The virtual inertia control (VIC) of wind turbine with directlydriven permanentmagnet synchronous generator (DPMSG) can act similarly to the conventional synchronous generator in inertia response and frequency control, thereby supporting the system frequency stability. However, because the wind speed is inconstant and changeable to a certain extent and the DPMSG is a complex nonlinear system, there are great difficulties in the virtual inertia optimal control of the DPMSG. Based on the design principle of the active disturbance rejection control (ADRC), this paper presents a new VIC strategy for the DPMSG from the perspective of power disturbance suppression in the system. The strategy helps fulfill the power grid disturbance estimation and compensation by means of the extended state observer (ESO) so as to improve the disturbanceresisting performance of the system. Compared with conventional proportionalderivative virtual inertia control (PDVIC), this method, which is of better adaptability and robustness, can not only improve the property of the DPMSG responding to the system frequency but also reduce the influence of wind speed disturbance. The simulation and experiment results have verified the effectiveness and feasibility of the VIC based on the ADRC.
1. Introduction
The wind turbine with DPMSG, which has low failure rate, high reliability and high power generation efficiency, has gradually become a dominant model in wind power industry
[1]
. At present, it can perform the maximum power point tracking (MPPT) control through the fullpower converter (FPC) for an efficient use of wind power. However, the rotating speed of the permanentmagnet synchronous generator (PMSG) is decoupled from the system frequency in this control mode, while the output power and rotating speed of DPMSG only vary with wind speed without responding to the frequency fluctuation. Thus, the system cannot be provided inertia and frequency support. With a continuous increase in wind power penetration, the number of connected conventional power plants will reduce. The decoupling effect of DPMSG will lead to a continuous decrease of system inertia only to have a serious influence on the frequency stability of the system
[2

4]
.
To enable wind turbine generators to give power support to the system like traditional synchronous generators when the frequency fluctuates, a deload control method for wind turbine generators was proposed in references
[5

7]
. In spite of improving the ability of the wind turbine generators to be involved in the frequency control, this method is not economical when largescale wind power connected to the grid, with the inertia time constant of MWlevel wind turbine generators up to 6 s
[2]
and the kinetic energy stored in the rotor being considerable in normal operating conditions of the turbine. References
[2
,
8]
and
[9]
offered a frequency response control method based on the kinetic energy of the rotor in wind turbines. The method introduces the auxiliary power related to the proportional and derivative terms of the frequency deviation on the basis of the MPPT control. When the system frequency drops, the DPMSG can release the kinetic energy stored in the rotor to get into the system inertia response and primary frequency control. Because the converter can adjust the active power quickly, the wind turbine generators can provide greater virtual inertia than their inherent inertia
[2]
. Therefore, this control method is also called PDVIC. Using the PDVIC, it is possible for the DPMSG to adjust the power output and participate in the frequency regulation when the frequency fluctuates and to quit the frequency response when the system is stable. Both enabling the DPMSG to be involved in the frequency response of the system and ensuring the electricitygenerating efficiency, this method has become the focal point of research.
The frequency response ability of the DPMSG is easily affected by the wind speed and the control parameters of the unit in practical operation. To bring the frequency response ability of units into full play under different working conditions, reference
[10]
has analyzed the frequency response ability of the DPMSG and proposed a method of optimizing and improving the frequency control of wind turbine generators based on PDVIC. The method can improve the frequency support ability of wind turbine generators to some extent. References
[11]
and
[12]
have proposed a smooth control method of wind farms power output based on the inertia control. The method can increase the frequency support time of the wind farm through the coordinated control of multiple units. However, the influence of the wind speed random disturbance has not been taken into account in
[11]
. Reference
[13]
has offered a design method of primary frequency control of wind turbine generators based on the fuzzy control principle. Although confirmed through experiments, the method still needs to be used for power reserve. Reference
[13]
only confirmed the characteristics of the wind turbine generators responding to the frequency deviation of the system but it did not confirm the relation between the output of the units and the frequency deviation under VIC.
The ADRC is a new control method, which overcomes the shortcomings of classic PID control
[14]
. The method can transform the nonlinear system into the linear integrator series structure through the dynamic compensation linearization so as to simplify the control design and eliminate the dependence upon the model of the controlled system. And it can implement the system disturbance estimation and compensation by use of the ESO so as to improve the ability to restrain the error and disturbance. Thus, it is of better adaptability and robustness
[15
,
16]
.
In this paper, the active disturbance rejection virtual inertia control (ADRVIC) of the DPMSG is proposed from the perspective of power disturbance rejection of the system according to the principle of ADRC. Firstly, a simplified model of the wind power integrated system (WPIS) is established for the design of ADRVIC. Then, the process of design and the method of applying the ADRVIC are presented based on this model. Finally, the effectiveness and feasibility of the ADRVIC are verified by comparing the ADRVIC and the PDVIC through the simulation and experiment system.
2. Principle of Conventional Virtual Inertia Control
The imbalance of generating power and load will lead to the change of frequency in power systems, while the mechanical inertia of the rotor in the traditional synchronous generator has a critical influence on the speed of variation in the system frequency. The principle is expressed as
[17]
:
where
H
is the inertia time constant of the system (s);
D
is the damping coefficient of the load; Δ
ω
^{*}
is the angular frequency deviation of the system (pu), Δ
ω
^{*}
=
ω
^{*}
−
ω_{n}
^{*}
, where
ω
^{*}
is the angular frequency of the system (pu),
ω_{n}
^{*}
is the rated angular frequency of the system (pu),
ω_{n}
^{*}
=1; Δ
P_{A}
^{*}
is the unbalance power of the system (pu), Δ
P_{A}
^{*}
=
P_{m}
^{*}
+
P_{w}
^{*}
−
P_{L}
^{*}
, where
P_{m}
^{*}
and
P_{L}
^{*}
are the output power of prime motor and the frequencyinsensitive load, respectively (pu);
P_{w}
^{*}
=
P_{w} /S_{B}
, where
P_{w}
is the gridconnected power of the DPMSG (Watt), SB is the total capacity of the synchronous generators (V·A). Before the VIC is introduced into the DPMSG, the DPMSG operates in the MPPT control mode. At this time,
P_{w}
^{*}
=
P_{MPPT}
^{*}
, where
P_{MPPT}
^{*}
=
P_{MPPT}
/
S_{B}, P_{MPPT}
is the output power of DPMSG in the MPPT control mode (Watt).
As shown in (1), the greater
H
is, the more slowly the system frequency changes, so the more stable the system is under the same unbalance power.
Because of the decoupling effect of the FPC, the DPMSG in the power system in a normal MPPT control mode cannot release or absorb the rotor kinetic energy like traditional synchronous generators when the system frequency fluctuates. Its rotational kinetic energy is “hidden” and almost has no contribution to the inertia of the system.
The conventional PDVIC makes the DPMSG change its output when the system frequency fluctuates mainly through the introduction of the auxiliary power related to the proportional and derivative terms of the system frequency deviation so as to simulate the properties of primary frequency control and inertia response of the traditional synchronous generators. The principle is expressed as
[10]
:
where
P_{VIC}
is the auxiliary output power of VIC (Watt);
k_{p}
and
k_{d}
are the proportional and derivative parameters,
k_{p}
>0,
k_{d}
>0 in practical projects.
After the VIC is introduced, the gridconnected power of the DPMSG is equal to the sum of the output power of MPPT control and VIC if the response time of the DPMSG is ignored, that is
So the response equation of the system frequency turns from (1) into:
where
P_{VIC}
^{*}
=
P_{VIC}/S_{B}
.
Combining with (2), (4) can be derived as follows:
where
k_{p}
^{*}
=
k_{p}/S_{B}
,
k_{d}
^{*}
=
k_{d}/S_{B}
.
As is shown in (5), the conventional PDVIC improves the stability of the system from the aspects of inertia and damping.
The PDVIC is simple in principle and clear in physical meaning, but it has difficulty in adjusting the parameters
k_{p}
and
k_{d}
and has poor adaptability under wind speed disturbance. Therefore, based on the design of ADRC, this paper has proposed a new VIC strategy from the perspective of reducing the disturbance of power.
3. Active Disturbance Rejection Virtual Inertia Control Method
 3.1 Mathematical model of the wind power integrated system
The system structure of the DPMSG which has been connected to the grid is shown in
Fig. 1
. The DPMSG contains the wind turbine, PMSG
[18]
, FPC and its control systems.
WPIS with DPMSG
Wind energy is captured through the wind wheel to drive the PMSG. Its rotor movement equation is expressed as:
where
J_{w}
is the rotational inertia of the DPMSG (kg·m
^{2}
),
ω_{w}
is the angular velocity of the wind turbine (rad/s),
P_{wind}
is the mechanical power which the wind turbine obtains from the wind (Watt).
P_{wind}
is expressed as
[19]
:
where
ρ
is the air density (kg/m
^{3}
),
R
is blade radius (m),
v
is wind speed (m/s),
C_{p}
is the power coefficient,
θ
is blade pitch angle (degree), and
λ
is tip speed ratio.
Normally, when the output power of the unit is less than the limited power, the blade pitch angle will be adjusted to zero. At this time,
C_{p}
is only a function of
λ
.
C_{p}
can reach its maximum
C_{pmax}
by adjusting
ω_{w}
thus to fulfill the MPPT control. At this time the corresponding
λ
equals the optimal top speed ratio
λ_{opt}
. The power extracted from the wind is expressed as
[19
,
20]
:
where
k
_{max}
is the coefficient used for the wind turbine to extract the maximum energy,
k_{max}
=0.5
ρπR
^{5}
C
_{pmax}
/
λ
_{opt}
^{3}
.
When the power system is in a steady state, the DPMSG operates in MPPT mode, with the auxiliary power
P_{VIC}
equals zero. When the system frequency fluctuates, the virtual inertia controller starts working. It adjusts the rotating speed and power output of the generator and regulates the rotor kinetic energy through the fast power control of the FPC, so that the DPMSG will be involved in the power system frequency regulation to damp the frequency fluctuation.
In the process of VIC, whether the DPMSG can participate in VIC is also related to its rotating speed. When the rotating speed of DPMSG is low, the kinetic energy of the rotor is relatively low, and releasing rotor kinetic energy may lead to unit halting. When the rotating speed is relatively high, keeping increasing rotor kinetic energy may make the unit’s rotating speed exceed the speed limit. In order to ensure the stable operation of the DPMSGs, when the rotating speed of a unit is lower than 0.6 pu or exceeds 1.1 pu,
P_{VIC}
is adjusted to zero and the unit will temporarily quit from VIC. Therefore, under different operating conditions, the reference power of VIC is set as follows
[4]
:
where
ω_{wn}
is the rated angular velocity of the wind turbine (rad/s).
When the larger wind speed causes the rotating speed to be greater than its rated value, the pitch angle control starts acting to increase the pitch angle and decrease the mechanical power obtained from the wind, thereby reducing the rotating speed. In this process, the output power of the unit will reach the upper limit of the FPC, which is generally determined as 1.0~1.2 pu. The pitch angle controller is usually a PI controller.
 3.2 Simplified model of the wind power integrated system
The wind power integrated system is a complex nonlinear system. Discussing the VIC method based on its detailed model will complicate the design of the controller. In ADRC, the unmodeled dynamics of the system can be regarded as internal disturbance and be compensated by the ESO. Therefore, a simplified model of the wind power integrated system can be built based on the physical principles of VIC. And based on the simplified model the design of ARDVIC can be discussed.
Both the DPMSG and the traditional synchronous generator will participate in the adjustment of the system frequency after the VIC is introduced. The structure of the system shown in
Fig. 1
can be simplified as shown in
Fig. 2
.
Simplified structure of WPIS with VIC
The VIC is mainly related to the electromechanical transient process of the system, so the electromagnetic transient process in the DPMSG system can be ignored in the simplified model. In references
[9]
and
[21]
, the DPMSG and FPC are equivalent to an inertia unit and their electromagnetic loss power is ignored, then
where
s
is the Laplace operator;
P_{wref}
is the reference power of the DPMSG (Watt),
P_{wref}
=
P_{MPPT}
+
P_{VIC}
;
T_{A}
is the inertia time constant of the PMSG and the FPC (s), its value being about 0.2 s. As the process of the system frequency response is commonly 10~30 s, the dynamics can be ignored in the study of system frequency response control. The output power of the DPMSG is supposed to follow the variation in reference power strictly, that is,
The above analysis shows that in the study of the DPMSG VIC, the response time of the DPMSG can be ignored in Eq. (3).
Fig. 2
shows that there is a certain relation between the active power component and the frequency of the system, which is as follows:
where Δ
P_{m}
^{*}
=
P_{m}
^{*}
−
P_{m0}
^{*}
, Δ
P_{w}
^{*}
=
P_{w}
^{*}
−
P_{w0}
^{*}
, Δ
P_{L}
^{*}
=
P_{L}
^{*}
−
P_{L0}
^{*}
,
P_{m0}
^{*}
,
P_{w0}
^{*}
and
P_{L0}
^{*}
are the original power of prime motor, DPMSG and frequencyinsensitive load respectively when the system is in a steady state, the relation of them is expressed as:
As for the DPMSG, the amount of power change is expressed as:
where Δ
P_{VIC}
^{*}
=
P_{VIC}
^{*}
−
P_{VIC0}
^{*}
, Δ
P_{MPPT}
=
P_{MPPT}
^{*}
−
P_{MPPT0}
^{*}
,
P_{VIC0}
^{*}
and
P_{MPPT0}
^{*}
are the VIC output power and the MPPT output power respectively when the system is in a steady state. At this time, the virtual inertia controller does not operate; that is,
P_{VIC0}
^{*}
=0, so
Supposing Δ
P
^{*}
=Δ
P_{m}
^{*}
+Δ
P_{MPPT}
^{*}
−Δ
P_{L}
^{*}
−
D
Δ
ω
^{*}
, the dynamic response equation of the system frequency which includes the VIC can be shown below based on (13), (15) and (16):
By
x
=Δ
ω
^{*}
, then (17) is derived as follows:
where
w
(
t
)=Δ
P
^{*}
/2
H
,
g
(
x,w
(
t
))=
w
(
t
),
u
(
t
)=
P_{VIC}
^{*}
,
b
=1/2
H
,
w
(
t
) is the external disturbance,
g
(
x,w
(
t
)) represents the combined effect of internal dynamics and external disturbance
[14
,
15]
,
x
is the state variable,
u
is the control variable,
y
is the output variable,
b
is the system parameter.
As shown in (18), the frequency response of the WPIS containing DPMSG can be simplified as a firstorder system, and the fluctuations of wind speed and load in this system can be treated as the disturbance of the system.
 3.3 Active disturbance rejection virtual inertia controller
The design of the active disturbance rejection virtual inertia controller is mainly based on the nonlinear system shown in (18). The nonlinear system control design is complicated while the linear system control design is relatively simple. The core of the ADRC is to implement the realtime observation of system disturbance with the ESO and compensate the disturbance in the control variable so as to realize the linearization. Supposing the accurate estimation of the total disturbance of the system
g
(
x, w
(
t
)) can be made, its value is expressed as:
Then the disturbance observation can be introduced into the control system as the compensated control variable:
where
u
_{0}
is the control variable without disturbance compensation.
By the action of control variable
u
, the nonlinear system shown in (18) turns into:
Now the nonlinear system in (18) is transformed into a linear system as shown in (21), the process of which is called dynamic compensation linearization. For the observation of the system disturbance, the state variable is firstly extended in the system shown in (18) to obtain the following expression:
where
x
_{1}
=
x
,
x
_{2}
is the extended state variable,
x
_{2}
=
g
(
x,w
(
t
)),
G
(
t
) is the unknown function. The realtime observation of
x
_{1}
and
x
_{2}
depends on the ESO. Reference
[14]
offered the method of designing the ESO. The algorithm is as follows:
where
e
is the tracking error of ESO,
z
_{1}
and
z
_{2}
are the observed quantity of the state variable
x
_{1}
and
x
_{2}
respectively,
β
_{1}
and
β
_{2}
are the control parameters, and
b
_{0}
is the factor of the disturbance compensation. When
b
is known,
b
_{0}
=
b
; when
b
is unknown,
b
_{0}
takes the estimated value of
b
.
fe
,
fe
_{1}
and
fal
(
e
,
α
,
δ
) are nonlinear function of
e
[14]
:
where
α
and
δ
are constants.
If
α
=1,
fal
(
e
,
α
,
δ
) will equal
e
. At this time,
e
can be used instead of
fe
and
fe
_{1}
in (23), thus to simplify (23) and obtain the following expression
[14]
:
Here is the linear implementation method of the ESO. After the state variable is extended, (21) will be turned into:
The ADRC aims at allowing
x
_{1}
tend to the reference value Δ
ω_{r}
^{*}
, where Δ
ω_{r}
^{*}
=0. As a result, the control variable
u
_{0}
in (26) is
where
k
_{0}
is the control parameter. For
z
_{1}
is the observed quantity of
x
_{1}
, so it can replace
x
_{1}
. The result is expressed as:
which is called linear state error feedback control law (LSEFL) of the system.
The final control variable can be derived from (20):
Based on (25) and (2829), it is possible to obtain the expression for the firstorder linear active disturbance rejection virtual inertia controller of the WPIS as following:
The structure of the controller in (30) is shown in
Fig. 3
. It shows that wind turbine generators can participate in the closeloop control of system frequency through ADRVIC. As for the stability of the closeloop system, based on reference
[22]
it can be proved that if
g
(
x, w
(
t
)) is bounded, which means there is a positive number
M
_{1}
and 
g
(
x,w
(
t
))≤
M
_{1}
, there will be
β
_{1}
> 0,
β
_{2}
> 0 and
k
_{0}
>0 making the closeloop BIBO stable. The detail proof process of the conclusion is shown in references
[15]
and
[22]
.
Structure of ADRVIC
 3.4 Application of the ADRVIC
The adopted algorithm needs to be discretized in practical application. The discretization method of (30) can be expressed as
[23]
:
where
h
is the control step of the controller. The smaller the value
h
takes, the stronger the control ability of the system is.
h
usually takes the value between 0.0001 and 0.1 for the linear ESO
[23]
.
The control parameters
β
_{1}
and
β
_{2}
can be adjusted according to the bandwidth of ESO
ω_{o}
[24]
. Deriving the characteristic equation of ESO from Eq. (25) and set its poles as
ω_{o}
, as in the following equation:
From Eq. (32) the following equation can be obtained:
Large
ω_{o}
can improve the performance of ESO, but it will also magnify the system noise. In practice, a compromise is made between the speed at which the observer tracks the states and its sensitivity to the sensor noises
[24]
.
For the firstorder system,
ω_{o}
is set as 1/2
h
, and Eq. (33) turns into
[23]
:
The control parameter
k
_{0}
can be set according to the bandwidth of the feedback system
[24]
:
where
ω_{c}
is the system bandwidth,
ω_{c}
=1/5~1/3
ω_{o}
.
However, in ADRVIC, parameters
u
_{0}
and
k
_{0}
both have actual physical meanings. If the tracking error of ESO is ignored, then
z
_{1}
≈Δ
ω
^{*}
. Considering Δ
ω_{r}
^{*}
=0, Eq. (28) turns into:
In power systems, the relation between the variation of conventional synchronous generator’s power output and the variation of system frequency is as follows
[17]
:
where Δ
P_{G}
^{*}
is the power output variation of synchronous generator (pu), and
R_{p}
is the frequency droop coefficient of the system.
In Eq. (30), the meaning of
u
_{0}
is the same as Δ
P_{G}
^{*}
, it represents the variation of generator’s power output when system frequency changes, and
k
_{0}
represents the proportional relation between the variation of generator’s power output and the frequency deviation. Thus in analogy to Eq. (37) the following equation is obtained:
In power systems,
R_{p}
=0.02~0.06
[17]
, thus
k_{0}
=16.7~50.0 in (38).
The control variable obtained from (31) practically refers to all the generators in the system, including all the DPMSG and traditional synchronous generators, while
P_{VIC}
is concerned with the single DPMSG, so the interrelationship of the DPMSG capacity and the system capacity needs to be considered. Suppose the system has
n
synchronous generators and
m
DPMSGs, each DPMSG with a power rating of
P_{DPMSG}
. For the
j
th DPMSG:
where
S_{SG,i}
is the rated capacity of the
i
th traditional synchronous generator,
P_{wn,j}
is the rated capacity of the
j
th DPMSG,
k_{VIC,j}
is the allocation coefficient of the
j
th DPMSG. According to the definition,
.
Eq. (40) shows that by using the allocation coefficient, the capacities of both DPMSGs and synchronous generators are considered, thus the coordinated control of DPMSGs and conventional synchronous generators is implemented.
According to (30) and (39), the power of the DPMSG participating in the system frequency response is expressed as:
In (41),
z
_{1}
and
z
_{2}
are the observed quantities of Δ
ω
^{*}
and
g
(
x,w
(
t
)) respectively,
g
(
x,w
(
t
)) contains the derivative term of the system frequency
d
Δ
ω
^{*}
/
dt
, so (41) is expressed as:
where
k_{ADRC1,j}
=
k_{VIC,j}
k
_{0}
,
k
_{ADRC2,j}
=
k_{VIC,j}
/
b
_{0}
.
The comparison of (42) and (2) indicates that the added auxiliary power in DPMSG is composed of the proportional and derivative terms of the system frequency deviation. Therefore the ADRVIC has the same basic function as the PDVIC so that the DPMSG can achieve the properties of frequency control similar to the traditional synchronous generators. However, what is worthy of note is that this algorithm incorporates the disturbances of the wind speed, DPMSG and grid into the total disturbance for the purpose of observation and compensation and that it is more suitable for wind turbine generators due to its strong ability of disturbance resisting.
4. Simulation Study
 4.1 Simulation platform
To verify the effectiveness of ADRVIC, a test system built on Matlab/Simulink is used for simulation study. As shown in
Fig. 4
, the system includes an equivalent wind farm and an equivalent thermal power plant. The wind farm with an installed capacity of 8 MW has four 2 MWrated DPMSGs while the thermal power plant with an installed capacity of 8.20 MW has one synchronous generator. In the system, the power of load0 and that of load1 are 10.20+j3.1 MVA and 1.12+j0.20 MVA respectively. Load0 is fixed and load1 is variable. S1 is used for the switching of load1. With the penetration of wind power is up to 49.3%, the system is a weak AC system.
Singleline diagram of simulation system
In the simulation system, the main parameters of the wind turbine generator are: rated power
P_{wn}
=2 MW, rated rotating speed
ω_{wn}
=1.65 rad/s, radius of the wind wheel
R
=42 m, rated wind speed
v_{n}
=11 m/s, and inertia time constant
H
_{w}
= 4.5 s. The capacity of the synchronous generator is
S_{n}
=8.2 MVA, and the inertia time constant is
H
= 6 s. The parameters of PDVIC are:
k_{p}
=20×10
^{6}
,
k_{d}
= 30×10
^{6}
[2
,
9]
. The parameters of ADRVIC are:
h
=0.01,
β
_{1}
=100,
β
_{2}
=2500,
k
_{0}
=40,
b
_{0}
=1/12.
 4.2 Case 1: sudden load changes
This case refers to the inertia response of the system when there is a sudden change in load under the condition of constant wind speed which is 10.7 m/s. In the simulation system, as the DPMSG units are of the same type, the response characteristic of each unit is also the same.
Fig. 5
and
Fig. 6
show the dynamic response of the system at the time when the variable load is switched in or out at 5 s. In the figures,
ω
,
P_{w}
,
ω_{w}
and
θ
denote the angular frequency of the system, the output of the DPMSG, the angular velocity and the blade pitch angle of the wind turbine respectively. The response curves marked in black, red and blue respectively represent three different situations, in which the ADRVIC and PDVIC are introduced and the VIC is not.
System inertia response for a sudden increase in load
System inertia response for a sudden decrease in load
As shown in
Fig. 5
, the variable load is switched in suddenly.
Fig. 5(a)
shows that the decreasing speed and magnitude of the system frequency are improved significantly with ADRVIC and PDVIC. Compared with PDVIC, ADRVIC improves more.
Fig. 5(b)
and
Fig. 5(c)
show that DPMSG releases the kinetic energy of the rotor to support the system frequency by increasing the output of the unit when frequency drops. Compared with PDVIC, ADRVIC can take full advantage of the inertia of the system and release the frequency regulation potential of the unit so as to improve the property of the system frequency.
As shown in
Fig. 6
, the variable load is switched out suddenly.
Fig. 6(a)
shows that ADRVIC can effectively reduce the rise rate and magnitude of the system frequency and is better than PDVIC in control performance.
Fig. 6(b)
and
Fig. 6(c)
show that DPMSG increases the kinetic energy of the rotor to support the system frequency by decreasing the output of the unit when frequency rises.
Fig. 6(d)
shows that the pitch angle control starts to increase the pitch angle and decrease the power extracted from the wind so as to stop the rotating speed of the unit from further rising when it exceeds the rated speed during the period of the DPMSG participating in the system frequency response.
As shown in
Fig. 5
and
Fig. 6
, the adjustment of the output and rotating speed of units through VIC can make them participate in the system frequency response and support the stability of system frequency when load disturbance causes the frequency to fluctuate. When the system is stable, the VIC will quit operation and the units will return to the MPPT control mode to put wind energy into full use. It is obvious that the introduction of VIC helps establish a new coupling relationship between the rotor and the system frequency, but the relationship does not affect the efficiency of power generation.
Fig. 7(a)
and
Fig. 7(b)
show the contrast effect of observation of ESO in ADRVIC respectively at the time of a sudden rise or drop in load. In the figures, the red curve denotes the practical power disturbance while black curve denotes the observed effect of ESO: Δ
P
^{*}
=
g
(
x,w
(
t
))×2
H
,
z
_{2}
is the observation of
g
(
x,w
(
t
)).
Fig. 7
shows that the ESO can track and estimate the system disturbance accurately under load disturbance, which provides a reliable basis for the compensation and suppression of power system disturbance.
Observed effect of ESO in ADRVIC at the time of a sudden rise or drop in load
 4.3 Case 2: wind speed variation
This case refers to the influence of variation in wind speed on the system under the condition of constant load which is 10.20+j3.1 MVA.
Fig. 8
and
Fig. 9
show the curves of system responses under two different conditions of wind speed. In the figures,
ω
,
P_{w}
,
ω_{w}
, and
θ
denote the angular frequency of the system, the output of the DPMSG, the angular velocity and the blade pitch angle of the wind turbine respectively. The black, red and blue curves respectively represent three different situations, in which the ADRVIC and PDVIC are introduced and the VIC is not.
For the highmedium wind speed, which averages 12 m/s, the curve of wind speed is shown in
Fig. 8(a)
. The inertia responses of the system in different control modes are shown in
Fig. 8(b)
to
Fig. 8(e)
.
Fig. 8(b)
shows that the high penetration of wind power in the system results in a relatively large frequency deviation caused by the changing wind speed under the traditional MPPT control, which will seriously influence the frequency stability of the system. The introduction of ADRVIC can reduce the fluctuation range of the system frequency and improve the stability of the system. Furthermore, ADRVIC is more effective than PDVIC.
Fig. 8(c)
and
Fig. 8(d)
show that ADRVIC can reduce the impact on the system by smoothing the output of the units; however, this will results in relatively great variation in the rotating speed. When the rotating speed exceeds the rated speed, the pitch angle control will start work to stop it from further rising. The changing curve of the pitch angle is shown in
Fig. 8(e)
.
System inertia response for highmedium wind speed
For the lowmedium wind speed, which averages 10 m/s, the curve of wind speed is shown in
Fig. 9(a)
. The inertia responses of the system in different control modes are shown in
Fig. 9(b)
to
Fig. 9(e)
. It can be seen from the figures that ADRVIC still functions well under the condition of lowmedium wind speed and even has a better effect than PDVIC.
System inertia response for lowmedium wind speed
Fig. 10(a)
and
Fig. 10(b)
show the contrast effect of observation of ESO in ADRVIC under the conditions of highmedium and lowmedium wind speed. The red curve denotes the practical power disturbance and the black curve denotes the observed effect of ESO. As shown in
Fig. 10
, the ESO can still track and estimate the system disturbance accurately under the condition of wind speed disturbance.
Observed effect of ESO in ADRVIC under the conditions of highmedium wind speed and lowmedium wind speed
 4.4 Case 3: variation in system parameters
This case refers to the adaptability of ADRVIC to the variation in system parameters. Case 1 and Case 2 demonstrate that ADRVIC has strong ability to suppress the system load disturbance and wind speed disturbance. Parameter
b
_{0}
is taken as actual value
b
in the algorithm,
b
=1/2
H
=1/12. But in the practical operation of the system, some units quit operation owing to an overhaul while others are connected to the grid due to an increase in load. As a result, the inertia time constant of the system which has been changing is difficult to obtain. For this reason, it is necessary to explore the influence of
b
_{0}
on the control performance of the algorithm.
The system simulation condition is the same as that in
Fig. 8
, namely the highmedium wind speed which averages 12 m/s. In this case, the inertia time constant of the system is 6s; that’s
b
=1/12, and
b
_{0}
takes the value of
b
, 2
b
and 0.5
b
respectively. The control performance of ADRVIC is shown in
Fig. 11
.
Fig. 11(a)
and
Fig. 11(b)
show the observed effect of ESO and the frequency response of the system respectively.
It can be seen from the
Fig. 11
that the response curves of the system overlap completely in the case of different parameters. Therefore, certain variation in parameter b0 will not influence the correct estimation of power disturbance by ESO or the effect of controlling the system frequency by ADRVIC. This illustrates that it is unnecessary to obtain the accurate parameters of the system in ADRVIC, which leads to reducing the dependence of ADRVIC on the grid parameters and ensuring the possibility of its practical application.
Response characteristics of ADRVIC with parameter b_{0} varying
5 Experiments
 5.1 Test bench
To demonstrate the possibilities of applying the control algorithm proposed in this paper to the practical DPMSG, a simulated wind power integrated experiment system is established on the basis of the governor 6RA7025 of Siemens and digital signal processor (DSP) TMS320F2812 of TI Corporation. The hardware structure is shown in
Fig. 12
.
Experimental platform configuration
The experiment system consists of wind turbine emulator (WTE), PMSG, FPC, interconnection transformer and independent grid. The WTE consists of governor 6RA7025, DC motor, flywheel and gearbox, among which the 6RA7025 controls the output mechanical torque of the DC motor and simulates the output characteristics of the wind turbine. The inertia time constant of the actual MWlevel wind turbine generators can be up to 6 s, while the inertia of the actual DC motor is very small (less than 0.5 s), so the flywheel is used to simulate the inertia characteristics of the MWlevel wind turbine generators. The gearbox is used for connecting the highspeed motor with the lowspeed PMSG.
The control structure of the WTE is shown in
Fig. 13
. With the configuration software in PC1, the reference torque of the DC motor is obtained from the samples of motor rotating speed
ω_{m}
, given wind speed
v
, and practical value of pitch angle θ according to the mathematical model of wind turbines. And the reference torque command is sent to 6RA7025 through PLC, to perform a closedloop control of the torque. The FPC implements the control of the generatorside and gridside converter through TMS320F2812. The control strategy of FPC can be seen from
Fig. 1
.
Control scheme for WTE
The independent power grid is made up of a simulative synchronous generator and equivalent load. The simulative synchronous generator is implemented with an inverter based on the virtual synchronous generator theory
[25]
. In actual implementation, the armature resistance and synchronous reactance of the synchronous generator are equivalently replaced by the filter reactance, and the inertia characteristics, frequency response characteristics and voltage regulation characteristics of synchronous generators are effectively simulated through the control system.
In the experiment system, the main parameters of the simulated wind turbine generator are: rated power
P_{wn}
=6.5 kW, rated rotating speed
ω_{wn}
=18 rad/s, radius of the wind wheel
R
=3.4 m, rated wind speed
v_{n}
=9.5 m/s, and inertia time constant
H_{w}
=5.7 s. The capacity of the independent grid is
S_{n}
=8 kVA, and the inertia time constant is
H
=6 s. The photo of the experiment system is shown in
Fig. 14
.
Test bench
 5.2 Experimental results
Under the condition of low wind speed condition, the inertia response properties of the system can be acquired. In the experiments, the wind speed is constant 7.5 m/s; the initial load of the system is 7kW; the system has a sudden addition of load disturbance of 2kW when t= 8 s. The inertia response curves of the system operating on different control modes are shown in
Fig. 15
.
Fig. 15(a)
~
Fig. 15(c)
show the response curves of the system frequency, rotating speed of PMSG and output of gridside converter respectively.
As shown in
Fig. 15
, the output and rotating speed of the PMSG do not respond to the variations in system frequency under the traditional MPPT control. Thus the system con not get frequency support. However, ADRVIC and PDVIC can get a new coupling relationship established between the wind turbines and the system frequency. When the frequency changes, the DPMSG can adjust its output and release the kinetic energy of the rotor to support the system frequency.
Fig. 15(a)
indicates that ADRVIC improves the system frequency more than PDVIC because it can fully release the kinetic energy of the rotor to provide more power support for the system. A comparison between
Fig. 15
and
Fig. 5
illustrates that the response characteristic curve of the experiment system is almost the same as that of the simulation system in the trend of variation though the two systems are at different power levels. Therefore, the ADRVIC proposed in this paper is effective and feasible in the practical DPMSG.
Inertia response curves of the system in different control modes
6. Conclusion
Based on the design principle of the ADRC, this paper has proposed the ADRVIC method for DPMSG and compared ADRVIC with conventional PDVIC through simulations and experiments. The results show that both of them can provide inertia and frequency support for the system under the condition of wind speed disturbance or load disturbance.
As ADRVIC participates in the frequency regulation through the observation and compensation of the power disturbance in the system, it can suppress the frequency fluctuation better than PDVIC.
The comparison of the control performances of ADRVIC using different control parameters shows that the phenom enon that the control parameter variation in a certain range has no effect on control of ADRVIC. Therefore, this method is characterized by better adaptability and robustness in practical systems.
Nomenclature
ω_{n} Rated angular frequency of the power system (rad/s). ω Angular frequency of the power system (rad/s). Δω Angular frequency deviation of the system (rad/s). H Inertia time constant of the power system (s). D Damping coefficient of the load. S_{B} Total capacity of the synchronous generators (Watt). P_{m} Output power of prime motor (Watt). P_{L} Frequencyinsensitive load of system (Watt). Rp Frequency droop coefficient of the system. J_{w} Rotational inertia of the DPMSG (kg·m^{2}). ω_{w} Angular velocity of the wind turbine (rad/s). P_{w} Gridconnected power of the DPMSG (Watt). P_{MPPT} Output power of MPPT control (Watt). P_{VIC} Auxiliary output power of VIC (Watt). k_{p}, k_{d} Control parameters of PDVIC. R Blade radius (m). V Wind speed (m/s). C_{p} Power coefficient. θ Blade pitch angle (degree). λ Tip speed ratio. x, x_{1}, x_{2} State variable. z_{1}, z_{2} Observed quantity of the state variable. β_{1}, β_{2} Control parameters of ESO. h Control step of the ADRC. k_{0}, k_{VIC} Control parameters of ADRVIC. ᅟ Subscripts and Superscripts ref Reference value. 0 Initial value. n Rated value. * Per unit value.
Acknowledgements
This work was supported by the National Basic Research Program of China (973 Program) (No. 2012CB215103), and the National Natural Science Foundation of China (No. 51377167).
BIO
Qiaoming Shi received his B.S. degree in electrical engineering from Xi’an Jiaotong University, China in 2010. He is currently studying for his Ph.D. degree at Xi’an Jiaotong University. His research interests include the develop ment of wind energy grid integration techniques.
Gang Wang received his B.S. and Ph.D. degrees from Tsinghua University, China in 1993 and 2008 respectively. He is currently employed as Professor at Naval University of Engineering, China. His research field includes the develop ment of stability control methods for wind power integrated system.
Lijun Fu received the B.S. degree in electrical engineering from Hunan University of Science and Technology in 1989, and the M.S. and Ph.D. degrees from Wuhan University, China respecttively in 1995 and 1997. He is currently employed as Professor at Naval University of Engineering, China. His research field includes the development of stability control methods for Microgrids.
Yang Liu received the B.S. degree in electrical engineering from Wuhan University of Technology in 2008, and the M.S. degree from Shanghai Maritime University, China in 2010. He is currently studying for his Ph.D. degree at Naval University of Engineering. His research interests include the development of voltage control methods for wind power plants.
You Wu received his B.S. degree from Tsinghua University, China in 2013. He is currently pursuing his M.S. degree at Naval University of Engineering. His research interests include the development of frequency control methods for wind power integrated system.
Li Xu received his B.S. degree from Hubei University of Technology, China in 2013. He is currently pursuing his M.S. degree at Naval University of Engineering. His research interests include the development of voltage control methods for wind power plants.
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