U.S. patent application number 14/808408 was filed with the patent office on 2017-01-26 for method and apparatus for use with grid connected inverters in distributed power generation.
The applicant listed for this patent is Suzan EREN, Praveen JAIN, Majid PAHLEVANINEZHAD. Invention is credited to Suzan EREN, Praveen JAIN, Majid PAHLEVANINEZHAD.
Application Number | 20170025943 14/808408 |
Document ID | / |
Family ID | 57837537 |
Filed Date | 2017-01-26 |
United States Patent
Application |
20170025943 |
Kind Code |
A1 |
EREN; Suzan ; et
al. |
January 26, 2017 |
METHOD AND APPARATUS FOR USE WITH GRID CONNECTED INVERTERS IN
DISTRIBUTED POWER GENERATION
Abstract
Systems, methods, and devices relating to the controlling of a
grid-connected inverter. A grid connected inverter is controlled by
a proportional-resonant controller which tracks the grid current.
To adjust for changes in grid conditions, an update block
dynamically and continuously adjusts coefficients used by the
controller to ensure high gains provided by the controller at the
grid frequency. A harmonic compensator is also provided to ensure
that high loop gains at harmonic frequencies of the grid frequency
are also provided for. To also adjust for changing grid conditions,
a second update block also continuously adjusts the coefficients
used by the harmonic compensator.
Inventors: |
EREN; Suzan; (Kingston,
CA) ; PAHLEVANINEZHAD; Majid; (Kingston, CA) ;
JAIN; Praveen; (Kingston, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
EREN; Suzan
PAHLEVANINEZHAD; Majid
JAIN; Praveen |
Kingston
Kingston
Kingston |
|
CA
CA
CA |
|
|
Family ID: |
57837537 |
Appl. No.: |
14/808408 |
Filed: |
July 24, 2015 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
Y02B 70/1441 20130101;
H02M 7/53873 20130101; H02M 2007/4815 20130101; H02M 7/539
20130101; H02M 1/12 20130101; H02M 2001/0025 20130101 |
International
Class: |
H02M 1/12 20060101
H02M001/12; H02M 7/44 20060101 H02M007/44 |
Claims
1. A system for controlling a grid connected inverter, the system
comprising: a proportional-resonant controller for sinusoidal
reference tracking of a reference grid current and for providing a
high gain at a specific line frequency, said controller receiving
said grid current; a first update law block for continuously
providing updated controller coefficients for said controller, said
first update law block receiving said grid current and a sinusoidal
signal related to said line frequency, said first update law block
adjusting said controller coefficients based on said grid current
and said line frequency; a harmonic compensator block for removing
current harmonics by providing high gains at harmonic frequencies
of said specific line frequency; a second update law block for
continuously providing compensator coefficients for said harmonic
compensator block, said second update law block receiving said grid
current and said line frequency, said second update law block
adjusting said compensator coefficients based on said grid current
and said line frequency; wherein outputs of said controller and
said compensator are combined to produce a duty cycle signal for
said inverter.
2. A system according to claim 1 wherein said controller
coefficients are given by: {circumflex over ({dot over
(a)})}=.gamma..sub.ae.sub.i sin(.omega..sub.lt) {circumflex over
({dot over (b)})}=.gamma..sub.be.sub.i sin(.omega..sub.lt) where
.omega..sub.l represents said line frequency; and e.sub.i
represents a difference between a reference grid current and an
output current of said inverter.
3. A system according to claim 1 wherein an output of said
controller is based on previous outputs of said controller.
4. A system according to claim 2 wherein an output of said
controller is given by:
u.sub.APR(k)=.zeta.(k)-(k-2)+u.sub.APR(k-1){circumflex over
(a)}(k)-u.sub.APR(k-2) where u.sub.APR(k) is the k.sup.th output of
said controller; and .zeta.(k) is a damping parameter for said
k.sup.th output of said controller.
5. A system according to claim 4 wherein the damping parameter is
given by: .zeta.(k)={circumflex over (b)}(k)e.sub.i(k)
6. A system according to claim 2 wherein said system is implemented
using: {circumflex over (a)}(k)=a.sub.0+.eta..sub.a(k)
.eta..sub.a(k)=.gamma..sub.ae.sub.i(k)sin(.omega..sub.lt)+.eta..sub.a(k-1-
) {circumflex over (b)}(k)=b.sub.0+.eta..sub.b(k)
.eta..sub.b(k)=.gamma..sub.be.sub.i(k)sin(.omega..sub.lt)+.eta..sub.b(k-1-
)
7. A system according to claim 1 further comprising a linear state
feedback loop, a result of said loop being combined with said
output of said controller and said output of said compensator to
result in said duty cycle for said inverter.
8. A method for controlling a grid connected inverter, the method
comprising: a) receiving a grid current at a controller for said
inverter and at a harmonic compensator block; b) receiving said
grid current and a line frequency for said grid at a first and a
second update blocks; c) determining controller coefficients for
said controller based on said grid current and said line frequency;
d) passing said controller coefficients to said controller; e)
determining compensator coefficients for said compensator block
based on said grid current and said line frequency; f) passing said
compensator coefficients to said compensator; g) determining a
controller output based on said grid current and said controller
coefficients; h) determining a compensator output based on said
grid current and said compensator coefficients; i) combining said
controller output and said compensator output to result in a duty
cycle for said inverter; j) sending said duty cycle to said
inverter.
9. A method according to claim 8 wherein step h) further comprises
combining a result of a linear state feedback loop with said output
of said controller and said output of said compensator to result in
said duty cycle for said inverter.
10. A method according to claim 8 wherein said controller
coefficients are given by: {circumflex over ({dot over
(a)})}=.gamma..sub.ae.sub.i sin(.omega..sub.lt) {circumflex over
({dot over (b)})}=.gamma..sub.be.sub.i sin(.omega..sub.lt) where
.omega..sub.l represents said line frequency; and e.sub.i
represents a difference between a reference grid current and an
output current of said inverter.
11. A method according to claim 10 wherein an output of said
controller is given by:
u.sub.APR(k)=.zeta.(k)-.zeta.(k-2)+u.sub.APR(k-1){circumflex over
(a)}(k)-u.sub.APR(k-2) where u.sub.APR(k) is the k.sup.th output of
said controller; and .zeta.(k) is a damping parameter for said
k.sup.th output of said controller.
12. A method according to claim 11 wherein the damping parameter is
given by: .zeta.(k)={circumflex over (b)}(k)e.sub.i(k)
Description
TECHNICAL FIELD
[0001] The present invention relates to control systems for
grid-connected DC/AC converters. More specifically, the present
invention relates to methods for controlling the output current of
a grid connected inverter used in distributed power generation.
BACKGROUND OF THE INVENTION
[0002] Distributed power generation is the key to global energy
sustainability. Extracting power from renewable energy sources with
a distributed generation platform seems to be the only sustainable
solution for future power generation. Grid-connected inverters are
the interface between the renewable energy power conditioning
systems and the utility grid. The grid-connected inverter is
responsible for delivering high quality power to the utility grid.
In particular, the control system of the inverter is responsible
for injecting a high quality current into the utility grid.
Regulatory standards for interconnecting renewable energy sources
with utility grids impose very strict requirements on the quality
of the output current. Particularly, the quality of the current
relates to its harmonic contents and its angle with respect to the
grid voltage. This angle is called Power Factor (PF).
[0003] The control system for the grid connected inverter is
responsible for shaping the output current of the inverter to a
nearly sinusoidal waveform. The reference signal for the inverter
output current is a sinusoidal waveform with a proper angle with
respect to the grid voltage. Ideally, the control system controls
the inverter output such that the inverter output current tracks
this sinusoidal waveform. The sinusoidal waveform has the same
frequency as the grid frequency (i.e. the line frequency). In order
to track the sinusoidal reference signal, the control loop should
have a very high gain at the frequency of the reference signal
(i.e. line frequency).
[0004] Proportional-Resonant (PR) controllers can be used to
provide high gain at the line frequency. These PR controllers are
commonly used to provide a very high gain at the frequency of the
reference signal by tuning the frequency of the PR-controller to
the grid frequency. Also, if a third-order LCL-filer is used at the
output of the inverter, a PR-controller, along with a linear
state-feedback, can be used to control the output current and to
thereby damp the resonance created by the LCL-filter. FIG. 1 shows
a typical closed-loop control system for a grid-connected inverter
used in distributed power generation according to the prior art. In
FIG. 1, a PR-controller is used to provide a high gain at the line
frequency. Also in FIG. 1, a harmonic compensator is used to
provide high gains at the harmonic frequencies for harmonic
rejection of the inverter output current. In addition, a linear
state-feedback is used to actively damp the resonance created by
the LCL-filter at the output of the inverter.
[0005] The digital implementation of the PR-controller has some
challenges. One of the main challenges is the effect of the
approximation used to discretize the PR controller. The transfer
function of the PR controller should be converted from the Laplace
domain (s-domain) to the discrete domain (z-domain) for the digital
implementation. This approximation creates a deviation of the
resonant frequency of the PR controller and, in turn, creates a
phase-shift between the output current of the inverter and the
reference signal. The other problem is the accuracy required to
implement the coefficient of the PR-controller in the discrete
domain in order to maintain the resonant frequency at the line
frequency. Due to the digital truncation, there might be a large
deviation in the resonant frequency of the discrete PR-controller
and the line frequency, leading to poor tracking of the reference
signal by the control system.
[0006] There is therefore a need for systems, methods, or devices
which address or mitigate the above issues with the prior art.
SUMMARY OF INVENTION
[0007] The present invention provides systems, methods, and devices
relating to the controlling of a grid-connected inverter. A grid
connected inverter is controlled by a proportional-resonant
controller which tracks the grid current. To adjust for changes in
grid conditions, an update block dynamically and continuously
adjusts coefficients used by the controller to ensure high gains
provided by the controller at the grid frequency. A harmonic
compensator is also provided to ensure that high loop gains at
harmonic frequencies of the grid frequency are also provided for.
To also adjust for changing grid conditions, a second update block
also continuously adjusts the coefficients used by the harmonic
compensator.
[0008] In a first aspect, the present invention provides a system
for controlling a grid connected inverter, the system comprising:
[0009] a proportional-resonant controller for sinusoidal reference
tracking of a reference grid current and for providing a high gain
at a specific line frequency, said controller receiving said grid
current; [0010] a first update law block for continuously providing
updated controller coefficients for said controller, said first
update law block receiving said grid current and a sinusoidal
signal related to said line frequency, said first update law block
adjusting said controller coefficients based on said grid current
and said line frequency; [0011] a harmonic compensator block for
removing current harmonics by providing high gains at harmonic
frequencies of said specific line frequency; [0012] a second update
law block for continuously providing compensator coefficients for
said harmonic compensator block, said second update law block
receiving said grid current and said line frequency, said second
update law block adjusting said compensator coefficients based on
said grid current and said line frequency;
[0013] wherein [0014] outputs of said controller and said
compensator are combined to produce a duty cycle signal for said
inverter.
[0015] In a second aspect, the present invention provides a method
for controlling a grid connected inverter, the method comprising:
[0016] a) receiving a grid current at a controller for said
inverter and at a harmonic compensator block; [0017] b) receiving
said grid current and a line frequency for said grid at a first and
a second update blocks; [0018] c) determining controller
coefficients for said controller based on said grid current and
said line frequency; [0019] d) passing said controller coefficients
to said controller; [0020] e) determining compensator coefficients
for said compensator block based on said grid current and said line
frequency; [0021] f) passing said compensator coefficients to said
compensator; [0022] g) determining a controller output based on
said grid current and said controller coefficients; [0023] h)
determining a compensator output based on said grid current and
said compensator coefficients; [0024] i) combining said controller
output and said compensator output to result in a duty cycle for
said inverter; [0025] j) sending said duty cycle to said
inverter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026] The embodiments of the present invention will now be
described by reference to the following figures, in which identical
reference numerals in different figures indicate identical elements
and in which:
[0027] FIG. 1 is block diagram of a typical closed loop control
system for a grid-connected inverter according to the prior
art;
[0028] FIG. 2 is a block diagram of a closed loop current control
system according to the prior art;
[0029] FIG. 3 is a Bode plot of the continuous-time transfer
function of one of the equations;
[0030] FIG. 4 shows the steady state error between the sinusoidal
reference signal and the grid current as caused by the discrete
approximation;
[0031] FIG. 5 illustrates the number of digital bits required to
digitally implement a coefficient in a digital implementation of a
PR controller;
[0032] FIG. 6 illustrates the resonant frequency deviation of the
PR controller due to coefficient inaccuracy because of
truncation;
[0033] FIG. 7 illustrates the steady state error due to grid
frequency variations;
[0034] FIG. 8 is a block diagram of the closed-loop control system
according to one aspect of the invention;
[0035] FIG. 9 is a block diagram illustrating the internal
structure of the advanced PR controller according to one aspect of
the invention along with the internal structure of the first update
block;
[0036] FIG. 10A details simulation results showing that, when the
present invention is used, the steady-state error is effectively
zero;
[0037] FIGS. 10B-10C show simulation results detailing that the
update law blocks according to one aspect of the invention
continuously adjust both the PR-controller coefficients such that
the steady-state error is maintained at zero;
[0038] FIG. 11 illustrates a magnification of the simulation
results to show that the steady-state error is pushed to zero;
[0039] FIG. 12 show simulation results of a grid-connected inverter
using the PR controller according to one aspect of the
invention;
[0040] FIG. 13 show experimental waveforms for the grid-connected
inverter with the PR-controller according to one aspect of the
invention.
DETAILED DESCRIPTION
[0041] In one aspect, the present invention relates to an improved
PR-controller which is able to precisely follow the line frequency
and to provide nearly perfect tracking of the reference signal. The
scheme of the invention adaptively tracks the line frequency and
tunes the PR-controller accordingly in order to achieve high gain
for the control loop and as well as zero phase-shift in the
reference signal tracking. One of the useful aspects of the
controller in the present invention is the very simple digital
implementation of the control system.
[0042] FIG. 2 shows a block diagram of the closed-loop current
control system for a grid-connected inverter with an LCL-filter
according to the prior art. According to FIG. 2, the current
control loop includes a main PR-controller 10 and a harmonic
compensator 20 along with a linear state-feedback controller 30.
The PR controller 10 is responsible for the sinusoidal reference
tracking of the grid current. The harmonic compensator 20 is
responsible for eliminating the current harmonics by providing high
loop gains at the harmonic frequencies. The linear state-feedback
30 guarantees the stability of the closed-loop control system by
placing the closed-loop poles on the left-half plane.
[0043] The PR controller in FIG. 2 is merely a bandpass filter,
which has a high gain at the line frequency. The transfer function
of the PR controller is given by:
H ( s ) = s s 2 + 2 .zeta. s + .omega. l 2 ( 1 ) ##EQU00001##
where .omega..sub.l is the centre frequency of the passband. This
structure allows for a very high gain at line frequency
.omega..sub.l. The width of the passband, or the quality factor of
the resonance, is adjusted by the damping parameter .zeta.. As
.zeta. increases, the phase transition becomes more gradual but the
reduction in the gain of the system is a more noticeable result.
Usually, the resonant controller is designed to have a very low
damping ratio, (i.e. .zeta..apprxeq.0), in order to have sufficient
gain for nearly perfect tracking of the sinusoidal signal. From
this, the transfer function of the PR controller is given by:
H PR ( s ) = s s 2 + .omega. l 2 ( 2 ) ##EQU00002##
[0044] In the circuit in FIG. 2, the PR controller has an almost
infinite gain at the grid frequency to render the steady-state
error to zero. Thus, the nearly perfect tracking of the error of
the fundamental component is achieved. However, due to the limited
bandwidth of the PR controller, it cannot compensate for the
harmonics. Such harmonics originate from non-linearities in the
system, such as quantization, signal conditioning circuits, and,
particularly, switching dead-time to prevent shoot-through. In
order to compensate for the presence of such distortions, the
harmonic compensator is used. The harmonic compensator has the same
structure as the PR controller. For each problematic harmonic, the
centre frequencies can be tuned for the respective harmonic
frequency. The harmonic compensator is usually tuned for the
3.sup.rd, 5.sup.th, 7.sup.th, and 9.sup.th harmonics. The transfer
function of the harmonic compensator is thus given by:
H HC = h = 2 , 3 , - k s s 2 + ( h .omega. l ) 2 ( 3 )
##EQU00003##
[0045] It should be noted that there are three main challenges with
the digital implementation of the PR controller as well as the
harmonic compensator. The first challenge relates to the discrete
approximation of the PR controller. The second challenge relates to
the truncation of coefficients due to the limited number of bits.
The third challenge relates to the frequency variations of the
grid. These three challenges cause a steady state error in the
tracking of the sinusoidal reference for the grid current. These
three challenges are described below in detail.
[0046] In order to digitally implement the PR controller, the
transfer function of the PR controller must be converted from the
continuous-time domain into a transfer function in the
discrete-time domain. The conversion of the transfer function from
the continuous-time domain to the discrete-time domain is carried
out through an approximation. There are three commonly used
approximations: the Forward Euler transformation, the Backward
Euler transformation, and the Bi-linear or Tustin's transformation.
The bilinear transformation results in a more precise approximation
compared to the other two transformations. The bilinear
transformation is given by:
s .fwdarw. 2 T s z - 1 z + 1 ( 4 ) ##EQU00004##
[0047] The z-domain equivalent of the continuous-time transfer
function of the PR controller given by:
H PR ( s .fwdarw. z ) = 2 T s z - 1 z + 1 ( 2 T s z - 1 z + 1 ) 2 +
.omega. l 2 ( 5 ) ##EQU00005##
[0048] From the above, the transfer function of the PR controller
in the z-domain is given by:
H PR ( z ) = b ( 1 - z - 2 ) 1 - az - 1 + z - 2 ( 6 ) where b = 2 T
s T s 2 .omega. l 2 + 4 ( 7 ) a = 2 4 - T s 2 .omega. l 2 4 + T s 2
.omega. l 2 ( 8 ) ##EQU00006##
and where T.sub.s is the sampling period.
[0049] FIG. 3 shows the Bode plot of the continuous-time transfer
function given by Eqn. (2) as well as the discrete-time transfer
function given by Eqn. (6). According to this figure, the resonant
frequency of the PR controller resulting from the discrete-time
transfer function deviates due to the discrete approximation
(bi-linear transformation) of the transfer function. This deviation
creates steady-state error in the tracking of the sinusoidal
reference signal. FIG. 4 shows the steady-state error between the
sinusoidal reference signal and the grid current caused by the
discrete approximation.
[0050] The second challenge in the digital implementation of the PR
controller is the truncation of the coefficients due to the limited
number of digits available to implement the PR controller. The
coefficients of the PR controller must be extremely precise in
order to maintain the accuracy in the resonant frequency. As an
example of the need for extreme precision, for a 60 Hz system with
a 25 kHz sampling frequency the PR coefficients are given by:
b=1.99988630 8620532 e-05, a=-1.99977261 7241063. In order to
approximate these coefficients with a reasonable accuracy, a very
large number of bits is required in a digital implementation. In
order to put this accuracy in perspective, the amount of bits
required to digitally implement the coefficient b is shown in FIG.
5. FIG. 6 shows the resonant frequency deviation of the PR
controller due to the truncation of the coefficients in the digital
implementation of the PR controller.
[0051] The third challenge in the digital implementation of the PR
controller is due to the frequency variations in the utility grid.
The frequency of the grid can vary in a specific range according to
the regulatory standards for interconnecting renewable energy
sources with a utility grid (e.g. IEEE1547). As distributed
generation power plants become more prevalent, the range of
frequency variation will be increased in order to accommodate
system transients. The frequency variations have an adverse impact
on the tracking of the resonant controller tuned to a fixed line
frequency. The discrepancy between the tuned frequency and the grid
frequency creates a steady-state error in the tracking of the
reference signal. It is possible to track the line frequency by a
PLL (phase locked loop) and to adaptively calculate the
coefficients based on Eqns. (7)-(8). However, this requires
extremely intensive calculations which would significantly increase
the complexity of the control algorithm. FIG. 7 shows the
steady-state error due to the grid frequency variations.
[0052] In one aspect, the present invention provides for an
advanced PR controller which uses an adaptive update law to improve
the performance of the conventional PR-controller. The adaptive
update law works by continuously and automatically updating the
coefficients of the PR-controller to remove the steady-state phase
error produced by the deviation in the resonant frequency. This
allows the PR-controller to offer near perfect tracking of the
reference signal. By adaptively changing the coefficients of the
PR-controller, it is also possible to remove the tracking error
produced by changes in the grid frequency. Normally, the
PR-controller has a very narrow band of high gain at the nominal
grid frequency. Any deviations in the frequency outside of this
very narrow band causes the gain to drop significantly. By using
the adaptive PR-controller, small changes in the grid frequency can
be compensated for by adaptively changing the controller
coefficients.
[0053] In FIG. 8, the block diagram of the closed-loop control
system according to one aspect of the invention is presented. In
FIG. 8, the system 10 has, as input, a reference current I.sub.ref
20. A multiplier 30 multplies this current 20 by
sin(.omega..sub.lt) from sine block 40. The result, i.sub.ref, is
added by summation block 50 to a negative of a feedback signal from
the output 60 of the system. The result from the summation block 50
is then fed to an advanced PR controller block 70 and to a first
update law block 80. The first update law block 80 sends its output
to the PR controller block 70 and also receives the output of the
sine block 40. The output feedback signal 60 is also sent to an
advanced harmonic compensator block 90 and to a second update law
block 100. This second update law block 100 sends its outputs to
the harmonic compensator block 90 and receives the output of a PLL
(phase locked loop) block 110. This output of the PLL block 110 is
the frequency (.omega..sub.l) of the output voltage signal and is
fed to the sine block 40.
[0054] The output of the advanced PR controller block 70 and the
output of the harmonic compensator block 90 are summed by a
summation block 120 along with the negative of the output of a
multiplier block 130. The multiplier block 103 multiplies the value
of X from a grid connected inverter 140 by the constant K. The
output d (duty cycle) of the summation block 120 is sent to the
inverter block 140. The output of the inverter block 140 is the
grid current i.sub.g and the grid voltage v.sub.g. The voltage
v.sub.g is fed to the PLL block 110 while the current i.sub.g is
sent to the grid and back to the system as the feedback signal
60.
[0055] As shown in FIG. 8, the update laws (from the first update
law block 80) of the advanced PR controller block 70 continuously
change the coefficients to produce smooth tracking with no
steady-state error. Furthermore, the advanced harmonic compensator
block 90 has a similar set-up, because it is also a collection of
PR-controllers with resonant frequencies tuned to the filtered
harmonic frequencies. Thus, the coefficients of the PR-controllers
within the advanced harmonic compensator block 90 are also
continuously updated to remove the steady-state error and thereby
produce nearly perfect tracking of the harmonic reference signals.
FIG. 9 shows the structure of the advanced PR-controller block 70
with its update laws block 80. In the advanced PR controller, the
coefficients of the control scheme are produced by the update laws.
The update laws use the value of the current error to make
adjustments to the nominal coefficients such that the steady-state
error is rendered zero. The update laws for the advanced
PR-controller in the present invention are given by:
{circumflex over ({dot over (a)})}=.gamma..sub.ae.sub.i
sin(.omega..sub.lt) (9)
{circumflex over ({dot over (b)})}=.gamma..sub.be.sub.i
sin(.omega..sub.lt) (10)
[0056] For clarity, it should be noted that e.sub.i in the
equations are, from FIG. 8, equal to e.sub.i=i.sub.ref-i.sub.g. As
well, it should be noted that .gamma..sub.a and .gamma..sub.b are
positive coefficients which determine the speed of the update
laws.
[0057] Referring to FIG. 9, the internal components of the advanced
PR controller 70 and of the first update laws block 80 are
illustrated. Within the controller block 70, the output of
summation block 50 is received as input 710 to the controller
block. This input 710 is received by a multiplier block 720 which
multiplies this input 710 by a second output 810 (controller
coefficient b(k)) of the update laws block 80. The result of the
multiplier block 720 is sent down two paths, the first being to a
summation block 730 and the second leading to two successive z
blocks 740, 750. Each of the z blocks apply 1/z to its input and
the net effect of the two blocks 740, 750 is to apply 1/z.sup.2 to
the result of the multiplier block 720. The result of block 750 is
then subtracted from the result of multiplier block 720 by
summation block 730.
[0058] On the other side of the controller block 70, the first
output 820 (controller coefficient a(k)) of the update block 80 is
multiplied by multiplier block 760 with the result of z block 770.
The result of z block 770 is also sent to another z block 780. The
result of z block 780 is subtracted from the result of multiplier
760 by summation block 790. The result from summation block 790 is
then added to the result from summation block 730 by summation
block 795. The result of summation block 795 is the output of the
controller 70.
[0059] Referring to the update laws block 80 in FIG. 9, the input
to this block is the function sin(.omega..sub.lt) received by the
muliplier block 830. This multiplier block 830 multiplies the input
to block 80 with the input to controller block 70. The output of
this multiplier block 830 is multiplied by multiplier block 840 by
.gamma..sub.a and the result is then fed to summation block 850.
The result of summation block 850 is passed through a z block 860
that applies 1/z to this result. As can be seen, the result of z
block 860 is sent to the summation block 850. The result of
summation block 850 is also added by summation block 870 to a value
a.sub.0 880. This value 880 is the previous value for variable a or
the first output 820 of the update block 80. This is also one of
the coefficients that the update block 80 updates. The result of
summation block 870 is then fed into a limiter block 880. The
output of the limited block 880 is the first output 820 of the
update block 80.
[0060] The bottom part of the update block 80 in FIG. 9 has the
components used to generate the updated coefficient that is the
second output 810 of the update block 80. The output of the
multiplier 830 is sent to a multiplier block 900 that multiplies it
by .gamma..sub.b. The result of multiplier block 900 is added by a
summation block 910 to the result of z block 920. The result of
summation block 910 is sent to z block 920. The result of summation
block 910 is also sent to summation block 930 which adds it to the
value b.sub.0 940. The result of summation block 930 is then sent
to a limited 950 and the output of this limiter 950 is the second
output of the update block 80.
[0061] It should be noted that the internal structure of the
harmonic compensator block is the same as that for the controller
block but with different inputs. From FIG. 9, it can be seen that,
for the controller block, the input is e.sub.i(k) and the input to
its corresponding update law block is sin(.omega..sub.lt). For the
harmonic compensation block, the input error signal is
e.sub.in=0-i.sub.g and the input to the corresponding update block
is sin(n.omega..sub.lt). As well, the compensator block and the
controller block may have different initial values for variables a
and b as based on Eqns. (7) and (8).
[0062] For further clarity, it should be noted that the values for
a.sub.0 and b.sub.0 in FIG. 9 are the initial values for the
variables a and b. These initial values are constant.
[0063] The digital implementation of the advanced PR controller in
the present invention is implemented through the following
equations:
u.sub.APR(k)=.zeta.(k)-.zeta.(k-2)+u.sub.APR(k-1){circumflex over
(a)}(k)-u.sub.APR(k-2) (11)
.zeta.(k)={circumflex over (b)}(k)e.sub.i(k) (12)
{circumflex over (a)}(k)=a.sub.0+.eta..sub.a(k) (13)
.eta..sub.a(k)=.gamma..sub.ae.sub.i(k)sin(.omega..sub.lt)+.eta..sub.a(k--
1) (14)
{circumflex over (b)}(k)=b.sub.0+.eta..sub.b(k) (15)
.eta..sub.b(k)=.gamma..sub.be.sub.i(k)sin(.omega..sub.lt)+.eta..sub.b(k--
1) (16)
[0064] Simulation results to demonstrate the efficacy of this
method can be seen in FIG. 10. FIG. 10A shows that the steady-state
error is effectively zero. FIG. 10B and FIG. 10C show that the
update laws make continuous adjustments to both of the advanced
PR-controller coefficients such that the steady-state error is
maintained at zero.
[0065] In FIG. 11, a magnification of the simulation results can be
seen. In this figure, it is clear that the advanced PR controller
pushes the steady-state error to zero.
[0066] FIG. 12 shows the simulation results of the grid-connected
inverter with the advanced PR controller in the present invention.
In this figure the grid frequency is 58 Hz. FIG. 12 shows that the
advanced PR controller can effectively compensate for grid
frequency variations.
[0067] FIG. 13 shows the experimental waveforms of the
rid-connected inverter with the advanced PR controller in the
present invention.
[0068] It should be noted that the adaptive PR controller and the
advanced harmonic compensator can both be implemented using a
general purpose computing device or may be implemented using an
application specific integrated circuit or ASIC. Similarly, the
update blocks may also be implemented using a general purpose
computing device or a dedicated computing device such as an
ASIC.
[0069] The embodiments of the invention may be executed by a
computer processor or similar device programmed in the manner of
method steps, or may be executed by an electronic system which is
provided with means for executing these steps. Similarly, an
electronic memory means such as computer diskettes, CD-ROMs, Random
Access Memory (RAM), Read Only Memory (ROM) or similar computer
software storage media known in the art, may be programmed to
execute such method steps. As well, electronic signals representing
these method steps may also be transmitted via a communication
network.
[0070] Embodiments of the invention may be implemented in any
conventional computer programming language. For example, preferred
embodiments may be implemented in a procedural programming language
(e.g. "C") or an object-oriented language (e.g. "C++", "java",
"PHP", "PYTHON" or "C#"). Alternative embodiments of the invention
may be implemented as pre-programmed hardware elements, other
related components, or as a combination of hardware and software
components.
[0071] Embodiments can be implemented as a computer program product
for use with a computer system. Such implementations may include a
series of computer instructions fixed either on a tangible medium,
such as a computer readable medium (e.g., a diskette, CD-ROM, ROM,
or fixed disk) or transmittable to a computer system, via a modem
or other interface device, such as a communications adapter
connected to a network over a medium. The medium may be either a
tangible medium (e.g., optical or electrical communications lines)
or a medium implemented with wireless techniques (e.g., microwave,
infrared or other transmission techniques). The series of computer
instructions embodies all or part of the functionality previously
described herein. Those skilled in the art should appreciate that
such computer instructions can be written in a number of
programming languages for use with many computer architectures or
operating systems. Furthermore, such instructions may be stored in
any memory device, such as semiconductor, magnetic, optical or
other memory devices, and may be transmitted using any
communications technology, such as optical, infrared, microwave, or
other transmission technologies. It is expected that such a
computer program product may be distributed as a removable medium
with accompanying printed or electronic documentation (e.g.,
shrink-wrapped software), preloaded with a computer system (e.g.,
on system ROM or fixed disk), or distributed from a server over a
network (e.g., the Internet or World Wide Web). Of course, some
embodiments of the invention may be implemented as a combination of
both software (e.g., a computer program product) and hardware.
Still other embodiments of the invention may be implemented as
entirely hardware, or entirely software (e.g., a computer program
product).
[0072] A person understanding this invention may now conceive of
alternative structures and embodiments or variations of the above
all of which are intended to fall within the scope of the invention
as defined in the claims that follow.
* * * * *