Artificial Neural Networks for Control.pdf

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 1
Artificial Neural Networks for Control
of a Grid-Connected Rectifier/Inverter Under
Disturbance, Dynamic and Power
Converter Switching Conditions
Shuhui Li, Senior Member, IEEE, Michael Fairbank, Student Member, IEEE, Cameron Johnson,
Donald C. Wunsch, Fellow, IEEE, Eduardo Alonso, and Julio L. Proaño
Abstract—Three-phase grid-connected converters are widely
used in renewable and electric power system applications. Tra-
ditionally, grid-connected converters are controlled with stan-
dard decoupled d-q vector control mechanisms. However, recent
studies indicate that such mechanisms show limitations in their
applicability to dynamic systems. This paper investigates how
to mitigate such restrictions using a neural network to control a
grid-connected rectifier/inverter. The neural network implements
a dynamic programming algorithm and is trained by using back-
propagation through time. To enhance performance and stability
under disturbance, additional strategies are adopted, including
the use of integrals of error signals to the network inputs and
the introduction of grid disturbance voltage to the outputs of
a well-trained network. The performance of the neural-network
controller is studied under typical vector control conditions and
compared against conventional vector control methods, which
demonstrates that the neural vector control strategy proposed
in this paper is effective. Even in dynamic and power converter
switching environments, the neural vector controller shows strong
ability to trace rapidly changing reference commands, tolerate
system disturbances, and satisfy control requirements for a
faulted power system.
Index Terms—Backpropagation through time, decoupled
vector control, dynamic programming, grid-connected
rectifier/inverter, neural controller, renewable energy
conversion systems.
I. INTRODUCTION
IN RENEWABLE and electric power system applications,
a three-phase grid-connected dc/ac voltage-source pulse-
width-modulated (PWM) converter is usually employed to
Manuscript received May 18, 2012; revised July 14, 2013; accepted
August 27, 2013. This work was supported in part by the U.S. National
Science Foundation under Grant EECS 1102038/1102159, in part by the Mary
K. Finley Missouri Endowment, and in part by the Missouri S&T Intelligent
Systems Center.
S. Li and J. L. Proano are with the Department of Electrical & Computer
Engineering, The University of Alabama, Tuscaloosa, AL 35487 USA (e-mail:
sli@eng.ua.edu; jlproano@crimson.ua.edu).
M. Fairbank and E. Alonso are with the School of Informatics, City Univer-
sity London, London EC1V OHB, U.K. (e-mail: michael.fairbank@virgin.net;
e.alonso@city.ac.uk).
C. Johnson and D. C. Wunsch are with the Department of Electrical &
Computer Engineering, Missouri University of Science and Technology, Rolla,
MO 65409-0040 USA (e-mail: dwunsch@mst.edu; cej@mst.edu).
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/TNNLS.2013.2280906
Fig. 1. Application of grid-connected rectifier/inverter in a microgrid.
interface between the dc and ac systems. Typical converter
configurations containing the grid-connected converter (GCC)
include: 1) a dc/dc/ac converter for solar, battery and fuel
cell applications [1], [2]; 2) a dc/ac converter for STATCOM
applications [3], [4]; and 3) an ac/dc/ac converter for wind
power and HVDC applications [4]–[8]. Fig. 1 demonstrates
the grid-connected dc/ac converter used in a microgrid to
connect distributed energy resources. Conventionally, this type
of converter is controlled using the standard decoupled d-q
vector control approach [5]–[8].
Notwithstanding its merits, recent studies indicate that this
control strategy is inherently limited due to its competing
nature [9], [10]. Issues reported in the literature include: 1) dif-
ficulty in tuning the proportional-integral (PI) controllers [3];
2) instability in low voltage applications [11]; 3) fluctuat-
ing dc-link voltage [12]; 4) malfunction such as unexpected
trips [5]; and 5) difficulty to synchronize for initial connection
of the GCC to the electric power grid [13].
For example, in [3], it is noted that tuning PI parameters
for a standard decoupled d-q vector controller in a STAT-
COM application is difficult. This finding is consistent with a
result reported in this paper, which shows that tuning the PI
gains is hard at a large sampling time. References [14]–[16]
show that the inner-current controller and the phase-locked
loop dynamics of conventional control techniques may be
affected significantly in weak ac-system connections. Ref-
erence [11] also informs of instable operability in such
2162-237X © 2013 IEEE

2 IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
conditions. Reference [12] indicates that there is a high
fluctuating dc-link voltage using the conventional GCC control
approach. References [5], [17], and [18] show that wind
farms periodically experience a high degree of imbalance and
harmonic distortions, which has resulted in numerous trips.
References [13] and [19] point out that using conventional
vector control methods, synchronization is always required
for initial connection of a GCC to the electric power grid.
References [20] and [21] indicate that the poor performance of
such technology has become an obstacle for GCCs in HVDC
transmission under challenging ac-system conditions.
To overcome the deficiencies, an adaptive control approach
was proposed recently that employs a direct-current control
(DCC) strategy [22], [23]. However, a major challenge of the
direct-current-based vector control mechanism is that no well-
established systematical approach to tuning the PI controller
gains exists, so that optimal DCC is hard to obtain. Other con-
trol methods have also been developed recently, direct power
control (DPC) [24]–[26] and predictive current control (PrCC)
[27]–[29] in particular. Notwithstanding their merits, all these
control methods show some limitations. This situation moti-
vates the development of neural-network-based optimal control
techniques for GCC vector control applications, as presented
in this paper.
In recent years, significant research has been conducted in
the area of dynamic programming (DP) for optimal control of
nonlinear systems [30]–[34]. Classical DP methods discretize
the state space and directly compare the costs associated with
all feasible trajectories that satisfy the principle of optimality,
guaranteeing the solution of the optimal control problem [35].
Adaptive critic designs constitute a class of approximate
DP (ADP) methods that use incremental optimization com-
bined with parametric structures that approximate the optimal
cost and the control [36]–[38]. Both classical DP and ADP
methods have been used to train neural networks for a large
number of nonlinear control applications, such as steering and
controlling the speed of a two-axle vehicle [39], intercepting
an agile missile [40], performing auto landing and control of
an aircraft [41]–[43], controlling a turbogenerator [44], and
tracking control with time delays [45]. As for GCC controllers,
neural networks have been primarily used to generate external
reference signals. In [46], a neuro-fuzzy external controller
is developed to generate reference ac bus voltage signal to
the PI controller of a STATCOM for coordinated optimal
control of the STATCOM and two synchronous generators.
In [47], an interface neuro-controller is proposed for coor-
dinated reactive power control between a large wind farm
equipped with doubly fed induction generators (DFIGs) and a
STATCOM, while the GCC controllers within both DFIGs and
the STATCOM have adopted conventional standard PI vector
control structures.
In [48], we developed a preliminary neural network vec-
tor control structure for a grid-connected rectifier/inverter in
renewable and electric power system applications. However
encouraging the results were, the design showed steady-state
errors and was unable to track targets properly under variable
system parameters. This paper has extended far beyond [48]
by developing an improved neural network design to overcome
Fig. 2. GCC schematic.
Fig. 3. Standard vector control structure.
these limitations and by testing the neural vector control
strategy in a more practical nested-loop control condition.
Moreover, a control signal can only be applied to an actual
system through power converters, which involves continuous
switching on and off of the converters [49] and hence distorts
the ideal control signal. This switching impact is carefully
evaluated in this paper.
The rest of this paper is structured as follows. The basic
topologies of the standard vector control method, DCC, DPC
and PrCC are briefly evaluated in Section II. Section III
proposes a neural network vector control configuration.
Section IV explains how to employ DP to achieve optimal
neural vector control for the GCC system. The performance
of the neural network vector control scheme is assessed in
dynamic and power converter switching environments in
Section V. Section VI analyzes the performance of the neural
vector controller in a nested-loop control condition. Finally,
this paper concludes with a summary of the main points.
II. CONVENTIONAL GCC CONTROL TECHNIQUES
Fig. 2 shows the schematic of the GCC, in which a dc-
link capacitor is on the left, and a three-phase voltage source,
representing the voltage at the Point of Common Coupling
(PCC) of the ac system, is on the right.
In the d-q reference frame, the voltage balance across the
grid filter is

vd
vq

= R

id
iq

+ L
d
dt

id
iq

+ ωs L

−iq
id

+

vd1
vq1

(1)
where ωs is the angular frequency of the grid voltage, and L
and R are the inductance and resistance of the grid filter. In
the PCC voltage-oriented frame [3], [50], the instant active
and reactive powers absorbed by the GCC from the grid are
proportional to the grid’s d- and q-axis currents, respectively,
as shown by (2) and (3)
p(t) = vdid + vqiq = vdid (2)
q(t) = vqid − vdiq = −vdiq. (3)

LI et al.: ARTIFICIAL NEURAL NETWORKS FOR CONTROL OF A GRID-CONNECTED RECTIFIER/INVERTER 3
A. Standard Vector Control
The standard vector control method for the GCC, widely
used in renewable and electric power system applications,
deploys a nested-loop structure consisting of a faster inner
current loop and a slower outer loop, as shown in Fig. 3
[3], [4], [50]. In this figure, the d-axis loop is used for dc-link
voltage control, and the q-axis loop is used for reactive power
or grid voltage support control. The control strategy of the
inner current loop is developed by rewriting (1) as
vd1 = −(Rid + L · did/dt) + ωs Liq + vd (4)
vq1 = −(Riq + L · diq/dt) − ωs Lid (5)
in which the bracketed item in (4) and (5) is treated as the
transfer function between the input voltage and output current
for the d- and q-axis loops, and the other terms are treated as
compensation items [3], [4], [50]. However, it was found that
the control signals generated by the d- and q-axis PI controllers
do not contribute in a right way in terms of the decoupled dq
control objectives [22]. Although there are compensation terms
in Fig. 3, they do not contribute in a feedback control principle.
Hence, this control structure has a competing control nature
[22], [48], which could result in malfunctions of the system.
B. Direct-Current Vector Control
The DCC [22], [23], developed recently to overcome the
deficiencies of standard vector control techniques, is consid-
ered as a pilot adaptive vector control strategy. The theoretical
foundation of the DCC is expressed in (2) and (3), i.e., the
use of d- and q-axis currents directly for active and reactive
power control of the GCC system. Unlike the conventional
approach that generates a d- or q-axis voltage from a GCC
current-loop controller, the DCC outputs a current signal by
the d- or q-axis current-loop controller (Fig. 4). In other words,
the output of the controller is a d- or q-axis tuning current
i
d or i
q, while the input error signal tells the controller how
much the tuning current should be adjusted during the dynamic
control process. The development of the tuning current control
strategy has adopted intelligent control concepts [23], e.g., a
control goal to minimize the absolute or root-mean-square
(RMS) error between the desired and actual d- and q-axis
currents through an adaptive tuning strategy. Nonetheless,
a major challenge of the DCC is that no well-established
systematical approach exists for tuning the controller PI gains,
so an optimal DCC controller is difficult to obtain. Actually,
the cross terms as shown in Fig. 4 imply that a neural network
vector controller could be a better fit to meet the GCC control
requirements.
C. Direct Power Control
The basic idea of the DPC approach, proposed by
Noguchi [24], is the direct control of active and reactive power.
In DPC, the inner current control loops and the PWM modula-
tor are not required because the converter switching states are
selected by a switching table based on the instantaneous errors
between the commanded and the estimated values of active and
reactive powers (Fig. 5). The active and reactive power errors
Fig. 4. GCC direct-current vector control structure.
Fig. 5. DPC configuration.
Fig. 6. Predictive current vector control structure.
are fed to hysteresis comparators and their outputs, together
with the system’s vector phase, are used to select from the
switching tables the best vector for the next control cycle.
DPC has the advantages of high dynamic response to demands
in active or reactive power and simplicity in implementation
[25], [26]. But, primary disadvantages of this control technique
are high harmonic distortion and unbalance in the system
current, variable switching frequency under different operating
conditions, and requirement of a high switching frequency
[26], which causes major impacts to a GCC system.
D. Predictive Current Control
The predictive control algorithm first estimates the model
parameters, including R and L of the grid filter and PCC
voltage [27]. The model is then used to predict the current
and to determine the voltage necessary to meet the control
objective for each control interval. In Fig. 6, the PrCC block
involves a current prediction equation to estimate the grid
current at the next sampling interval and a control equation
to determine the next GCC control voltage [27], [28].
A PrCC has a fast current tracking response, which permits
the minimization of the dc-bus capacitance, increases the
voltage loop bandwidth, and reduces harmonic distortions in
ac current waveforms [28], [29]. However, a PrCC becomes

Fig. 7. GCC neural vector control structure. va1,b1,c1 stands for the GCC output voltage in the three-phase ac system and the corresponding voltages in
dq-reference frame are vd1 and vq1. va,b,c is the three-phase PCC voltage and the corresponding voltage in dq-reference frame are vd and vq . ia,b,c stands
for the three-phase current flowing from PCC to GCC and the corresponding currents in dq-reference frame are id and iq . v∗
d1 and v∗
q1 are d- and q-axis
voltages from neural controller and the corresponding control voltage in the three-phase domain is v∗
a1,b1,c1.
unstable when the programmed filter inductance differs from
its actual value. In addition, if the resistive part of the filtering
inductors is not accurately measured and programmed, the
predictive control presents a steady-state error. Since filter
parameters vary along with inverter operation, it is difficult
to achieve an adequate static and dynamic performance [29].
In summary, in order to meet to the optimal GCC control
requirements it is important to develop new methods that
integrate the advantages of different conventional control tech-
niques and at the same time avoid their shortcomings. Our
neural-network controller proposal is a step in that direction.
III. STRUCTURE OF GCC VECTOR CONTROL USING
ARTIFICIAL NEURAL NETWORKS
The neural-network-based vector control structure of the
GCC current-loop is shown in Fig. 7, in which the converter
output voltage, grid PCC voltage, and grid current are consis-
tent with those shown in Fig. 2. The neural network, known
here as the action network, is applied to the GCC through a
PWM mechanism to regulate the GCC output voltage va1,b1,c1
in the three-phase ac system. The ratio of the GCC output
voltage to the output of the action network is a gain of kPWM,
which equals to Vdc/2 if the amplitude of the triangle voltage
waveform in the PWM scheme is 1 V [49].
The integrated GCC and grid system is described by (1),
which is rearranged into the standard state-space represen-
tation as shown by (6), where the system states are id and
iq, grid PCC voltages vd and vq are normally constant, and
converter output voltages vd1 and vq1 are the control voltages
that are to be specified by the output of the action network.
For digital control implementation and the offline training of
the neural network, the discrete equivalent of the continuous
system state-space model from (6) must be obtained [51] as
shown by (7), where Ts represents the sampling period, k is
an integer time step, F is the system matrix, and G is the
matrix associated with the control voltage. In this paper, a
zero-order-hold (ZOH) discrete equivalent is used to convert
the continuous state-space model of the system in (6) to the
discrete state-space model in (7). We used Ts = 1 ms in all
experiments
d
dt

id
iq

= −

R f /L f −ωs
ωs R f /L f

id
iq

−
1
L f

vd1
vq1

+
1
L f

vd
vq

(6)

id(kTs + Ts)
iq(kTs + Ts)

= F

id(kTs)
iq(kTs)

+ G

vd1(kTs) − vd
vq1(kTs) − vq

. (7)
The discrete system model in Eq. (7) can be written more
concisely as

idq (k + 1) = F ·
idq (k) + G ·

vdq1 (k) −
vdq

(8)
The action network makes the control decision
vdq1 (k) at each
time step k in the above equation. The action network is a
fully connected multi-layer perceptron [52], and its position
and role in the GCC architecture are shown in Fig. 7. As
indicated in Fig. 7, the inputs to the neural network are

idq (k) ,
idq (k) −
i∗
dq (k) , and
s(k), where
s(k) represents an
integral term defined below in (9). Since each of these inputs is
a 2-dimensional vector (with d and q components), the action
network has 6 inputs in total. The action network we used
had 2 hidden layers of 6 nodes each, and 2 output nodes,
and short-cut connections between all pairs of layers, with
hyperbolic tangent functions at all nodes. With the inputs and
weight vector
w, we will denote the action network as the
function A

idq (k) ,
idq (k) −
i∗
dq (k) ,
s(k),
w

. The integral-
term input,
s(k), is defined by

s(k) =
k
0

idq (t) −
i∗
dq (t)

dt (9)
Prior work with this sort of neurocontroller utilized a
similar set of neural inputs [46], except that in that work

the integral input
s(k) was not present. This system produced
good tracking performance during testing when the system
equation (8) was identical to that under which the network was
trained, but when the system equation (8) was varied slightly
(for example if the inductance L or resistance R of the plant
deviated slightly), then the tracking system showed a steady-
state error. In this case the system was unable to track the
reference dq current exactly. This is due to the fact that the
feed-forward network was trained to act on slightly different
plant dynamics than it was actually experiencing. The extra
integral input term, given by (9) and introduced in this paper,
is designed to resolve this steady-state tracking error.
For a trained neural-network controller, the integral term
would provide a history of all past errors by summing them
together. If there is an error in a given time step, it gets added
to the integral term for the next time step. Thus, the integral
term will only be the same as it was last time step if there is no
error in this time step, preventing the neural-network controller
from staying at a non-target value after the controlled system
reaches its steady state unless

idq =
i∗
dq

. The other terms
drive a controlled variable closer to the reference, and as the
error becomes smaller, the integral term’s difference from its
value for the prior time step diminishes, reducing its steady-
state error influence and allowing the system to home in on
the target.
For a reference dq current
i∗
dq (k), the control action
applied to the system is expressed by:

vdq1 (k) = kPW M · A

idq (k) ,
idq (k) −
i∗
dq (k) ,
s(k),
w

(10)
where A (•) represents the action network as described above.
IV. TRAINING NEURAL NETWORK FOR OPTIMAL VECTOR
CONTROL OF A GCC
A. DP in GCC Vector Control
DP employs the principle of optimality and is a very useful
tool for solving optimization and optimal control problems.
According to [34], the principle of optimality is expressed
as: “An optimal policy has the property that whatever the
initial state and initial decision are, the remaining deci-
sions must constitute an optimal policy with regard to the
state resulting from the first decision.” The typical struc-
ture of the discrete-time DP includes a discrete-time system
model and a performance index or cost associated with the
system [37].
The DP cost function associated with the vector-controlled
system is
J(
x( j),
w) =
K
k= j
γ k− j
· U(
idq(k),
i∗
dq(k)) (11)
where γ is the discount factor with 0 ≤ γ ≤ 1, K is the
trajectory length used for training, and U(·) is defined as
U(
idq(k),
i∗
dq(k)) = (id(k) − i∗
d (k))2 + (iq(k) − i∗
q (k))2.
(12)
The function J(·), dependent on the initial time j and the
initial state
idq( j), is referred to as the cost-to-go of state

idq( j) in the DP problem. The objective of the DP problem is
to choose a vector control sequence,
vdq1(k), k = j, j+1,…,
so that the function J(·) in (11) is minimized.
B. Backpropagation Through Time Algorithm
The action network was trained to minimize the DP cost
of (11) by using the backpropagation through time (BPTT)
algorithm [53]. BPTT is gradient descent on J(
x( j),
w) with
respect to the weight vector of the action network. BPTT
can be applied to an arbitrary trajectory with an initial state

idq ( j), and thus be used to optimize the vector control
strategy. In general, the BPTT algorithm consists of two steps:
a forward pass which unrolls a trajectory, followed by a
backward pass along the whole trajectory which accumulates
the gradient descent derivative. Algorithm 1 gives pseudo code
for both stages of this process. Lines 1–9 evaluate a trajectory
of length K using (8)–(12). The integral inputs defined by
(9) are approximated by a rectangular sum, in line 7 of the
algorithm.
The second half of the algorithm calculates the desired
gradient, ∂ J/∂
w. This would then be used for optimization
of the function J(
x( j),
w) by using multiple iterations and
multiple calls to Algorithm 1. In this code, the variables
J−
idq(k), J−
s(k) and J−
w are workspace column vectors
of dimension 2, 2, and dim(
w), respectively. These variables
hold the “ordered partial derivatives” of J with respect to
the given variable name, so that for example J−
idq(k) =
∂+ J/∂
idq(k). This ordered partial derivative, as defined by
Werbos [53], [54], represents the derivative of J with respect
to
idq(k), assuming all other variables which depend upon

idq(k) in lines 5–8 of Algorithm 1 are not fixed, and thus
their derivatives will influence the value of J−
idq(k) via
the chain rule. The derivation of the gradient computation
part of the algorithm (lines 11–19) is exact, and was derived
following the method described in detail by [54], which is
referred to as generalized backpropagation [53], or automatic-
differentiation [55]. In the pseudo code, the vector and matrix
notation is such that all vectors are columns; differentiation
of a scalar by a vector gives a column. Differentiation of a
vector function by a vector argument gives a matrix, such that
for example (dA/dw)ij =dAj /dwi.
In lines 16–18, the algorithm refers to derivatives of the
action network function A(·) with respect to its arguments,

idq(k),
s (k), and
w. These derivatives would be calculated
by ordinary neural-network backpropagation, which needs to
be implemented as a sub-module, and should not be confused
with BPTT itself. The BPTT pseudo code also requires the
derivatives of the function U(·), which can be found directly
by differentiating (12). The pseudo code uses matrices F and
G which represent the exact model of the plant; there was no
need for a separate system identification process or separate
model network. For the termination condition of a trajectory,
we used a fixed trajectory length corresponding to a real time
of 1 second (i.e. K = 1000). We used γ = 1 for the discount
factor.

Algorithm 1 DP Based BPTT Algorithm for GCC Vector
Control
1: J ← 0
2:
s(0) ←
0 {Integral input}
3: {Unroll a full trajectory}
4: for k = 0 to K-1 do
5:
vdq1 (k) ← kPW M · A

idq (k) ,
idq (k) −
i∗
dq (k) ,
s(k),
w

{Control action}
6:
idq (k + 1) ← F ·
idq (k) + G ·

vdq1 (k) −
vdq

{Calculate next state}
7:
s (k + 1) ←
s (k) +

idq (k) −
i∗
dq (k)

· Ts
8: J ← J + γ k · U

idq (k) ,
i∗
dq (k)

9: end for
10: {Backwards pass along trajectory}
11: J−
w ← 0
12: J−
idq (K) ← 0
13: J−
s (K) ← 0
14: for k = K-1 to 0 step -1 do
15: J−
vdq1 (k) ← GT · J−
idq (k + 1)
16:
J−
idq (k) ← kPW M
d

A

idq (k),
idq (k)−
i∗
dq (k),
s(k),
w

d
idq (k)
·
J−
vdq1 (k) + Ts J−
s(k + 1) + FT J−
idq (k + 1)
+ γ k ·
∂

U

idq (k),
i∗
dq (k)

∂
idq (k)
17:
J−
s (k) ← J−
s(k + 1) + kPW M·
∂

A

idq (k),
idq (k)−
i∗
dq (k),
s(k),
w

∂
s(k) ·
J−
vdq1 (k)
18:
J−
w ← J−
w + kPW M·
∂

A

idq (k),
idq (k)−
i∗
dq (k),
s(k),
w

∂
w(k) J−
vdq1 (k)
19: end for
20: {on exit, J−
w holds ∂ J
∂
w for the whole trajectory}
Fig. 8. Reference dq current trajectory for training neural controller.
C. Training the Neural Controller
To train the neural controller, the system data of the inte-
grated GCC and grid system is specified for a typical GCC in
renewable energy conversion system applications [6], [7], [22].
These include: 1) a three-phase 60 Hz, 690 V voltage source
signifying the grid; 2) a reference voltage of 1200 V for the
dc link; and 3) a resistance of 0.012 and an inductance of
2 mH standing for the grid filter.
The training was repeated for 10 different experiments,
with each experiment having different initial weights. For
each experiment, the training procedure includes: 1) randomly
Fig. 9. Average DP cost per trajectory time step for training neural controller.
generating a sample initial state idq( j); 2) unrolling the tra-
jectory of the GCC system from the initial state; 3) randomly
generating a sample reference dq current trajectory; 4) training
the action network based on the DP cost function in (11) and
the BPTT training algorithm; and 5) repeating the process
for all the sample initial states and reference dq currents.
For each experiment, 10 sample initial states were generated
uniformly from id = [100 A, 120 A] and iq = [0 A, 20 A].
Each initial state was generated with its own random seed.
Each trajectory duration was unrolled during training for a
duration of 1 s, and the reference dq current was changed
every 0.1 s. Ten reference current trajectories were generated
randomly, with each trajectory having its own seed too.
Fig. 8 shows a randomly generated reference current trajectory.
The weights were initially all randomized using a Gaussian
distribution with zero mean and 0.1 variance. Training used
RPROP [56] to accelerate learning, and we allowed RPROP
to act on 10 trajectories simultaneously in batch update mode.
For each experiment, training stops at 1000 iterations and the
average trajectory cost per time step over the 10 trajectories
was calculated. The trained network with the lowest average
trajectory cost from the 10 experiments is picked as the final
action network.
The generation of the reference current considered the phys-
ical constraints of a practical GCC system. Both the randomly
generated d- and q-axis reference currents were first chosen
uniformly from [−500 A; 500 A], where 500 A represents
the rated GCC current in this paper. Then, these randomly
generated d- and q-axis current values were checked to see
whether their resultant magnitude exceeds the GCC rated
current limit and/or the GCC exceeds the PWM saturation
limit. From the neural network standpoint, the PWM saturation
constraint stands for the maximum positive or negative voltage
that the action network can output. Therefore, if a reference dq
current requires a control voltage that is beyond the acceptable
voltage range of the action network, it is impossible to reduce
the cost (11) during the training of the action network.
The following two strategies are used to adjust randomly
generated reference currents. If the rated current constraint is
exceeded, the reference dq current is modified by keeping the
d-axis current reference i∗
d unchanged to maintain active power
control effectiveness (13) while modifying the q-axis current
reference i∗
q to satisfy the reactive power or ac bus voltage
support control demand (14) as much as possible as shown by
[22] and [23]
i∗
q new = sign(i∗
q ) ·

i∗
dq max
2
− (i∗
d )2. (13)

Fig. 10. Vector control of GCC in power converter switching environment.
If the PWM saturation limit is exceeded, the reference q-axis
current is modified by
v∗
q1 = −i∗
d X f v∗
d1 =

v∗
dq1 max
2
− (v∗
q1)2
i∗
q =
(v∗
d1 − vd)
X f
(14)
which represents a condition of keeping the q-axis voltage
reference v∗
q1 unchanged so as to maintain the active power
control effectiveness while modifying the d-axis voltage refer-
ence v∗
d1 to meet the reactive power control demand as much
as possible [22], [23], [48].
Fig. 9 shows the average DP cost per trajectory time step
for one successful training of the action neural network. As
the figure indicates, the overall average trajectory cost dropped
to small number quickly, demonstrating good learning ability
of the neural controller for the vector control application.
V. PERFORMANCE EVALUATION OF TRAINED NEURAL
VECTOR CONTROLLER
To evaluate the performance of the neural network vector
control approach and compare the neural controller with the
conventional standard and DCC vector control methods, an
integrated transient simulation system of a GCC system is
developed by using power converter switching models in
SimPowerSystems (Fig. 10). The power converter is a dc/ac
PWM converter. The dc voltage source represents the dc-link.
The converter switching frequency is 1980 Hz, and loss of
the power converter is considered. In the converter switching
environment, the evaluation can be made under close to real-
life conditions, which includes: 1) real-time computation of
PCC voltage space vector position; 2) measurement of instant
grid dq current and PCC dq voltage; and 3) generation of
the dq control voltage by the controller in the PCC voltage-
oriented frame [23]. The PCC bus is connected to the grid
through a transmission line that is modeled by an impedance.
A fault-load is connected before the PCC bus for the purpose
to evaluate how the controller behaves when a fault appears
in the grid. For digital control implementation of the neural
or conventional controllers, the measured instantaneous three-
phase PCC voltage and grid current pass through a ZOH block.
The ZOH is also applied to the output of the controller before
being connected to the converter PWM signal generation
block.
A. Ability of Neural Controller to Track Reference Current
The reference current is generated randomly within the
acceptable GCC current range for the neural controller track-
ing validation. Fig. 11 presents a case study of tracking the
reference current by using neural vector controller in the
power converter switching environment. The sampling time
is Ts = 1 ms. In the figure, initial system states can be
generated randomly and the reference dq currents can change
to any values, within the converter rated current and PWM
saturation limit, that are not used in the training of the neural
network. At the beginning, both GCC d- and q-axis currents
are zero, and the d- and q-axis reference currents are 100 A
and 0 A, respectively. After the start of the system, the neural
controller quickly regulates the d- and q-axis currents to the
reference values. When the reference dq current changes to
new values at t = 2 s and t = 4 s, the neural controller restores
d- and q-axis current to the reference currents immediately
[Fig. 11(a)]. However, due to the switching impact, the actual
dq current oscillates around the reference current. An exam-
ination of the three-phase grid current shows that the current
is properly balanced [Fig. 11(b)]. For any command change
of the reference current within the converter rated current and
PWM saturation limit, the system can be adjusted to a new
reference current immediately, demonstrating strong optimal
control capability of the neural vector controller. Since the
rated GCC current used in this paper is 500 A, for a d-axis
reference current i∗
d within [−500 A, 500 A], the q-axis current
i∗
q cannot exceed the lower value calculated from (13) and (14).
B. Comparison of Neural Controller With Conventional
Standard and DCC Vector Control Methods
For the comparison study, the current-loop PI controller is
designed by using the conventional standard and the direct-
current vector control methods, respectively, as shown in
Section II. For the conventional standard vector control struc-
ture (Fig. 3), the gains of the digital PI controller are designed
based on the discrete equivalent of the system transfer func-
tion, as shown in (4) and (5) [7]. For the DCC vector control
structure (Fig. 4), the gains of the digital PI controller is tuned
until the controller performance is acceptable [22]. With the
sampling time of Ts = 1 ms, no stable PI gains were obtained
for the conventional standard vector control approach; for the
DCC vector control method, it is easier to get a stable PI gain
but the actual dq current oscillates around the reference current
much higher than that of the neural-network controller.
Figs. 12 and 13 present the performance of the standard
and DCC vector controllers under the same conditions used
in Fig. 11 but with a smaller sampling time of 0.1 ms. Even so,
compared to the neural-network controller having the sampling
time of 1 ms, the actual dq current of the standard and DCC
vector controllers oscillates worse than that of the neural-
network controller and there are more distortion and unbalance
in the three-phase grid current.
The comparisons were also conducted for many other
reference dq current cases. All the case studies showed that
the neural-network controller always performs better than both
conventional and DCC vector control mechanisms. In general,

Fig. 11. Performance of neural vector controller [Ts =1 ms (a) dq current
(b) three-phase current].
Fig. 12. Performance of conventional standard vector controller [Ts = 0.1 ms
(a) dq current (b) three-phase current].
the neural-network controller can get to a reference current
very quickly and stabilize around the reference with very small
oscillations. This may give the neural-network controlled GCC
system the following advantages: 1) low harmonic current dis-
tortion; 2) small ac system unbalance; 3) reduced sampling and
computing power requirement; and 4) improvement of GCC
connection to the grid without synchronization. In particularly,
the synchronization for GCC grid connection has been an
issue investigated by many researchers in the field [13], [19].
The advantage of the neural network vector controller in this
perspective may result in important impact in developing new
microgrid control technologies and overcome many existing
challenges for control and operation of a microgrid.
C. Ability to Track Fluctuating Reference Current
GCCs are typically used to connect wind turbines and solar
photovoltaic (PV) arrays to the electric power grid. Due to
Fig. 13. Performance of DCC vector controller [Ts = 0.1 ms (a) dq current
(b) three-phase current].
Fig. 14. Performance of neural vector controllers under a variable reference
current condition in power converter switching environment (Ts = 1 ms).
variable weather conditions, the power transferred from a
wind turbine or PV array changes frequently, making the
GCC reference current vary constantly over the time. Over
periods shorter than one hour, for example, wind speed can
be approximated as the superposition of a slowly varying mean
speed Vw plus N sinusoidal components having frequencies
ωi , amplitudes Ai and random phases φi as shown by [57]
vw(t) = Vw +
N
i=1
Ai cos(ωi t + φi ). (15)
Based on (15), a variable d-axis reference current is gen-
erated as shown in Fig. 14, while q-axis reference current is
zero (i.e., zero reactive power), which corresponds to typical
wind power production under a fluctuating and gusty wind
condition. Due to the motor sign convention used in Fig. 2,
power generation from a wind turbine is represented by
negative d-axis current values as shown in Fig. 14. Again, the
figure shows that the neural network performs very well in
tracking the variable reference current in the power converter
switching environment.
D. Performance Evaluation Under Variable Parameters
of GCC System
GCC stability has been one of the main issues to be
investigated in conventional vector controls. In general, such

Fig. 16. GCC neural vector control structure when considering voltage disturbance impact. Vd n and Vq n are the d and q components of the nominal GCC
voltage. In the PCC voltage oriented frame Vq n = 0 V and therefore Vq n is not listed in the figure. kPWM is the gain of the GCC and equals to Vdc/2.
Fig. 15. Performance of neural vector controller under variable grid-filter
inductance (Ts = 1 ms). (a) Actual inductance is 60% above the nominal
inductance. (b) Actual inductance is 40% below the nominal inductance.
(c) Actual inductance is 50% below the nominal inductance.
studies primarily focus on the GCC performance for either
system parameter changes or for unbalanced or distorted ac
system conditions. For instance, in [1], a small-signal model is
used for a sensitivity study of the GCC under variable system
parameter conditions. In [58], a control strategy is developed
to improve the GCC performance under variable system con-
ditions. In this paper, the neural control method is investigated
for two variable GCC system conditions, namely: 1) variation
of grid-filter resistance and inductance and 2) variable PCC
voltage.
Fig. 17. Performance of neural vector controllers for short-circuit ride
through (a) PCC bus voltage in per unit, (b) dq grid current, and (c) three-
phase grid current.
It was found that the neural-network controller is mainly
affected by variation of the grid-filter inductance but not the
resistance. Fig. 15 shows how the neural vector controller
is affected as the grid-filter inductance deviates from the
its nominal value used in training the network. In general,
if the actual inductance is smaller than the nominal value,
the performance of the neural controlled GCC deteriorates
[Fig. 15(b) and (c)]. If the actual inductance is larger than
the nominal value, the performance of the controller is almost

Fig. 19. Neural vector controller in nested-loop control condition.
Fig. 18. Nested-loop GCC neural vector control structure.
not affected (Fig. 15a). However, as the actual inductance
is higher than the nominal inductance, it is easier for the
GCC to get into the PWM saturation as explained in [22]
and [23], particularly for generating reactive power conditions.
The study shows that when the actual inductance is over 50%
below the nominal value, the impact becomes significant and
high distortion and unbalance are found in the grid current
[Fig. 15(c)]. A comparison study also demonstrates that the
neural controller is much more stable and that it performed
better than both conventional standard and DCC vector control
methods under the variable grid-filter inductance conditions.
Regarding the variation of the GCC voltage, a special
technique is employed in this paper to prevent the neural
controller from being affected by the GCC voltage variation.
Assume that the nominal and disturbance components of the
PCC dq voltage are
vdq n and
vdq dis, respectively. Then, (6)
can be rewritten as
d
dt

idq = −Fc ·
idq − (
vdq1 − [
vdq n +
vdq dis])/L f (16)
where Fc is the continuous system matrix. Since the training
of the neural network in Section IV does not consider PCC
voltage disturbance, the neural controller will be unable to
track the reference demand or lose stability if a high voltage
disturbance appears on the PCC bus. One way to overcome the
disturbance impact is to introduce d- and q-axis disturbance
voltage terms to the network inputs. However, this makes the
training more difficult and the improvement is not evident or
worse. Instead of using the disturbance voltage as network
inputs, this paper introduces the disturbance voltage to the
output of a well trained action network, with the intention
of neutralizing the disturbance. This makes the final control
voltage applied to the system become

vdq1(k) = kPWM · [A(
idq(k),
w) +
vdq dis/kPWM] (17)
where
vdq =
vdq n +
vdq dis is the actual PCC voltage. With
the introduction of the disturbance voltage to the output of the
action network, the neural network vector control structure,
different from Fig. 7, is shown by Fig. 16. The performance
evaluation demonstrates that this strategy is very effective to
maintain neural network performance under distorted PCC
voltage conditions.
Fig. 17 presents how the neural controller performs under
variable PCC voltage caused by a fault. The fault starts at
1 s and is cleared at 3 s, which causes a voltage drop on the
PCC bus during this time period [Fig. 17(a)] depending on
the fault current levels. As it can be seen from Fig. 17(b),
the neural vector controller can still effectively regulate the
dq current even under a voltage drop of more than 80% at
the PCC caused by a fault, demonstrating strong short-circuit
ride-through capability of the neural controller. For many
other cases, the neural vector controller demonstrates excellent
performance from various aspects. At the start and end of the
fault, there is a high peak in the dq current. However, it is
necessary to point out that this peak does not mean a high
grid current but represents a rapid transition from the previous
three-phase current state to a new one [Fig. 17(c)].
VI. EVALUATION OF NEURAL VECTOR CONTROLLER IN
NESTED-LOOP CONTROL CONDITION
In many renewable and microgrid applications, the GCC
control has a nested-loop structure consisting of a faster inner
current loop and a slower outer control loop that generates d-
and q-axis current references, i∗
d and i∗
q, to the current loop
controller [7], [22]. Fig. 18 shows the neural network in the
nested-loop control condition, in which the d-axis loop is used
for dc-link voltage control and q-axis loop is used for reactive
power or grid voltage support control [22], [23]. The error
signal between measured and reference dc voltage generates
a d-axis current reference to the neural network through a PI
controller while the error signal between actual and desired
reactive power generates a q-axis current reference. Fig. 19
shows the schematics of the neural vector controller in a
ac/dc/ac converter structure, which is the typical situation for
grid integration of distributed energy resources as shown in
Fig. 1. In Fig. 19, the left side represents the grid and the
right side represents a renewable energy source (RES) such
as a wind turbine. The power transfers from the RES through
the dc-link capacitor and the GCC to the grid.

Fig. 20. Performance of neural controller in nested-loop control condition.
(a) DC link voltage. (b) Instantaneous active/reactive power waveforms.
(c) Grid three-phase current waveforms.
Fig. 20 shows the performance of the neural control
approach in the nested-loop structure. Before t = 4 s, the
RES generates an active power of 100 kW while the GCC
reactive power reference is 100 kVar, i.e., the GCC should
absorb reactive power from the grid. The initial dc-link voltage
is 1200V. Although no synchronization control is employed
at the start of the system, both the dc-link voltage and the
GCC reactive power are adjusted around the reference values
quickly and have very small oscillations by using the neural-
network control. At t = 4 s, the active power generated
by the RES changes to 200 kW, which causes more active
power delivered to the grid through the dc-link and the GCC.
The reactive power reference is unchanged. Therefore, the
dc-link voltage increases, but with the neural network vector
control, the dc-link voltage are quickly regulated around the
reference value. At t = 8 s, the reactive power reference
changes from 100 kVar to −25 kVar, i.e., the GCC should gen-
erate reactive power to the grid. At t = 12 s, the reactive power
reference changes from −25 kVar to 50 kVar, i.e., a condition
of absorbing reactive power. In general, for all the reference
changes, the neural-network controller demonstrates very good
performance to meet the nested-loop control requirements.
VII. CONCLUSION
Three-phase grid-connected rectifier/inverters are used
widely in renewable, microgrid and electric power system
applications. This paper analyzes the limitations associ-
ated with conventional vector control methods for the grid-
connected converters. Then, a neural-network based vec-
tor control method was developed. The paper described
how the vector controller was developed based on a
dynamic-programming technique and trained via a backprop-
agation through time algorithm.
The performance evaluation demonstrates that the neural
controller can track the reference d- and q-axis currents effec-
tively even for highly random fluctuating reference currents.
Compared to standard vector control methods and direct-
current vector control techniques, the neural vector control
approach produces the fastest response time, low overshoot,
and, in general, the best performance.
To improve neural controller performance and stability
under disturbance conditions, we used additional strategies.
These include adding integrals of error signals to the network
inputs and introducing grid disturbance voltage to the outputs
of a well-trained network rather than to the inputs of the
network. We have proved that these strategies are effective.
In both power converter switching environments and nested-
loop control conditions, the neural network vector controller
demonstrates strong capability in tracking reference command
while maintaining a high power quality. Under a fault in the
grid system, the neural controller exhibits a strong short-circuit
ride-through capability.
For future work, we plan to purchase equipment and develop
hardware experiment system for a laboratory setup as shown
by Fig. 19. We believe that the successful hardware experi-
ment would accelerate the commercialization of the proposed
neural network vector control technology in power and energy
industry.
ACKNOWLEDGEMENT
The authors would like to thank the reviewers for their
helpful comments which contributed to an improved paper.
REFERENCES
[1] E. Figueres, G. Garcera, J. Sandia, F. Gonzalez-Espin, and J. C. Rubio,
“Sensitivity study of the dynamics of three-phase photovoltaic inverters
with an LCL grid filter,” IEEE Trans. Ind. Electron., vol. 56, no. 3,
pp. 706–717, Mar. 2009.
[2] C. Wang and M. H. Nehrir, “Short-time overloading capability and
distributed generation applications of solid oxide fuel cells,” IEEE Trans.
Energy Convers., vol. 22, no. 4, pp. 898–906, Nov. 2007.
[3] A. Luo, C. Tang, Z. Shuai, J. Tang, X. Xu, and D. Chen, “Fuzzy-PI-
based direct-output-voltage control strategy for the STATCOM used in
utility distribution systems,” IEEE Trans. Ind. Electron., vol. 56, no. 7,
pp. 2401–2411, Jul. 2009.
[4] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galván,
R. C. P. Guisado, M. Á. M. Prats, J. I. León, and N. Moreno-
Alfonso, “Power-electronic systems for the grid integration of renewable
energy sources: A survey,” IEEE Trans. Ind. Electron., vol. 53, no. 4,
pp. 1002–1016, Jun. 2006.
[5] L. Xu and Y. Wang, “Dynamic modeling and control of DFIG based
wind turbines under unbalanced network conditions,” IEEE Trans. Power
Syst., vol. 22, no. 1, pp. 314–323, Feb. 2007.
[6] A. Mullane, G. Lightbody, and R. Yacamini, “Wind-turbine fault
ride-through enhancement,” IEEE Trans. Power Syst., vol. 20, no. 4,
pp. 1929–1937, Nov. 2005.
[7] R. Pena, J. C. Clare, and G. M. Asher, “Doubly fed induction generator
using back-to-back PWM converters and its application to variable speed
wind-energy generation,” IEE Proc. Electr. Power Appl., vol. 143, no. 3,
pp. 231–241, May 1996.
[8] B. C. Rabelo, W. Hofmann, J. L. Silva, R. G. Oliveira, and S. R. Silva,
“Reactive power control design in doubly fed induction generators for
wind turbines,” IEEE Trans. Ind. Electron., vol. 56, no. 10, pp. 4154–
4162, Oct. 2009.

[9] S. Li and T. A. Haskew, “Transient and steady-state simulation of
decoupled d-q vector control in PWM converter of variable speed wind
turbines,” in Proc. 33rd Annu. Conf. IEEE IECON, Nov. 2007, pp. 2079–
2086.
[10] S. Li and T. A. Haskew, “Analysis of decoupled d-q vector control in
DFIG back-to-back PWM converter,” in Proc. IEEE Power Eng. Soc.
General Meeting, Jun. 2007, pp. 1–7.
[11] P. Fischer, “Modeling and control of a line-commutated HVDC trans-
mission system interacting with a VSC STATCOM,” Ph.D. dissertation,
School Electr. Eng., Royal Inst. Technol. Stockholm, Stockholm, Swe-
den, 2007.
[12] U. I. Dayaratne, S. B. Tennakoon, N. Y. A. Shammas, and J. S. Knight,
“Investigation of variable DC link voltage operation of a PMSG based
wind turbine with fully rated converters at steady state,” in Proc. 14th
Eur. Conf. Power Electron. Appl., Sep. 2011, pp. 1–10.
[13] J. Rocabert, G. M. S. Azevedo, A. Luna, J. M. Guerrero, J. I. Candela,
and P. Rodíguez, “Intelligent connection agent for three-phase grid-
connected microgrids,” IEEE Trans. Power Electron., vol. 26, no. 10,
pp. 2993–3005, Oct. 2011.
[14] D. Jovcic, L. A. Lamont, and L. Xu, “VSC transmission model for
analytical studies,” in Proc. IEEE Power Eng. Soc. General Meeting,
vol. 3. Jul. 2003.
[15] M. Durrant, H. Werner, and K. Abbott, “Model of a VSC HVDC
terminal attached to a weak ac system,” in Proc. IEEE CCA, Jun. 2003,
pp. 178–182.
[16] L. Harnefors, M. Bongiornos, and S. Lundberg, “Input-admittance
calculation and shaping for controlled voltage-source converters,” IEEE
Trans. Ind. Electron., vol. 54, no. 6, pp. 3323–3334, Dec. 2007.
[17] I. Codd, “Windfarm power quality monitoring and output comparison
with EN50160,” in Proc. 4th Int. Workshop Large-scale Integr. Wind
Power Transmiss. Netw. Offshore Wind Farm, Oct. 2003, pp. 1–6.
[18] B. I. Nass, T. M. Undeland, and T. Gjengedal, “Methods for reduction
of voltage unbalance in weak grids connected to wind plants,” in Proc.
IEEE Workshop Wind Power Impacts Power Syst., Jun. 2002, pp. 1–7.
[19] A. Timbus, R. Teodorescu, F. Blaabjerg, and M. Liserre, “Synchroniza-
tion methods for three phase distributed power generation systems—
An overview and evaluation,” in Proc. 36th IEEE Power Electron.
Specialists Conf., Jun. 2005, pp. 2474–2481.
[20] L. Zhang, “Modeling and control of VSC-HVDC links connected to
weak AC systems,” Ph.D. dissertation, School Electr. Eng., Royal Instit.
Technol., Stockholm, Stockholm, Sweden, 2010.
[21] L. Zhang, L. Harnefors, and H.-P. Nee, “Power-synchronization control
of grid-connected voltage-source converters,” IEEE Trans. Power Syst.,
vol. 25, no. 2, pp. 809–820, May 2010.
[22] S. Li, T. A. Haskew, Y. Hong, and L. Xu, “Direct-current vector control
of three-phase grid-connected rectifier-inverter,” Electric Power Syst.
Res., vol. 81, no. 2, pp. 357–366, Feb. 2011.
[23] S. Li, T. A. Haskew, and L. Xu, “Control of HVDC light systems using
conventional and direct-current vector control approaches,” IEEE Trans.
Power Electron., vol. 25, no. 12, pp. 3106–3118, Dec. 2010.
[24] T. Noguchi, H. Tomiki, S. Kondo, and I. Takahashi, “Direct power
control of PWM converter without power-source voltage sensors,” IEEE
Trans. Ind. Appl., vol. 34, no. 3, pp. 473–479, May/Jun. 1998.
[25] D. Zhi, L. Xu, and B. W. Williams, “Improved direct power control
of grid-connected DC/AC converters,” IEEE Trans. Power Electron.,
vol. 24, no. 5, pp. 1280–1292, May 2009.
[26] J. A. Restrepo, J. M. Aller, J. C. Viola, A. Bueno, and T. G. Habetler,
“Optimum space vector computation technique for direct power control,”
IEEE Trans. Power Electron., vol. 24, no. 6, pp. 1637–1645, Jun. 2009.
[27] J. C. Moreno, J. M. Espí Huerta, R. G. Gil, and S. A. González,
“A robust predictive current control for three-phase grid-connected
inverters,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1993–2004,
Jun. 2009.
[28] J. M. Espí Huerta, J. Castelló-Moreno, J. R. Fischer, and
R. García-Gil, “A synchronous reference frame robust predictive current
control for three-phase grid-connected inverters,” IEEE Trans. Ind.
Electron., vol. 57, no. 3, pp. 954–962, Mar. 2010.
[29] J. M. Espí, J. Castelló, R. García-Gil, G. Garcerá, and E. Figueres, “An
adaptive robust predictive current control for three-phase grid-connected
inverters,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3537–3546,
Aug. 2011.
[30] A. Al-Tamimi, M. Abu-Khalaf, and F. L. Lewis, “Adaptive critic designs
for discrete time zero-sum games with application to H∞ control,” IEEE
Trans. Syst., Man, Cybern. B, Cybern., vol. 37, no. 1, pp. 240–247,
Feb. 2007.
[31] S. N. Balakrishnan and V. Biega, “Adaptive-critic-based neural networks
for aircraft optimal control,” J. Guid. Control Dyn., vol. 19, no. 4,
pp. 893–898, Jul. 1996.
[32] S. N. Balakrishnan, J. Ding, and F. L. Lewis, “Issues on sta-
bility of ADP feedback controllers for dynamical systems,” IEEE
Trans. Syst., Man., Cybern. B, Cybern, vol. 38, no. 4, pp. 913–917,
Aug. 2008.
[33] S. Mohahegi, G. K. Venayagamoorth, and R. G. Harley, “Adaptive
critic design based neuro-fuzzy controller for a static compensator in
a multimachine power system,” IEEE Trans. Power Syst., vol. 21, no. 4,
pp. 1744–1754, Nov. 2006.
[34] R. E. Bellman, Dynamic Programming. Princeton, NJ, USA: Princeton
Univ. Press, 1957.
[35] D. E. Kirk, Optimal Control Theory: An Introduction. Englewood Cliffs,
NJ, USA: Prentice-Hall, 1970, chs. 1–3.
[36] D. V. Prokorov and D. C. Wunsch, “Adaptive critic designs,” IEEE Trans.
Neural Netw., vol. 8, no. 5, pp. 997–1007, May 1997.
[37] F. Y. Wang, H. Zhang, and D. Liu, “Adaptive dynamic programming:
An introduction,” IEEE Comput. Intell. Mag., vol. 4, no. 2, pp. 39–47,
May 2009.
[38] H. He, N. Zhen, and F. Jian, “A three-network architecture for on-line
learning and optimization based on adaptive dynamic programming,”
Neurocomputing, vol. 78, no. 1, pp. 3–13, 2012.
[39] G. G. Lendaris, L. Schultz, and T. T. Shannon, “Adaptive critic design
for intelligent steering and speed control of a 2-axle vehicle,” in Proc.
IJCNN, vol. 3. Jul. 2000, pp. 73–78.
[40] D. Han and S. N. Balakrishnan, “Adaptive critic based neural networks
for control-constrained agile missile control,” in Proc. Amer. Control
Conf., vol. 4. Jun. 1999, pp. 2600–2604.
[41] G. Saini and S. N. Balakrishnan, “Adaptive critic based neurocontroller
for autolanding of aircraft,” in Proc. Amer. Control Conf., Jun. 1997,
pp. 1081–1085.
[42] S. N. Balakrishnan and V. Biega, “Adaptive-critic-based neural networks
for aircraft optimal control,” J. Guid., Control, Dyn., vol. 19, no. 4,
pp. 893–898, 1996.
[43] K. KrishnaKumar and J. Neidhoefer, “Immunized adaptive critics for
level-2 intelligent control,” in Proc. IEEE Int. Conf. Syst., Man Cybern.,
vol. 1. Oct. 1997, pp. 856–861.
[44] G. K. Venayagamoorthy, R. G. Harley, and D. C. Wunsch, “Comparison
of heuristic dynamic programming and dual heuristic programming
adaptive critics for neurocontrol of a turbogenerator,” IEEE Trans.
Neural Netw., vol. 13, no. 3, pp. 764–773, May 2002.
[45] H. Zhang, R. Song, Q. Wei, and T. Zhang, “Optimal tracking control
for a class of nonlinear discrete-time systems with time delays based on
heuristic dynamic programming,” IEEE Trans. Neural Netw., vol. 22,
no. 12, pp. 1851–1862, Dec. 2011.
[46] S. Mohagheghi, G. K. Venayagamoorthy, and R. G. Harley, “Optimal
neuro-fuzzy external controller for a STATCOM in a 12-bus benchmark
power system,” IEEE Trans. Power Del., vol. 22, no. 4, pp. 2548–2558,
Oct. 2007.
[47] W. Qiao, R. G. Harley, and G. K. Venayagamoorthy, “Coordinated
reactive power control of a large wind farm and a STATCOM using
heuristic dynamic programming,” IEEE Trans. Energy Convers., vol. 24,
no. 2, pp. 493–503, Jun. 2009.
[48] S. Li, M. Fairbank, D. C. Wunsch, and E. Alonso, “Vector control of
a grid-connected rectifier/inverter using an artificial neural network,”
in Proc. IJCNN, Jun. 2012, pp. 1–7.
[49] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics:
Converters, Applications, and Design, 3rd ed. New York, NY, USA:
Wiley, Oct. 2002.
[50] J. Dannehl, C. Wessels, and F. W. Fuchs, “Limitations of voltage-
oriented PI current control of grid-connected PWM rectifiers with
LCL filters,” IEEE Trans. Ind. Electron., vol. 56, no. 2, pp. 380–388,
Feb. 2009.
[51] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control
of Dynamic Systems, 3rd ed. Reading, MA, USA: Addison-Wesley,
1998.
[52] C. M. Bishop, Neural Networks for Pattern Recognition. London, U.K.:
Oxford Univ. Press, 1995.
[53] P. J. Werbos, “Backpropagation through time: What it does and
how to do it,” Proc. IEEE, vol. 78, no. 10, pp. 1550–1560,
Oct. 1990.
[54] P. J. Werbos, “Neural networks, system identification, and control in the
chemical process industries,” in Handbook of Intelligent Control. New
York, NY, USA: Van Nostrand Reinhold, 1992, ch. 10, pp. 339–343.

[55] P. J. Werbos, “Backwards differentiation in AD and neural nets: Past
links and new opportunities,” in Automatic Differentiation: Applications,
Theory, and Implementations (Lecture Notes in Computational Science
and Engineering), H. M. Bücker, G. Corliss, P. Hovland, U. Naumann,
and B. Norris, Eds. New York, NY, USA: Springer-Verlag, 2005,
pp. 15–34.
[56] M. Riedmiller and H. Braun, “A direct adaptive method for faster
backpropagation learning: The RPROP algorithm,” in Proc. IEEE Int.
Conf. Neural Netw., vol. 1. Apr. 1993, pp. 586–591.
[57] B. G. Rawn, P. W. Lehn, and M. Maggiore, “Control methodology to
mitigate the grid impact of wind turbines,” IEEE Trans. Energy Convers.,
vol. 22, no. 2, pp. 431–438, Jun. 2007.
[58] S. Alepuz, S. Busquets-Monge, J. Bordonau, J. A. Martínez-Velasco,
C. A. Silva, J. Pontt, and J. Rodríguez, “Control strategies based on
symmetrical components for grid-connected converters under voltage
dips,” IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 2162–2173,
Jul. 2009.
Shuhui Li (S’99–M’99–SM’08) received the B.S.
and M.S. degrees in electrical engineering from
Southwest Jiaotong University, Chengdu, China, in
1983 and 1988, respectively, and the Ph.D. degree
in electrical engineering from Texas Tech University,
Lubbock, TX, USA, in 1999.
He was with the School of Electrical Engineer-
ing, Southwest Jiaotong University, from 1988 to
1995, where his fields of research interest included
modeling and simulation of large dynamic systems,
dynamic process simulation of electrified railways,
power electronics, power systems, and power system harmonics. From 1995
to 1999, he was engaged in research on wind power, artificial neural networks,
and applications of massive parallel processing. He joined Texas AM
University, Kingsville, TX, USA, as an Assistant Professor, in 1999, and an
Associate Professor in 2003. He was with Oak Ridge National Laboratory,
Oak Ridge, TN, USA, for simulation system development on supercomputers
in 2004 and 2006. He joined the University of Alabama, Tuscaloosa, AL,
USA, as an Associate Professor, in 2006. His current research interests include
renewable energy systems, smart grids, smart microgrids, power electronics,
power systems, electric machines and drives, FACTS, distributed generation,
and applications of artificial neural networks in energy systems.
Michael Fairbank (S’12) received the B.Sc. degree
in mathematical physics from Nottingham Univer-
sity, Nottingham, U.K., in 1994, and the M.Sc.
degree in knowledge based systems from Edinburgh
University, Edinburgh, U.K., in 1995. He is currently
a Ph.D. student with City University London, Lon-
don, U.K.
He has been independently researching ADPRL
and neural networks since that time, while pursing
careers in computer programming and mathemat-
ics teaching. His current research interests include
backpropagation through time, applied to control problems, adaptive dynamic
programming, and neural-network learning algorithms, especially for recurrent
neural networks.
Cameron Johnson received the B.S. and M.S.
degrees in physics from the University of Missouri
at Rolla, Rolla, MO, USA, in 2004 and 2006,
respectively, and the M.S. and Ph.D. degrees in
computer engineering from the Real-Time Power
and Intelligent Systems Laboratory in 2008 and
2011, respectively.
He went to work for L-3 Communications in 2012,
after a semester with the Applied Computational
Intelligence Laboratory. Interested in the advance-
ment of nano-robotics, and realizing that there was
work to be done in controls and their processing, he shifted to studying
computational intelligence at that point. He works for that company today,
with personal research interest and expertise in neural networks and swarm
intelligence and a professional desire to apply computational intelligence to
intellectual work the way factories applied automation to physical labor during
the latter part of the industrial revolution.
Donald C. Wunsch (F’07) received the Execu-
tive M.B.A. degree from Washington University, St.
Louis, WA, USA, the M.S. degree in applied mathe-
matics and the Ph.D. degree in electrical engineering
from the University of Washington, Seattle, WA,
USA, and the B.S. degree in applied mathematics
from the University of New Mexico, Albuquerque,
NM, USA. He also completed the Jesuit Core Hon-
ors Program, Seattle University, Seattle, WA, USA.
He is the Mary K. Finley Missouri Distinguished
Professor with the Missouri University of Science
and Technology (Missouri ST), Rolla, MO, USA. He was with Texas Tech
University, Boeing, Rockwell International, and International Laser Systems.
He has published over 300 publications including nine books. His research has
been cited over 7000 times. His current research interests include clustering,
adaptive resonance and reinforcement learning architectures, hardware and
applications, neurofuzzy regression, traveling salesman problem heuristics,
robotic swarms, and bioinformatics.
Dr. Wunsch is an INNS fellow and former INNS President. He has
served as an IJCNN General Chair and on several boards, including the St.
Patrick’s School Board, the IEEE Neural Networks Council, the International
Neural Networks Society, and the University of Missouri Bioinformatics
Consortium. He has also chaired the Missouri ST; Information Technology
and Computing Committee. Furthermore, he has produced 16 Ph.D. recipients
in computer engineering, electrical engineering, and computer science, and he
has attracted over $8 million in sponsored research.
Eduardo Alonso is a Reader in computing with City
University London, London, U.K. He is an expert on
artificial intelligence focused on machine learning
methods for systems and control, and as models
for computational neuroscience. He has published
dozens of papers in artificial intelligence journals
and volumes, and is contributing to The Cambridge
Handbook of Artificial Intelligence. He has edited
special issues for the journals Autonomous Agents
and Multi-Agent Systems and Learning Behav-
ior, and the book Computational Neuroscience for
Advancing Artificial Intelligence: Models, Methods and Applications.
He has acted as an OC and PC of the International Joint Conference on Arti-
ficial Intelligence (IJCAI) and the International Conference on Autonomous
Agents and Multiagent Systems (AAMAS), served as a Vice-Chair of The
Society for the Study of Artificial Intelligence and the Simulation of Behaviour
(AISB), and is a member of the U.K. Engineering and Physical Sciences
Research Council (EPSRC) Peer Review College.
Julio L. Proaño received the B.S. degree from the
New Jersey Institute of Technology, Newark, NJ,
USA.
He is a Graduate Student with the Electrical and
Computer Engineering Department, University of
Alabama, Tuscaloosa, AL, USA. He came to the
field of electrical engineering after extensive practi-
cal experience as a Mechanical and Electrical Tech-
nician, which he has complemented with internships
and volunteer positions. His graduate work focuses
on power systems, renewable energy systems, power
electronics, and real-time simulations.
Dr. Proaño has been supported by the National Science Foundation’s Bridge
to the Doctorate Fellowship.

Artificial Neural Networks for Control.pdf

More Related Content

Similar to Artificial Neural Networks for Control.pdf (20)

Recently uploaded (20)

Artificial Neural Networks for Control.pdf