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A Feedback Linearization Control Scheme for the Integration of Wind Energy Conversion Systems into Distribution Grids Federico Delfino, Member, IEEE, Fabio Pampararo, Renato Procopio, Member, IEEE, and Mansueto Rossi
Abstract—This paper focuses on the development of a control strategy for integration of wind energy conversion systems (WECS) into the electrical distribution networks with particular attention to the combined provision of energy and ancillary services. Typically, a WECS is composed by a variable speed wind turbine coupled with a direct driven permanent magnet (DDPM) synchronous generator. This configuration offers a considerable flexibility in design and operation of the power unit, as its output is delivered to the grid through a fully controlled frequency converter. Here, a new control scheme to regulate electrical and mechanical quantities of such generation unit is proposed, aimed both at reaching optimal performances in terms of power delivered to the grid and at providing the voltage support ancillary service at the point of common coupling. The control scheme is derived resorting to the feedback linearization (FBL) technique, which allows both decoupling and linearization of a non linear multiple input multiple output system. Several numerical simulations are then performed in order to show how the flexibility of the DDPM wind generator can be fully exploited, thanks to the use of the FBL approach, which assures independent control of each variable and significant simplifications in controller synthesis and system operation, thus making it easier to integrate WECS into modern day smart grids. Index Terms—Direct drive, feedback linearization, permanent magnet synchronous generator, wind power.
I. Introduction
T
HE INCREASED penetration of renewable energy resources into the power delivery infrastructures is an effect of the adoption at world level of governmental policies aimed at facing climate changes and at designing a long term energy scenario where power supply systems are technologically improved to become more efficient and more “friendly” toward environmental issues [1]–[6]. Among the different renewable production technologies, wind power is the most promising for large scale applications, due to its investment costs, which are lower than the costs for power produced from other renewable systems, and thanks to the growing technological progress, which is making available Manuscript received September 15, 2010; revised February 25, 2011; accepted May 25, 2011. The authors are with the Department of Naval and Electrical Engineering, University of Genoa, Genova I-16145, Italy (e-mail: federico.
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSYST.2011.2163002
wind turbine for large-sized power plants (on shore and offshore) and, at the same time, compact and low-speed triggered systems, suitable for residential uses [7]. However, many utilities are reluctant to install significant wind capacity because of the intermittent nature of the resource, which prevents wind power plants to be controlled in the same way as conventional fossil fuel “bulk” units. Thus, research in the field is presently very focused on the development of suitable control strategies [8], [9], to improve wind power integration into distribution networks and to regulate it into a dispatchable resource. Among the different kinds of wind generation systems, those based on direct driven permanent magnet (DDPM) are gaining attention and growing fast in terms of new installations, as it is expected that current developments in gearless energy transmission with powerelectronic grid interfaces will lead to a new generation of quiet, efficient, and economical wind turbines. In these systems, optimum wind energy extraction is achieved by operating the wind turbine generator in variable-speed/variable-frequency mode, according to the wind speed, by maintaining the tip speed ratio to the value that maximizes aerodynamic efficiency. The DDPM machine, jointly with new power-electronic controls, has thus become an important and very employed actor in the distributed generation world; it allows improving reliability of the wind mill and reducing maintenance expenses, since its gearbox can be eliminated. In the light of this state-of-the-art, the aim of this paper is to present a new control scheme for integrating WECS into the power grids. In particular, the following issues are faced: 1) optimal WECS performances, i.e., tracking of the maximum power extraction from the wind turbine; 2) optimal operating conditions of the permanent magnet synchronous generator (PMSG), which works at minimum stator current; 3) DC link voltage control; 4) control of the reactive power injection into the power grid, in order to perform a voltage support at the point of common coupling (PCC); 5) voltage support during grid fault conditions. Such goals can be achieved by applying feedback linearization (FBL) technique [10]–[14] at the control synthesis stage, taking advantage of some peculiarities characterizing such a technique, as the possibility to reduce a nonlinear
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multiple-inputs, multiple-outputs system to a number of single input, single output linear systems, without resorting to mathematical approximations (like the small signal analysis); this makes it easier to design the regulators transfer functions and allows a decoupled (independent) control of each regulated variable. This paper is organized in six parts. In Section II the whole system model is derived, considering separately wind turbine, synchronous generator, machine side pulse-width modulation (PWM) inverter, DC link, network side PWM inverter and grid, while in Section III the theory necessary to apply the FBL and to synthesize the control is outlined. The next two sections present simulations results aimed at highlighting the system behavior both in normal operating conditions and in the event of faults. In particular, Section IV is devoted to a simulation campaign, performed in order to test the WECS response to wind speed fluctuations and reference variations, showing also its ability to deliver reactive power to the grid when the generated active power is low. Beside this latter kind of ancillary services, utilities and transmission system operators (TSOs) are becoming more demanding in terms of requirements the system must fulfil during low voltage and fault conditions [15]–[17]; in order to assess the performances of the proposed control scheme also when these contingencies occur, in Section V the fault ride through capacity of the system is tested using as a reference a voltage drop profile of the kind prescribed by E.ON Netz GmbH [16]. Finally, in Section VI some conclusions are drawn.
II. Wind Energy Conversion System The considered WECS consists of a permanent magnet synchronous generator driven by a wind turbine, a machine side PWM inverter, an intermediate DC circuit, and a grid side PWM inverter, as indicated in Fig. 1. In the following, the mathematical models used to represent each one of these components will be outlined. A. Wind Turbine Model The output mechanical power of the wind turbine is given by [9] 1 (1) P = ρAVw3 cp (β, γ) 2 where ρ (kg/m3 ) is the air density, A (m2 ) is the area swept by the blades, Vw (m/s) is wind speed, cp is the performance coefficient, β (°) is the pitch angle of turbine blades, and γ is the tip speed ratio expressed as follows: 2.237 · Vw γ= (2) ωmec being ωmec (rad/s) the mechanical rotor speed. The performance coefficient cp has been approximated using the following nonlinear function: 1 cp = γ − 0.022β2 − 5.6 e−0.17γ . (3) 2 When the turbine operates with β = 0, for each instantaneous wind speed, ωmec must be set to the value corresponding
to the maximum active power extraction from the wind. The value of γ that maximizes the coefficient cp for each pitch angle β is obtained by solving ∂cp 1 = 1.952 − 0.17 · γ e−0.17γ = 0. (4) ∂γ 2 Once (4) is solved in the variable γ, γopt = 11.48, one can insert the solution into [2] and then compute the optimal machine angular frequency ωopt by using the following expression: 2.237 · Vw · p ωopt = (5) 11.48 where p is the pole pair of the generator (ωopt = p · ωmec ). If the active power or the mechanical speed becomes greater than their rated value, the pitch control mode (β#0) is activated acting as a limiter for those quantities. B. PMSG Model The PMSG dynamic equations are expressed in the “d-q reference” frame. The model of electrical dynamics in terms of the machine d-q axes voltages and currents is v∗md = Rs imd + Lsd imd + ωe Lsq imq
(6)
v∗mq = Rs imq + Lsq imq − ωe Lsd imd − ωe p
(7)
while the model for the mechanical dynamic is J Ce − Cm = ωe p
(8)
where the electromagnetic torque Ce can be expressed as Ce = p Lsq − Lsd imd imq − imq p (9) and the wind turbine torque Cm is defined as Cm = P ωmec .
(10)
The quantities appearing in the previous relationships are here defined as J: moment of inertia, p : main flux, Lsd , Lsq : d-q synchronous inductances, and Rs : stator resistance. C. PWM Inverter Machine Side For the machine side PWM converter, which acts as rectifier to connect the machine to the DC link, we used a first harmonic model, expressed in the “d-q reference” frame of the permanent magnet generator (11) vmd = 3/2ma /2 · VmDC · cos δ vmq = − 3/2ma /2VmDC · sin δ.
(12)
The converter d-q axes voltages vmd , vmq differ from that of the machine (v∗md , v∗mq ) because of the presence of the parameters Lfm and Rfm (see Fig. 1), modeling a series filter. In (11) and (12), ma and δ are the converter modulation index and phase. Transforming these parameters in rectangular coordinates, we can define Umd and Umq as follows: Umd = ma cos δ
(13)
Umq = −ma sin δ.
(14)
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Fig. 1.
3
Wind energy conversion system.
Equations (11) and (12) do not take into account the inverter losses; a simple way to consider these losses in the first harmonic model is to add an “equivalent resistance,” whose value is heuristically set to four thirds of the static switch resistance, Rpwm [18]. This way, and using the definitions (13) and (14), (11) and (12) have to be modified as follows: vmd = 3/2VmDC /2 · Umd − 4/3Rpwm imd (15) vmq =
3/2VmDC /2 · Umq − 4/3Rpwm imq .
(16)
D. DC Link The DC link electrical behavior is described simply by the Kirchhoff’s laws (Fig. 1) VDC = RmDC imDC +
LmDC imDC
+ VmDC
(18)
= 0. imDC + inDC + CDC VDC
(19)
E. Grid Side PWM Inverter The equations for the grid side inverter are identical to those of the machine side inverter (20) vnd = 3/2VnDC /2 · Und − 4/3Rpwm ind 3/2VnDC /2 · Unq − 4/3Rpwm inq
vnd = Rind + Lind + ωLinq + vgridd =
3/2VnDC /2 · Und (22)
vnq = Rinq + Linq − ωLind + vgridq =
3/2VnDC /2 · Unq . (23)
The d-q reference frame has been chosen so that vgridq = 0, while vgridd has been set to the rate value; this way, the active and reactive power delivered to the grid becomes Pn = vgridd ind
(24)
Qn = vgridd inq .
(25)
(17)
VDC = RnDC inDC + LnDC inDC + VnDC
vnq =
voltages vgridd , vgridq , and the quantities defined in the previous section is the following:
(21)
where Und , Unq , and Rpwm have the same meaning of the analogous quantities already defined for the previous converter. This time, the d-q reference frame adopted for the AC side converter phase voltages and currents rotates at the network angular frequency.
III. Control System In order to apply the FBL, the equations representing the system have to be rewritten in the form [10] x = f (x) + g (x) u (26) y = h (x) where u is the input variables vector, x is the vector of the system state variables, and y the output variables vector. Based on (6), (7), (8), (19), (22), and (23), and neglecting the DC link series parameters (thus VmDC = VDC = VnDC and the DC link model reduces to a power balance between the converters and the DC link capacitor), the system state vector can be identified as follows: T (27) x = imd imq ωm VDC ind inq
F. Grid Model
while the system input variables are represented, in our case, by the converter parameters Umd , Umq , Und and Unq T u = Umd Umq Und Unq . (28)
The system is supposed to be connected to an infinite bus through a resistance R = Rtr− LV/MV +Rfn +Rl +Rtr− MV/HV and an inductance L = Ltr− LV/MV + Lfn + Ll + Ltr− MV/HV modeling two (LV/MV and MV/HV) transformers longitudinal parameters, a series filter and a MV line parameters (as seen from the transformer low voltage side), respectively. With the equivalent resistance Rpwm also included in R, the link between grid axes
As a consequence, considering the equations derived in the previous sections, and defining Lmd = Lsd + Lfm (29) Lmq = Lsq + Lfm (30) Rm = Rs + Rfm + 4 3 Rpwm .
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f(x) and g(x) can be written in the following forms: −Rm imd − ωm Lmq imq /Lmd ⎢ ⎢ 2 −Rm imq + ωm Lmd imd + ωmp /Lmq ⎢ p Lsq − Lsd imd imq − imq p /J − pCm /J f (x) = ⎢ ⎢ 0 ⎢ ⎣ −Ri − ωLi nq − vpccd /L nd −Rinq + ωLind /L
⎤
⎡
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
(31) ⎡
VDC /Lmd 0 √ ⎢ 3 ⎢ 0 ⎢ g (x) = √ ⎢ 2 2 ⎣ −imd /CDC 0 0
0 VDC /Lmq 0 −imq /CDC 0 0
0 0 0 −ind /CDC VDC /L 0
⎤
0 0 ⎥ ⎥ 0 ⎥ −inq /CDC ⎥ ⎦ 0 VDC /L
.
Fig. 2. Block diagram of the equivalent linearized system and of the regulators (the symbol ∗ indicates the reference values).
In a similar way, for the control output h3 = inq
(32) As system output variables, we chose the following quantities: T h (x) = ωm imd inq VDC . (33) This way, we can directly control the machine angular frequency (in order to set its value to the optimal one), the DC link voltage and the reactive power delivered to the grid [according to (25), by regulating inq ], while, by acting on imd , we can minimize the machine current. The goal of the feedback linearization is to obtain a transformed system whose states are the output variables and, eventually, some of their derivatives. This structure is achieved by considering each one of the outputs and, repeatedly, applying to it the Lie derivatives [10] along the vector f and along the vector g·u, until at least one input variable appears in the latter; as an example, for the output h1 = ωm we have to compute
Lf,h1 = ∇h1 , f = [0, 0, 1, 0, 0, 0] , f Lg,h1 = ∇h1 , gu = [0, 0, 1, 0, 0, 0] , gu = 0
(34)
where the symbol · , · represents the scalar product and ∇(.) is the gradient with respect to state variables. Since in the last expression none of the inputs appear explicitly (actually, the expression is identically zero), we have to apply the Lie derivatives once again, this time to Lf,h1 ⎧ 2 Lf,h = ∇Lf,h1 , f = ⎪ 1 ⎪ ⎪ ⎪ p2 C (ωm ) ⎪ ⎨= , 0, 0, 0 , f Lsq −Lsd imq , Lsq −− Lsd imd −p , J p Lg Lf h1 = ∇Lf,h1 , gu = ⎪ ⎪ √ 2 ⎪ Umq Umd ⎪ Umq 3p VDC ⎪ ⎩= √ Lsq −Lsd imq + Lsq − Lsd imd . − p J 8
Lmd
Lmq
Lmq
(35) As can be seen, now the inputs u1 and u2 (i.e., Umd and Umq ) appear in the last expression. For the output h2 = imd ⎧ ⎨ Lf,h2 (x) = ∇h2 , f = [1, 0,0, 0, 0, 0], f V U DC md . ⎩ Lg,h2 (x) = ∇h2 , gu = 38 Lmd
(37)
and for the control output h4 = VDC ⎧ ⎨ Lf,h4 (x) = ∇h4 , f = 0 Lg,h4√(x) =∇h4 , gu = ⎩ = − 3/8 Umd imd + Umq imq + Und ind + Unq inq /CDC . (38) Taking into account the Lie derivatives definition and (26), from the previous results it follows that [10] ⎧ ω = L2f,h1 (x) + Lg Lf h1 (x, u) ⎪ ⎪ ⎨ m imd = Lf,h2 (x) + Lg h2 (x, u) (39) i = Lf,h3 (x) + Lg h3 (x, u) ⎪ ⎪ ⎩ nq VDC = Lf,h4 (x) + Lg h4 (x, u) . Now, if we define a set of fictitious input variables Vi (i = 1, ..., 4) so that V1 = L2f,h1 (x) + Lg Lf h1 (x, u) (40) Vi = Lf,hi (x) + Lg hi (x, u) , i = 2, ..., 4 by combining (39) and (40) (i.e., by equating the two l.h.s.), it is apparent that, as anticipated, the system has been reformulated in terms of the new state variable ωm and ω m , imd , inq , and VDC , with ωm (and ωm ) depending (linearly) only on the fictitious input V1 , imd on V2 and so on (the system has also a sixth new state variable, corresponding to an “internal dynamics;” see [10] for details). The stability of the zero dynamics (sufficient to ensure the stability of the internal one) has been verified but here all the steps are not reported for simplicity. Thanks to this result, the very simple control scheme of Fig. 2 can be applied, where Rhi are the regulators. In order to employ this scheme, a relation between the actual and the fictitious inputs is needed. So, if we rewrite (40) as
(36)
So, for this output we can stop at the first order derivative.
Lf,h3 (x) = ∇h3 , f = [0, √ 0, 0, 0, 0, 1] , f Lg,h3 (x) = ∇h3 , gu = 3/8VDC Umq /L
Lg Lf h1 (x, u) = V1 − L2f,h1 (x) = TN1 (x) Lg hi (x, u) = Vi − Lf,hi (x) = TNi (x) , i = 2, ..., 4
(41)
or E (x) · u = TN (x)
(42)
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where the matrix E depends only on the system parameters (e.g., J, CDC , and so on) and x, then the required relationship is
Umd
Umq
Und
Unq
T
= E−1 (x) · TN (x) .
(43)
We verified that the matrix E(x) is invertible; this check is not reported here for brevity. As anticipated, among the reference values in Fig. 2, that referring to imd is chosen in order to minimize the stator current module (and then the generator Joule losses), for each value of the electrical torque Ce . The peculiarities of the proposed control strategy if compared with conventional ones can be highlighted as follows. Traditional controls usually adopt some sort of multi-level architecture like the one proposed in [19]; an external level (corresponding to a number of outer control loops with their P or PI regulators) is responsible for maintaining the wind turbine at the optimum speed, making at the same time the grid side converter deliver the desired reactive power and the active power corresponding to the mechanical one produced by the wind turbine (or, as an alternative to the former, performing voltage regulation). The outputs of this outer level are the reference signals for the converter axis currents, controlled by inner loops (equipped with another set of PI regulators), and constituting an intermediate control level whose outputs are the converter parameters Umd , Umq , Und , and Unq . In [19], a third level, named “internal,” is identified as the one responsible for producing, on the basis of these latter parameters, the actual control signals to the converters switches; furthermore, another control loop is used to regulate the DC link voltage. So, from an “architectural” point of view, a first difference between traditional schemes and the one proposed in this paper can be identified in the fact that this latter does not need such a “hierarchical” structure, treating the system as a whole and requiring in principle only a regulator per each control channel. Furthermore, in traditional control schemes, the “practical” decoupling, for instance, of active and reactive powers delivered to the grid is usually obtained by a proper choice of the regulators (and of the related proportional and integral gains); as an example, in [19], the steady-state decoupling of these powers is achieved by means of the two inner loop PI conventional controllers and proper feedback of the grid side converter output currents. Even if a decoupled control is implemented for the grid side converter, a cross coupling still exists between the two grid side axis currents and the DC link voltage [apparent in (22) and (23)], so this control cannot be considered as fully decoupled. This problem is faced in [19] by trying to maintain the DC link voltage as constant as possible by means of the associated PI regulator. Similar considerations hold for the scheme presented in [20], where the DC link voltage is maintained close to the specified reference level by acting on the active power delivered to the grid, in order to make it match that of the power input to the generator side converter. On the contrary, in the proposed approach, the actual decoupling of all control channels is a priori guaranteed by the FBL theory both in transient and in steady state. A third important difference can be identified which has practical implications in the control system design, i.e., in
5
TABLE I Modeled System Parameters Parameter Description Value Pm Rated generator power 2 MW Vm Rated generator voltage (L to L) 4 kV p Number of pole pairs 11 J Moment of inertia 2.525∗106 kgm2 p PM flux 166.8 Wb Lsd Stator d-axis inductance 0.367 H Lsq Stator q-axis inductance 0.250 H Rs Stator resistance 0.08 Lfn Filter inductance 33 mH Rfn Filter resistance 0.078 L Inductance between grid side conv. and grid 0.0295 H R Resistance between grid side conv. and grid 0.086 CDC DC link capacitance 100 μF
the choice of regulators types and in their proportional and integral gains settings. This task is usually accomplished by an heuristic procedure, perhaps making use of trial and error through several simulations, in a way similar to that outlined in [20] for the grid side converter controller; the proportional gain of this controller was chosen by increasing its value until borderline stability was reached and then taking the 25% of this “limit” gain to provide a conservative margin of 4. The integral gain term was then chosen as the 10% of the proportional one to ensure a small influence on the loop gain margin. The application of the FBL makes this same task straightforward; as the whole system is reduced to the elementary scheme of Fig. 2, the closed loop behavior of each control channel with a given regulator and related gain values can be predicted a priori. An application example of this feature is illustrated in Section V. IV. Simulations in Normal Operation The simulations have been performed on a real system, whose electrical parameters are listed in Table I. In order to test the efficiency of the new FBL-based control scheme, different disturbances and reference variations have been considered, with the aim to highlight the system ability to: 1) generate or absorb reactive power to or from the grid, even when the active power is low (Fig. 3); 2) respond to wind speed Vw variations (Fig. 4); 3) work at optimal current, machine side; Im decreased to the minimum value at t = 30 s (Fig. 9). As previously stated, one of the main advantages of this method is the complete decoupling of each control channel; as a matter of fact, the step variations imposed to h2 = imd at t = 30 s or h3 = inq at t = 5 s (Figs. 8, 3, respectively) to minimize the machine current in order to decrease the generator losses and to regulate the reactive power at the grid side, do not affect the machine speed (Fig. 6). This means that after the beginning of the simulation, the machine speed is set to the optimum speed value which guarantees maximum power extraction for the actual wind speed magnitude (performance coefficient cp close to its maximum value), until the wind rises
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Fig. 4.
Wind speed.
Fig. 5.
Pitch angle of turbine blades.
Reactive power and its reference at the grid-side.
at t = 10 s, without being affected by modification of h3 . Since the new VW would make both generated power and rotor speed exceed their rated values, the pitch angle is increased (Fig. 5) in order to limit the rotor speed. As anticipated, the variation of h2 at t = 30 s does not affect the machine speed, which remains constant till the wind decreases to 5 m/s (t = 80 s), the pitch angle is set back to zero and the speed control loop regulates ωm in order to reach the new optimal value. Fig. 7 shows that both the active power Pm generated by the machine and that delivered to the grid Pn , follow the behavior of ωm , as expected. As far as the behavior of the reactive power delivered to the grid is concerned (Fig. 3), since the regulator is purely proportional and the transfer function between V3 and h3 = inq is an integrator, the response of the control loop (the third one in Fig. 2) is that of a simple pole, whose time constant can be tuned by varying the regulator proportional gain; this means that the closed-loop response of this control channel can be “shaped” in a very straightforward way. Similar considerations could be done for the other control channels, but the feature is of particular interest for this one, as the reactive power, being an important ancillary service, is subjected to stringent regulations by system operators [17], [18], especially in terms of the system response time when given reference variations are considered; the developed control scheme can help the designer in fulfilling these requirements at the control synthesis stage. Most importantly, by comparing Figs. 3 and 7, it is evident that every variation of the active power delivered to the grid has no effect (not even transient) on the reactive power (and vice versa); when, after about 80 s, the active power falls below 0.2 MW (i.e., below the 10% of the rated power), the system continues to inject into the grid the same value of the reactive power till t = 100 s when, in response to a reference variation, the reactive power exchanged with the grid becomes negative. This latter result highlights the system ability to generate or absorb the required value for the reactive power, even if the active power is low. Finally, Fig. 9 shows the effective reduction of machine current (−6%) comparing a control which would impose imd = 0 and the proposed approach. The picture is related to the generator working point at t = 50 s. The red line is
the hyperbole defined by (9), that can be seen as a constraint (imd and imq values must ensure the required electromagnetic torque), while the blue line is the circle that represents the current absolute value. As a matter of fact, the curves corresponding to constant absolute values of the machine current are circles in the imd , imq plane; among them, the one identifying the allowable minimum for the current module is the one tangent to (9); this is because the function gradient and the constraint gradient have to be parallel in the minimum point. As a consequence, the couple (imd , imq ) that minimizes the machine current, providing at the same time the required electromagnetic torque, is the one identified by the label “new working point” in Fig. 9. Figs. 8 and 10 show how, in response to the step imposed to h2 = imd at t = 30 s, imq , after a transient, reaches the “optimum” value corresponding to this point.
V. Behavior During Fault Ride Through Fault ride through capabilities is nowadays demanded by a number of TSO grid codes [15], [16] both for conventional and renewable generation units. Prescriptions differ considerably in terms of the shape of the limit curves for the voltage [17] (which identify the severest voltage drop the generation unit must withstand) and also in terms of the behavior the generator must comply with during the fault (essentially, the active and reactive currents to be injected into the grid). Here, the voltage limit curve (Fig. 11, VPCC ) and the prescription about the reactive current to be delivered as indicated
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Fig. 6.
Machine angular frequency and its reference (optimal value).
Fig. 9.
Fig. 7.
Active power at machine and grid side.
Fig. 10.
Reactive current at machine side.
Fig. 8.
Active current at machine side.
Fig. 11.
Voltage profile requested by E.ON for fault ride-through.
by E.ON Netz [16] are taken as a reference. In particular, as far as the latter aspect is concerned, for a voltage drop/rise (with respect to the rated value) exceeding a dead band of ±10%, the reactive current fed to the grid must be equal to (V − grid− pre − fault − V − grid) · In− rated Inq− ref = 2 · V − grid− rated +Iq− pre−fault (44) while for a drop greater than 50%, at least the rated value must be guaranteed. Fig. 12 graphically represents the constraint imposed by (44). Furthermore, the voltage control must take place within 20 ms after fault recognition, by providing the required current.
7
Machine current minimization.
As illustrated in Fig. 11, the fault ride through transient takes place at t = 0 s; the grid voltage drops to zero and in response, the control system raises the reference for Inq from the pre-fault value to the rated one (Fig. 15). The actual value of Inq follows its reference with a time behavior given by the third control loop sketched in Fig. 2. The resulting voltage support action can be appreciated in Fig. 11; as can be seen, the PCC experiences a voltage drop less severe than the one affecting the grid. Reactive and active powers delivered to the grid during the fault are shown in Figs. 13 and 14, respectively; it can be observed that the reactive power fed to the grid does not
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Fig. 12. Principle of voltage support by reactive current injection during grid faults specified by E.ON (reproduction from [16]).
Fig. 13.
Reactive power at the PCC.
vanish, thanks to the just highlighted voltage support at the PCC. After 150 ms, the grid voltage starts rising linearly and, when the 0.5 pu value is reached, the reactive current is decreased as prescribed by (44); in the same time interval, the active power increases and, after a transient, finally reaches the pre-fault value. On the contrary, the final values of both reactive power and Inq differ from the pre-fault ones as, according to the prescribed limit curve, the grid voltage after the fault is lower than 0.9 pu and, as a consequence, the system must continue to deliver reactive power. The cited constraints about the control system response time of 20 ms can represent an example of how easily the system transient behavior can be “shaped,” thanks to the inherent simplicity of the block diagram of the equivalent linearized system in Fig. 2. Using a purely proportional regulator, the Inq closed loop transfer function is simply F (s) =
RInq RInq /s = 1 + RInq /s s + RInq
(45)
i.e., a simple pole whit time constant τ = 1/Rinq ; so, if we consider the steady state reached after, say, 4τ, we can calculate the value of Rinq that allows us to fulfill the constraint 0.02 s = 4 · τ → RInq =
4 = 200. 0.02
(46)
Fig. 14.
Active power at the PCC.
Fig. 15.
Reactive current at the grid side.
Fig. 16. Reactive current at the grid side (first 50 ms of the transient) for different Rinq values.
Fig. 16 shows (in an extended view of the first 50 ms of the transient) the response obtained for Inq with different values of Rinq ; the diagram confirms the obtained value. VI. Conclusion and Perspectives of Future Work This paper discussed issues related to the management of wind renewable energy in distribution networks. The presented control scheme, together with the mathematical model needed for its implementation, offers the possibility of a fully decoupled control of the main variables which characterize WECS
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. DELFINO et al.: A FEEDBACK LINEARIZATION CONTROL SCHEME FOR THE INTEGRATION OF WIND ENERGY CONVERSION SYSTEMS
operation, allowing to regulate the reactive power injected into the grid independently from the maximum power point tracking and maintaining, at the same time, the DC link voltage at its rated value and the generator at its maximum power factor. Moreover, the very simple system structure resulting from the application of the FBL greatly simplifies the regulators synthesis, thus making it easier to meet regulatory constraints on control loop dynamic behavior. It should be underlined that such features can help integrating wind distributed generation resources in modern smart grids, in view of their ever growing application both for active power production and ancillary services provision [21]. Future research activities will be devoted to the extension of the presented approach to systems equipped with short-term storage for power smoothing applications.
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[19] M. G. Molina, A. G. Sanchez, and M. Rizzato Lede, “Dynamic modeling of wind farms with variable-speed direct-driven PMSG wind turbines,” in Proc. IEEE/PES T&D Transmission Distribution Conf. Expos. Latin America, Nov. 2010, pp. 1–8. [20] G. Ramtharan, A. Arulampalam, J. B. Ekanayake, F. M. Hughes, and N. Jenkins, “Fault ride through of fully rated converter wind turbines with AC and DC transmission systems,” IET Renewable Power Generation, vol. 3, no. 4, pp. 426–438, 2009. [21] H. Weber and M. Kleimaier, “Grid integration of wind generation,” in Proc. Int. CIGRE’ Symp. Integr. Wide-Scale Renewable Resources Into Power Delivery Syst., Jul. 2009, pp. 1–6.
Federico Delfino (M’03) was born in Savona, Italy, on February 28, 1972. In 1997, he received the M.S. degree (with honors) in electrical engineering and the Ph.D. degree, both from the University of Genoa, Genoa, Italy, in 1997 and 2001, respectively. He is currently an Associate Professor with the Department of Naval and Electrical Engineering, University of Genoa. He is the author or co-author of more than 90 scientific papers published in reviewed journals or presented at international conferences. His current research interests include mainly power system transients, integration of renewables into the power delivery systems, and smart power grids. Dr. Delfino is a member of the European Commission Task Force on Smart Grids—Expert Group 3: Roles and Responsibilities of Actors involved in the Smart Grids Deployment and a member of the Italian Expert Committee on Energy Efficiency, at the Economic Development Ministry.
Fabio Pampararo was born in Genova, Italy, on February 14, 1984. In 2008, he received the M.S. degree with honors in electrical engineering from the University of Genoa, Genova, where he is currently pursuing the Ph.D. degree with the Department of Naval and Electrical Engineering. He works on power quality improvement in distribution networks, electric machine modeling, power systems control, and integration of renewables into the power delivery system. He is the author or coauthor of more than ten scientific papers published in reviewed journals or presented at international conferences.
Renato Procopio (M’03) was born in Savona, Italy, on March 6, 1974. He received the Bachelors cum laude degree in electrical engineering in 1999 and the Ph.D. degree in 2004, both from the University of Genoa, Genova, Italy. He is currently a Researcher with the Department of Naval and Electrical Engineering, University of Genoa. He works on power systems control and optimization, power quality improvement in distribution networks, and power system transients. He is the author or co-author of more than 80 scientific papers published in reviewed journals or presented at international conferences.
Mansueto Rossi was born in Savona, Italy, on April 10, 1974. In 2000, he graduated cum laude in electrical engineering from the University of Genoa, Genova, Italy, where he received the Ph.D. degree in 2004. He is currently a Researcher with the Department of Naval and Electrical Engineering, University of Genoa. He is the author or co-author of more than 80 scientific papers published in reviewed journals or presented at international conferences. His current research interests include power system transients, smart power grids, and power system control and optimization.
