MPC-Based Power Tracking Control for a Wind Energy Conversion
System with PM Synchronous Generator
JIANG Haiping, JIAO Xiaohong, REN Lina
Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China
E-mail: jiaoxh@ysu.edu.cn
Abstract: In consideration of the intrinsic
properties such as nonlinearity, uncertainties and randomness of the Wind Energy
Conversion System (WECS) based on Permanent Magnet Synchronous Generator (PMSG), the Model Predictive Control (MPC)
method is utilized to realize the power tracking control of the system. A simplified second-order linear model by the pre-feedback
and the forward difference are adopted to improve the feasibility of the MPC algorithm. In addition, a fast computing method,
the Continuation/GMRES (C/GMRES) method, is employed to obtain the control sequence. Simulation results verify the
effectiveness of the designed model predictive controller, in term of the power tracking ability of the system under the varying
load demand and parameters perturbation.
Key Words: Wind energy conversion system, model predictive control, GMRES, power tracking control
1 Introduction
Electric power generation using the clean, infinite and
available wind resource is of important significance to
energy conservation and environmental protection, as well as
PMSG has obvious advantages in high efficiency, high
reliability, low weight, etc, which make the PMSG-based
WECS is receiving considerable attention throughout the
world
[1,2]
.
The WECS is a kind of system which is difficult to control,
because the power from wind depends on the random wind
speed which could result in complexity to the WECS, and the
nonlinear aerodynamic performance of Wind Turbine (WT)
maybe lead to the WECS uncertainties. To deal with this
situation some advanced methods have been utilized, such as
adaptive control
[3]
, robust control
[4]
, etc. However each
method has its own disadvantages. Specially, the adaptive
control relies heavily on the system structure, and the
uncertain parameters must be unknown constant or slow
time-varying; the robust control is not so strict about the
system structure, but the boundary of the uncertain
parameters should be known.
MPC is a kind of model-based optimal control which has
already been used in the PMSG control system
[5,6]
. This
optimal approach computes the next control action by
minimizing the cost function according to the predicted
behavior of system. Hence, to some extent, the effect of the
nonlinearity, uncertainties and randomness in the WECS can
expect to be reduced
[7]
. In general, constraints are necessary
to guarantee the PMSG performance, but the concomitant
computational burden is inevitable. Therefore, most of the
research on PMSG with the MPC focuses on the simplified
model. When solving the problem, we usually generalize it
into a quadratic programming problem and complete it with
iterative approaches, whereas there is little concern about the
computational speed of iterative approaches
[8,9]
.
*
This work is supported by Ph.D. Programs Foundation of Ministry of
Education of China under Grant 20111333110001, National Natural
Science Foundation (NNSF) of China under Grant 61304025, and Natural
Science Foundation of Hebei Province under Grant F2014203234.
In this paper, considering the maximum output power of
the WECS is enough to meet the load demand, we adopt a
MPC method with low computational cost to achieve the
power tracking control of the system within a narrow range
of the wind speed. More specially, a second-order linearized
model of PMSG and the forward difference are utilized to
reduce the computational cost, and the Generalized
Minimum Residual (GMRES) method is used to realize the
fast computation
[10]
. The effectiveness of the model
predictive controller is verified under MATLAB/Simulink.
2 PMSG-based Wind Generation Control System
The block diagram of the considered PMSG-based wind
generation control system is shown in Fig. 1. The system
consists of WT, PMSG, a converter, an inverter, a load and a
controller.
w
V
PMSG
Converter
d
u
q
u
WT
PWM
Generator
Controller
Inverter
&Load
abc
dq
Expect
Calculator
Fig. 1: The block diagram of the PMSG-based WECS
The energy captured by the WT depends on the wind
speed, the blade pitch and the rotor speed. The aerodynamic
torque of the WT can be described as:
23
0.5 , ,
wwpwww
TRVCV
US Z T Z
(1)
where
U
is the air density,
R
is the blade radius,
w
V
is the
wind speed,
p
C
is the power coefficient which is a function
of the rotor speed of the WT
w
Z
and the pitch angle
T
.
The WT coaxially connects to and directly drives the
PMSG in the considered WECS. The equation of the drive
train can be described by:
g
we mg eq
d
TTB J
dt
Z
Z
(2)
Proceedings of the 34th Chinese Control Conference
Jul
28-30, 2015, Han
zhou, China
4079