to fulfill the ratings given in Table 5.1 and 5.2. Table 5.3. Comparing the design specification of the four different industrial generators with the generator in the lab Description Symbol G1 G2 G3 G4 G5 Unit Stator inner diam. D si m Active length l a m Air gap length g 8.3 (4) mm Number of slots Q s Slots per pole per phase q s 3 2 1/4 2 1/2 2 1/2 6 Coil pitch q s,coil 9 6 NA NA 15 Circuits per phase c s Conductors per slot n s Dampers per pole n D Field turns per pole N F /2 26 1/2 18 1/2 42 1/2 There exists rough analytical estimates which relates the design specification to the ratings. The general generator formula 3 q s n s U = k 1 2π f D si l a ˆB 2 c δ, (5.1) s estimates the terminal voltage. ˆB δ is the fundamental air gap flux density (normally slightly above 1T) and k 1 is the fundamental winding factor. The 33

34 fundamental winding factor is calculated from [31] k 1 = ) π ( 6 qs,coil π ) sin q s sin( π 6q s 6qs ). (5.2) An important parameter for exciation systems is the reduction factor, relating the field current and field voltage in the equivalent circuit to the real ones. An analytical estimation in [32] states that the field winding reduction factor is equal to 6 q s n s k f = k 1 k c, (5.3) π N f c s where k c is a correction factor related to the longitudinal reaction of the machine. The relation between the stator referred and the rotor referred field voltage is u f d = k f u f (5.4) i f d = i f k f, (5.5) used in the equivalent circuit of the synchronous generator. Also the field winding parameters in real quantities yields R f = R f k 2 f (5.6) L f = L ad + L f d. (5.7) M f = k 2 f 2 L ad. (5.8) 3 k f The equivalent circuit parameters can be extracted from the standard parameters in Table 5.4. G1 WD corresponds to the experimental generator without damper bars, whereas G1 CD shows the standard parameters with continuous damper bar connection. 34

35 Table 5.4. Standard parameters comparing the test rig generator with four different industrial generators Symbol G1 WD G1 CD G2 G3 G4 G5 Unit X l pu X du pu X qu pu X d pu X q pu X d pu X d pu X q pu T do s T d s T do s T d s T qo s T q s T a s From the synchronous generator standard parameters, the main inductances are obtained from simply subtracting the leakage (L ad = L d L l and L aq = L q L l ). The other equivalent circuit parameters are obtained according to [29, 33], yielding L f d = L ad L d L l L d L d L 1d = (L d L l) L d L l L d L d L q L l L 1q = L aq L q L q R f d = L ad + L f d ω base T do R 1d = L 1d + L d L l ω base T do R 1q = L aq + L 1q ω base T qo (5.9) (5.10) (5.11) (5.12) (5.13) (5.14) R a = 2L d L q T a (L d + (5.15) L q) The following relations exists between the open circuit time constants and the short circuit time constants T do = X d T d, (5.16) X d 35

36 T do = X d X d T qo = X q X q T d, (5.17) T q. (5.18) Table 5.5 shows the standard parameter in per unit quantities, whereas Table 5.5 outputs the parameters in actual quantities for the power-invariant reciprocal dq-system. The real rotor-referred quantities are given in Table 5.7. Table 5.5. Equivalent circuit parameters of the generators in per unit Symbol G1 WD G1 CD G2 G3 G4 G5 Unit L l pu L ad pu L aq pu L f d pu L 1d pu L pl NA NA NA NA pu L 1q pu R f d pu R 1d pu R 1q pu R a pu Table 5.6. Equivalent circuit parameters of the generators Symbol G1 WD G1 CD G2 G3 G4 G5 Unit L l mh L ad mh L aq mh L f d mh L 1d mh L pl NA NA NA mh L 1q mh R f d mω R 1d mω R 1q mω R a mω Table 5.7. Real field winding parameters of the four different generators Symbol G1 G2 G3 G4 G5 Unit k f L f H M f mh R f Ω 36

37 5.2 Field-wound exciter parameters Due to the small size and lower market value in comparison to a generator or a turbine, exciters have not been sufficiently focused upon [34]. All conventional exciters studied in this thesis have equal design parameters with slight modifications (See Table 5.8). Table 5.8. Generic design parameters for all exciters Description Parameter Value Unit Number of poles p 18 Slots per pole per phase q r 3 Number of parallel circuits c r 6 Number of conductors per slot n r 8 Number of field winding turns per pole n f 240 Coil pitch in number of slots q r,coil 8 Fundamental winding factor k Rotor outer diameter D ro 1.7 m Table 5.9 compares the specification of three different exciters with equal design parameters given in Table 5.8. The behavior of exciter X1 with a rotating thyristor bridge is investigated in Paper II. Exciter X1 is in operation on an industrial power plant including a wireless communication system for thyristor triggering. The different exciters are fitted into generators with different mechanical speeds, which results in slight variations in the electrical frequency of the rotor armature winding. For exciters with a rotating thyristor bridge, the field voltage time response is directly proportional to the electrical frequency. This is because the thyristor bridge is triggered only 6 times per electrical period. Table 5.9. Specification of three different exciters with generic design parameters Description Parameter X1 X2 X3 Unit Apparent power S kva Power factor cos(ϕ) Terminal voltage U V Rated I A Rated generator field voltage U F V Rated generator field current I F A Rated exciter field voltage U f V Rated exciter field current I f A Electrical frequency f Hz Mechanical speed n rpm Air gap length g mm Active length l a m The power factor of the the different exciters are specified only for rotating diode bridge operation. For the specification of a fast-response brushless 37

38 excitation system with a rotating thyristor bridge, this would not be a valid assumption. At higher firing angles, the commutation interval tends to be small as a result of high commutation voltages. The phase currents in the rotor armature have a square wave shape. The relation between the rms value of the armature currents and the generator field current becomes then 2 I = 3 I f. (5.19) Including the both the effect of the displacement and distortion of the currents, the true power factor becomes PF = 1 cos(α) cos(α), (5.20) π2 6 6 where the firing angle (α) accounts for the displacement power factor. Normally the ceiling voltage of a fast-response exciter is attained at 10 firing angle. For a ceiling voltage factor of 2, the steady state operating firing angle tends to be about 60 (Paper II). This suggests the actual steady state power factor is about The problem of a low power factor could be solved with other power electronic interfaces, like a rotating capacitor and a dual quadrant chopper (Paper IV). In recommended exciter design, the direct axis synchronous reactance should be about 1.22 per unit [34]. Also, the direct axis transient reactance is proposed to be 0.26 per unit. Among the exciters investigated in this thesis, X2 have parameters close to this recommended practice (see Table 5.10). Paper III investigates the design of an outer pole PM exciter with a direct axis synchronous reactance of about 0.2 per unit. This is a general trend when comparing field wound synchronous machines with permanent magnet machines [35]. Table Standard parameters of different exciters Description Parameter X1 X2 X3 Unit Leakage reactance X l pu Commutating reactance X com pu D-axis synchronous reactance X d pu Q-axis synchronous reactance X q pu D-axis transient reactance X d pu D-axis subtransient reactance X d pu Q-axis subtransient reactance X q pu Open circuit time constant T do s Short circuit time constant T d s Armature time constant T a s The final per unit equivalent circuit parameters are given in Table The rotor of the exciters are solid, with no added damper bars. However a small 38