Real-time Power-Hardware-In-the-Loop Discrete Modeling of PMSM Wind Turbines F. Huerta, M. Prodanović and P. Matatagui Electrical Systems Unit Institute IMDEA Energy Móstoles, Spain
[email protected] Abstract— Increasing global interest in clean and distributed energy systems emphasizes the importance of power electronics technologies in grid integration of renewable energy resources. High penetration of renewables such as wind turbines introduces new challenges for the grid stability seeking appropriate solutions. From a technical and economic point of view any application and testing of new management schemes in real power networks is risky. To overcome these obstacles, hardwarein-the-loop (HIL) technologies appear as a suitable and logical option, because they make equipment or control algorithm evaluation easier, faster and more economical. This paper addresses the hardware-in-the-loop discrete time modeling of a permanent magnet synchronous machine (PMSM) wind turbine (WT). The discrete time modeling has been considered and used so that the developed models can be executed in real-time on an industrial computer. In addition, some features of the Smart Energy Integration Lab (SEIL) — a purposely build lab environment for implementation of grid scenarios and the HIL system used for the implementation are presented. Finally, the paper experimentally validates the design methodology for real-time emulation of wind turbines. Keywords— modeling; hardware-in-the-loop; wind turbine; real-time implementation; grid integration component
I.
INTRODUCTION
Interest in renewable energy resources we have witnessed in the past decades will not decline in the years to come. Main drivers such as climate change, energy independence, obsolescence of fossil fuels or risks and controversies regarding use of nuclear energy have impelled scientific community and governments to support renewable energies. European Union set ambitious energy and climate goals by 2020 and 2050 frameworks [1]. Countries such as Denmark, Germany or Spain have increased their renewable generation mix during the past decades and even the giants such as China or USA have recently turned their attention to clean and inexhaustible energies [2]. However, the rapid growth in renewable production entails risks and challenges. High penetration of renewable energies based on intermittent sources can compromise the grid stability and reliability and continuity of the electricity supply. Because of this, grid integration of renewable and distributed resources is still one of the hot topics where a key piece is the development of tools that facilitate the analyses of grid integration scenarios.
Hardware-in-the-loop (HIL) environments combine hardware elements and software models in a closed loop simulation, in which a real-time target (RTT) runs the software model and the communication —including acquisition and actuation— interface between software and hardware. HIL techniques benefit from flexibility of simulation and fidelity and verisimilitude of using real devices. Applied on the study of grid integration of renewable energy resources, HIL systems allow easily overcoming some technological barriers. Widely used in fields such as the automotive sector or the aircraft industry, application of HIL technology in power electronics systems has become relatively significant during the past decade, emerging the concept of power-hardware-in-the-loop (PHIL). Between the existing applications of HIL to power electronics system [3-8], some of them focus on grid integration [9], but yet those proposals place emphasis on the device standpoint and emulate grid connection [10]. There exists a wide knowledge base for modeling of wind turbines (WTs), making it possible to find many approaches which address the model considering different degrees of complexity [11], including concrete effects on the mechanical elements of the turbine [12] or modeling for HIL applications [13]. However, modeling has generally been more oriented to computer simulation, considering continuous time frame and without taking into consideration important aspects like discrete time implementation, possible algebraic loops or the computational burden which are crucial and restrictive in real-time HIL implementations. This paper tackles two objectives. Firstly, the paper deals with real-time discrete modeling of one of the most popular renewable energy generator: a permanent magnet synchronous machine (PMSM) wind turbine (WT). This model will be emulated on a HIL system as part of an analysis or control evaluation of WT grid integration strategies. Secondly, the paper introduces the HIL test bed: the Smart Energy Integration Lab (SEIL). The laboratory represents a completely automatized power electronics facility and allows execution of grid integration experimental tests on up to five independent islanded or grid connected microgrids. The paper is divided into five sections, including this introduction. In Section II, the discrete time model of the PMSM WT is described in detail. Section III describes the SEIL facilities. Section IV presents the grid integration
experimental tests that verify the proposed methodology. Finally, section V discusses conclusions and future works. II.
PMSM WIND TURBINE MODELING
The paper considers two modeling methodologies that are described in Fig. 1. In Methodology A, the model includes WT and PMSM modeling. A voltage source converter (VSC) implements the WT plus PMSM model response and requires an additional back-to-back converter to connect the system to the grid. Methodology B includes the modeling of the back-toback converter and its control algorithms in addition to WT and PMSM blocks. The complete model is emulated by using only one VSC connected to the grid. The first methodology is suitable for the development and evaluation of generator control algorithms, the study of transient responses or the analysis of grid integration strategies from generator’s point of view. Methodology B is more useful tool for evaluation of microgrid control strategies like development of power dispatching algorithms or analysing grid integration of renewable resources from the power network point of view. The implementation of the wind turbine model on the RTT (PMSM and back-to-back converter including the control algorithms) is divided into two parts as shown in Fig. 2: (a) the RT software wind-turbine model and (b) the control algorithms of the physical VSC. As part of the information flow, the RT wind turbine model calculates the current value that would inject the wind generator using as inputs a wind profile and the measured grid voltage. This current value is used as reference to the VSC’s current control, which regulates the real injected current. The following subsections deal with Tustin’s discrete time modeling of a variable speed PMSM WT with full rated power converter, see Fig. 3. Each element of the PMSM WT is modeled as an independent block. This pursues two objectives: on one hand, WT elements with slow dynamic could be implemented using bigger time steps than faster WT components in order to optimize computational burden; on the other hand, a library of WT components can be created, those WT blocks could be then easily re-used in the implementation of other WT topologies.
Fig. 1. Real-time implementation methodologies of a full-rated converter PMSM wind turbine model.
• Grid-side converter control A. 3-blades rotor model Wind turbines transform the kinetic energy of the air flow passing through the swept area of the blades into mechanical torque on the rotor shaft of the turbine. Airflow power is given by [14]
Pair =
1 ρπ r 2 vw3 2
(1)
As it was mentioned before, converter control and modulation algorithms should be also included into the modeling. The modeled WT components in next subsections are: • 3-blades rotor • Pitch actuator
Fig. 2. HIL implementation of a full-rated converter PMSM wind turbine based on described methodology B.
• Shaft and gearbox • PMSM • Back-to-back converter • Output filter: L and LCL topologies • Modulation • Generator-side converter control
Fig. 3. PMSM wind turbine with L filter (Type IV).
where ρ is the air density (1.225 kg·m-3 at 15 ºC), r is the rotor radius and vw is the wind speed. The wind turbine extracts only a fraction of the wind power, which is denominated the wind turbine power coefficient, Cp. The extracted mechanical power is then
Pm = C p ( λ , β ) ⋅ Pair
(2)
where Cp is a nonlinear function of the tip speed ratio, λ, and the pitch angle, β, and can be expressed as in [15] ⎛ 116 ⎞ C p ( λ , β ) = 0.22 ⋅ ⎜ − 0.4 β − 5 ⎟ ⋅ e ⎝ λi ⎠
−12.5
λi
(3)
where 1 1 0.035 = − 3 λi λ + 0.08β β + 1
(4)
The tip speed ratio is defined as the quotient between tip speed and wind speed
λ = ω m r vw
(5)
Fig. 5. Block diagram for pitch angle control.
where τpitch is its time constant, Ts is the sample period and β* = kp · (ωrot – ωref). The proportional control, kp, forces wind-turbine rotational speed, ωrot, to tackle a reference rotational speed, ωref, which would be determined by using a Maximum Power Point Tracking (MPPT) algorithm [11]. C. Shaft and gearbox model Single-mass drivetrain model is suitable for evaluating the impact of wind fluctuation, whilst two-mass model should be used when evaluating grid stability [14]. With the increasingly size of wind turbines, three-mass model or higher should be considered. The scope of the paper is limited to one-mass and two-mass models. 1) The one-mass model: A single-mass drivetrain model is obtained lumping together all inertia component. If frictions and stiffness are neglected as in [16], the discrete-time model using Tustin’s approximation is given by
Equations (3-4) constrains β ≥ 0. The relationship between Cp and λ according to β is shown in Fig. 4.
Ts
k = ω gen
J eq
Eventually, the rotor shaft torque is obtained by Trot = Pm ωm
(6)
B. Pitch actuator model Fig. 5 shows the pitch actuator scheme. If pitch angle and pitching limitations are neglected, the pitch actuator can be modeled as
β k +1 = (1 − Ts τ pitch ) β k + (Ts τ pitch ) β k* 0.45
β = 4
0.3
β = 8
β = 6 β = 10
C
P
0.25 0.2 0.15
5
10 λ
15
Trot′ = Trot η g
(10)
ωrot = ωgen η g
(11)
2) The two-mass model: Assuming that the moment of inertia for the shafts and the gearbox are negligible compared with the moment of inertia of the wind turbine or generator, the two-mass drivetrain model can be expressed using Tustin’s discretization as
′k = ωrot 0
(9)
and
0.1 0.05 0
J eq = J gen + J rot η g2
where is ηg the gearbox ratio, ωrot is the angular velocity of the rotor shaft, ωgen is the angular velocity of the generator shaft, Tgen is the torque of the generator shaft and J are the inertia moments.
β = 2
0.35
(8)
defining
(7)
β = 0
0.4
k
k −1 ∑ (Tgenj + Trot′ j ) + ωgen j = k −1
2
Ts
k
∑ (Trot′ j − Deq Δω j − K s,eq Δθ j ) + ωrot′k −1 (12)
2
′ J rot
j = k −1
20
Fig. 4. Power coefficient (Cp) depending on tip speed ratio (λ) for different pitch angle values (β).
k ωgen =
Ts
2
J gen
k
∑ (T
j =k −1
j gen
k −1 + Deq Δω j + K s ,eq Δθ j ) + ωgen
(13)
′k = Ts 2 (ωrot ′k + ωrot ′k −1 ) + θ rot ′k −1 θ rot
(14)
k k k −1 k −1 θ gen = Ts 2 (ω gen + ω gen ) + θ gen
(15)
where Δω = ω’rot – ωgen, Δθ = θ’rot – θgen, Deq and Ks,eq are the damping and stiffness and
′ Trot ωrot θ′ = = rot = η g Trot′ ωrot θ rot
(16)
′ = J rot η g2 J rot
(17)
1 1 1 = + 2 K s , eq K s , rot η g K s , gen
(18)
D. Permanent Magnet Synchronous Machine Model Under certain assumptions, the PMSM can be represented by a synchronous-frame nonlinear model [17] whose Tustin’s discrete model is expressed as
idk =
iqk =
TS
2
Lq
TS
k
vdj − Rs idj + ωs Lq iqj ) + idk −1 ( ∑ j = k −1
(19)
∑ ( vqj − Rs iqj − ωs Ld idj − ωs λaf ) + iqk −1 j = k −1
(20)
3P ⎡λaf iq + ( Ld − Lq )id iq ⎤⎦ 2 ⎣
(21)
2
Ld k
Tgen =
where P is the number of pole pairs, λaf is the permanent magnet flux linkage, Ld = Lq = Ls are the dq axis inductances, Rs is the stator resistance, vdq and idq are the dq axis stator voltage and current, and ωs is the electrical speed
ωs = Pωgen
(22)
E. Back-to-back converter model 1) Voltage-source converter VSC model: The VSCs of the back-to-back converter can be modeled as [18]
⎡vai ⎤ ⎢ i ⎥ VDC ⎢ vb ⎥ = 3 ⎢ vci ⎥ ⎣ ⎦ i iDC = ⎡⎣ S ai
i ⎡ 2 −1 −1⎤ ⎡ Sa ⎤ ⎢ −1 2 −1⎥ ⎢ S i ⎥ ⎢ ⎥⎢ b⎥ ⎢⎣ −1 −1 2 ⎥⎦ ⎢⎣ Sci ⎥⎦
Sbi
Sci ⎤⎦ ⋅ ⎡⎣iai
ibi
ici ⎤⎦
k VDC =
TS
k
⎛
j = k −1
⎝
∑ ⎜i
2
CDC
r, j DC
i, j − iDC −
VDCj ⎞ k −1 ⎟ + VDC RDC ⎠
(25)
where CDC and RDC are the dc-link capacitor and an associated r i parallel resistance, iDC ,k and iDC ,k are the dc-link currents of the PMSM-side VSC and the grid-side VSC, respectively. F. Output filter model 1) L-filter model: An output L filter can be modeled by using Tustin’s approximation as ixk =
TS
2
Lf
k
∑ (u
j = k −1
j x
− exj − R f ixj ) + ixk −1
(26)
where x = a, b, c, Lf and Rf are the filter inductance and resistance, ux is the converter output voltage, ex is the grid voltage and ix is the current. 2) LCL-filter model: Due to the coupling between the LCL-filter’s variables, the filter model must be expressed in the state-space representation in order to be implemented in discrete-time. The continuous-time LCL-filter model can be written as
⎧ ′ ⎡ i1,dq ⎤ ⎪ ⎡ i1,dq ⎤ ⎡u ⎤ ⎢ ⎥ ⎪ i2,dq = A ⋅ ⎢ i2,dq ⎥ + B ⋅ ⎢ dq ⎥ ⎢ ⎥ ⎢ ⎥ ⎪ ⎣ edq ⎦ ⎢uc ,dq ⎥ ⎪ ⎢⎣uc ,dq ⎥⎦ ⎣ ⎦ ⎨ ⎪ ⎡ i1,dq ⎤ ⎡udq ⎤ ⎪G ⎢ ⎥ ⎪ ydq = C ⋅ ⎢ i2,dq ⎥ + D ⋅ ⎢ e ⎥ ⎣ dq ⎦ ⎪ ⎢uc ,dq ⎥ ⎣ ⎦ ⎩
(27)
where A and B are as described in [19], C = I if all the filter variables were measured and D is a zero matrix. The model is discretized by using the approximation based on the Cayley Transform [20]
Tustin’s
⎧⎪ Aσ = (σ + A )(σ − A )−1 , Bσ = 2σ (σ − A )−1 B ⎨ −1 −1 ⎪⎩Cσ = 2σ C (σ − A ) , Dσ = D + C (σ − A ) B where σ = 2 / TS. The discrete-time LCL-filter model is then given by
(23)
T
(24)
where Sabc are the modulation pulses. 2) DC-link model: The DC link is modeled as in Fig. 6, being the Tustin’s approximated discrete-time model Fig. 6. Diagram of the considered DC-link model.
(28)
⎧ ⎡ i1,kdq+1 ⎤ ⎪ ⎢ k +1 ⎥ ⎪ ⎢ i2,dq ⎥ = ⎪ ⎢u k +1 ⎥ ⎪ ⎣ c ,dq ⎦ ⎨ ⎪ ⎪ yG k = C σ ⎪ dq ⎪⎩
⎡ i1,kdq ⎤ ⎡udqk ⎤ ⎢ ⎥ Aσ ⋅ ⎢ i2,k dq ⎥ + Bσ ⋅ ⎢ k ⎥ ⎣ edq ⎦ ⎢ k ⎥ ⎣uc ,dq ⎦ ⎡ i1,kdq ⎤ ⎡udqk ⎤ ⎢ ⎥ ⋅ ⎢ i2,k dq ⎥ + Dσ ⋅ ⎢ k ⎥ ⎣ edq ⎦ ⎢uck,dq ⎥ ⎣ ⎦
(29)
G. Modeling of the modulation scheme The most popular modulation schemes can be considered: sinusoidal pulse-width Modulation (PWM), sinusoidal PWM with third-harmonic injection or Space-Vector Modulation (SVM). A simplified option is to use the duty cycle instead of the modulation pulses in (23-24). If a low level of detail is only required, another way for model reduction is to assume the simplified average model and approximate the VSC as a gain * GVSC = 1 and then vabc = vabc . Computational time delays, z-j,
Fig. 7. Generator-side control: field-oriented control (FOC) structure.
k *k − j = vabc . implicit in digital controllers, can be included as vabc
H. Generator-side control modeling Direct-torque control (DTC) and field-oriented control (FOC) are some of the most popular control strategies for the control of PMSM. Because of the space restriction, this paper only considers FOC whose structure is depicted in Fig. 7. I.
Grid-side control modeling Some typical control strategies applied to the grid-side converter are vector control or direct power control. However, only a voltage-oriented control (VOC) is considered in this paper because of the space limitations. Its structure is shown in Fig. 8.
III.
Fig. 8. Grid-side control: voltage-oriented control (VOC) diagram.
the RTTs for the control of each converter by using Matlab/Simulink and the Triphase toolbox [21] to design the algorithms. The embedded RTTs are based on Nexcom NISE 6140 industrial computers. The models are designed and built by using Simulink and linked to the converter hardware through the Triphase toolbox [21]. It is possible to store the models on the RTT hard drive, thus creating a model library on it. High level control covers the control of the microgrid by means of two NI compactRIO - 9022 and a conventional PC and uses NI LabVIEW to design connection, monitoring and
POWER-HARDWARE-IN-THE-LOOP FACILITY
The modeling validation has been performed in the PHIL laboratory SEIL of Institute IMDEA Energy, showed in Fig. 9. The SEIL facility combines power and control electronics systems, thus achieving a highly configurable power electronics laboratory especially designed for grid integration studies.
Fig. 9. The Smart Energy Integration Laboratory (SEIL).
The power electronics system consists of four 15 kVA three-phase AC/DC VSCs (configurable by pairs as 15 kVA back-to-back converters); two 75 kVA three-phase AC/DC VSCs (configurable as a 75 kVA back-to-back converter); a DC/DC converter of 90 kW; a lithium ion battery system of 47.5 kWh; a programmable balanced resistive load of 30 kW; a programmable unbalanced resistive load of 10 kW per phase; and a configurable matrix three phase AC bus bars system, which can be arranged forming up to five isolated or grid connected microgrids. The SEIL hardware system diagram is depicted in Fig. 10. Two main components form the control electronics system: four RTTs and a SCADA system based on two NI compactRIOs. The control system is structured in two hierarchical levels, see Fig. 11. Low level control is applied on
Fig. 10. Scheme of the SEIL power electronics system.
TABLE I. r Jrot P Ls CDC Lf
K
control algorithms.
• PMSM • Back-to-back converter
K pfoc,cc K
The current, DC-link voltage and speed control loops in the VOC and FOC have been implemented by using PI controllers. Table I lists the model parameters. The wind-turbine model has been designed assuming a 600 kW generation system, operating at VDC = 1200 V and connected to a 690 Vll,rms – 50 Hz grid. The outputs of the model have been emulated by scaling the system to 50 kW and implemented in a power-controlled 75 kVA VSC, operating at VDC = 700 V and connected to a 400 Vll,rms - 50 Hz grid. That kind of configuration are common in microgrids power dispatching experiments in which the transient response is not critical. For the experimental test, the pitch angle has been set at 10º and a wind speed pattern is applied. The generator speed reference is set at 125 rad/s. Table II presents the experimental set up. Fig. 12 shows the dq grid current reference and the real injected grid current during the wind speed transitions. Fig. 13 shows from top to bottom: 1) wind speed input, 2) WT rotor shaft torque, angular velocity, 5) PMSM active power, 6)
3 kΩ 0.1 Ω
1.3
Kivoc ,cc
594
1
voc i ,vc
10
1.3
Ki foc ,cc
594
81
foc i , sc
159
K
K
8 kHz
EXPERIMENTAL SET UP
Wind-turbine model Emulator Pwind-turbine 600 kW Pemulator Vll,rms 690 V Vll,rms VDC 1200 V VDC Experimental Set Up β*
10 º
* ωgen
50 kW 400 V 700 V 125 rad/s
DC-link voltage and 7) real grid-injected active power. The results validate the methodology introduced for the modelling of PMSM WT turbines. V.
CONCLUSIONS
The paper proposes a discrete time modeling of a PMSM wind turbine oriented to RT emulation in grid integration scenarios. In addition, the paper briefly presents a HIL system used for the implementation: the Smart Energy Integration idq (A) 60 current (A)
The VSC modulation has been simplified by using the duty cycle. The model considers wind speed (vw), pitch angle (β), and grid voltages (eabc), as inputs; and grid-injected active and reactive powers (Pinj and Qinj) as outputs.
0.6 Wb 0.36 Ω
Implementation parameters 125 μs fsw TABLE II.
40 20 0 90
95
100 105 tim e (s) iabc (A)
110
115
95
100 105 tim e (s)
110
115
50 current (A)
• VOC structure
foc p , sc
Ts
• L filter • FOC structure
voc p ,vc
1:80 90 kg·m2
Field-oriented control
IV. RESULTS The proposed modeling methodology and architecture has been validated in the SEIL. A RT discrete-time model has been developed and implemented and it includes: • One-mass drivetrain
Wind turbine parameters 22 m ηg 10000 kg·m2 Jgen PMSM parameters 10 λaf 0.278 mH Rs DC-link model 4.4 mF RDC L filter 1 mH Rf Voltage-oriented control
K pvoc,cc
Fig. 11. SEIL control system: hierarchical structure.
• 3-blades rotor motor
600 KW PMSM WT MODEL PARAMETERS
0
-50 90
Fig. 12. Grid current reference and real injected grid current during a wind speed transition.
w ind (m / s)
20 10 0 90
[5] 95
100
(N· m / s)
3
105
110
115
T rot
5
x 10
[6]
2 1 90
95
100
105
110
115
105
110
115
[7]
(N· m / s)
T gen 0 -2000 -4000 90
[8] 95
100
[9]
w gen (rad / s)
130 125 120 90
95
100
105
110
115
[10]
Pgen (kVA)
300 200 100 0 90
95
100
105
110
115
[11]
V DC (V)
1300
[12]
1200 1100 90
95
100
105
110
115
[13]
(kVA)
Pinj 30 20 10 0 90
95
100 105 tim e (s)
110
115
Fig. 13. Experimental results of the implementation of a HIL PMSM WT model during a wind speed transition.
Laboratory. This kind of model based approach introduces great flexibility in analyzing and testing renewable energy integration strategies. The experimental results validate and demonstrate the usefulness of the modelling approach as the model dynamic response resembled closely the emulated PMSM.
[14] [15]
[16] [17]
[18]
ACKNOWLEDGMENT This work has received financial support by the Community of Madrid Government, the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (INP-2012-0154-PCT-120000-ACT1).
[19]
[20]
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