Distributed Model Predictive Active Power Control for Large-Scale Wind Farm Based on ADMM Algorithm
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Distributed Model Predictive Active Power
Control for Large-Scale Wind Farm Based
on ADMM Algorithm
Shuai Xue, Houlei Gao(B) , Bin Xu, and Yitong Wu
School of Electrical Engineering, Shandong University, Jinan 250061, China
houleig@sdu.edu.can
Abstract. This paper provided a distributed model predictive control (DMPC)
for the active power of a large-scale wind farm. The active power produced by
each wind turbine (WT) was regulated by DMPC to reduce the fatigue loads
and to track the dispatch command obtained from the transmission system oper-
ator (TSO). Model predictive control (MPC) and alternating direction multiplier
method (ADMM) were adopted in the proposed DMPC, which can make the com-
putational pressure lower and improve the scalability of the wind farm. This study
used a wind farm model containing 80 WTs to test the applicability of DMPC
scheme.
Keywords: Large-scale offshore wind farm · Model predictive control · ADMM
algorithm · Active power control
1 Introduction
Recently, developing renewable sources has gradually become the consensus of various
countries and governments [1]. Among the renewable energy technologies, offshore
wind power is developing more and more rapidly due to its advantages such as stable
resource conditions and proximity to the load center. According to research by GWEC,
by 2025, the worldwide growth of offshore wind power capacity in each year will exceed
20 GW, and by 2030 it will exceed 30 GW. The offshore wind power capacity installed
in the next 10 years will exceed 205 GW [2].
As offshore wind farms get larger and larger, its influence on the power system also
increases, higher requirements should be put forward for the active power control system
of large-scale wind farms. In this context, it is of great significance to propose a more
economical and efficient active power control strategy.
In the active power control of a wind farm, a controller is installed to receive the power
dispatch command from TSO and distributes it to each WT according to a certain strategy.
The main objective of wind farm dispatch schemes is power tracking [3, 4]. In [5], an
optimal control method was proposed to maximize outputs of WTs while minimizing
the line loss, which is based on the ultra-short-term forecasting. In [6], a bi-level control
method was proposed for better active power dispatch by achieving fair active power
© Springer Nature Singapore Pte Ltd. 2021
K. Li et al. (Eds.): LSMS 2021/ICSEE 2021, CCIS 1468, pp. 201–209, 2021.
https://doi.org/10.1007/978-981-16-7210-1_19202 S. Xue et al.
sharing and decreasing the fatigue loads of WTs. In [7], a new auxiliary damping control
method was proposed to suppress the subsynchronous resonant oscillation of the nearby
turbo-generator. The authors of [8] proposed a closed-loop framework for the active
power control while reducing structural loads caused by wakes during the interaction of
a fully developed wind farm flow with the atmospheric boundary layer.
In previous studies, the active power control methods of wind farms can be divided
into centralized methods and distributed methods according to different topological
structures. The performance of centralized control relies heavily on the central controller.
As the scale of wind farms grow, the central controller’s computational pressure will be
greater. In distributed control strategies, each WT is equipped with a separate controller
and each controller solves the control problem in parallel, so that the computational
burden can be effectively reduced. However, as wind farms grow in size, the number of
iterations and the resulting communication delay will greatly influence the convergence
time.
Therefore, a DMPC method for large-scale wind farms is proposed with centralized
communication and distributed computing. Based on the framework of ADMM, the
original optimization problem can be divided into multiple problems that can be solved
simultaneously in each WT controller. Part of the problems are solved in the central con-
troller, and others are solved locally in each WT controller. Therefore, the computational
pressure of the central controller can be effectively reduced. At the same time, as part of
the optimization problem is solved in parallel in each WT controller, the convergence
speed is not affected by the increase in the scale of the wind farm.
2 Architecture of DMPC
2.1 Configuration of a Wind Farm
Figure 1 shows the structure of a typical large-scale offshore wind farm, which is con-
nected to the onshore AC grid through the voltage-source-converter high-voltage-direct-
current (VSC-HVDC) system. The power output of each WT is collected through col-
lector substations, collected to the high-voltage (HV) transmission cable through the
Fig. 1. Configuration of a VSC-HVDC connected offshore wind farmDistributed Model Predictive Active Power Control 203
step-up transformer, and then sent to the onshore AC grid through a wind farm side
voltage-source -converter(WFVSC).
2.2 Concept of DMPC
The structure of DMPC proposed in this paper is shown in Fig. 2. A central controller
is adopted in the wind farm and several WT controllers are set for each WT.
The proposed active power control scheme is based on the MPC and ADMM. Lin-
earize the mathematical model of the WT at the operating point, and then formulate the
optimization problem. The control object of the optimization problem is to track the
power dispatch command from the TSO while prolonging the operation life of WTs.
Through the ADMM algorithm framework, the original optimization problem can be
divided into multiple optimization problems. These sub-problems can be solved in par-
allel on the central controller and the WT controllers, and the global optimal solution
is obtained through continuous iteration between the central controller and the WT
controllers.
Pavi
WF
Meas.
z, Pref
WT1
WT controller1
x, Meas.
ref
PWF
central z, Pref
WT2
controller
WT controller 2
x, Meas.
z, Pref
WTi
WT controller i
x, Meas.
Fig. 2. Control structure of DMPC
3 DMPC Active Power Control of Wind Farm
The DMPC method regulates the output produced by each WT to track the dispatch
command from TSO while minimizing the fatigue loads.
In this paper, the WT shaft load and the structural load of the tower are used to
measure the fatigue load [9]. The fatigue load can be effectively reduced by reducing
the fluctuation of the shaft torque of the WT and the thrust of the tower.
3.1 Predictive Model
The WT model used to study DMPC is based on the 5 MW nonlinear variable speed
WT system of NREL [10]. The dynamic characteristics of the pitch angle servo system204 S. Xue et al.
should be considered when establishing the nonlinear model of the WT because it makes
a big difference to the state of the WT.
The aerodynamic model of the WT is as follows
0.5πρR2 VW3 CP (λ, θ )
Ta = , Ft = 0.5πρR2 VW3 Ct (λ, θ ). (1)
ωr
Where Ta is the aerodynamic moment; R is the blade length; ωr is the rotor speed; VW
is the effective wind speed; θ is the pitch angle; CP is the power coefficient; Ct is the
thrust coefficient and λ is the tip speed ratio.
Model the drive system as follows
ηg2 Jg ηg Jr
Ts = Ta − Jr ω̇r = Ta + . (2)
Jr + ηg2 Jg Jr + ηg2 Jg
Where ηg is the transformation ratio of the gearbox; Tg is the torque of the generator;
Jr is the rotor mass and Jg is the generator mass.
The generator model of a WT can be described as
PWT 1 1
Tg = , ω̇f = − ωf + ωg . (3)
μg ωf τf τf
Where μg is the efficiency of the generator, τf is the filter time constant and ωf is the
filtered speed.
The model of the pitch angle servo system is as follows
KP Ki
θ ref = ( + )(ωf − ωgrated ) , β = (K0 + K1 θ )θ. (4)
Kc sKc
Where Kp and Ki respectively represent the proportional gain and integral gain of the PI
controller. Kc = K0 + K1 θ , where K0 and K1 are constants.
Assuming that the operating point is t 0 and the wind speed does not change dramat-
ically over short periods of time, define the state values of the WT at t0 time as Ta,0 ,
Tg,0 , θ0 , ωg,0 , ωf ,0 and PWT ,0 . It can be deduced that the incremental state space model
at the operating point is expressed as
ẋ = A x + B u + E , y = C x + D u. (5)
Where x = [ ωg , ωf , β]T , u = PrefW and y = [ Ts , Ft ]T . The state
space matrix is as follows
⎛ ⎞ ⎛ ⎞
ηg ∂Ta ηg PWT ,0 ηg ∂Ta
2
ηg2 PWT ,0
⎜ Jt ∂ωg μg Jt ω2 Jt ∂β ⎟ ⎜ μg Jt ωf2,0 ⎟
⎜ f ,0
⎟
A=⎜ 1
− τf 1
0 ⎟B=⎜⎝ 0 ⎠
⎟
⎝ τf ⎠
Kp Kp
τf − τf +Ki 0 0
⎛ ⎞ ⎛η ⎞
ηg2 Jg ∂Ta ηg Jr PW ,0 ηg2 Jg ∂Ta ηg Jr (Ta,0 − ηg Tg,0 )
g
Jt
Jt ∂ωg μg Jt ω2 Jt ∂β ⎜ ⎟
C=⎝ f ,0 ⎠D= μg Jt ωf ,0 E=⎝ 0 ⎠.
∂Ft ∂Ft 0
∂ωg 0 ∂β Ki (ωf ,0 − ωgrated )Distributed Model Predictive Active Power Control 205
Therefore, the discretized state space equation of the WT can be expressed as
x(k + 1) = Ad x(k) + Bd u(k + 1) + Ed . (6)
y(k) = Cd x(k) + Dd u(k). (7)
3.2 Optimization Problem Formulation
MPC is essentially a model-based finite time-domain optimal control algorithm, which
is dedicated to decomposing the optimization control problem of a longer time span
into several shorter time spans. The method of optimizing the control problem, and still
pursuing the optimal solution to a certain extent [11].
When designing the objective function, first consider making the shaft torque and
the thrust of the tower as small as possible to reduce fatigue load, thereby prolonging
the operating life of WTs; secondly, it is also necessary to consider fair distribution of
the active power between WTs in the wind farm. Therefore, the objective function can
be expressed as
NT
ref 2 2 2
min PWT ,i (k) − Ppd ,i + Ts,i (k) QT
+ Ft,i (k) QF
. (8)
QP
i=1
Where Ppd ,i is the power reference for WT-i when proportional dispatch (PD) method is
adopted, QP is the weighting coefficient to ensure the fair distribution of active power,
QT and QF are the weighting coefficients to minimize the changes in the shaft torque
and tower thrust of WTs. Ppd ,i can be obtained by the following formula
avi
PWT
ref ,i
Ppd ,i = PWF · avi
. (9)
PWF
The constraints of the optimization problem should be considered from both a single
WT and the wind farm as a whole. For the wind farm, the sum of the outputs produced
by each WT should track the dispatch command given by TSO, namely
NT
ref ref
PWT ,i = PWF . (10)
i=1
For a WT, its power output should be within the range of available power of the WT,
namely
ref
0 ≤ PWT ,i ≤ PWT
avi
,i , ∀i ∈ NT . (11)206 S. Xue et al.
3.3 Solution Based on ADMM
The ADMM algorithm is a widely used method for solving distributed optimization
problems. ADMM algorithm has many excellent characteristics, such as simple form,
decomposability, nice convergence and high robustness [12, 13]. The standard form of
ADMM is as follows
min f (x) + g(z)
. (12)
s.t. Ax + Bz = c
In the formula: f and g are convex functions;x ∈ Rn ; z ∈ Rm ;A ∈ Rp×n ;B ∈ Rp×m ;c ∈
Rp .
The steps of the ADMM algorithm can be expressed as follows
step1 : xk+1 = arg min L(x, z k , λk )
z
step2 : z k+1
= arg min L(xk+1 , z, λk ).
z
step3 : λ k+1
= λ + ρ(Axk+1 + Bz k+1 − c)
k
(13)
Where ρ is the iteration step size of the ADMM algorithm.
Due to the special structure of the active power control problem, that is, the objective
function is the sum of multiple decoupled objective functions, and the constraints are
coupled with each other, so the ADMM algorithm can be used to disassemble the problem
into multiple sub-optimization problems. Through iterative calculation with the central
controller, the constraints are gradually satisfied. In order to deal with the constraints,
variables z are introduced and the original problem is rewritten into ADMM form.
⎧
⎪ min f ( u) + g( z)
⎪
⎪
⎪
⎪ s.t. u = z
⎪
⎪
⎪
⎪
⎪
⎪ NT
⎪
⎪ (i) 2
⎪
⎪ f ( u) = PWT + ui − Ppd ,i
⎪
⎪
,0 QP
⎪
⎪ i=1
⎪
⎨ ⎛ ⎞
NT 2 2
⎝ ∂T s,i ∂Ft,i ⎠ .
⎪
⎪ g( z) = zi + zi
⎪
⎪
ref
∂PWT ,i
ref
∂PWT ,i
⎪
⎪ i=1
⎪
⎪
QT QF
⎪
⎪ N N
⎪
⎪
T T
⎪ ref
ui = PWF − ,0 , ∀i ∈ NT
i
⎪
⎪ PWT
⎪
⎪
⎪
⎪ i=1 i=1
⎪
⎩ (i) (i)
0 − PWT ,0 ≤ ui ≤ PWT avi
,i − PWT ,0 , ∀i ∈ NT
(14)
Among them, f ( u) needs the information of TSO, and its optimization can be car-
ried out in the central controller; the part g( z) is only related to the information of each
WT and can be completed locally in each WT controller. The two parts of optimiza-
tion problems are processed in parallel, and then iterative calculations are performed
according to the ADMM algorithm, and finally converges to the optimal solution.Distributed Model Predictive Active Power Control 207
4 Case Study
In order to test the performance of the DMPC scheme proposed in this paper, a wind farm
model with 80 5 MW-WTs was established based on the MATLAB/Simulink platform
according to the wind farm structure in Fig. 1. The SimWindFarm toolbox is used to
dynamically simulate the wind conditions. The performance of DMPC is compared with
the simulation result of the PD con scheme based on the available power.
The control performance of DMPC method is analyzed by selecting WT-1 as the
representative WT. The simulation results of WT-1 are shown in Fig. 3.
106
4.5
4
3.5
Active power (W)
3
2.5
2
1.5
DMPC
1 PD
0.5
0
0 100 200 300 400 500 600
Time s
106
4
3.5
3
Shaft torque (Nm)
2.5
2
1.5
1 DMPC
PD
0.5
0
0 100 200 300 400 500 600
Time s
10 105
8
6
Thrust force (N)
4
2
0
DMPC
PD
-2
-4
0 100 200 300 400 500 600
Time s
Fig. 3. Simulation results
As can be seen from the figure above, the proposed DMPC scheme has good con-
vergence, and the output of the optimized WT is relatively close to that of PD scheme.
At the same time, compared with PD scheme, under the DMPC scheme, the variation of
the shaft torque of WTs and the thrust of tower is smaller, and the output of the WT is208 S. Xue et al.
smoother. Therefore, the DMPC scheme in this paper can minimize the fatigue load of
WTs while prolonging the service life under the premise of meeting the requirements
of active power dispatching.
In addition, the optimization problem of the DMPC scheme is disassembled into
two parts, one of which is solved locally in WTs in parallel, the other part is solved in
the central controller. As part of the data is solved in WT controllers, this control can
relieve the calculation pressure of the central controller. At the same time, because the
information transmitted between the central controller and the WT controllers is not
sensitive, DMPC also has certain privacy protection capabilities.
5 Conclusion
In this paper, a distributed model predictive control scheme for large-scale wind farms is
proposed based on MPC and ADMM. It can be concluded by simulation experiment that
the wind farm can effectively track the dispatch command from TSO, and minimize the
variation of shaft torque and tower thrust of WTs, thereby minimizing the fatigue load.
The DMPC scheme reduces the calculation pressure of the central controller, enhances
the scalability of the wind farm as part of the optimization problem is solved in parallel
in each WT controller, and effectively reduces the fatigue load of WTs. At the same
time, because the information transmitted between the central controller and the WT
controllers is not sensitive, DMPC also has certain privacy protection capabilities.
References
1. U.S. Energy Information Administration. http://www.eia.gov/ieo
2. GWEC: Global Offshore Wind. J. Annual Market Report 2020 (2020)
3. Mitra, A., Chatterjee, D.: Active power control of DFIG-based wind farm for improvement
of transient stability of power systems. J. IEEE Trans. Power Syst. 31(1), 82–93 (2015)
4. Zhao, H., Wu, Q., et al.: Optimal active power control of a wind farm equipped with energy
storage system based on distributed model predictive control. J. IET Gener. Transm. Distrib.
10(3), 669–677 (2016)
5. Li, D., Wang, S., et al.: Method for wind farm cluster active power optimal dispatch under
restricted output condition. J. DRPT. 1981–1986 (2015)
6. Huang, S., Wu, Q., et al.: Bi-level decentralised active power control for large-scale wind
farm cluster. J. IET Renew. Power Gener. 12(13), 1486–1492 (2018)
7. Bin, Z., et al.: An active power control strategy for a DFIG-based wind farm to depress the
subsynchronous resonance of a power system. J. Int. J. Electr. Power Energy Syst. 69, 327–334
(2015)
8. Vali, M., Petrović, V., et al.: An active power control approach for wake-induced load alle-
viation in a fully developed wind farm boundary layer. J. Wind Energy Sci. 4(1), 139–161
(2019)
9. Zhao, H., Wu, Q., et al.: Fatigue load sensitivity-based optimal active power dispatch for wind
farms. J. IEEE Trans. Sustain. Energy. 8(3), 1247–1259 (2017)
10. Jonkman, J., Butterfield, S., et al.: Definition of a 5-MW reference wind turbine for offshore
system development. In: National Renewable Energy Lab.(NREL). Golden, CO, USA (2009)Distributed Model Predictive Active Power Control 209
11. Chen, H., Zhang, J., et al.: Asymmetric GARCH type models for asymmetric volatility char-
acteristics analysis and wind power forecasting. Prot. Control Mod. J. Power Syst. 4(1), 1–11
(2019)
12. Chang, T.-H., Liao, W.-C., et al.: Asynchronous distributed ADMM for large-scale optimiza-
tion—Part II: Linear convergence analysis and numerical performance. J. IEEE Trans. Signal
Process 64(12), 3131–3144 (2016)
13. Boyd, S., Parikh, N., et al.: Distributed optimization and statistical learning via the alternating
direction method of multipliers (2011)You can also read
