A comparison of fault-tolerant control strategies for a ... - ESRGroups

J. Electrical Systems 13-3 (2017): 472-488 Sana Toumi1,2, Yassine Amirat3, Regular paper Elhoussin Elbouchikhi3, A comparison of fault-tolerant control Mohamed strategies for a PMSG-based marine Trabelsi1, current turbine system under generatorMohamed side converter faulty conditions Benbouzid2,4, M. Faouzi Mimouni5

JES Journal of Electrical Systems

This paper describes fault-tolerant control strategies for a Permanent Magnet Synchronous Generator (PMSG)-based Marine Current Turbine (MCT) dealing with the generator-side converter under faulty conditions. MCT system mainly used PI controllers. However, this type of controllers is very sensitive to faulty conditions such as an open circuit faults in the generator-side converter. As consequence, the MCT system represents a high decrease in its power generation and dynamic performances. In this faulty context, firstly, a fault tolerant structure consists in requiring only minimum hardware modifications to the converter is proposed. In the second part, a backstepping and a second-order sliding mode nonlinear control are therefore investigated for fault-tolerant control purposes. A comparison between the different control strategies is proposed to prove the most robust one.

Keywords: Marine current turbine; permanent magnet synchronous generator; generator-side converter; open-circuit fault; fault-tolerant structure; fault-tolerant control; backstepping; secondorder sliding mode control. Article history: Received 7 November 2016, Accepted 19 June 2017

1. Introduction Nowadays, marine tidal energy has become an important issue of significant interest achieving a spectacular increase [1]; it has been shown that 48% of the European tidal resource is in the UK, 42% in France and 8% in Ireland [2-3]. However, marine current turbine systems are exposed to environmental constraints due to their geographic location weather conditions (immersed systems). These constraints make marine systems suffering from higher failures rate mainly related to the blades, the electric generator, and even the power converter. Moreover, industrial surveys have presented that about 70% of converter faults are related to power switches [4-5]. This rate will increase if these faults are taken into account and can lead to the performances degradation of the whole system and its accelerated aging process [6-7]. Indeed, despite the fact that Insulated Gate Bipolar Transistors (IGBTs) are rugged, they suffer from failure due to excess thermal and electrical stress. These failures can be broadly categorized as short-circuit faults, open-circuit faults, and intermittent gate misfiring faults. In fact, IGBT’s open-circuit faults are usually linked to the loss of bonding wires of the control signal or to a short-circuit fault causing rupture of the transistor [8]. Moreover, this fault can arise when the switches are destructed by an accidental over 1

Ecole Nationale d’Ingénieurs de Sousse, UR ESIER, Sousse, Tunisia (e-mail: [email protected]) University of Brest, FRE CNRS 3744 IRDL, Brest, France (e-mail: [email protected]) 3 ISEN Brest, FRE CNRS 3744 IRDL, Brest, France (e-mail: [email protected], [email protected]) 4 Shanghai Maritime University, 201306 Shanghai, China 5 Ecole Nationale d’Ingénieurs de Monastir, UR ESIER, Monastir, Tunisia (e-mail :[email protected]) 2

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J. Electrical Systems 13-3 (2017): 472-488

current or a fuse connected with series for short protection is blown out. In this context, when an open-circuit fault occur, the converter cannot synthesize balanced output voltages, hence providing large torque ripple and increasing current harmonics distortion [9-10]. In the literature, several fault-tolerant topologies have been studied to allow the continuous operation of the converter and to ensure the behavior of the marine current turbine system after a fault occurrence [11-12]. Two solutions have been proposed [13]; a first solution consists in incorporating a fourth converter leg in order to isolate the faulty one by using isolating devices and replacing it with the fourth one via connecting devices. The second solution consists in modify the standard converter topology by adding extra bidirectional switches to bypass the faulty IGBT [14]. The second solution will be adopted. In fact, in the case of an open-circuit fault, conventional control techniques are very sensitive to faulty conditions and their consequences. Therefore, robust fault-tolerant control techniques are needed. In the literature, many fault-tolerant control strategies have been proposed such as the input-output linearization control [15], the passivity-based control [16], the backstepping control [17-18], and the second-order sliding modes [3]. The backstepping control and the second-order sliding mode control strategies have been widely studied and developed for the control and state estimation problems. Indeed, these techniques achieve a good performance in both steady and transient modes, even in the presence of load torque disturbances and parameter variations [19], [3]. In this context, the main objective of this paper is firstly to propose a fault-tolerant structure that require minimum hardware modifications and allow bypassing the impact of an open-circuit fault. Second, a backstepping control and a second-order sliding mode control strategies will be applied in faulty conditions. However and after a comparison between these two techniques, the second-order sliding mode control will be adopted as a solution of choice for a PMSG-based MCT fault tolerant control when dealing with the generator-side converter open-circuit faults [20]. This paper is organized as follows; in section II, a description of the MCT modeling and its control is given. In section III, fault-tolerant structures are discussed. In section IV, backstepping and second-order sliding mode control strategies are analyzed. In section V, simulation results are presented. The conclusion is presented in section VI. 2. Notation Notations used throughout the paper are given below. Indexes: Stator index s d,q Synchronous reference frame index Constants: MCT MPPT PMSG IGBT PWM

Marine Current Turbine Maximum Power Point Tracking Permanent Magnet Synchronous Generator Insulated Gate Bipolar Transistor Pulse width modulation Mechanical power

473

S. Toumi et al : A comparaison of fault-tolerant control strategies…

λ β

ρ r vt

R

L p

Jt

Ω ω

f ψ φ , φ , γ , γ , Γ , Γ Γ , Γ α , α , β , β

Power coefficient Tip speed ratio Blade pitch angle Fluid density Turbine radius Tidal velocity Voltage (Current) Mechanical (electromagnetic) torque Resistance Inductance Pole-pair number Permanent magnet flux Turbine and PMSG inertia Turbine speed Electrical speed Viscosity coefficient Flux Spring tide current velocity Neap tide current velocity Uncertain bounded functions Lower bound of φ1 and φ2 respectively Lower bound of γ1 and γ2 respectively Upper bound of γ1 and γ2 respectively Positive constants

3. Marine current turbine modeling and control 3.1. MCT modeling Figure 1 depicts an MCT basic structure. This structure is composed by a marine turbine, a permanent magnet synchronous generator coupled to a DC-bus via a three-phase converter.

Fig. 1. Marine current turbine basic structure.

3.1.1. Resource model

474


The gravitational interaction of the earth, the moon and the sun is created the marine currents [21]. Since the moon is so much closer to the earth than the sun, its pull has more influence on the tides; marine currents are resulted about 32% from the sun and 68% from the moon. In fact, the moon gravitational pull forces the ocean to bulge outwards on opposite sides of the earth, which causes a increase in the water level in places that are aligned with the moon and a decrease in water levels halfway between those two places. This rise in water level is accompanied by a horizontal movement of water called the tidal current [22]. Tidal current data are given by the SHOM (French Navy Hydrographic and Oceanographic Service, Brest, France) and are available for various locations in chart form. The available SHOM charts give, for a specific site, the current velocities for spring and neap tides. These values are given at hourly intervals starting at 6h before high waters and ending 6h after. Therefore, knowing tide coefficient, it easy to derive a simple and practical model for tidal current velocities vt. vt = vn t +

(C − 4 5 ) ( v s t − v n t ) 95 − 45

(1)

Where C is the tide coefficient which characterize each tidal cycle (95 and 45 are, respectively, the spring and neap tide medium coefficient). This coefficient is determined by astronomic calculation of earth and moon positions. vst and vnt are, respectively, the spring and neap tide current velocities. For example, 3 hours after the high tide in Brest, vst = 1.8knots and vnt = 0.9knots; therefore, for a tide coefficient C = 80; vt = 1.58knots. Then, this first-order model is used to calculate the tidal velocity each second. 3.1.2. Marine turbine model The conversion of kinetic energy into mechanical energy is achieved by using a marine turbine rotor. A marine turbine mechanical power has the same dependence to that of a wind turbine and is given by [23-24] Pm =

1 C ( λ, β )ρπ r 2 vt3 2 p

(2)

Cp represents the rate of mechanical power extracted by the turbine from the fluid stream. For typical MCTs, the maximum value of Cp for normal operation is estimated to be in the range of 0.35-0.5 [25]. For a given turbine, the Cp can be expressed as an expression of the blade pitch angle β and the tip speed ratio λ (3) [26-27]. In this paper, the MCT is not pitched. Figure 2 illustrates the Cp curve for simulations. λ =

rΩ vt

(3)

475


Fig. 2. Marine current power coefficient curve.

3.1.3. Generator model The PMSG was chosen as a candidate for the system [28] thanks to its compactness, its high efficiency and the possibility to eliminate gearbox, in case of a direct-drive system, which reduces maintenance [29-30]. Dynamic modeling of PMSG can be expressed in d-q reference system as follows [31]  dΩ Jt =  dt  d i R  sd = −  dt L di  sq = − R i  dt L sq   Te m 

T m − Te m − f Ω is d + p Ω is q +

φa

− p Ω is d − p L 3 p φ a is q = 2

(4)

vsd L +

vsq L

3.1.4. Generator-side converter model As shown in Fig. 3, the generator-side converter is composed by three legs, each leg features two semiconductor switches (Tk, Tk+3, k=1, 2, 3) with antiparallel connected freewheeling diodes (Dk, Dk+3). The switches of the same leg are controlled by a PWM using logic control signals Sk (k = 1, 2, 3) also known as gate signals [32]. The kth gate signal denoted Sk switch is defined by

1 ! "# $#% &' "!! 0 ! &' "# $#% "!!

(5)

3.2. MCT control The control system of marine current turbine based on the traditional linear PI controller used in conventional field oriented control technique, mainly consist of a Maximum Power Point Tracking (MPPT) control, PI speed controller, two current PI controllers, abc/dq conversion, dq/abc conversion and a PWM bloc to give the control signals of the converter switches. The control scheme is presented in Fig. 4.

476


Fig. 3. Generator-side converter topology.

vtide vtide Ω PM SG

DC Bus PWM PW M

M arine turbine

θ p

∫

vs1

PARK i sd

PI

vsd-ref vsd1!

T em-ref

Ωref Ω réf Ω

PI

2! 3p ! "φ#a

vs3

PARK -1

i sq

i sd-ref M PPT

vs2

vsq-ref D ecoupling

vsq1!

i sq-ref PI

Fig. 4. Marine current turbine control scheme based on PI controller.

The control system is defined in the s-domain as follows  1 (v sd + ω ψ sq )  isd = R + L s  1 i = (v − ω ψ sd )  sq R + L s sq

(6)

where  ψ sd = Lisd + φa   ψ sq = Lisq

(7)

The electromagnetic torque is given by this equation

477


Tem =

3 p φa isq 2

(8)

Indeed, an MPPT-based variable speed technique has been adopted for the MCT [33]. This strategy consists in controlling the rotor speed to maintain the turbine tip ratio λ at its maximum value in order to obtain a maximum value of the turbine power coefficient Cp and finally achieve the expected maximum power by the MCT. The expression of the turbine speed reference calculated by the conventional MPPT is given by [24] Ω ref =

v t λ opt

(9)

r

Therefore, the reference of the rotational speed control loop is adjusted so that the turbine will operate around the maximum power for the current tidal velocity. If the tidal velocity exceeds 2.3m/s (given by the SHOM), the extracted power will be limited to 7.5kW. The turbine extractable power under different tidal velocities is calculated by (2). The d-axis current reference is maintained equal to zero in order to minimize resistive losses and therefore minimize current for a given torque [34], so, the generator torque can be controlled directly by the quadratic component (8) [35]. The q-axis current reference is calculated by the speed loop controller [36]. The required d-q components of the converter voltage vector are derived from two PI currents controllers. Then, a decoupling block is added the compensation terms to improve the dynamic response. Finally, PWM bloc is used to generate the control signal to implement the vector control of the generator. 4. Proposed fault-tolerant strategies 4.1. First structure As shown in Fig. 5, the first structure presents a four-leg converter with the capability of isolating a faulty one using specific devices such as fuses in the figure and activating the fourth auxiliary leg. There is no modification in the digital control code apart from the deviation of the switching commands from the faulty leg to the fourth one. This technique could cause adverse effects to the behavior of the machine and presents a large number of switches, which makes this solution expensive. 4.2. Second structure The second structure is illustrated by Fig. 6, it is based in a few modified standard converter consists in adding three Triac (pair of back-to-back thyristors) in series with the three phases generator and connecting it to the mid-point of the split DC bus capacitor link. This strategy is known with its advantages as simple circuit topology, good compatibility, low-cost and strong fault-tolerant capability. In healthy conditions, the three Triacs are switched off witch makes the converter operate in exactly the same way as that of a standard converter [37]. In faulty conditions, for example, when an open-circuit fault is sensed in the leg of the phase A, the control algorithm sends the gate driven signals out to turn on the Triac TRa which given a post-fault topology with the phase A terminal of the PMSG connected directly to the middle point of the DC bus capacitor.

478


5. Proposed fault-tolerant control Due to PI control sensitivity to faulty conditions that leads to lack of robustness and effectiveness [3], [38], some non linear control such as the backstepping control and the second-order sliding mode control are adopted as solution of choice for a PMSG-based MCT fault tolerant control when the converter deals with switches open-circuit faults.

Fig. 5. First fault-tolerant structure for converter.

Fig. 6. Second fault-tolerant structure for converter.

5.1. Backstepping control The Backstepping control is applied to replace the traditional linear PI controller used in conventional field oriented control strategies. It is based on Lyapunov theory to ensure the stability of the whole system. The main idea of the Backstepping control design is to decompose a complex nonlinear control design into smaller and simple ones [39]. Its algorithm is divided into two steps, which each step gives a reference for the next step. According to (4), the dynamic modeling of PMSG can be expressed by  dΩ  dt   disd =   dt  disq =   dt

= f1 v f2 + sd L v sq f3 + L

(10)

where the functions f1 to f3 are defined as

479


 1 T −  f1 = Jt m   R f2 = −  L  R   f 3 = − isq L 

1 1 Tem − fΩ Jt Jt isd + p Ω isq

(11)

φ − p Ω isq − p a L

Step1: The rotor speed tracking error is defined by e Ω = Ω ref − Ω

(12)

The derivate of (12) gives & & e&Ω = Ω ref − Ω

(13)

(13) can be rewritten as follows & e&Ω = Ω ref − f1

(14)

A first Lyapunov function is defined as v1 =

1 2 e 2 Ω

(15)

Using (12), the derivate of (15) gives & v&1 = eΩ (Ω ref − f1 )

(16)

(16) can be defined as follows 2 v&1 = −k1eΩ

(17)

(17) must be negative definite, so k1 should be positive to ensure a stable tracking which gives

e&Ω = −k1eΩ

(18)

Then, the quadratic current reference can be deduced as follows i sq−ref =

2J t Tm f & ( − Ω − k1eΩ − Ω ) réf 3 pφ a J t Jt

(19)

Step 2: The direct and the quadratic current tracking errors are defined by esd = isd − ref − isd  e = isq − ref − isq  sq

480

(20)


or isd-ref = 0 and according to (19), (20) becomes  esd = −i sd   2Jt Tm f &  esq = 3pφ ( J − J Ω − k1eΩ − Ωréf ) − i sq a t t 

(21)

The derivate of (20) gives / . ,

012 −412 − 5

1678 1

9

0:2 4:;<= 2 − 4:2 4:;<= 2 −5

167> 1

9

(22)

Using (10), (22) becomes 012 −! +

B ? A 0:2 4:;<= 2 − !' + 7> A78

B

(23)

A second Lyapunov function is defined as

v2 =

1 2 2 2 (e Ω + esd + esq ) 2

(24)

The derivate of (24) gives v&2 = eΩe&Ω + esde&sd + esqe&sq

(25)

According to (23), (25) can be rewritten as follows 1 1 2 − k e2 − k e2 + e (k e + i& v&2 = −k1eΩ 2 sd 3 sq sd 2 sd sq−ref − f3 − vsq ) + esq (k3esq − f2 − vsd ) L L

(26)

where k2 and k3 are positive parameters to ensure a faster dynamic of the rotor speed and the stator currents. (26) should be negative definite to ensure the stability tracking, so, quantities between parenthesis must be equal to zero  1  k2 esd + i&sq−ref − f3 − vsq = 0  L  1  k3esq − f2 − vsd = 0  L 

(27)

Then, the stator voltages are deduced as follows   vsq = L(k2 esd + i&sq−ref − f3 )  vsd = L(k3esq − f2 )  

(28)

5.2. Second-order sliding mode control

481


Second-order sliding mode is clearly appropriate to achieve simple control algorithms and chattering-free phenomenon in a finite-time [38]. In conventional sliding mode control design, the control target is to move the system state into sliding surfaces S = 0. Second-order sliding mode control aims for 2 0 where the system states converge to zero at the intersection of S and 2 in the state space. The proposed control approach will be designed using the super-twisting algorithm [40]. This algorithm is divided into five steps. First, the speed reference is given by the MPPT strategy and the optimal electromagnetic torque, which ensures the rotor speed convergence to Ωref, is computed using

;<= = − CDE − E<= F − G E<= 2 − !E<=

(29)

where α is a positive constant. Then, the current references are deduced as follows

1;<= = 0 ? :;<= =

'HI

(30)

Then, the second-order sliding mode algorithm is used to ensure the currents convergence to their references, the sliding surfaces is given by

= 1 − 1;<= = : − :;<=

(31)

The derivate of (31) gives

J

2 = 41 2 − 41;<= 2 K = L (M, N ) + O (M, N)1

(32)

and

2 = 4: 2 − 4:;<= 2 J K = L (M, N) + O (M, N):

(33)

where φ1(t,x), φ2(t,x), γ1(t,x) and γ2(t,x) are uncertain bounded functions that satisfy

L > 0; |L | > ; 0 < T < O < T L > 0; |L | > ; 0 < T < O < T

(34)

The proposed second order sliding mode controller contains two parts [41]

1 = U + U = V + V :

(35)

where

U2 = −C WX# ( ) U = −Y | | WX# ( ) and

482

(36)


V2 = −C WX# ( ) V = −Y | | WX# ( )

(37)

To ensure the convergence of the sliding manifolds to zero in finite-time, the gains can be chosen as follows / . ,

Y6 ≥

C6 >

HZ

[\Z HZ [`Z (aZ &HZ ) 4 _ ; [\Z [\Z (aZ ;HZ )

0 < c ≤ 0.5

= 1, 2

(38)

6. Performance evaluation results The overall control system based on the FTC strategy is shown in Fig. 7. The simulated PMSG-based MCT parameters are given in the Appendix. Figure 8 represents an example of marine current velocity in the Raz de Sein (potential site for the MCT project off the coast of Bretagne in France) during 20s based on tidal current data given by the French Navy Hydrographic and Oceanographic Service (SHOM). It can be seen that the peak marine current velocity can reach 2.3m/s. Waveforms given by Figs. 9 to 11 show the three phase currents in different faulty conditions. At t = 0.7s, a faulty condition is considered and applied to the upper switch (T1) by keeping gate-signal S1 permanently in ‘off’ state. It is observed that the phase current ia is no more negative. We also note that the healthy phases b and c don’t have the same peak current value. At t = 0.8s, a multiple open-circuit fault for the upper switch (T1) and the lower switch (T4) is applied, the phase current ia drops to zero. In this case, the current transient for both healthy phases b and c has the same peak current value unlike the first case. This condition is very important for using the fault-tolerant structure. Indeed, the healthy phases must withstand the current transient and the device must withstand the transient thermal stress caused by the power losses. In fact, the maximum currents peaks must not overcome the maximum admissible current of the device. At t = 0.9s, the fault-tolerant structure is used. The threephase currents represent a small increase in their amplitudes values, then, it stabilize and we obtain a three sinusoidal currents with constant frequency equal to 50Hz (Fig. 12). The PMSG generated power (Fig. 13), its rotor speed (Fig. 14), and its torque (Fig. 15) are deeply correlated with the marine current velocity waveform (Fig. 8). As shown in these figures, by using PI control, the power, the speed, and the torque have some ripple at the faults occurrences, which proves that this technique is not useful and doesn’t present any robustness and effectiveness against faults. By using Backstepping control, the ripples are smaller than the case of PI control, which proves that this technique effectively does not have a good response against generator-side converter faults. But, by using the secondorder sliding mode control, the achieved results, clearly show the system almost power and dynamic performances degradation-free in comparison to PI-based control and backstepping control. These results clearly show the high-order sliding modes superiority in terms of faulttolerant control effectiveness.

483


vtide AC-DC Ω PMSG θ

ʃ

p

MCT

DC Bus PWM Park

vs2

vs1

vs3

Park-1 i sd

i sq

Ωref

vsd-ref

vsd1

MPPT

FTC Strategy

vsq-ref

Decoupling vsq1

Fig. 7. The proposed fault-tolerant control structure. 40 30 2

20 10

1.5

ia (A)

M a rin e c u rre n t s p e e d (m /s )

2.5

1

0 -10 -20

0.5

-30 0

0

2

4

6

8

10

12

14

16

18

-40 0.65

20

0.7

0.75

0.8

40

30

30

20

20

10

10

ic (A)

ib (A )

40

0

-10

-20

-20

-30

-30 -40

0.8

0.9

1

time (s)

Fig. 10. Current ib.

484

0.95

1

1.05

1.1

0

-10

0.7

0.9

Fig. 9. Current ia.

Fig. 8. Marine current velocity.

-40

0.85

time (s)

time (s)

1.1

0.7

0.8

0.9

1

time (s)

Fig. 11. Current ic.

1.1

J. Electrical Systems 13-3 (2017): 472-488 4000

40

ia ib ic

20

3000

10

iabc (A)

Power with Second-Order SMC Power with PI Control Power with Backstepping Control

3500

P M S G P o w e r (W )

30

0 -10 -20

2500 2000 1500 1000 500

-30

0

-40 0.92

0.93

0.94

0.95

0.96

0.97

-500

0.98

time (s)

0

2

4

8

10

12

14

16

18

20

time (s)

Fig. 12. Three-phase current iabc (f = 50Hz).

Fig. 13. PMSG power.

250

40

Rotor speed with Second-order SMC Rotor speed with PI Control Rotor speed with Backstepping Control

200

Torque with Second-Order SMC Torque with PI Control Torque with Backstepping Control

35

P M S G T o rq u e (N .m )

P M S G ro to r s p e e d (rd /s )

6

150

100

50

30 25 20 15 10 5

0

0

2

4

6

8

10

12

14

16

18

20

0

0

2

4

6

8

time (s)

10

12

14

16

18

20

time (s)

Fig. 14. PMSG rotor speed.

Fig. 15. PMSG torque.

Appendix: PMSG-based MCT parameters.

MCT

PMSG

Converter

Parameter

Value

Turbine blade radius

0.87m

Number of blades

3

Fluid density

1027.68kg/m3

Rated Power

7.5 kW

Stator resistance

0.173mΩ

d-axis inductance

0.951mH

q-axis inductance

0.951mH

Permanent magnets flux

0.112Wb

System total inertia

1.3131*106 kg.m2

Viscosity coefficient

8.5 10-3Nm/s

Turn-on time

0.13µs

Turn-off time

0.445µs

Dead-time

4µs

Duty-cycle frequency

5kHz

DC-bus voltage

600V

7. Conclusion This paper dealt with the comparison of three fault-tolerant approaches including classical PI, backstepping, and high-order sliding mode controls for a permanent magnet 485


synchronous generator-based marine current turbine experiencing open-circuit fault in power switches of its generator-side converter. These three control approaches and more specifically the second-order one have adopted for fault-tolerant control purposes to maintain the marine system optimal power and dynamic performances under faulty conditions. The achieved results clearly show the superiority of the second-order sliding mode control in terms of fault-tolerance effectiveness over the other strategies. Further investigations should however be carried out to evaluate other possible faulttolerant control approaches such as model predictive control as recently shown to be effective for marine renewable applications [42]. Moreover, investigations on resilient generator-side converters are also expected [43]. References [1]

[2] [3]

[4]

[5]

[6]

[7]

[8] [9]

[10]

[11]

[12]

[13] [14] [15]

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