# Instrumentation & Measurement Magazine 25-5 - 12

```an SPSAPF HCD are proposed, collectively called a view correction
for evaluating an SPSAPF HCD. Thirdly, the proposed
view correction is verified by experimental results. Finally,
main conclusions are summarized.
The Three Most Fundamental
Theoretical Bases
According to Fourier series, the Fourier series of the singlephase
be expressed as
i
L()  
n 2
t   nq
t
** *
I tIq
p sin( ) cos( )  I nt I


[ sin( )
np
   *
pci iit
i tt t
** *
1
In (1), I T i ()
*  2 /

pL sin( )
T
current amplitude. I T2 / ()cos()
mental reactive current amplitude. **
*
q 
L
( ) 
i t it i t
i t it i t
 
hL 1
h
() () () ( )
* cos( )]
nt
(1)
t t dt is the fundamental active
T
 it t dt is the fundait
I
fundamental active current. ** *
the fundamental currents. **
and harmonic currents. **
currents. T is the period of iL
series, a precondition for (1) is that iL
it Ipq1 ( )  t

c () () ()Lp is the reactive
 
() () () is the harmonic
(t), and ω=2π/T. From Fourier
(t) is a periodic non-sinusoidal
current satisfying the Dirichlet conditions.
Operating Principle of SPSAPF
A typical block diagram of the principle of an SPSAPF is
presented in Fig. 1 [4], [12], [19]. The SPSAPF consists of a harmonic
current detection circuit, a harmonic current control
circuit, a driving circuit, and a main circuit. Moreover, us
the source voltage. is(t) is the source current, iL
(t) is
(t) is the singlephase
nonlinear load current, and id(t) is the harmonic current
reference detected by the harmonic current detection circuit.
id
'(t) is the harmonic current compensation value controlled
pp sin( ) is thet
t I
sin( ) cos( ) is
(t) [4], [12], [13], [17], [18] can
by the harmonic current control circuit and provided by the
SPSAPF.
id(t)=ih
Under ideal conditions, id'(t)=id
*(t). The SPSAPF can compensate ic
Compensating ic
(t); and id
*(t) or ih
(t)=ic
*(t).
*(t): When the SPSAPF compensates ic
(t). To detect id
*(t), its
RHCD implementing the function of the harmonic current
detection circuit should detect id
(t), the RHCD
should detect Ip, the detected fundamental active current amplitude.
Then ip(t)=Ip sin(ωt), the detected fundamental active
current. Thus, id(t)=iL
(t)-ip
(t), the detected reactive and harmonic
currents; this equation is called a relation between id(t)
and ip(t).
rent source. Theoretically, the SPSAPF should provide ic
*(t): is
id'(t)=ic
Under ideal conditions, id'(t)=id
*(t), the power source should provide ip
(t) and id
'(t)=ic
(t)=ip
(t)=ic
*(t) and is
The SPSAPF can be considered as a current-controlled cur*(t):
*(t).
*(t);
thus,
is(t)=iL(t)-id'(t)=iL(t)-ic*(t)=ip*(t) according to Fig. 1, Kirchhoff's
current law, and (1). Therefore, both id
(t)=ip
(t) accurately. From the function of the RHCD, it follows that
the higher the detection accuracy of the RHCD is, the more effective
the RHCD should ideally be.
*
Compensating ih
*(t): When the SPSAPF compensates ih
(t). To detect id
sin(ωt)+Iq
(t)=iL
(t)-i1
*(t),
its HCD implementing the function of the harmonic current
detection circuit should detect id
(t), the HCD
should detect Ip and Iq, the detected fundamental active current
amplitude and the detected fundamental reactive current
amplitude, respectively. Then i1
tected fundamental currents. Thus, id
(t)=Ip
(t) and i1
(t).
cos(ωt), the de(t),
the detected
harmonic currents; this equation is called a relation between
id
power source should provide i1
conditions, id'(t)=id
(t) and id
(t)=ih
In theory, the SPSAPF should provide ih
*(t): is
*(t): id
(t)=i1
*(t); thus, is
i h*(t)=i l
'(t)=ih
(t) accurately. From the
function of the HCD, it is obtained
that the higher the
detection accuracy of the
HCD is, the more effective
the HCD should ideally be.
*
*(t)
'(t)=ih
(t)-id
*(t); the
*(t). Under ideal
(t)=iL
'(t)=iL
(t)from
Fig. 1,
Kirchhoff's current law,
and (1). Therefore, both
id
*(t) and is
(t)=i1
*(t) are
implemented, and the function
of the HCD is to detect
ih
*(t)
are implemented, and the function of the RHCD is to detect
ic
*(t) or
Essential Function of
SPSAPF
The above conclusions are
not entirely correct. The
function of the SPSAPF is
to compensate ic
*(t) or ih
Fig. 1. Block diagram of the principle of an SPSAPF.
12
IEEE Instrumentation & Measurement Magazine
*(t)
accurately. However, the
August 2022
```

# Instrumentation & Measurement Magazine 25-5

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