Campus Monterrey
School of Engineering and Sciences
Model-Based Predictive Rotor Current Control Strategy for Indirect Power Control of a Doubly Fed Induction Generator Driven by an
Indirect Matrix Converter
A dissertation presented by
Alejandro Olloqui Mu ˜noz
Submitted to the
School of Engineering and Sciences
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
in
Information Technologies and Communications Major in Electronics
Monterrey, Nuevo Le´on, November, 2021
To Jesus Christ, my Lord and Savior.
“Yours, O Lord, is the greatness and the power and the glory and the victory and the majesty, indeed everything that is in the heavens and the earth; Yours is the dominion, O Lord, and You exalt Yourself as head over all.” — 1 Chronicles 29:11
“I can do all things through Christ who strengthens me.” — Philippians 4:13
To my beloved wife Rachel, to my parents Manuel and Rosario, to my brother Manuel and my sister Rosario, to my friends and partners; thank you all for your unconditional confidence, support, patience, wise counsel and encouragement.
iii
Thank you Lord for your infinite mercy and love. Thanks to my beloved wife and my family, thanks to my friends and partners for their unconditional confidence, support, patience, wise counsel and encouragement.
Thanks to Professor Manuel Mac´ıas, Professor Osvaldo Micheloud, and to the Power Elec- tronics Lab at Tecnol´ogico de Monterrey for their support on tuition.
Thanks to Professor Marco Rivera and to the Power Electronics Research Group at Universi- dad de Talca, Curic´o Campus, Chile. Fondecyt Regular Project 1191028 and Fondap SERC Chile 15110019.
Thanks to Consejo Nacional de Ciencia y Tecnolog´ıa (Conacyt) for the support granted.
iv
Indirect Power Control of a Doubly Fed Induction Generator Driven by an Indirect Matrix Converter
by
Alejandro Olloqui Mu˜noz Abstract
Wind energy conversion systems, which are in continuous development, are formed by three main elements, generator, converter, and control algorithms. Each element has its own tech- nical challenges but all together they intend to cover the same objective, which is to get the maximum power from the wind with fast and adaptive control techniques to ensure power quality and grid compliance.
This work has a special focus on the doubly fed induction generator (DFIG), which still holds an important market share in the wind energy industry. The DFIG shows advantages over synchronous generators in terms of weight and size, and favorable characteristics such as decoupled active and reactive power control over a wider speed range, and partial scale of the power converter rating when used at rotor terminals.
The full power capability of the generator is the aggregate sum of rotor and the stator when operating at super-synchronous speed and with a bidirectional power interface with low loses, high efficiency and variable output voltage amplitude, frequency, phase, and sequence.
The indirect matrix converter (IMC) is light, it can handle high power densities and it can operate in harsh condition environments. The IMC, just as the conventional matrix converter (MC), would require a modulator or a complex conventional control strategy. Model predic- tive control (MPC) is a relatively new control technique for the IMC, specially due to the use of the discrete nature of power converters and its simplicity for implementation and intuitive approach.
Model-based predictive rotor current control (MB-PCC) is proposed for a doubly fed induction machine (DFIM) driven by an indirect matrix converter. In this strategy active and reactive power, as well as the synchronization process, are controlled using the control of rotor currents with a dynamic reference calculated from active and reactive stator power set points and the dynamic model of the DFIM in coordination with the grid parameters. The grid synchronization process is carried out only by setting the P-Q power set points to zero and once completed, the control strategy can be applied in all four P-Q operating regions of the DFIM in a variable speed scenario.
This strategy was implemented in a simulation using Gecko Circuits®, and in a 5.5 kW test rig. First, the stator active and reactive power references Ps∗, Q∗s are decoupled into a stator current reference; second, the rotor electrical angular frequency ωr and angle θr, the grid voltage amplitude, angular frequencyωg and angleθg are integrated in the DIFG model;
third, rotor currents are solved for a stator-fixed time-varyingαβ reference frame; forth, the rotor current prediction takes into account the twenty-four valid combinations of the IMC
v
liseconds. This was the time required to guarantee full synchronization conditions applying zero power reference (Ps∗ = 0, Q∗s = 0). During the synchronization process, a very small voltage ripple in the stator voltage caused an overshoot in the stator current of only 1 Ampere.
Right after the synchronization, the power reference can be changed within the nominal power limits as required. However, in simulation, the power reference was changed from zero to 3 kW and 3 kvar, and in the experimental rig the steps were limited to 500 W and 500 var due to setup limitations and in order to emulate a reduced scale grid. With the latter, the feasibility of the proposed control technique was proven both by simulation and implementation in an experimental rig rated to 5.5 kW.
vi
List of Figures
2.1 WECS topology with a DFIG and a power converter on the rotor terminals. . 7
2.2 DFIG equivalent circuit rotational synchronous to an arbitrary angular speedω. 8 2.3 Electromagnetic torque and angular speed of the rotor for each operating mode of the DFIG. . . 9
2.4 Conventional back-to-back converter. . . 10
2.5 Power topology of the conventional direct matrix converter. . . 10
2.6 Wind energy conversion system with DFIG technology controlled by an IMC on the rotor side. . . 12
2.7 Conventional indirect matrix converter. . . 13
2.8 DFIG equivalent circuit fixed to the stator (αβ). . . 14
2.9 Field oriented control applied to DFIG. . . 16
2.10 Influence of the rotor currents over active and reactive power during motoring mode. . . 17
2.11 Comparison of FOC and DTC algorithms for the squirrel cage induction ma- chine. . . 18
2.12 Hysteresis comparator for active power control. . . 18
2.13 Flux orientation and rotation during motoring mode of the DFIG. . . 19
3.1 Block diagram of the indirect power control using predictive rotor current control strategy. . . 27
4.1 IMC wired. . . 29
4.2 Power interface for 18 signals optically isolated. . . 30
4.3 Snubber circuit for the inverter side of the IMC. . . 31
4.4 Different configurations for current transducers. . . 32
4.5 Measuring system composed of transducers and a conditioning circuit for each channel. . . 33
4.6 DFIG attached to a torque transducer, a prime motor and an encoder. . . 34
4.7 Control platform formed by an FPGA and a DSP. . . 35
4.8 Setup: dSPACE, converter, power interface, optical interface, FPGA, trans- ducers. . . 36
4.9 Left: Encoder, motor and drive, DFIG. Right: Reduced-scale grid. . . 37
4.10 Control platform formed by an FPGA and a dSPACE. . . 38
4.11 Example of an S-function used to implement the MPC algorithm in Simulink®. 39 4.12 dSPACE block diagram including RTI’s external interrupt signal, analog to digital acquisition and conditioning blocks. . . 39
vii
current reference for the MPC strategy. . . 40
4.14 dSPACE block diagram outputs including the next switching state for the IMC and digital to analog output to the oscilloscope. . . 40
5.1 GeckoCIRCUITS menu. . . 42
5.2 Rotor current reference with reference equal to zero (left) and with a step in the value. . . 43
5.3 Synchronization process and closure of grid contactor. . . 44
5.4 Acquired rotor currents and reference value for each phase. . . 45
5.5 Predictive control of the stator active and reactive power using model predic- tive current control. . . 45
5.6 Close look of the DFIG active and reactive power to see the ripple and dy- namic response during a step change. . . 46
5.7 Experimental test rig. . . 47
5.8 Stator and rotor current, stator and grid voltage during synchronization at con- stant speed of 950 rpm. . . 48
5.9 Rotor current control with step on the active and reactive power reference at constant speed of 950 rpm. . . 49
5.10 Rotor current control with step on the active power reference at constant speed of 950 rpm. . . 49
5.11 Close look of the DFIM active power to see the ripple and dynamic response during a step change. . . 50
A.1 Equivalent circuit of a mutual coupling between one stator phase and its cor- responding rotor phase of a DFIG. . . 53
A.2 Complex vector representation of a three-phase induction motor. . . 57
B.1 Line currents and phase voltages for calculation of power factor and powers for no-load test. . . 68
B.2 Line currents and phase voltages for calculation of power factor and powers for blocked-rotor test. . . 69
B.3 Block diagram in Simulink. . . 70
B.4 Current vs. speed (simulation results). . . 71
B.5 Current vs. speed (experimental results). . . 72
C.1 Switching pattern for the optimal vectors. . . 74
C.2 Block diagram of the modified predictive rotor current control strategy. . . 75
viii
List of Tables
4.1 DFIG simulation parameters. . . 37
A.1 Stator and rotor coupling inductances. . . 55
B.1 Power factor calculation from no-load test. . . 67
B.2 Active powerPN Lfrom no-load test. . . 68
B.3 Power factor calculation from blocked-rotor test. . . 69
B.4 Active powerPBRfrom blocked-rotor test. . . 69
B.5 Calculated parameters of the equivalent circuit of the DFIG. . . 70
ix
Abstract v
List of Figures viii
List of Tables ix
1 Introduction 1
1.1 Motivation . . . 2
1.2 Problem Statement and Context . . . 2
1.2.1 Wind Power System . . . 2
1.2.2 Generator . . . 3
1.2.3 Power Converter . . . 3
1.2.4 Control Strategy . . . 3
1.3 Hypothesis . . . 4
1.4 Solution Overview and Contribution . . . 5
2 The DFIG in Wind Energy Conversion Systems 7 2.1 Electrical Generator Topology . . . 7
2.2 Power Converter Topologies . . . 8
2.3 DFIG-Based WECS Driven by an Indirect Matrix Converter . . . 11
2.4 Conventional Control Methods . . . 14
2.4.1 Passive and Partial Active Control of Speed . . . 14
2.4.2 Vector Control . . . 15
2.4.3 Hysteresis Control . . . 16
2.5 Modern Power Control Strategies for the DFIG . . . 19
2.5.1 Sliding-Mode Control . . . 19
2.5.2 Fuzzy Control . . . 20
2.5.3 Model-Based Predictive Control . . . 20
2.6 Discussion . . . 21
3 Indirect Power Control for the DFIG using MBPCC 23 3.1 Rotor Current Reference Generation . . . 24
3.2 Indirect Power Control Using MBPC . . . 25
3.2.1 Cost Function . . . 26
3.2.2 Block Diagram of the Control Strategy Proposed . . . 26
x
4.1 Prototype I: Wired IMC Using Terminal Blocks to Drive a 5 HP DFIG . . . . 28
4.1.1 Wired Indirect Matrix Converter . . . 28
4.1.2 Power Interface and Drives . . . 29
4.1.3 Protection Systems . . . 30
4.1.4 Sensing and Conditioning Systems . . . 32
4.1.5 Encoder and Torque Transducer . . . 34
4.1.6 Digital Platform . . . 34
4.2 Prototype II: IMC Using Isolated Switch Modules . . . 35
4.2.1 Entire Test Rig Hardware Redesign . . . 36
4.2.2 Digital Control Platform Redesign . . . 37
4.3 Implementation of the Control Strategy . . . 38
5 Results 42 5.1 Simulation Results . . . 42
5.2 Experimental Results . . . 47
6 Conclusion 51 A DFIG Model inαβ system 53 A.1 Complex Vector Representation of Three-phase Variables . . . 54
A.2 Turns Ratio Transformation . . . 56
A.3 Transformation to a Rotating Reference Frame . . . 57
A.4 DFIGαβ Dynamic Model . . . 59
A.4.1 αβ Rotor Currents . . . 59
A.4.2 αβ Stator Currents . . . 61
A.5 Transformation of Stator and Rotor a, b, c Quantities to Stationary q− and d−axis . . . 61
B Parametrization of the DFIG 63 B.1 Introduction . . . 63
B.1.1 Nomenclature . . . 64
B.1.2 Direct Current Test . . . 65
B.1.3 No Load Test or Idle-Running Test . . . 65
B.2 Experimental tests . . . 66
B.2.1 Parametrization . . . 67
B.2.2 Validation . . . 70
C Extended Work 73 C.1 Predictive Rotor Current Control with Fixed Switching Frequency . . . 73
Bibliography 85
xi
Introduction
Renewable energy sources not only reduce the dependence on fossil fuels but also diversify the energy sources. Its development is intended to generate clean and sustainable energy by means of no greenhouse emissions and reduce the footprint with a competitive cost. Hydro power is still leading as the most prominent renewable energy source but solar power and wind power are continuously growing with new installations and new short-term and long- term projections around the world.
The dependence on fossil fuels is still there but there is also an energy transforma- tion worldwide for which the development of the renewable energy is focused in economic competitiveness, to somehow, displace generation from imported fuel sources with relatively expensive high cost. However, the levelized cost of electricity (LCOE) values for wind and solar technologies are not directly comparable with the LCOE values for other technologies that may have a similar average annual capacity factor, there is a continuous improvement of the technology aiming higher power density and efficiency.
Wind power cost presents regional variations that may be attributed to local labor mar- kets and availability of energy sources but this technology finds opportunities not only in windy sites but also in regions with lower quality wind resources that offer low cost of opera- tion and high value considering environmental regulations or tax credits, for example.
The wind energy conversion systems (WECS) are one of the fastest growing and one of the most promising renewable technologies, with few tens of kW in late 80’s and now with multi-MW systems installed worldwide [1]. With a 27.7% average growing for 2018, WECS contributed with a capacity of more than 0.3 GW in the world; 98% of its growth in the last eighteen years [2]. Its research is emphasized in greater efficiency, better power control, maximum energy capture, and recently grid codes and fault ride-through compliance [3].
A general structure for distributed systems is formed by hardware and software. The first element composed by an input power source, a power conversion unit and a load system;
and the second element composed by input power controller and a grid side controller. In this case the input power source is the wind, and the power extraction not only depends on the rotor diameter or the blade design, but also have a strong correlation with the turbine topology and the control algorithms, including synchronization and power control.
1
1.1 Motivation
This work has a special focus on three main elements, generator, converter, and control al- gorithms, each of them in continuous development. Four types of generators have been used in wind energy conversion systems, such as the doubly fed induction generator (DFIG), the squirrel cage induction generator (SCIG), permanent magnet synchronous generator (PMSG), and electrically excited synchronous generators (EESG). The generators are driven by differ- ent types of converters using an extended list of control algorithms, some of them described in this work. An example of the adaptability and development of a topology is the use of the SCIG. In the early development of the latter technology, some turbine systems were based on this type of generator directly connected to the grid with a soft starter used to reduce the inrush currents during start up, and several years after in modern turbines, it is used along with a full scaled converter as an intelligent interface with the grid.
Increased wind power penetration comes with new technical challenges such as maxi- mum power extraction from the power source and protection of the input-side converter which are important in lower quality wind resource sites. Other challenges apply to the grid side controller which controls active and reactive power generated to the grid, controls dc-link voltage, ensures high quality of the injected power, and grid synchronization, among others.
So, a larger rotor diameter is normally used to increase the swap area and maximize the thrust in lower quality wind resource, maximum electrical power extraction from the mechanical input given, and control algorithms and topology take place to ensure power quality and grid compliance.
The main reason that motivates the research arises from the selection of each of the main elements of the energy conversion system based on the features described in the literature along with a new control strategy that allows smooth synchronization and maximum power production with the minimum ripple.
1.2 Problem Statement and Context
1.2.1 Wind Power System
In the early development of the wind power systems, the energy was generated at variable frequency mainly due to the shaft speed and the number of electromagnetic poles, and then converted to grid frequency by a power converter [4, 5]. Later, different strategies were imple- mented to diminish problems in transmission lines caused by variable power output of large wind turbines [6], such as pitch control, stall control and control techniques applied to a power converter used as an intelligent interface between the wind turbine and the grid.
In the literature, several types of generators, converters and control strategies have been discussed and studied as distributed power systems [7, 8, 9]. These studies include control algorithms and trends in technology in power converters [10], power quality and maximum wind power capture [11], reliability and performance [12, 13], ride-through improvement [14, 15], life cycle cost of the system including power electronics, and others.
1.2.2 Generator
The DFIG, also called wound rotor induction machine (WRIM), occupies close to fifty percent of the wind energy market these days [11]. At the beginning, the control of speed and torque of the WRIM, was based on external resistors connected to the slip rings to reduce starting current and modify the speed-torque characteristics of the motor. Now with the aim on higher efficiency, an electronic converter replaces external resistors as a regenerative system, allow- ing bidirectional power flow and extending the range of the variable speed operation [16]. For decades different topologies of power converters have been developed for the WRIM, starting from current-fed naturally commutated converters as diode bridges and cycloconverters, to PWM voltage-fed back-to-back converters, and more recently to direct frequency converters as the matrix converters [10] and its derived topologies [17].
The DFIG has become popular in variable speed WECS, presenting several advantages over synchronous generators in terms of weight and size. Other advantages can include greater torque/cost ratio, decoupled active and reactive power control over a wider speed range, and partial scale of the power converter rating when used at rotor terminals. In this configuration power handling capability of the generator is the aggregate sum of rotor and the stator when operating at super-synchronous speed. In order to achieve this, the power converter has to play an important role, it must satisfy many requirements, such as bidirectional power flow, high power quality, fast response, low losses, among others [7]. The matrix converter holds the requirements already mentioned, it is an intelligent interface between the grid and the rotor circuit of the wind turbine generator (WTG). It allows bidirectional power flow as required in a DFIG-based WECS and offers a relatively small and lightweight converter solution to reach great efficiency, high power quality and density.
1.2.3 Power Converter
The indirect matrix converter (IMC) is an interesting and lightweight alternative to the conven- tional back-to-back converter (BBC) mainly due to the advantage of handling higher power densities in terms of volume and to operate in environments with harsh temperatures and pres- sures. Favorable features of the indirect matrix converter allow a compact converter capable of operating in adverse atmospheric conditions to control ac machines and other non-linear loads. Moreover, model predictive control implemented in an IMC gives similar dynamic response to classical control methods that rely on space vector modulation (SVM) but with a simpler concept as will be explained in subsequent paragraphs and sections [18].
Recent studies show that matrix converter’s topologies are suitable for high frequency applications, where the conduction losses are dominant, and for high-inertia loads since the IMC does not have energy-storage elements other than the input filter [19].
1.2.4 Control Strategy
In conventional DFIG control systems, vector control (VC) decouples the rotor current into torque or flux components on a synchronous dq flux-oriented reference frame. Following the same concept, rotor current components can be decoupled into active and reactive power
components. The main disadvantage of VC is the use of linear controllers which don’t con- sider the discrete operation of the power converter and need to be carefully tuned to get good performance and stability for the whole operating range of the load [20, 21].
The concept of direct power control (DPC) applied to the DFIG was originally developed to control the power factor on PWM rectifiers and extend the principle of direct torque control (DTC) for induction motors [22]. DPC is based on instantaneous active and reactive power control comparators without internal current control loops and without any extra modulation blocks. In DPC the converter’s switching state is selected using look-up tables (LUTs) based on the instantaneous errors between commanded and calculated values of active and reactive power.
The direct power control strategy provides an alternative that minimizes the use of machine parameters and reduces the complexity of vector control algorithms. However, it presents drawbacks and/or advantages depending on the strategy used for the vector orienta- tion as follows:
• Voltage-oriented DPC requires high sampling frequency, it has variable switching fre- quency and high output power ripple, and its performance deteriorates during starting and low-speed operations.
• In rotor-flux-oriented DPC the estimated rotor flux can be significantly affected by the machine parameter variations, specially near synchronous speed.
• In stator-flux-oriented DPC the estimated stator flux simplifies the control system and reduce the impact of the machine parameters on system performance since stator flux accuracy can be guaranteed.
• DPC based on grid virtual-flux is less sensitive to grid disturbances, it needs lower sampling frequency, and has higher dynamics and easier power estimation; it offers accurate flux estimation and better active and reactive power calculation and control since stator voltage is relatively stable, harmonic-free, and with a fixed frequency.
There are discrepancies on the strategy to use in order to achieve active and reactive power control of a DFIG generation system connected to the grid. Conventional power con- trol techniques for DFIGs in generation systems such as vector control (VC) are characterized by using pulse width modulation [23] or space vector modulation (SVM) to control the power converter [11] and in general involves relatively complex calculations and requires extra cur- rent loops carefully tuned to ensure system performance and stability under the whole operat- ing range of the system [24]. Direct control techniques such as direct power control and direct torque control, establish a direct relation between the controlled variables and the state of the converter’s switches [25] where the fast estimation of the correct power output of the DFIG is often the main disadvantage resulting in variable switching frequency and high power ripple [26].
1.3 Hypothesis
Renewable energy sources play and important role in the global energy market and it is clear that wind energy conversion systems are in continuous development. It is also clear that the
challenges are focused in the topology and in the control strategy.
Many methods have been proposed in the literature to overcome the complexity and rip- ple problems such as mixed schemes which have been presented using membership functions [27, 28], model-based predictive control (MBPC) [29], DPC applying a modulation strategy as PWM [21], SVM [30] or predictive direct power control (PDPC) [31], among others.
Model predictive control (MPC) is now presented as an attractive alternative to the clas- sical current control and direct control methods for power converters and drives since it holds the advantages of DPC in terms of the missing modulator and internal control loops. It also simplifies the complexity of DFIG control with reliable and fast performance in both steady and transient states. MPC uses a cost function that minimizes the error between a reference and the control variable taking into account the discrete and non-linear nature of the power converter along with other constraints, such as the power loses due to excessive switching.
The MPC strategy has been used to control the DFIG rotor current using an arbitrary refer- ence and a dynamic reference that allows the synchronization process [29].
The IMC-DFIG system is chosen to further prove that the MBPC is simple, intuitive and easily implemented to control loads with complex dynamics.The DFIG is still widely used in variable speed wind turbine systems presenting advantages over other topologies as the syn- chronous generators in terms of the cost, weight and size [1, 10]. Matrix converters (MCs) satisfy the requirements of wind energy conversion systems with great features, such as the voltage and current rating, high power density, bidirectional power flow, low total harmonic distortion (THD), sinusoidal input and output currents, controllable input displacement power factor, among others [32]. In general, MCs can operate in environments with harsh tempera- tures and pressures [33] and its reactive power handling capability is limited only by the active power output to the converter and the input displacement power factor [34, 35]. The indirect matrix converter not only holds the same features of the conventional direct matrix converter but also is easier to control and allows secure commutation [19, 36, 37].
1.4 Solution Overview and Contribution
The proposed control scheme takes the advantages of virtual-flux DPC to estimate the power flow to the grid and to calculate independently the references for the active power and reactive power output to the grid from the machine terminals, so maximum energy can be handled from the wind [38]. Also, finite-states model predictive control is proposed to determine the best switching state of the indirect matrix converter in order to achieve proper synchronization to the grid, and to deliver maximum power to the grid with the minimum ripple.
The contribution of this work is intended to cover four objectives:
• First. Overcome the complexity and ripple problems of classical control methods such as vector control and direct power control by developing and intuitive predictive control algorithm.
• Second. Complete assessment of the DFIG dynamic model to decouple power refer- ences into a simple representation of the rotor current reference to achieve both, syn- chronization process to the grid and power control with the same strategy.
• Third. Include non-linearities of the indirect matrix converter in a predictive algorithm.
• Fourth. Develop a modified MBPC strategy to reduce the power ripple without increas- ing the sampling frequency, achieving fixed frequency in the input side of the converter.
The DFIG in Wind Energy Conversion Systems
2.1 Electrical Generator Topology
In a typical DFIG-based wind turbine system (WTS) the power converter is relatively small because it is located at the rotor side (Scherbius configuration) and typically rated to one third of total machine power. The Scherbius system shown in Fig. 2.1 allows bidirectional power flow in the rotor circuit so that operation of the machine in the four quadrants is possible. This system is formed by the wind turbine, gearbox, generator and a partial-rated power converter.
This converter is used as a power quality interface and is rated to one third of machine power since it is located at the rotor side of the machine. A gearbox between the wind turbine rotor (LSS - low speed shaft) and the generator (HSS - high speed shaft) is still a requirement for this topology since a multi-pole low-speed DFIG is not technically feasible [7].
LSS Ps, Qs HSS
Pg, Qg
vin iin
vs, is vg, ig
vout iout Power
Converter
AC-Grid DFIG
Contactor
Rotor Stator Transformer
Wind Turbine Rotor Fixed Ratio
Gearbox
Figure 2.1: WECS topology with a DFIG and a power converter on the rotor terminals.
The DFIG topology, also called WRIM or slip ring induction machine is widely used 7
as generator in variable speed wind turbine systems. This topology shows some advantages over the SCIG, over the EESG and PMSG in terms of the cost, weight, and size [10]. How- ever, DFIG presents drawbacks against the PMSG in terms of total reactive power handling capability [39].
+
− +
−
+ −
+ −
replacements
λs λsr
is vs
isr
vsr
Rs Ls− LM Lsr− LM Rsr
LM
j(ω − ωr)λsr jωλs
Figure 2.2: DFIG equivalent circuit rotational synchronous to an arbitrary angular speedω.
The DFIG operating regions are defined mainly by the direction of the power flow from the rotor or from the stator to the grid, and clearly depend on the shaft speed as it can be seen in Fig. 2.3. The DFIG can produce extra power when it is operating at super-synchronous speed, where nominal power can be extracted from the stator and one third of rated power from the rotor.
The DFIG can be modeled with an equivalent electrical circuit depending on the refer- ence frame used to represent the equations. The reference frame can be stationary fixed to the stator (αβ) or to the rotor (xy), or rotational synchronous to an arbitrary angular speed ω (dq).
The αβ reference frame is selected since the main constraints are imposed directly on the stator and the two-axis transformation, known by Clarke transformation, simplifies the computational load. In this equivalent circuit, rotor equations are referred to the stator using the turns ratio and transformingabc rotor equations in a two-axis equivalent system xy and later into adq system rotating at −ωrwithq axis aligned to phase a in the rotor.
2.2 Power Converter Topologies
The introduction of power converters instead of diode-bridges or cycloconverters allowed bidirectional power flow with a wider range of speed control limited only by the rotor voltage rating of the DFIG. Conventionally, the power converter is designed considering a back-to- back voltage source converter (BBVSC) controlled mainly using pulse width modulation, such as fixed-PWM, sinusoidal-PWM, modified-shape-PWM, or SVM, etc. This topology allows low distortion of stator, rotor and supply currents, as well as independent torque and flux control of the DFIG [23].
The back-to-back converter is formed by two voltage source inverters (VSI) connected by a dc-link allowing bidirectional power flow between the grid and the rotor. One of the VSIs known as grid side converter (GSC) controls the input displacement power factor and the dc-link voltage level. The other inverter, the rotor side converter (RSC), controls the rotor current or flux to drive the DFIG.
As
As
As
As
As
As
As
As Bs
Bs
Bs
Bs
Bs
Bs
Bs
Bs
Cs
Cs
Cs
Cs
Cs
Cs
Cs
Cs ar
ar
ar
ar
ar
ar
ar
ar br
br
br br
br br
br br cr
cr
cr cr
cr cr
cr cr Tem> 0
Tem< 0 Tem
ωr ωsync
ωr> ωsync ωr< ωsync
M ode I M ode II
M ode III M ode IV
Figure 2.3: Electromagnetic torque and angular speed of the rotor for each operating mode of the DFIG.
The matrix converter is a simple and compact power circuit that directly connects the ac-source with any arbitrary ac-load without the need for large storage elements, making this topology suitable for many applications where weight and size are important issues. With this converter, generation of output voltage with different amplitude and frequency, sinusoidal in- put and output current waveforms, as well as operation with unity displacement power factor and regenerative capability are made possible. One challenge of MCs used to be the commu- tation of bidirectional switches but this issue has been solved with multi-step commutation techniques and the use of new technologies in power elements. Due to these characteristics,
is vs
io vo idc
vdc
iin vin
Lf
Cf
Rf
Ll
Rl
n N
Cf f
Rf f
Lf f
Sr1 Sr3 Sr5
Sr4 Sr6 Sr2
Si1 Si3 Si5
Si4 Si6 Si2
Figure 2.4: Conventional back-to-back converter.
in recent years MCs have shown continuous and fast development related to the creation of new topologies and control methods, including industrial applications with standard units for high and medium voltage using cascade connections [17, 33, 40, 41, 42].
iA
iB
iC
ia ib ic
SAa SAb SAc
SBa SBb SBc
SCa SCb SCc
Figure 2.5: Power topology of the conventional direct matrix converter.
The power topology of the MC is presented in Fig. 2.5. It consists of bidirectional switches to directly connect the input side with the load side without any intermediate dc- link storage element. An input filter is connected at the input side of the converter with two purposes [33]:
• To avoid over-voltage due to short-circuiting the impedance of the power supply, by cause of the fast commutation of currents.
• To eliminate high-frequency harmonics in the input currents.
Such as in each converter, the operation of the direct MC (DMC) is restricted to some operation constraints: the load current cannot be interrupted abruptly, due to the inductive nature of the load, and the operation of the switches cannot short-circuit two input lines, owing to the presence of capacitors in the input filter. These restrictions can be expressed by:
SAy + SBy + SCy = 1, ∀ y = a, b, c (2.1)
The relations between the input and output variables of the MC are given by:
vo = T(Sij) vi (2.2)
ii = T(Sij)Tio (2.3)
where T(Sij) is the instantaneous transfer matrix defined as:
T(Sij) =
SAa SBa SCa
SAb SBb SCb
SAc SBc SCc
(2.4)
Equations (2.3) and (2.4) are the basis of all modulation and control methods, which consist of selecting appropriate combinations of on and off switches to achieve the desired output voltages.
As presented in [40, 41, 42], there are several topologies of MCs. The main differences between them are given by the number of switches, operation constraints and applications.
The most important advantages of these extensions are: the increment of output voltage con- trol range and the reduction of the switching frequency harmonics, losses and common mode voltage. The most common and used topology where predictive control has been implemented is the DMC, shown in Fig. 2.5. One challenge of this converter is the safe commutation of the nine switches (eighteen IGBTs in total) and its modulation, which is very complex. Addi- tionally, in the operation of a DMC with predictive control, a critical issue has been the high sampling frequency needed, but nowadays this problem has been solved due to the technolog- ical progress in fast and powerful microcontrollers.
Many authors have used this converter in [18, 38, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60] to apply different techniques for a large number of applications.
For this converter, twenty-seven different switching states must be evaluated every sampling instant in order to select the one that minimizes the cost function. The current control on the output side of the converter is a very well studied issue, especially for motor drive and grid interconnection applications. Some aspects considered in the control of the DMC are the amplitude and phase control of the input currents in order to operate with unity, capacitive or inductive power factor. Another relevant issue that has been objective for study with predictive control, in consideration for the safe operation of the DMC, is the reduction of the distortion in the input currents produced by input filter resonances due to the commutation and several perturbations in the ac-supply. Due to the large number of power semiconductors of the DMC, some authors have studied also the increment of the efficiency of the converter by reducing the switching losses and frequency.
2.3 DFIG-Based WECS Driven by an Indirect Matrix Con- verter
The wind turbine system presented in this proposal uses the IMC to drive the DFIG as in a Scherbius system showed in Fig. 2.6. In this WTS the power converter is rated to one third of machine power since it is located at the rotor side of the DFIG.
ωT
ωm
as
as
bs
bs cs
cs
br br
ar ar
cr cr Ps, Qs
Pg, Qg
vf if
is vs vg ig
vr
ir
iin
vin
Lf
Cf
Rf
Sr1 Sr3 Sr5
Sr4 Sr6 Sr2
vdc
idc
Si1 Si3 Si5
Si4 Si6 Si2
Indirect Matrix Converter AC-Grid
Filter
DFIG Transformer
Wind Turbine Gearbox
Rectifier Inverter
Figure 2.6: Wind energy conversion system with DFIG technology controlled by an IMC on the rotor side.
The configuration of the IMC is divided in two stages: the rectifier and the inverter. This characteristic becomes an advantage when using the zero dc-link current switching scheme, which allows a safe operation of the converter and a reduction of the switching losses. In particular, the mathematical model of the rectifier stage has the phase voltage vinand dc-link currentidcas inputs and the dc-link voltagevdcand input current iin, as outputs. This is shown in equations (2.5) and (2.6):
vdc = Sr1− Sr4 Sr3− Sr6 Sr5− Sr2 vin (2.5)
iin=
Sr1 − Sr4
Sr3 − Sr6 Sr5 − Sr2
idc (2.6)
The inputs and outputs of each stage of the converter are related by the associated switch- ing states. For the inverter this relation involves the output current ir and dc-link voltagevdc
as inputs, and the dc-link currentidc and the output voltage vr as outputs, as can be seen in equations (2.7) and (2.8):
idc = Si1 Si3 Si5 ir (2.7)
vr =
Si1− Si4 Si3− Si6
Si5− Si2
vdc (2.8)
Not all the possible switching states are allowed. There are some constraints which are mandatory for the safe operation of the converter:
• Input phases of the rectifier stage cannot be short circuited thus, only nine valid rectifier states can be used.
• Output phases of the inverter stage cannot be disconnected thus, from all possible only eight inverter states are allowed.
vf
if
vr
ir
iin
vin
Lf
Cf
Rf
Sr1 Sr3 Sr5
Sr4 Sr6 Sr2
vdc
idc
Si1 Si3 Si5
Si4 Si6 Si2
Filter
Rectifier Inverter
Figure 2.7: Conventional indirect matrix converter.
Additionally, there must always be a positive dc-link voltage to avoid forward biasing on the freewheeling diodes in the inverter. Therefore, the valid states for the rectifier are reduced to only three at any instant and the number of total switching states for the IMC is reduced to twenty-four.
The indirect matrix converter shown in Fig. 2.7 is other topology where important con- tributions of predictive control have been done, such as reported in [27, 36, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72]. The IMC, in contrast to the DMC, presents a more simple modulation and commutation known as zero dc-link current strategy [17, 72], which allows to reduce the commutation losses and thus increase the efficiency of the converter. The main challenge in this topology is to ensure a positive dc-link voltage while working with a unity displacement power factor at the input side [62, 63, 64, 65, 66, 67, 68, 70, 71, 72]. For this converter there are seventy-two valid switching states to be evaluated in the cost function each sampling time, nine given by the rectifier side and eight by the inverter side. But as only a pos- itive dc-link voltage is allowed at any time, the number of valid switching states in the rectifier side that can be applied at any specific time are reduced to only three, thus, the total number of valid switching states that are evaluated in the cost function are reduced to twenty-four.
The Scherbius system shown in Fig. 2.6 allows bidirectional power flow in the rotor circuit and operation of the DFIG both below and above its synchronous speed.
This αβ reference frame is selected since the constraints are imposed directly on the stator variables and the two-axis reference simplifies the control variables. To avoid many trigonometric coupling terms in the differential equations, it is possible to represent the rotor equations by a stator referred (dq) rotating at (ω − ωr) with ω = 0 and the q−axis aligned to thear−winding.
vsα = Rsisα+ Ls
disα
dt + Lm
disrα
dt (2.9)
vsβ = Rsisβ+ Ls
disβ
dt + Lm
disrβ
dt (2.10)
+ − +
− +
−
λs λsr
is vs
isr
vsr
Rs Ls− LM Lsr− LM Rsr
LM
j(ω − ωr)λsr
Figure 2.8: DFIG equivalent circuit fixed to the stator (αβ).
vrαs = Lmdisα
dt + ωrLmisβ+ Rsrisrα+ Lsrdisrα
dt + ωrLsrisrβ (2.11) vrβs = −ωrLmisα+ Lm
disα
dt − ωrLsrisrα+ Rrsisrβ + Lsrdisrβ
dt (2.12)
For a thorough explanation of how the equations (2.9) to (2.12) were obtained the reader is encouragingly referred to [73].
2.4 Conventional Control Methods
Different control techniques have been extensively investigated to drive the DFIG in stand- alone and grid-connected systems. Some of the main techniques and topologies are presented as a background.
Conventional power control techniques of DFIG in generation systems can be classified as direct or indirect [74]. Indirect control is often related to vector control and it is charac- terized by using modulation such as PWM [23, 75] and SVM to control the power converter [11, 76, 77]. Direct control techniques such as direct power control and direct torque con- trol, establish a direct relation between the controlled variables and the state of the converter’s switches [25, 78, 79].
2.4.1 Passive and Partial Active Control of Speed
• Fixed external resistors attached to rotor terminals to change (X/R) characteristics of the rotor - This technique is considered obsolete for its low efficiency in variable speed WECS.
• External resistors plus electronics (e.g. OptiSlip of Vestas) - This technique controls the slip variation and reduce the mechanical stress of the system using electronic com- ponents to change the resistance applied to the rotor depending on the operating point.
This strategy may be used in a few turbines in operation but has low efficiency and may cause some mechanical stress to the system when applied.
• OptiSlip plus pitch control - Dynamic selection of rotor resistance with pitch control augments the slip range control and improve the dynamic response against disturbances.
• Rectifier and active breaking in the dc-link (e.g. OptiSpeed of Vestas) - A diode bridge or other naturally commutated electronic component is used instead of the external resistors to allow extra power to flow between the rotor power resistor in the dc-link.
The main disadvantage of passive control of speed is its low efficiency because of the dissipation of energy in the external resistors to drive the machine. Some improvements were made to diode bridge converters in Scherbius systems. However, the current-fed convert- ers and the cycloconverters produce high harmonic content in the rotor current, which are reflected to the stator [10].
2.4.2 Vector Control
Vector control is a linear control strategy and it has been applied widely to drive squirrel-cage induction machines where torque and flux are controlled. This is achieved by modelling the machine as a linear and time-invariant (LTI) system where the stator currents are controlled using adq rotating frame aligned with the rotor flux.
Vector control is also known as field oriented control (FOC) and is the most popular power control method used in the industry. In field-oriented control applied to the induction motors, the quadrature component of stator currentisqhas to be controlled to control the stator active powerP and the direct component of stator current isd has to be controlled to control the stator reactive powerQ.
VC’s applications have been also extended to DFIGs where the stator is connected to the grid and the rotor is fed by a back-to-back converter, for example. In order to control active and reactive power,dq components of the rotor current have to be controlled [23] as shown in Fig. 2.9.
In Fig. 2.10airdis set to zero, i.e. the reactive power is fed completely from stator side andirqis varied from zero to rated power. With this consideration the locus ofλrvaries along A-B, which indicate predominant change in angleδp betweenλsand λr and a small change in the magnitude ofλr. The change in the slip angleδp would definitely result in a change in active power handled by the stator.
In Fig. 2.10b the stator active power demand is maintained constant, soirq is constant andirdis varied from zero to rated value, then the locus ofλrvaries along C-D, resulting in a predominant change in magnitude ofλr, and a small variation of the angleδp. The change in reactive power is then handled by the magnitude of the flux.
Active and reactive power control of DFIG is achieved by controlling rotor currents irq and ird, respectively, as in a conventional oriented control where the magnetizing flux is calculated adding and subtracting the leakage flux vector to rotor or stator flux vectors as it is shown in Fig. 2.10a and Fig. 2.10b.
Conventional control systems usually take stator and rotor currents in adq rotating frame aligned with rotor flux and the rotor currents are controlled using a rotating frame aligned with stator flux. It decouples the rotor currents into active power (or torque) and reactive
+-
+-
++
++
+ - + -
ω∗r
ωr ωr
ωslip
ωslip
θslip
θs θr SVM
Sr1...Sr6
DFIG
Converter
Flux Calculator Compensation
Grid is vs isr
i∗dr i∗qr
idr
iqr
vdr
vqr
dq abc
d/dt d/dt
PI
PI PI
sw
SWup: Speed mode,SWdown: Current mode
Figure 2.9: Field oriented control applied to DFIG.
power (or flux), and adjust them separately into a reference frame fixed to the flux. The mentioned control systems require accurate information of machine parameters and they need to be carefully tuned to ensure system performance and stability under normal and abnormal conditions [23].
Many non-linear plants can be modeled as LTI systems where the goal is to keep the system state near some operating point. Some of the effects of plant non-linearities can be taken into account in the framework of an LTI plant and its controller, leading to an opti- mization problem. As non-linearities are included, the complexity of the controller design increase. Linear control systems often form the core or basis of control for non-linear sys- tems. Even when the controller becomes a time-varying system, when it is implemented on a digital control processor, a proper selection of sampling rates can solve the problem.
One of the drawback of this VC system is the large amount of computing effort to run the complex algorithm in real time. A significant amount of work is also needed to tune the PI regulators, it is sensitive to the machine parameters variation and it cannot take into account the discontinuities of a discrete converter. FOC involves relatively complex calculations and requires extra current loops carefully tuned to ensure system performance and stability under the whole operating range of the system [80].
2.4.3 Hysteresis Control
Direct control strategies provide an alternative that minimizes the use of machine parameters and reduces the complexity of vector control algorithms as it is shown in Fig. 2.11. DTC
λs
λsr δP
A
B
d − axis q − axis
sub-synchronous
λms
isq
isd
irq is vs
(a) Active power control
λs
λsr δP
C D
d − axis q − axis
λms
isq
irq ird vs
isr
(b) Reactive power control
Figure 2.10: Influence of the rotor currents over active and reactive power during motoring mode.
based on line voltage needs high sampling frequency, it has variable switching frequency and high output power ripple, and its performance deteriorates during starting and low-speed operations.
Direct Torque Control
Direct torque control is a strategy to control the electromagnetic torque and flux of an induc- tion machine using hysteresis comparators and available states of the converter system in use.
Each state of the converter produces a specific rotor flux vector, both in amplitude and phase, depending on the rotor speed and position, and on the stator flux vector. The electromagnetic torque in this technique is calculated as the cross product of the stator and rotor flux vectors.
The DTC technique has also been used to control the electrical torque in the DFIG because the algorithm can be applied in a straightforward manner achieving good dynamic performance [25].
When the control relies on the flux orientation, the magnetizing current can be provided entirely from the stator, entirely from the rotor or from both the stator and the rotor using the equivalent model equations and proper reference conversion. In rotor-flux-oriented direct power control voltage vectors are selected using rotor-flux position, rotor-flux error and active power error and when the machine is operating near synchronous speed, the rotor supply
+-
T∗ λ∗
T−1
i∗s ǫi Current
Component
PWM PI
vs
is θr
i∗sT i∗sλ
Si, Sr
IM
Encoder
orque and
(a) Field-oriented control algorithm.
+-
+-
T∗
λ∗
ǫT
ǫλ
vs
vs
is
Si, Sr Switching IM
Table
Torque and Flux Calculator
Tk λk
(b) Direct torque control algorithm.
Figure 2.11: Comparison of FOC and DTC algorithms for the squirrel cage induction ma- chine.
frequency can be very low and rotor flux estimation can significantly be affected by machine parameters. On the other hand, stator-flux-oriented direct power control is less sensitive to grid disturbances, it needs lower sampling frequency, and has higher dynamics and easier power estimation.
Direct Power Control
The concept of direct power control was originally developed to control the power factor on PWM rectifiers and holds the same principle as the DTC for induction motors. DPC is based on the instantaneous active and reactive power control comparators without internal current control loops and without extra PWM blocks. In DPC the converter’s switching state is selected using look-up tables based on the instantaneous errors between commanded and calculated values of active and reactive power [81].
Ps Ps∗
Ps∗∗
Pband
A B
C
Figure 2.12: Hysteresis comparator for active power control.
In DPC the converter’s switching state is selected using LUTs based on the instantaneous errors between commanded and calculated values of active and reactive power. Stator reactive power is proportional to the direct component of the rotor flux and stator active power is proportional to the quadrature component of the rotor flux component where the direct axis in this reference frame is aligned to the stator flux vector.
λs
λr
∆|λs|
|λs|∗
δP Θ(1)
Θ(2) Θ(3)
Θ(4)
Θ(5) Θ(6)
d − axis
q − axis θe
sub-synchronous super-synchronous V (1, 0, 0)
V (1, 1, 0) V (1, 1, 0)
Figure 2.13: Flux orientation and rotation during motoring mode of the DFIG.
This DPC scheme offers accurate flux estimation and better active and reactive power calculation and control since stator voltage is relatively stable, harmonic-free, and with a fixed frequency [74]. Active power is adjusted controlling the power angleδP and reactive power is adjusted controlling the magnitude of rotor flux as it is shown in Fig. 2.13 based on the premises described for VC and shown in Fig. 2.10a and Fig. 2.10b. A typical output for DPC is shown in Fig. 2.12.
The direct power control is also used to drive induction machines including the DFIG because of its simplicity. The difficulty arises near synchronous speed when it is difficult to know the rotor flux vector’s magnitude and angle.
2.5 Modern Power Control Strategies for the DFIG
In DPC, the converter’s switching states are selected by a table based on the instantaneous errors of control variables [22], then the key point of the DPC implementation is a correct and fast estimation of the power output of the WTS and the main disadvantage is the resulting variable switching frequency and high power ripple [26]. In order to overcome complexity and ripple problems, mixed schemes have been presented using membership functions [82, 83], model predictive control [37], sliding-mode control [78, 84, 85, 86, 87], or using direct power control applying a modulation strategy as PWM [21], SVM [30] or a predictive sequence [31, 88].
2.5.1 Sliding-Mode Control
Sliding-mode control is a variable structure control for non-linear systems with uncertainties.
In wind energy conversion systems, the DFIG is subject to stochastic operating conditions
