Detailed Description
1. Method for acquiring expected rotating speed of wind turbine
(1) Wind turbine output characteristics
The mechanical energy output by the wind turbine is
Pm=0.5ρπR2Cpv3(1)
Cp=0.5176(116/β-0.4θ-5)exp(-21/β)+0.0068λ (2)
In the formula, PmIs the power of the wind turbine; cpIs the wind energy utilization coefficient; λ is tip speed ratio; theta is a pitch angle; v is the wind speed. Defining tip speed ratio λ of
In the formula, ωmIs the wind turbine rotor speed (rad/s); r is the wind turbine blade radius.
According to the formula (2), CpIs a nonlinear function of λ and θ, and at rated wind speed, θ is usually made 0, so CpOnly with respect to lambda. By calculation, when λ ═ λoptWhen not equal to 8.1, Cp=Cpmax0.488. At this time, the maximum power obtained by the wind turbine is as follows:
Pmax=0.5ρπR2Cpmaxv3(5)
from the tip speed ratio definition of equation (4), at the optimum tip speed ratio λ ═ λoptWhen the speed is 8.1, the expected rotating speed of the wind turbine is as follows:
thus, in theory, the maximum output mechanical torque T of the wind turbinemIs composed of
Or
(2) Direct-drive PMSM wind power system MPPT control
When the wind power generation system operates, the rotating speed of the wind turbine needs to be controlled, namely when the electromagnetic torque T iseMechanical torque TmAnd viscous friction torque B omegamThe conditions are satisfied: t ism-Te-BωmWhen the value is 0, the wind power system enters a steady state. Neglecting viscous friction torque B omegamWhen desired, the desired speed of the wind turbine may be defined as
Wherein,(constant) and
Te=1.5pniq[id(Ld-Lq)+ψf](10)
under a synchronous rotating coordinate system d-q, the mathematical model of the PMSM is as follows:
physical significance of each parameter: u. ofd、uqD-q axis components of the stator voltage, respectively; i.e. id、iqAre the d-q axis components of the stator current, respectively; l isd、LqRespectively d-q axis inductance components (H); rsIs the stator resistance; psifIs the rotor permanent magnet flux linkage (Wb); omegamIs the mechanical angular velocity (rad/s) of the fan and the electrical angular velocity ω of the motoreIs omegae=pnωm;pnIs the number of pole pairs; t ismIs the fan torque (Nm); b is the damping coefficient (Nms); j is moment of inertia (kgm)2)。
As can be seen from the formulas (10) and (11), the direct-drive PMSM wind generating set is a typical MIMO nonlinear strong coupling object. Wherein u isdAnd uqRespectively, the control input, T, of the systemmExternal wind energy disturbance input; i.e. id、iqAnd ωmRespectively, are the status outputs of the system. For the purpose of theoretical analysis, the constant parameters were defined as: b0=-1.5pnψfAnd the associated perturbation components are: d1=(pnLqiqωm-Rsid)/Ld,d2=-(pnLdidωm+pnψfωm+Rsiq)/Lq,d3=[Tm-Bωm-1.5pnid(Ld-Lq)]The system (11) can then be defined as a perturbing system:
wherein, | d1|<∞、|d2|<∞、|d3|<∞。
Considering that there is a measurement error in the state quantity of the PMSM due toAnd a disturbance component d1、d2And d3There is uncertainty, and therefore, how to apply effective control to the perturbation system (12) is the core technology of the present invention, i.e., perturbation-aware control technology of MPPT.
2. Tracking Differentiator (TD)
When the wind speed changes randomly under the rated wind speed, in order to realize the maximum power point tracking of wind energy, the expected rotating speed of the fan is required to respond quickly, or the expected rotating speed of the fan is required to change along with the change of the wind speed. Since the desired rotation speed of the fan is a time-varying physical quantity, it is necessary to obtain differential information of the desired rotation speed when the control is applied to the rotation speed of the fan. In consideration of the fact that a specific mathematical model of the desired rotational speed of the fan cannot be ascertained, it is difficult to obtain differential information of the desired rotational speed by the conventional method. Therefore, the invention uses the tracking differentiator technology to obtain the tracking signal of the expected rotating speed of the fan and the differential signal thereof, on one hand, the difficult problem that the differential information of the expected rotating speed of the fan is difficult to obtain can be effectively solved, and on the other hand, the contradiction between rapidity and overshoot existing in the control process can be effectively solved. The specific method comprises the following steps:
(1) tracking differentiator technique
Let the fan expect an angular velocity ofAnd v is1And v2Are respectivelyAnd a differential signal, defining a tracking error asThe corresponding tracking differentiator (TDm) model is then:
wherein z isv> 0 is the gain factor of TDm, as in FIG. 1.
(2) Tracking differentiator stability analysis
Theorem 1. assume that the desired acceleration of the wind turbine is bounded:then if and only if zvAt > 0, the rotational speed tracking differentiator (13) is expected to be globally asymptotically stable.
And (3) proving that: error tracking based on rotational speedAnd combined with (13), there can be obtained:thus is provided with
Is provided withAnd (3) performing Las transformation on the formula (14) to obtain:
consider that: v2(s)=sV1(s)、Therefore, the temperature of the molten metal is controlled,substituting formula (15) to obtain:namely, it is
Because the system (16) is a signal at the expected rotating speedThe error dynamics system under excitation can be known according to the signal and system complex frequency domain analysis theory, when z isvThe error dynamics system (16) is globally asymptotically stable > 0, so long asThen there are:thus, the rotational speed tracking differentiator (13) is expected to be globally asymptotically stable. ByIt is known that, when t → ∞ is:as in fig. 1.
3 speed loop disturbance state estimation
(1) Rotating speed loop state observer
Using z31And z32To estimate the rotational speed omega respectivelymAnd disturbance d3. The observation error is set as follows: e.g. of the typezm=z31-ωmThen the corresponding disturbance observer DOm is:
wherein z iso> 0, thereby realizing z31≈ωm、z32≈d3As in fig. 2.
(2) Stability analysis of rotating speed loop observer
Theorem 2. assuming the disturbance state of the rotating speed ring is bounded: | d3If and only if zo > 0, the disturbance observer (17) is globally asymptotically stable.
And (3) proving that: from equation (17) and equation (12) 3, the state observation error system can be obtained as follows:
is provided withSubjecting formula (19) to Lass transformation and arrangement to obtain
The disturbance observation error system shown in the formula (20) is in a disturbance state d3The observation error dynamics system under excitation of (1) if the disturbance state is bounded: | d3If and only if z is | < ∞oThe error system (20) is globally asymptotically stable > 0, andthe disturbance observer (17) is thus globally asymptotically stable.
MPPT-aware Controller (MPPT-DPC) design
Aiming at the control problem of a direct-drive PMSM wind turbine generator, an outer ring is set for rotating speed control, an inner ring is set for current control, and the outer ring is generally set for current controlWith desired current of d-axis of inner ring being zero, i.e.
(1) Design of rotary speed ring disturbance sensing controller (DPCm)
Setting the actual mechanical angular speed of the direct-drive PMSM wind power system to omegamSince the desired angular velocity of the fan is a time-varying physical quantity, the present invention uses the TD to determine the desired angular velocityPerforming tracking and obtaining corresponding differential information, i.e. Therefore, the fan angular velocity tracking control error can be expressed as:
em=v1-z31(21)
according to equation 3 of the system (12), the differential signal with the tracking error is:
it is apparent that equation (22) is a first order Disturbance Error System (DEDS). Perturbing the state quantity i of formula 3 in the system (12)q(q-axis current) as a virtual control quantity of a rotation speed control link, and in order to make DEDS (digital imaging System) be globally asymptotically stable, the q-axis current i is definedqDesired instruction ofComprises the following steps:
wherein z ism>0、zo>0,ezm=z31-ωm. And (3) a rotating speed ring disturbance sensing controller (DPCm) as shown in figure 3 (a).
Due to the fact thatAndd-q axis current expected instructions are provided for PMSM inner loop current control links respectively, so that a theoretical basis is laid for designing an inner loop current controller, and the following are introduced respectively:
(2) d-axis current disturbance sensing controller (DPCd) design
The current tracking control error of the d axis of the inner ring is set as follows:in combination with equation 1 of the system (12), the differential signal of the error is:
it is apparent that equation (24) is a first order perturbation error system (DES). Defining the d-axis disturbance perception control law as follows:
wherein z isd>0,d-axis current disturbance sensing controller (DPCd), FIG. 3 (b).
(3) q-axis current disturbance sensing controller (DPCq) design
The current tracking control error of the q axis of the inner ring is set as follows:
in combination with equation 2 of the system (12), the differential signal of the error is:
defining a q-axis current disturbance perception control law as follows:
wherein z isq>0,q-axis current disturbance sensing controller (DPCq), fig. 3 (c).
And integrating the TDm, the DPCm, the DPCd and the DPCq together to form an MPPT disturbance perception controller (MPPT-DPC) of the direct-drive PMSM wind generating set, as shown in figure 4.
5. Disturbance perception control system stability analysis
In order to ensure the stability of the direct-drive PMSM wind power control system, a rotating speed loop disturbance sensing controller (DPCm), a d-axis current disturbance sensing controller (DPCd) and a q-axis current disturbance sensing controller (DPCq) are required to be stable. The stability of the three disturbance sensing controllers is theoretically analyzed below.
(1) D-axis current disturbance sensing controller (DPCd) stability analysis
Theorem 3. hypothesis perturbationMoving d1The method has the following steps: | d1If and only if z is | < ∞dA d-axis current disturbance sensing controller (DPCd) represented by equation (25) at > 0:
is globally asymptotically stable. Wherein the tracking control error ed=-id、LdIs the d-axis inductance component.
And (3) proving that: substituting a d-axis current disturbance perception control law (25) into a Disturbance Error System (DES) shown in a formula (24) to obtain:
is provided withIn view ofThe formula (29) is subjected to Lass transformation and is finished to obtain
The expression (30) is a disturbance d1An excited error dynamics system. Obviously, as long as | d1If and only if z is | < ∞dAt > 0, the error dynamics system (30) is globally asymptotically stable, i.e.:therefore, the d-axis current disturbance sensing controller (DPCd) shown in equation (25) is globally asymptotically stable, and is verified.
(2) q-axis current disturbance sensing controller (DPCq) stability analysis
Theorem 4. assume that the differential of the q-axis desired current is bounded:and disturbance d2The method has the following steps: | d2I < ∞, then if and only if the gain parameter zqQ-axis current disturbance sensing controller (DPCq) shown in equation (28) at > 0:
is globally asymptotically stable.
Wherein,Lqis the q-axis inductance component.
And (3) proving that: sensing and controlling law u for q-axis current disturbanceq(28) Substituting the Disturbance Error System (DES) shown in an expression (27) to obtain:
is provided withIf it is notThen there isIs then provided withIn view ofThe formula (31) is subjected to Lass transformation and is finished to obtain
Equation (32) is a bounded perturbationAn excited error dynamics system. Obviously, as long as|d2L < ∞ thus hasThen if and only if zqAt > 0, the error dynamics system (32) is globally asymptotically stable, i.e.:therefore, the q-axis current disturbance sensing controller (DPCq) shown in equation (28) is globally asymptotically stable, and is verified.
(3) Rotational speed loop disturbance sensing controller (DPCm) stability analysis
Theorem 5, suppose|d2If and only if z is | < ∞mAnd when the speed is more than 0, the rotating speed ring disturbance perception controller (DPCm) shown in the formula (23):
is globally asymptotically stable. Wherein e ism=v1-z31、v1Is the desired angular velocity of the fanV is a tracking signal of2Is thatDifferential tracking information of (z)32Is to the disturbance d3Is a state estimate of, i.e. z32≈d3。
And (3) proving that: due to disturbance of the state quantity i of formula 3 in the system (12)q(q-axis current) as a virtual control quantity of a rotation speed control link, and the control aim is to enable the q-axis current iqTracking expected command currentFrom theorem 4, as long asAnd | d2If and only if z is | < ∞qAt > 0, the q-axis current disturbance perception controller (DPCq) shown in equation (28) is globally asymptotically stable, i.e.:thus, is composed ofIt is known that, when t → ∞,the disturbance perception error system shown in an expression (22) is substituted to obtain:
setting the initial state of the rotation speed error as follows: e.g. of the typem(0) Not equal to 0, the solution of equation (33) is:
and is
Obviously, as long as|d2If and only if z is | < ∞mWhen the pressure is higher than 0, the pressure is higher,and isIndicating that the speed error can be approached to the origin from any non-zero starting point, i.e.And zmThe larger the rotation speed error is, the faster the rotation speed error approaches the origin from any initial point which is not zero, and therefore, the rotation speed loop disturbance sensing controller (DPCm) shown in the formula (23) is globally asymptotically stable and is proved to be stable.
6. Gain parameter stabilization method for direct-drive PMSM wind power MPPT control system
Because the direct-drive PMSM wind power MPPT control system not only comprises a rotating speed loop disturbance perception controller (DPCm), a current loop disturbance perception controller DPCd and a DPCq, but also comprises functional components such as a tracking differentiator and a rotating speed loop disturbance observer, and the like, 5 gain parameters are involved in the control system totally and need to be stabilized. Although theorems 1 to 5 prove that: when z isvWhen the rotation speed is more than 0, the tracking differentiator of the expected rotation speed is stable in a global asymptotic mode; when z isoWhen the rotating speed is more than 0, the rotating speed ring disturbance observer is globally asymptotically stable; when | diL [ ∞ (i ═ 1,2,3), and zd>0、zq>0、zmWhen the current loop controller and the rotating speed loop controller are both globally asymptotically stable when the current loop controller and the rotating speed loop controller are more than 0, which shows that the relevant gain parameters of the invention have large setting margin. However, in addition to ensuring the global asymptotic stability, the tracking differentiator, the disturbance observer, and the current loop controller and the rotational speed loop controller are required to have a fast response speed and a high tracking accuracy, or a high observation accuracy, or a high tracking control accuracy. Therefore, the 5 relevant parameters are required to be valued in an optimal range, and if the values are too small, the response speed is reduced, and if the values are too large, the oscillation phenomenon is caused. Setting h as an integral step length, and setting related gain parameters as follows:
(1)zd=zq=zm=zcwherein, z is more than or equal to 700c≤1000;
(2)100≤zv≤500;
(3)zo=1/(2h)。
7. Simulation experiment and analysis of direct-drive PMSM wind power control system
In order to verify the effectiveness of the disturbance perception control method of the MPPT of the direct-drive PMSM wind power generation system, the following simulation experiment is carried out. A schematic diagram of an MPPT control system of a direct-drive PMSM wind generating set is shown in fig. 5, and the influence of a PWM inverter is ignored in a simulation experiment. The relevant simulation conditions are set as follows:
(1) three-phase PMSM related parameters
pn=40,Ld=Lq=5mH,Rs=0.01Ω,ψf=0.175Wb,J=0.05kgm2,B=0.008Nms;
(2) Fan related parameter
The blade radius R is 5m, and the air density rho is 1.29kg/m3Pitch angle β is 0;
(3) disturbance perception control system related parameters
Let the integration step h be 1/4000,get zd=zq=zm=850;zv=300;zo=1/(2h)。
Example 1. permanent magnet synchronous generator speed omega at 7m/s wind speedmQuadrature axis current iqWind turbine output torque TmAnd generator electromagnetic torque TeWind energy utilization coefficient CpThe iso-curve is shown in fig. 6. FIG. 6 shows that the control method of the present invention not only has fast response speed and high steady-state tracking accuracy, but also has the maximum wind energy utilization coefficient C of the wind turbinepmaxTo 0.483.
Example 2. at the time of 2.5s, when the wind speed suddenly drops from 7m/s to 6m/s, the rotating speed omega of the permanent magnet synchronous generatormQuadrature axis current iqWind turbine output torque TmAnd generator electromagnetic torque TeWind energy utilization coefficient CpThe isocurves are shown in FIG. 7. FIG. 7 further shows that the control method of the present invention not only has fast response speed and high steady-state tracking accuracy, but also has the maximum wind energy utilization coefficient C of the wind turbinepmaxTo about 0.483. Fig. 7 verifies that the MPPT control method of the present invention has a fast tracking performance and a high tracking accuracy in an extreme case of sudden wind speed change.
Example 3 random wind speed v, permanent magnet synchronous generator speed omega in extreme case of rated random wind speed and sudden change of wind speedmQuadrature axis current iqWind turbine output torque TmAnd generator electromagnetic torque TeWind energy utilization coefficient CpThe isocurve is shown in figure 8. FIG. 8 further shows that the control method of the present invention not only has fast response speed and high steady-state tracking accuracy, but also has the maximum wind energy utilization coefficient C of the wind turbinepmaxCan reach 0.478-0.488. Fig. 8 verifies that the MPPT control method of the present invention has a fast tracking performance and a high tracking accuracy in an extreme case of a sudden change of random wind speed.
8. Conclusion
PID controllers, Sliding Mode Controllers (SMC) and Active Disturbance Rejection Controllers (ADRC) based on a cybernetic strategy (error based elimination of errors) are three major mainstream controllers widely used in the field of control engineering today. However, the gain parameter of the conventional PID controller changes with the change of the working condition state, and the disturbance resistance is lacked, so that the difficulty of parameter stabilization exists; the strong disturbance rejection capability of a Sliding Mode Controller (SMC) is obtained by sacrificing the dynamic quality of a system, so that an irreconcilable contradiction exists between the disturbance rejection capability and high-frequency buffeting; although the Active Disturbance Rejection Controller (ADRC) has strong disturbance rejection capability, the number of parameters involved in the controller is large, and some non-linear smooth functions have the problem of large calculation amount. The Disturbance Perception Controller (DPC) integrates the advantages of three main flow controllers, has the characteristics of high response speed, high control precision, good robust stability and strong disturbance resistance, has a simple structure, small calculated amount and large setting margin of gain parameters, and does not need to re-stabilize the gain parameters under the extreme condition that the working condition state is suddenly changed. Simulation results of the three examples show that under the working conditions of completely different wind speeds, the Disturbance Perception Controller (DPC) with completely the same gain parameter realizes effective control of the MPPT of the direct-drive PMSM wind power generation system, so that the correctness of theoretical analysis of the invention is verified.
The method has important theoretical and practical significance for realizing the MPPT control of the direct-drive PMSM.