Degree project
Integrating Wind Power into The
Electric Grid
Predictive Current Control Implementation
Author: Ahmad Badran
Supervisor: Pieternella Cijvat
Examiner: Sven-Erik Sandström
Date: 2020-November
Course code: 5ED36E, 30 hp
Level: Master
Department of Physics and
Electrical Engineering
Faculty of Technology
Summary
Renewable power production currently shows a quick expansion commanded by wind and solar power. The increasing penetration of wind power into the power system dominated by variable-speed wind turbines among the installed wind turbines will require further development of control methods. Power electronic converters are widely used to improve power quality in conjunction with the integration of variable speed wind turbines into the grid.
In this thesis the main interest is the integration of variable speed wind turbines into a grid via controlling the grid side inverter. Different types of wind turbine generators will be highlighted with their connection scheme to the grid, and wind power and wind turbine power formulas will be briefly described including maximum power point tracking (MPPT).
A detailed model of a predictive current control (PCC) method will be implemented for the purpose of control of the grid connected converters. The injected active and reactive power to the grid will be controlled to track their reference value. The PCC model predicts the future grid current by using a discrete-time model of the system for all possible voltage vectors generated by the inverter. The voltage vector that minimizes the current error at the next sampling time will be selected and the corresponding switching state will be the optimal one.
The basic concept and operation of Model predictive control (MPC) are described. It includes three different reference frames (abc, αβ and dq) and corresponding mathematical transformations (abc / αβ) and (αβ/ dq). A two-level voltage source converter with Predictive current control (PCC) is used as an implementation of the MPC. An optimum switching state is selected automatically to control the inverter voltage vectors in order to minimize a certain cost function.
Finally, a model is implemented in Matlab / Simulink and simulation results are presented for different sampling times and different power factors. Parameters such as overshoot, rise time and Total harmonic distortion are analyzed. Based on the simulation results for the different sampling times, the increase of the sampling time will cause increased ripple in the grid current. Moreover, when the operation mode is changed from PF=1 to PF=0.8, overshoot is noticed to increase when the sampling time is 100 μs. Changing the wind speed showed a decoupled relation between id and iq, where the id had varying values while iq maintained its value.
On the other hand, for the sampling time of 20 μs, a high performance in tracking the reference current is shown, with a low rise time, low ripple and very little overshoot.
Abstract
The increasing penetration of wind power into the power system dominated by variable-speed wind turbines among the installed wind turbines will require further development of control methods. Power electronic converters are widely used to improve power quality in conjunction with the integration of variable speed wind turbines into the grid. In this thesis, a detailed model of the Predictive Current Control (PCC) method will be descripts for the purpose of control of the grid-connected converter. The injected active and reactive power to the grid will be controlled to track their reference value. The PCC model predicts the future grid current by using a discrete-time model of the system for all possible voltage vectors generated by the inverter. The voltage vector that minimizes the current error at the next sampling time will be selected and the corresponding switching state will be the optimal one. The PCC is implemented in Matlab/simulink and simulation results are presented.
Keywords:
Model predictive control, Wind turbine, Predictive current control, Inverter, Simulink, Active power, Reactive power.
Preface
I would like to express my deepest thanks to my supervisor Pieternella Cijvat for her excellent guidance, advice and input during this work.
I would like to thank my wife Ruba for supporting me for the whole period of my master's study. Thank you to my mama, sister and brothers for encouragement. My dad! I am sure that you would be proud of me but unfortunately, you passed away too early so I would like to dedicate this work to your soul.
A special thanks to Jonas Wågenberg _Kalmar Energy for motivating.
Ahmad Badran
Table of Contents
Summary ___________________________________________________ III Abstract ____________________________________________________ IV Preface ______________________________________________________ V Table of Contents _____________________________________________ VI Acronyms __________________________________________________ VIII 1. Introduction ________________________________________________ 1 1.1. Background ... 11.2. Purpose and objectives ... 2
1.3. Limitations ... 2
1.4. Method ... 3
2. Basics of Wind Energy Conversion Systems ______________________ 4 2.1. Wind power and extracted turbine power ... 4
2.2. Maximum power point tracking (MPPT) ... 4
2.3. Types of wind turbines generators ... 6
2.3.1. Fixed speed wind turbine __________________________________ 6 2.3.2. Variable speed wind turbine _______________________________ 6 3. Model Predictive Control (MPC) _______________________________ 8 3.1. Introduction ... 8
3.2. Fundamental of model predictive control ... 9
3.3. Reference frame transformation ... 10
3.3.1. Mathematical transformation equations ______________________ 11 4. Power electronics in wind power systems ________________________ 12 4.1. Back to back converter ... 12
4.2. Predictive control in power electronics ... 14
5. Implementation and Results ___________________________________ 16 5.1. Predictive current control scheme ... 16
5.1.1. Measurement and synthesis of feedback signals _______________ 16 5.1.2. Calculation of the reference currents i*αβ block and V*dc ________ 20 5.1.3. Prediction of the future grid currents iαβ(K+1) __________________ 21 5.1.4. Cost function minimization _______________________________ 22 5.2. Working principle of the control algorithm ... 22
5.2.1. Timing diagram of the control algorithm ____________________ 23 5.3. Control scheme implementation ... 23
5.4. Simulation results ... 25
5.4.1. Simulation results for a sampling time of 20 μs ... 26
5.4.1.1. Total Harmonic Distortion (THD) ________________________ 29 5.4.2. Simulation results for a sampling time of 100 μs ... 30
5.4.2.1. Total Harmonic Distortion (THD) ________________________ 32 6. Discussion and analysis ____________________________________ 33 7. Conclusion and future work _________________________________ 34 References __________________________________________________ 35 Appendix A _________________________________________________ 37
Acronyms
2L Two-Level (Converter) AC Alternating Current BTB Back-to-Back DC Direct Current
FCS-MPC Finite Control-Set Model Predictive Control FSWT Fixed-Speed Wind Turbine
GSC Grid-side Converter
HVAC High-Voltage Alternating Current HVDC High-Voltage Direct Current IGBT Insulated Gate Bipolar Transistor MPC Model Predictive Control
MPPT Maximum Power Point Tracking MSC Machine Side Converter
PCC Predictive Current Control
PLL Phase-locked loop
PF Power Factor
SRF Synchronous reference frame
VSI Voltage Source Inverter VSC Voltage Source Converter VSWT Variable-Speed Wind Turbine WT Wind Turbine
1. Introduction
This chapter presents the basis and the objectives of this study. The project limitations that have been considered in this current work are given, in addition to the methods that are used to achieve project objectives.
1.1. Background
Wind energy is playing an important role in the energy markets nowadays. Wind power energy and wind production in the world have been increased to reach about 1300 TWh in 2018 compared to 2008, when it was only 200 TWh [3], as can be seen in figure 1.1.
Fig. 1.1. Comparison of the electricity generation by wind power in the world in 2008 and 2018 (Data source: [3]).
In the European Union, electricity generation by oil has decreased in the last decade to reach 53 TWh in 2019 compared to 205 TWh in 2009. On the other hand, the energy generation by renewable sources has been dramatically increased to reach 740 TWh, where the energy production through wind energy is the dominant sector, as shown in figure 2.1 [3].
Fig. 1.2. Electricity generation by source, in the European Union 2019 (Data source: [3]).
18% 58% 23% 1% Solar PV Wind Biofuels Solar thermal
1.2. Purpose and objectives
The integration of high penetration levels of wind power into the power system may require a step-by-step redesign of the existing power system and development control methods for the wind turbines.
The requires for acceptance of more renewables sources in the grid and integrate them enable power electronic converters to play an important role in this technology transformation. The use of the power electronic converters technology in grid-connected operation has significantly improved over the past years [5]. Power electronic converters offer enhanced wind energy efficiency. In addition, power electronic converters help comply with the grid code and improve the power quality for output electrical power of variable-speed wind turbines (VSWTs). The development of a control system in addition to a power converter is important to achieve an efficient operation of VSWTs [5].
The control system that can be implemented by digital control platforms is used to control wind turbines to feed high quality power to the utility grid. Finite Control-Set Model Predictive Control (FCS-MPC) in the form of Predictive Current Control (PCC) opens the doors for controlling a wind turbine with optimal control performance, as will be proven in the present work. The PCC for the grid side converter will be the main focus in the current work to control the injected active and reactive power to the grid and ensure the grid synchronization to achieve the high performance of the VSWTs.
The objective of this thesis can be summarized as follow:
• Analyzing the system consisting of wind turbines, grid and power electronic converters.
• Modeling of the grid side converter.
• Implementation of the control method predictive current control (PCC). 1.3. Limitations
The limitations that are considered in the present thesis work are listed as follow:
• The generator rotates at a speed more than the synchronous speed and the power flow is considered from the GSC to the grid.
• The turbine is working at the maximum rated wind speed. The power that is extracted from the turbine is the rated power.
• The machine side converter can be assumed in this case as a DC current source with rated DC current.
• The DC link maintains its reference value.
• The losses in the power electronics and the mechanical parts are neglected and the inverter works at its rated power.
1.4. Method
By means of a literature search, a basic introduction to wind turbines and grid-side converters is presented. Different methods of control are described. Due to the complexity of the control system, Matlab/ Simulink will provide a platform that supports system-level design to achieve the thesis objectives most simply. The aim of using the Matlab /Simulink model is to apply the control scheme and build a model for the control system. A predictive current control (PCC) model will be implemented for the grid side converter in a different subsystem to control the active and reactive power injected into the grid. Furthermore, the PCC control algorithm for the grid side inverter will be applied by using the Matlab function block. The simulation is implemented for two different sampling times: 100 and 20 μs, in the interest of demonstrating the different characteristics of the output signal. Many articles and books have been used in this work for understanding grid-side converters, the principles of model predictive control and the control scheme, as referred in the references list.
2. Basics of Wind Energy Conversion Systems
In this chapter, the wind power and wind turbine power formulas will be presented in terms of the maximum power point tracking (MPPT) method. The different types of wind turbines generators will be highlighted with their connecting scheme to the grid.
2.1. Wind power and extracted turbine power
Wind power is the use of wind to provide mechanical power through wind turbines. Since the wind has air mass, the wind holds kinetic energy which can be translated to power and expressed as follows:
[2]:
Pw =
1 2 𝜌 A 𝑣
3 (1.1)
where A is the area [m2]. v is the wind speed [m/s] and ρ is the air density [kg/m3]. According to Betz´s law, about 59% of the wind kinetic energy can be extracted and transformed into mechanical energy when the wind hits the blades in the wind turbine. This value is a theoretical maximum, but the actual value depends on the conversion efficiency of the turbine. Hence, the achievement of the maximum value of the power coefficient Cp will produce maximum efficiency [2].
𝑃m = Pw × Cp=
1
2 Cp (𝛽, 𝜆) 𝜌 A 𝑣
3 (1.2)
where Cp (power coefficient) is the ratio of power produced by a wind turbine
divided by the total wind power flowing into the turbine blades at a specific wind speed.
For the new generation of high-power WTs, the Cp value ranges between 0.32 and
0.52 [1]. The power coefficient Cp is related to the two characteristics (𝛽, λ). The
angle 𝛽 is the pitch angle, while λ is the ratio between the tip speed of rotor blades to the speed of wind at hub height and it can be calculated as following [1]:
λ = 𝑣 𝑡𝑖𝑝
𝑣 𝑤𝑖𝑛𝑑 = 𝑅 𝜔𝑚
𝑉 𝑤𝑖𝑛𝑑 (1.3)
where ωm is the rotational speed of the rotor in rad/s and R is the rotor radius in m.
2.2. Maximum power point tracking (MPPT)
The MPPT control system ensures maximum extraction of the power from the wind. In VSWTs, a reference rotation speed that ensures an optimal operation well be generated. Hence, the operating point of the turbine will maintain its maximum power for different wind speeds [4], as shown in figure 2.1.
Fig. 2.1. Turbine mechanical power as a function of ωm for various wind speeds.
By regulation of the rotational speed of the generator, an optimal power coefficient
Cp can be obtained and the maximum power at a specific wind speed will be
extracted from the wind [4]. For a large wind speed, regulation of the rotational speed can be achieved by pitch control, where rotor blades can be turned on their longitude axis from the hub. By turning the blades, the angle of attack 𝛽 can be adapted and the rotational speed can be controlled [1]. The relation between Cp
and λ when β equals zero degrees is shown in figure 2.2.
Fig. 2.2. The relation among generated mechanical powers and rotor speeds for different wind speeds.
It can be noticed that at the rated wind speed (14 m/s) the maximum mechanical power for the turbine can be obtained for pitch angle equal to 0.
2.3. Types of wind turbines generators
2.3.1. Fixed speed wind turbine
The generator of the fixed speed wind turbine is directly connected to the power grid and has a rotational speed that corresponds to the grid frequency. A simple generator with only two poles (N and S) would then need a rotational speed of 3,000 rpm [revolutions/minute] to give 50 Hz [1].
Fixed-speed wind turbines have many advantages, such as being powerful, simple, reliable and the cost of its electrical parts is low. On other hand, they provide limited power quality control and uncontrollable reactive power consumption [2]. The squirrel cage induction generator is common to use in FSWT, where the generator is directly connected to the grid through a soft starter. The rotational speed is regulated via a three-stage gearbox, while the capacitor bank is used as a reactive power compensator [2], as shown in figure 2.3.
Fig. 2.3. Squirrel-cage induction generator wind turbine.
2.3.2. Variable speed wind turbine
During the past few years, the variable-speed wind turbine has become the dominant type among the installed wind turbines and has become more popular than the fixed-speed WT [1]-[2].
The reason to vary the rotor speed is to capture the maximum aerodynamic power in the wind, as the wind speed varies. The advantages of variable-speed wind turbines are increased energy capture, improved power quality and maximum power point tracking (MPPT) system can be implemented. The disadvantage of this type of turbines is that they could not be connected directly to the grid without power electronic converters. Moreover, they suffer from losses in power electronics and the initiation cost is higher than the fixed speed wind turbine [1]. There are two different configurations of variable speed wind turbines that are commonly used:
1) Type 3 variable speed wind turbine:
In this type, the power electronic converter is connected between the rotor and the grid, as can be seen in figure 2.4. The rated power of the converter is 30% of the
generator rated power and the turbine’s generator is a double phase induction generator DFIG. The type 3 wind turbine is one of the dominating technologies because of its lower losses and lower cost [5].
Fig. 2.4. Wind turbine with doubly fed induction generator. 2) Type 4 variable speed wind turbine:
In this type, the power electronic converter is connected between the stator and the grid, as shown in figure 2.5. The power electronic converter is a full-scale power converter and a wound rotor synchronous generator WRSG or permanent magnet synchronous generator PMSG is common to use in this type [5].
Fig. 2.5. Wind turbine with PMSG or WRSG generator.
These kinds of configurations are usually connected to the grid through a step-up transformer, that increases the voltage level from 400 / 690 V to a high voltage of 10 kV. [5]
3. Model Predictive Control (MPC)
The basic concept and operation of model predictive control are described in this chapter. The three different reference frames abc, αβ and dq in addition to the mathematical transformation between (αβ/ abc) and (dq/ αβ) are also presented. 3.1. Introduction
In recent years, the MPC has been used heavily in power system balancing models and power electronics. The operation principle of the MPC is to take current control actions to minimize future errors. MPC is available under different names [5], such as dynamic matrix control, horizon control, generalized predictive control, dynamic linear programming and model algorithmic control.
Finite control-set MPC (FCS-MPC) was proposed almost a decade ago for a two-level voltage source converter (2L-VSC). FCS-MPC has been tried for a wide range of low, medium and high-power converter topologies and power conversion applications. The differences between the FCS-MPC strategy and the classical linear control for a 2L-VSC will be presented in table 1 [5].
Table1. Comparison of the linear control with the PI regulator and FCS-MPC
FCS-MPC Linear Control
Model Discrete-Time (DT)
Model Linear model Controller
Design Cost Function
Definition PI Adjustment Nature off Controller Nonlinear Liner Modulation not required PWM Switching Frequency variable but controllable Fixed Transient
3.2. Fundamental of model predictive control
Figure 3.1 shows the operating principle of the MPC, where the reference controls trajectory x∗, set constant to simplify the analysis. The MPC is formulated in terms of the district time DT by allowing the variables to change their values at discrete sampling time Ts. An approximate discrete-time model (DT) for the first order
continuous-time (CT) state-space equation can be obtained by applying the forward Euler method, where the present sample is k and the future sample is k +
1, as follows [5]
X (k + 1) = Φx (k) + Γu(k) (3.1)
and
Φ ≈ I + ATs, Γ ≈ BTs (3.2)
where Γ is the input or control matrix in discrete-time and Φ is the state matrix in discrete time.
Fig. 3.1. Operating principle of MPC (source: Wikipedia
https://en.wikipedia.org/wiki/Model_predictive_control, model predictive control. Martin Behrendt / CC BY-SA 3.0)
The principle of the MPC mainly consists of three parts/components as demonstrated below [5]:
1) Prediction: this step involves the time model that is used to predict the future value of the variable. The control input sequence u where the predictive future values of the state variable x for a prediction horizon Np.
2) Optimization: the predictions are evaluated by a cost function that defines the system control objectives, where the predicted that minimizes the cost function will be selected as an optimal action. The definition of the cost function is an important design stage.
3) Receding Horizon Strategy: the first element of the optimal input sequence u(k) is applied to the plant. As a result, the state variable x moves toward the reference x*. The process of measuring new feedback variables, predicting
future system behavior and optimizing selection is repeated during each sampling interval.
3.3. Reference frame transformation
The reference theory is a mathematical transformation used to simplify the modeling of the three-phase circuits, power electronics, electrical machine and the control scheme.
The types of references frames are listed as follows [5]:
1. Natural reference frame(abc): the reference frame has a speed ω of zero and a 120-degree phase displacement.
2. Stationary reference frame (αβ): the speed of the reference frame ω is still zero and the variables are represented as two-phase variables with 90-degree displacement. The transformation of three-phase time-varying quantities (abc) to two-phase time-varying quantities (αβ) simplifies the modeling and the analysis. The αβ-frame is used to obtain the voltage’s vectors for the output inverter.
3. Synchronous reference frame (dq): this reference frame rotates at a
synchronous angular speed ω. The dq frame is used in the present work in the grid voltage orientation scheme (closed-loop current control) where the
abc/dq0 transformation (also named as Park transformation) is used to reduce
the complexity and to simplify control design and analysis. The q axis of the
dq0 coordinate system is leading the d axis by 90 degrees. This transformation
allows any system to operate an independent control for the active d-axis and the reactive q-axis components of the currents [10].
Moreover, it allows the representation of any transient event between phases (balances or not). Furthermore, (PI) offers an effective and reliable control solution when the quantities are DC in nature.
3.3.1. Mathematical transformation equations
The transformation matrix between αβ to abc reference frame is shown in equation 3.3. The synchronous reference frame dq can be obtained from stationary reference frame αβ with help of the angle between phase a and the d-axis, as shown in equation 3.4 [5].
The transformation matrix between the stationary and synchronous frame: 𝑉𝛼 𝑉𝛽 = 2 3 × ( 1 −½ ½ 0 √3 2 − √3 2 ) ( 𝑉𝑎 𝑉𝑏 𝑉𝑐 ) (3.3)
The transformation matrix between natural and stationery frame:
𝑉𝑑 𝑉𝑞 = ( 𝑐𝑜𝑠Ø 𝑠𝑖𝑛Ø −𝑠𝑖𝑛Ø 𝑐𝑜𝑠Ø) × 𝑉𝛼 𝑉𝛽 (3.4)
4. Power electronics in wind power systems
This chapter is subdivided into three parts. The first part analyses the two-level volt source converter configuration. The all possible number of the switching state and the inverter voltage vectors will be presented in the second section. The third section will demonstrate the implementation of model predictive control in power electronics.
4.1. Back to back converter
The three phase two-level voltage source converter (2L-VSC) is the most widespread power electronic converter used to integrate variable speed wind turbines into the grid [6]. The 2L-VSC consist of two parts, a machine side converter, and a grid-side converter as seen in figure 4.1. The capacitator makes it possible to decouple the control of the two converters without affecting the other side of the converter [6].
The machine side converter (MSC) and the grid side converter (GSC) consist of three legs each leg has two IGBTs connected with diodes to insure a path for the current during the switching [5].
The reasons for the use of insulated gate bipolar transistors (IGBTs) are to operate at higher switching frequencies and to increase power quality and density [5].
Fig. 4.1. Voltage source inverter power circuit.
The possible number of switching states for a three-phase 2L-VSC is 23=8, with two switching vectors [1] and [0] in each phase. Hence, only one switch is conducting in each phase at any time instant.
The switching states of the converter are determined by the gating signals sa, sb and sc as follows [6]:
Sa={0 𝑖𝑓 𝑆1 = 0 "off" 𝑎𝑛𝑑 𝑆4 = 1 "𝑜𝑛" 1 𝑖𝑓 𝑆1 = 1 "𝑜𝑛" 𝑎𝑛𝑑 𝑆4 = 0 "off" Sb={0 𝑖𝑓 𝑆2 = 0 "off" 𝑎𝑛𝑑 𝑆5 = 1 "𝑜𝑛" 1 𝑖𝑓 𝑆2 = 1 "𝑜𝑛" 𝑎𝑛𝑑 𝑆5 = 0 "off" (4.1) Sc={0 𝑖𝑓 𝑆3 = 0 "off" 𝑎𝑛𝑑 𝑆6 = 1 "𝑜𝑛" 1 𝑖𝑓 𝑆3 = 1 "𝑜𝑛" 𝑎𝑛𝑑 𝑆6 = 0 "off"
The eight possible switching states will produce eight voltage vectors [V0 … V7]T.
The six active voltage vectors V1 to V6 will produce nonzero output voltage while
switching vectors V0 [000] and V7 [111] will produce no output voltage [6], as
shown in figure 4.2.
Fig. 4.2.Voltage vectors that are generated by the inverter.
The voltage vectors for a 2L-VSC with respect to the negative DC-bus N in the stationary reference frame αβ are given by [5]:
𝑉𝛼(𝑘) 𝑉𝛽(𝑘)= 2 3𝑉𝑑𝑐 ( 1 −1 2 1 2 0 √3 2 − √3 2 ) 𝑆1 𝑆2 𝑆3 (4.2)
The express of the equation will give eight different voltage vectors that can be written as follow: v0 = 0. v1 = 2/3 Vdc. v2 = 1/3 Vdc + j√3 3 Vdc. v3 = -1/3 Vdc +j √3 3 Vdc. (4.3) v4 = -2/3 Vdc
v5 = -1/3 Vdc - j√3 3 Vdc.
v6 = 1/3 Vdc - j√3 3 Vdc.
v7 = 0.
4.2. Predictive control in power electronics
The predictive control presents several advantages that can be applied to a variety of systems, nonlinearities and constraints, which make it suitable for the control of power converters. In addition, a multivariable case can be considered, and the resulting controller is easy to implement [7]. Several control schemes have been proposed for the control of power converters and drives [5], as can be seen in figure 4.3.
Fig. 4.3. Basic methods of converter control.
Wind generator output voltage and frequency changes concern the rotational speed (wind speed). The generator output terminals can be directly coupled to the grid in fixed speed wind turbines type or can be coupled through a power electronic converter in variable speed wind turbines which are sorted as type 3 and type 4 wind turbines [8], as was presented in chapter 2.3.2.
The AC output voltage for the generator is converted to DC voltage by a rectifier (AC/DC converter) and then back to AC with a fixed voltage magnitude and frequency by an inverter (DC/AC). In most WTs, the configuration of both AC/DC and DC/AC converters is known as a back-to-back (BTB) connected converter [5], as depicted in figure 4.4.
By using BTB many advantages can be obtained concentrate on the full power controllability, simple to apply with few components, which in return results in lower cost and reliable performance [9].
The grid side converter is a common and substantial element for connecting wind turbine generators to the grid. The GSC is in charge of the DC-bus voltage control, grid synchronization and grid reactive power control. Therefore, the digital control of GSCs is important in the successful and efficient operation of Type 3 and 4 wind energy conversion systems (WECs) [5].
The machine-side converter or AC/DC rectifier draws more energy from wind by performing the MPPT by using a generator speed or torque regulation. For Type 4 WECs, the BTB is connected between the generator and the grid. On the other hand, in the Type 3 WECs, the BTB connected between the rotor circuit and the grid, while the stator terminals of DFIG are directly connected to the utility grid via a step-up transformer [5], as was explained in section (2.3.2),
5. Implementation and Results
This chapter presents the predictive current control scheme for a three-phase grid side inverter. A Simulink model of the PLL and the control scheme are presented step-by-step. The predictive current control algorithm is explained in detail. The results are demonstrated in two different sampling time Ts=20, 100 μs and for
different operation mode PF=1 and leading power factor of PF=0.8. 5.1. Predictive current control scheme
The Model predictive control explained in chapter 3 is implemented by means of a Predictive current control scheme. The cost function is then focusing on comparing the grid current with a reference current. The control block diagram for the predictive current control of grid-connected 2-level voltage source inverters (2L-VSI) is shown in figure 5.1.
Fig. 5.1. The predictive current control scheme for a grid-side inverter.
The control scheme is consisting of four main blocks:
• Block (1): Measurement and synthesis of feedback signals block.
• Block (2): Calculation of the reference current i*αβ block. • Block (3): Prediction of the future grid currents iαβ(K+1) block.
• Block (4): Cost function minimization block.
5.1.1. Measurement and synthesis of feedback signals
The three-phase grid voltages vabc will be the input of the phase-locked loop (PLL)
The grid voltage angle θg presents the angle between phase a in the three-phase
system and d-axis as is seen in figure 5.2. It a very important step in the transformation of variables from abc to the dq reference frame. It also helps in the design of the current predictive control system for GSC [5].
Fig. 5.2. Grid voltage vs and current vectors are in dq and αβ frame.
The use of PLL forces the d-axis of the synchronous reference frame to synchronize with the grid voltage vector, Vs. Hence, vqg becomes zero on the
active and the reactive power equations in the SRF.
Pg = Re (Sg) = 1.5 (vdg idg + vqg iqg) (5.1)
Qg = Im (Sg) = 1.5 (vqg idg − vdg iqg) (5.2)
For vqg = 0 the design of the control scheme becomes easy and the linear
relationship between (Pg and idg) & (Qg and iqg) can be obtained as followed:
Pg = +1.5 vdg idg (5.3) Qg = −1.5 vdg iqg (5.4)
5.1.1.1 PLL model
The simulation model for PLL has been built by using MATLAB, as depicted in figure 5.3. The simulation blocks contain two subsystems to make the transformation between abc/αβ and from αβ to dq0.
The PI controller is used to force the q-axis grid voltage vqg to zero value. The PI controller showing how the output frequency Δω is far from the central frequency
ωo which is added as a feed forward.
Adding an angular frequency term ωo=2π50 will improve the initial dynamic performance [5].
The output signal will be an input for the integrator block 1/s to produce the grid voltage angle θg. To ensure that θg changes between 0 and 2π, a modulus function
block is used. The modulus function block (mod) is used to make sure that θg changes between 0 and 2π, as seen in figure 5.6.
Fig. 5.3. MATLAB simulation model for PLL.
5.1.1.2. PI block design for PLL block
In a proportional-integral controller (PI), the proportional term Kp has an effect of
reducing the rise time, while the steady-state error will not be eliminated. However, the integral controller term Ki will have the effect of eliminating this.
The different values of Kp are considered in the design of the PI controller to
achieve the optimal value. Figure 5.4 shows the steady-state tracking error decreases as the proportional feedback gain increases, while the rise time increases as Kp increases. Moreover, the figure shows an unstable system could be obtained
for Kp=5.
Time[sec] Fig. 5.4. The output voltage vqg for different values of the proportional term Kp
(0.5, 5, 1).
[V
Figure 5.5 reveals the advantage of adding an integral term to the controller. This will help in reducing the steady-state error compared to the case where only a proportional term is used, where three scenarios have been tested for different values of ki = 250, 100, 0 with fixed kp. The figure also shows increasing the value
of ki will make the transient response worse.
Time[sec] Fig. 5.5 The output voltage vqg for different values of integral term Ki (250, 100, 0) with Kp =
0.5.
It can be concluded that the use of the PI controller with parameters (Kp = 0.5 & Ki= 100) will give a good performance for the PLL mode and these values will
be adopted thought the project.
5.1.1.3 PLL simulation results
Figure 5.6 shows the simulation results of the three-phase grid voltages Vabc and
the stationary reference-frame voltages Vαβ in per unit. It can be noticed that the
phase α is shifted by 90 degrees from phase β and it is in phase with the grid voltage in the neutral reference frame Va. The peak value of the grid voltage angle θg is aligned with the Va peak value. The dq-axes voltages are estimated according
to the value of θg.
[V
Fig. 5.6. Transformation of the grid voltages. (a) grid voltage in the natural reference frame (b) αβ reference (c) grid voltage angle (d) the q- axis grid voltage vqg.
It can be noticed in figure 5.6 (d) that the q- axis grid voltage vqg is equal to 0 after
a short overshoot. Hence, the grid voltage orientation is achieved and a linear relation between (Pg and idg) & (Qg and iqg) is obtained.
5.1.2. Calculation of the reference currents i*αβ block and V*dc
The DC link in the two-level voltage converter provides complete decoupling between the generator and the grid. For the machine side converter (MSC), the DC link makes the rectifier output voltage more smoothly. On the other hand, the grid DC link acts as a voltage source for the grid side inverter (GSI).
The DC link voltage is closely dependent on the active power [12] and the GSC regulates the net DC-bus voltage at its reference value V*dc [5].
The DC-bus voltage reference value V*dc is selected to be higher than the peak grid
line-to-line voltage 𝑉𝑔_𝑙𝑙 as [5] Va Vb Vc Vα Vβ a b a c d [sec]
V*dc =√2
𝑚𝑎𝑉𝑔_𝑙𝑙 (5.6)
By setting a modulation index ma = 0.8, about 20% margin will be allowed for the adjustment during transients. Hence, the value of V*
dc can be obtained as [5]
V*dc = 3.062 Vg_ph (5.7)
The injected active power to the grid Pg* is related to the wanted grid PF, while
the turbine active power is related to the extracted power from the wind. The implementation of the maximum power point tracking system makes it possible to extract the maximum power from the wind and deliver it to the GSI. By neglecting the losses in the power electronic and the mechanical losses the active power Pg
on the AC side will equal to the DC Power [5]:
Pg= 1.5 idg vdg = idc Vdc (5.8)
The reference current in the d axis of the synchronous reference frame can be calculated as:
i*dq=P*g/1.5 vdg (5.9)
On the other hand, the reactive power is controlled by the imaginary current component of the grid side converter iqg. The delivered reactive power Q*g to the
grid is determining according to the grid operator’s command [5]. Hence the reference current in the q axis of the SRF can be calculated as:
i*qg= Q*g /-1,5 vdg. (5.10)
The reference current in the stationary reference frame i*αβ can be obtained by
transforming (dq / αβ) with help of the grid angle θg.
5.1.3. Prediction of the future grid currents iαβ(K+1)
In this block, the predictive current value of the grid in the stationary reference frame at time instant (k+1) is given by [5]:
iαβ(K+1) = (1 – (ri Ts /Li)) iαβg(k) + (Ts/Li) vαβ(k) - (Ts/Li) vαβg(k) (5.11)
where vαβ(k) can be calculated from equation 4.1, vαβg(k) is the primary step up transformer voltage in the stationary reference frame. ri is the internal resistance
of the grid filter that is equal to 1.9e-3 Ohm and Li is the grid-filter inductance
5.1.4. Cost function minimization
In this block the absolute error between the eight predicted currents
i
αβ(K+1)andthe reference currents i*αβ(k) are evaluated by a cost function g(k) which is given
as [5]:
g(k)=
abs (i
αβ(K+1)- i
*αβ(k) ) (5.12)5.2. Working principle of the control algorithm
Fig 5.7 presents a flow diagram of the control algorithm in detail. The predictive current in equation 5.11 can be estimated by using the measurement ig(k), vg (k), and all switching states of the voltage vector V(i) that are presented in equations 4.2 and 4.3, respectively. The algorithm calculates the predictive current for all possible switching S1, S2, S3, S4, S5, S6, S7 and S8. Then the predictive current for each switching state will be evaluated by the cost function presented in equation 5.12. The switching state that produces minimum cost function value is selected as the optimal switching state Sopt.
5.2.1. Timing diagram of the control algorithm
For the real-time implementation of the control algorithm, increasing the horizon length Np results in complexity of the overall MPC [6]-[7]. Hence, the prediction
horizon is selected to be a one-sample-ahead prediction horizon with NP =1. In the
sampling time instant t(k) the grid current and voltage will be measured, while the minimization of the future grid current error for all possible switching and their corresponding voltage vectors will be evaluated by the cost function. The switching state that minimizes the future current error will be selected as an optimal switching stat for the next sampling time t(k+1). After that, the state variables of the system at sampling time t(k+1) are considered as an initial condition for the prediction for t(k+2), these procedures will be repeated during the time of processing. The timing of the different tasks for the control algorithm is shown in figure 5.8.
Fig. 5. 8. The timing of different tasks for the control algorithm. 5.3. Control scheme implementation
The implementation of the control scheme shown in figure (5.1) is done by the Simulink environment in MATLAB, see figure 5.9.
Fig. 5.9. Simulink model for the control scheme.
The simulation model was divided into five main blocks:
1. In block number 1, the reference currents were generated by using the controlled current source block in the MATLAB Simulink library.
The reference currents id and iq that were defined in MATLAB m-file can be
calculated by equations 5.9 and 5.10 respectively. The MATLAB m-file should be run before the simulation start. The transformation between dq to αβ reference frame as shown in equation 3.4 with the help of the grid voltage angle θg is needed to provide the reference current i*αβ to the control algorithm
block.
2. The control algorithm, which was explained in section 5.2, was applied in the MATLAB function block (block number 2). The inputs signals are ri, Li, Vdc,
Ts, i(k), vg(k) and the reference current i*αβ, where the output is the optimal
switching state Soptabc. The internal resistance inductance of the grid r
i, Li, and
Vdc can be defined in the m.file as well.
3. The inverter output voltage with respect of grid neutral n will be calculated inside block 3 as shown in figure 5.10. While the one phase grid current ia can
be calculated as:
Via-Vag = Li
𝑑 𝑖𝑎
𝑑𝑡 +ri ia (6.10)
By applying the Laplace transform to equation (6.10) the phase a grid current (ia) can be written as :
ia =
1
𝐿 .𝑠+𝑟𝑖 (Via -Vag) (6.11)
ib and ic can be calculated as was done for ia.
Fig. 5.10. Simulink model for the inverter voltage output and measurement current calculation.
4. The phase locked loop which was explained in chapter 5.1.1 represents block number 4.
5. The step-up transformer 690/10 KV with the apparent power of 3.6 MVA and the three-phase voltage source that acts as the grid will form the fifth block. 5.4. Simulation results
Simulations of a grid side inverter controlled by the current predictive control method have been carried out with Matlab/Simulink. The parameters of the simulated system are defined in table 2.
Table 2: Simulink parameters
Parameter Value
Grid line voltage 690 (V) Converter nominal power 3 (MVA)
Frequency 50 (Hz)
Vdc 1.2198e+03(V)
ri 1.9e-3 (Ω)
Transformer primary voltage(line) 690 (V) Transformer secondary voltage(line) 10 (KV) Transformer nominal power 3.6 (MVA)
Start time 0 (S)
Stop time 0.25 (S)
Solver type Fixed step
Solver Ode5
There are two different sampling times: Ts=20 μs and 100 μs will be tested in this
simulation to study the system response for different power factor scenarios in each tested sampling time.
5.4.1. Simulation results for a sampling time of 20 μs
The two different operation modes have been considered in this simulation. The first one is the operation through feeding a pure active power to the grid with power factor PF=1, as can be seen in figure 5.11.
Fig. 5.11. Comparison of the grid current Iαβ (marked in black and pink lines, respectively) with the reference current I* αβ (marked in red and blue lines, respectively) for PF=1, Ts=20 μs.
The second operation mode is the operation through feeding power with lead phase angle PF=0.8 at 0.1 sec, as shown in figure 5.12.
[A
]
Fig. 5.12. The grid current in the three different reference frames abs, αβ and dq when the power factor changes from 1 to 0.8 at 0.1 sec, for sampling time Ts=20 μs.
Figure 5.13 shows the phase angle between the voltage and current for phase a when the power factor is 0.8. The current is divided by a factor 5 to scale the axis.
Fig. 5.13. The phase shift between Va and ia for PF=0.8 and Ts=20 μs, where ia is the phase a grid
current divided by 5 in A and the voltage Va is the phase a grid voltage.
[A ] [sec] Va [V ], ia [ A] [sec]
The step response for the system has been simulated for a step input signal as can be seen in figure 6.14. The rise time is found to be 15.840 μs.
Fig. 5.14. Step response for the system, Ts=20 μs.
During 1.0 to 0.93 (PU) wind speed conditions at 0.1 sec, the grid active power Pg
changes from 3.0 MW to 2.4 MW which is corresponding to grid current of id = 2.8400e+03 A. The grid reactive power Qg corresponds to iq =0 and is maintained
zero by implementing the PCC scheme, see figure 5.15.
[A
]
Fig. 5.15. The grid current in the three different reference frames abs, αβ and dq when the wind speed changes from 1 to 0.93 pu at 0.1 sec for sampling time Ts=20 μs.
5.4.1.1. Total Harmonic Distortion (THD)
MATLAB/ Simulink computes the total harmonic distortion (THD) in a grid current signal by applying a Fast Fourier Transform (FFT). The THD is defined as the ratio of the sum of the powers of all harmonic components and the power of the fundamental frequency. For a number of signal cycles equal to 11, as depicted in figure 5.16 with start time 0.02 sec and stop time 0.23 sec, the THD will be calculated.
Fig. 5.16. Selected signal for the FFT analysis. Ts=20 μs.
Figure 5.1 shows the THD and the harmonic magnitude of the fundamental frequency concerning the harmonic order for 11 cycles of the grid current signal.
[A
]
Fig. 5.17. The THD through feeding a pure active power for 11 cycles of the grid current signal when Ts=20 μs.
5.4.2. Simulation results for a sampling time of 100 μs
Similar to the previous procedure that was used in section 5.4.1 with the sampling time of 100 μs instead of 20 μs. The two different operation modes have been shown in figures 5.18 and 5.19, respectively.
Fig. 5.18. Comparison of the grid current Iαβ (marked in gray and red lines, respectively) with the reference current I*αβ (marked in black and green lines, respectively) for PF=1, Ts=100 μs.
Simulation results for the operation mode through feeding a power with lead phase angle corresponding to PF=0.8 at 0.1 sec are shown in figure 5.19.
[A
]
Fig. 5.19. The grid current in the three different reference frames abs, αβ and dq when the power factor changes from 1 to 0.8 at 0.1 sec, for sampling time Ts=100 μs.
The step response for the system can be seen in figure 6.19, where the rise time for a sampling time of 100 μs is equal to 79.2 μs.
Fig. 5.20. Step response for the system, Ts=100 μs.
[A ] [A ] [sec] [sec]
5.4.2.1. Total Harmonic Distortion (THD)
For numbers of cycles equal to 11, as can be seen in figure 5.2, the THD percentage through feeding a pure active power to the grid is found to be THD=9.08%, see figure 5.22.
Fig. 5.21. Selected signal for FFT analysis. Ts=100 μs.
Fig. 5.22. The THD through feeding a pure active power for 11 cycles of the grid current signal when Ts=100 μs.
6. Discussion and analysis
In this chapter, results that were obtained for two different sampling times of Ts= 20 and Ts= 100 μs through feeding a pure active power with PF =1 and feeding
power with a leading power factor of 0.8 will be discussed and analyzed deeply.
The results for a sampling time of 20 μs show a high performance of tracking the reference current with low ripple in the grid current, as can be seen in figure 5.11. By contrast, the grid current’s ripple is considerably increased when the sampling time increases to 100 μs, as can be noticed in figure 5.18. This is expected, however, as other parameters are kept constant.
Ejecting reactive power to the grid as was presented in figure 5.13 will produce a leading phase angle shift equal to 36 °. A changing in the injected active and reactive power has been simulated for a sampling time of 20 and 100 us, as was shown in figures 5.12 and 5.19, respectively. It can be noticed that, the change in operation mode at 0.1sec increases the overshoot on the grid current for a sampling time of 100 μs compared to the sampling time of 20 μs.
The rise time for the system when Ts=20 μs has been found equal to 15.840 μs.
On the contrary, the rise time is greatly increased and reaches 79.2 μs for a sampling time of 100 μs, as is shown in figure 5.20. The difference is proportional, as is expected.
Since the power is proportional to the cube of the speed (P ∝ V3), the drop in wind
speed from 1 (pu) to 0.92 (pu) will cause a drop in the feeding of the active power to the grid. As a result, the corresponding d component of the grid current will change from id = 3.5e+03 A to id = 2.84e+03 A, as can be seen in figure 5.15. On
the other hand, the grid reactive power Qg which corresponded to iq=0 is
maintained at zero. Hence, the id and iq of the current are decoupled. This is also
expected, as the PF was maintained at 1.
The total harmonic distortion for the grid current with the sampling time of 20 μs was found to be 1.92%, as can be seen in figure 5.19 while the THD for sampling time Ts=100 μs was raised to 9.08%, see figure 5.22. In the power systems, lower
THD indicates lower peak currents, less heating and lower electromagnetic emissions. Hence, the sampling time of 20 μs is most likely to be implemented in a real time.
Similarly, the model predictive control algorithm is possible to implement by a Digital Signal Processor, and this opens the door to implementing this algorithm in a real time.
7. Conclusion and future work
In this thesis, the use of the grid side inverter to control the active and reactive power for variable speed wind turbines has been presented in detail. The maximum power point tracking method and different types of wind turbines were presented. The types of reference frames and their transformation matrixes with a brief explanation was demonstrated. The role of the power electronics in the integration of wind power into the grid was mentioned with the implementation of the predictive current control in the power electronics. The use of the PLL helped in the synchronization with the grid and made the reference current calculation simpler. The use of the PI controller with parameters Kp = 0.5 and Ki= 100 gave
a good performance for the PLL mode.
The model predictive control principle and its components were shown and explained step by step. For the predictive current control strategy and its practical implementations, minimization of the current error and selection of the optimal voltage vector were done by applying the control algorithm. The control scheme for the PCC has been implemented in Matlab/Simulink where the predictive current was obtained by using a discrete-time model of the system.
Based on the simulation results for the different sampling times, the increase of the sampling time will cause an increased ripple in the grid current. Moreover, for two different operation modes changing between PF=1 and PF= 0.8 at 0.1sec, the overshoot was noticed to be increased when the sampling time was 100 μs. On the other hand, for the sampling time of 20 μs, the high performance of tracking the reference current with a low value of rise time has been noticed. A change in wind speed showed a decoupled relation between id and iq, where id had varying values while iq maintained its value.
This work can be extended by implementing predictive current control to the machine side converter of the DFIG wind turbines to maximize the harvested power from the wind for different wind speeds. The electromagnetic torque or the
d component of the rotor current will be controlled to produce an optimal wind
speed corresponding to the maximum power. The control procedure will be similar to the GSC, where the referenced d component of the rotor current is produced from the error signal between a measured rotational speed and its reference. The corresponding switching state that minimizes the future error will be implemented for the next sampling time.
References
[1]. T. Ackermann, "Wind power in power systems," John Wiley \& Sons, 2005, pp. 52-80.
[2]. T. Wizelius, Wind Power Projects: Theory and Practice, Routledge, 2015.
[3]. "IEA – International Energy Agency," IEA, [Online]. Available:
https://www.iea.org/data-and-statistics?country=WORLD&fuel=Energy%20supply&indicator=Electricity %20generation%20by%20source. [Accessed 20 09 2020].
[4]. J. S. a. O. M. Thongam, "MPPT control methods in wind energy conversion systems," 1, no. InTech, pp. 339--360, 2011.
[5]. Yaramasu, V., & Wu, B, Model predictive control of wind energy conversion systems, John Wiley \& Sons, 2016.
[6]. Rodriguez, J., Pontt, J., Silva, C. A., Correa, P., Lezana, P., Cortés, P., & Ammann, U, ”Predictive current control of a voltage source inverter,” IEEE transactions on industrial electronics, vol. 54, nr IEEE, pp. 495--503, 2007.
[7]. Cortés, P., Kazmierkowski, M. P., Kennel, R. M., Quevedo, D. E., & Rodríguez, J, “Predictive control in power electronics and drives” IEEE Transactions on industrial electronics, vol. 55, pp. 4312-4324, 2008. [8]. F. Blaabjerg, R. Teodorescu, M. Liserre, and A. Timbus, “Overview of control and grid synchronization for distributed power generation systems,” IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398–1409, October 2006.
[9]. Blaabjerg, Frede, et al. "Power electronics-the key technology for renewable energy system integration." 2015 International Conference on Renewable Energy Research and Applications (ICRERA). IEEE, 2015. [10]. Teodorescu, R., Liserre, M., & Rodriguez, P , "Grid converters for photovoltaic and wind power systems," vol. 29, no. John Wiley \& Sons, 2011.
[11]. Franklin, G. F., Powell, J. D., Emami-Naeini, A., & Sanjay, H. S, Feedback control of dynamic systems, London: Pearson London, 2015.
[12]. F. Blaabjerg,” Control of Power Electronic Converters and Systems: Volume 2,” Control of Power Electronic Converters and Systems: Volume 2, Academic Press, 2018, pp. 269-298.
Appendix A
1 % Variable for control algorithm
2 clear 3 4 ri=1.9e-3;%ohm 5 f=50;%Hz 6 Ts=100e-06;%Sample time S 7 vg_line=690;%Voltage 8 Vdc=3.062*(vg_line/sqrt(3));% Dc voltage 9 vdg=sqrt(2)*(vg_line/sqrt(3));% peak voltage 10 vqg=0;%By using PLL
11 wg=2*3.14*f;%rad/s 12 Li=0.084e-3;%H
13 S=3e6;% converter apparent power in VA 14
15 prompt = 'Insert the operation capacity for the inverter as % = '; 16 Sc=input(prompt);
17 Si= (Sc*S)/100; 18
19 prompt = 'Insert the wanted delivered power factor PF ='; 20 cos_alpha=input(prompt);
21
22 if (cos_alpha > 1 );
23 prompt = 'Error PF should be between (0 to 1)pleae re_insert the wanted
PF = '; 24 cos_alpha=input(prompt); 25 Pg=cos_alpha*Si 26 Qg=sqrt(Si.^2 - Pg.^2) 27 100 28 else 29 30 Pg=cos_alpha*Si 31 Qg=sqrt(Si.^2 - Pg.^2) 32 33 end 34 35 Sg=sqrt(Pg.^2+ Qg.^2); 36 Id_ref=Pg/(1.5*vdg); 37 Iq_ref=Qg/(1.5*vdg);
%---Control Algorithm---
1 function [Sa , Sb ,Sc] = Matlab_Function(ri, Li,I_ref,Vdc,Ts,vg,I_k)
2 if isempty(i_pre), i_pre = 0+1i*0; 3 end
4 % define the measured current and reference current 5 6 Ik_ref =I_ref(1)+1i*I_ref(2); 7 8 Ik=I_k(1)+1i*I_k(2); 9 10 vgab=vg(1)+1i*vg(2); 11 12 i_pre=Ik; 13
14 % Initialize values for the cost function and switching state 15
16 g_opt=inf; 17 S_opt=0; 18
19 % voltages vectors output for three-phase inverter in the alpha-beta reference frame 20 21 v0 = 0; 22 v1 = 2/3*Vdc; 23 v2 = 1/3*Vdc + 1j*sqrt(3)/3*Vdc; 24 v3 = -1/3*Vdc +1j*sqrt(3)/3*Vdc; 25 v4 = -2/3*Vdc; 26 v5 = -1/3*Vdc - 1j*sqrt(3)/3*Vdc; 27 v6 = 1/3*Vdc - 1j*sqrt(3)/3*Vdc; 28 v7 = 0; 29 30 v_inverter_output = [v0 v1 v2 v3 v4 v5 v6 v7]; 31 32 states = [0 0 0;1 0 0;1 1 0;0 1 0;0 1 1;0 0 1;1 0 1;1 1 1]; 33 34 35 36 37 for i = 1:8
39 v_o1 = v_inverter_output(i); 40 % Current prediction at instant k+1
41 ik1 = (1 - ri*Ts/Li)*Ik + Ts/Li*(v_o1)-Ts/Li*(vgab); 42 % Cost function
43 g = abs(real(Ik_ref - ik1)) + abs(imag(Ik_ref - ik1)) 44
45 if (g<g_opt)
%selection of the optimal cost function 46 g_opt = g;
%selection of the optimal switching ststes 47 S_opt = i;
48 end 49 end
50 % Output optimal switching states 51 Sa = states(S_opt,1); 52 Sb = states(S_opt,2); 53 Sc = states(S_opt,3); 54 55 end
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