# Instrumentation & Measurement Magazine 25-5 - 13

```function of the SPSAPF is superficial and extrinsic and thus,
is easily accepted. Then, what is the essential function of the
SPSAPF? The essential function of the SPSAPF is to make is
(t)
sinusoidal and is implemented to achieve the goal of improving
power quality.
View Correction
View Correction for Evaluating an SPSAPF RHCD
When iL
T
id'(t)=id
(t) and id
*(t); hence, is
(t)=iL
(t)-id
'(t)=iL
(t)-ic
*(t)=ip
(t) changes periodically, the precondition for (1) is sat*
 (2 / )T i t
*sin(ωt) is sinusoidal. Under ideal conditions,
(t)=ic
*(t)
according to Fig. 1, Kirchhoff's current law, and (1). Consequently,
the essential function of the SPSAPF to render is
(t)
sinusoidal is implemented, and the function of the RHCD is to
detect ic
*(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 is. As a result, when iL
(t) changes periodically,
it is correct that the higher the detection accuracy of
the RHCD is, the more effective the RHCD is.
When iL
(1) is not satisfied. Therefore, IpL( ) sin( )t dt is not qL and I T i t( )cos( )t dt are not constants, and thus
a constant, and thus ip*(t)=Ip
(t) changes non-periodically, the precondition for
*  (2 / )T i t
T
*sin(ωt) is not sinusoidal. Hence,
by rendering id'(t)=ic*(t) and is(t)=ip*(t), the essential function
of the SPSAPF to render is
(t) sinusoidal is not implemented.
(t)
(t);
(t) and ip
(t). For
However, it is necessary, logical, and feasible to render is
approximately sinusoidal. Under ideal conditions, id'(t)=id
consequently, is(t)=iL(t)-id'(t)=iL(t)-id(t)=ip(t) from Fig. 1, Kirchhoff's
current law, and the relation between id
this reason, is(t) is approximately sinusoidal if ip
ingly, to render is(t) approximately sinusoidal, id
render ip(t)=iL
(t)-id
(t) is. Accord(t)
should
(t) approximately sinusoidal. In theory, the
closer ip(t) is to sinusoidal, the more effective the RHCD is; and
the higher the detection accuracy of the RHCD is, the more
effective the RHCD is also. However, both statements are inconsistent:
When iL
(t) changes non-periodically, the closer
(t) is to sinusoidal, the lower the detection accuracy of the
RHCD is, and vice versa. Thus, the RHCD should have sufficiently
high detection accuracy and render ip
(t) approximately
sinusoidal at the same time; both should be simultaneously
satisfied as much as possible. Furthermore, to render ip
proximately sinusoidal, the optimal solution is that Ip
* slowly and smoothly because ip
*sin(ωt). As a result, when iL
track Ip
ip*(t)=Ip
(t)=Ip
(t) apshould
sin(ωt)
and
(t) changes non-periodically,
it is not correct that the higher the detection accuracy of
the RHCD is, the more effective the RHCD is.
In summary, when iL
(t) changes periodically, it is correct
that the higher the detection accuracy of an SPSAPF RHCD is,
the more effective the RHCD is. However, when iL
(t) changes
non-periodically, it is not correct that the higher the detection
accuracy of the RHCD is, the more effective the RHCD is. The
RHCD should have sufficiently high detection accuracy and
render ip
(t) approximately sinusoidal, Ip
should
ip
(1) is not satisfied. Therefore, both IpL( ) sin( )t dt
*  (2 / )
T
i1*(t)=Ip
*sin(ωt)+Iq
*cos(ωt) is not sinusoidal. Consequently, by
making id'(t)=ih*(t) and is(t)=i1*(t), the essential function of the
SPSAPF to make is(t) sinusoidal is not implemented. However,
it is necessary, logical, and feasible to make is
sinusoidal. Under ideal conditions, id'(t)=id
(t) approximately
(t); accordingly,
is(t)=iL(t)-id'(t)=iL(t)-id(t)=i1(t) according to Fig. 1, Kirchhoff's
current law, and the relation between id(t) and i1
son, is(t) is approximately sinusoidal if i1
is(t) approximately sinusoidal, id
(t) should make i1
(t)-id
(t). For this rea(t)
is. Hence, to make
(t)=iL
(t)
approximately sinusoidal and have sufficiently high detection
accuracy at the same time; both should be simultaneously
satisfied as much as possible. In addition, to make i1
proximately sinusoidal, the optimal solution is that Ip
* slowly and smoothly, and Iq
sin(ωt)+Iq
(t) apshould
track
Ip
i1(t)=Ip
Iq
cos(ωt) and that i1
a result, when iL
*(t)=Ip
*. The reasons are that
*sin(ωt)+Iq
*cos(ωt). As
(t) changes non-periodically, it is not correct
that the higher the detection accuracy of the HCD is, the more
effective the HCD is.
In conclusion, when iL
(t) changes periodically, it is correct
that the higher the detection accuracy of an SPSAPF
HCD is, the more effective the HCD is. Nevertheless, when
iL
(t) approximately sinusoidal
Iq
(t) changes non-periodically, it is not correct that the
higher the detection accuracy of the HCD is, the more effective
the HCD is. The HCD should have sufficiently high
detection accuracy and make i1
at the same time; both should be simultaneously satisfied as
much as possible. In addition, to make i1
sinusoidal, Ip should track Ip
* slowly and smoothly, and Iq
(t) approximately sinusoidal at the same time; both
should be simultaneously satisfied as much as possible. Furthermore,
to render ip
August 2022
(t) approximately
*
.
These insights are called the view correction for evaluating
an SPSAPF HCD.
The view correction for evaluating an SPSAPF RHCD and
that for evaluating an SPSAPF HCD are together called a view
correction for evaluating an SPSAPF HCD.
IEEE Instrumentation & Measurement Magazine
13
isfied. Therefore, IpL( ) sin( )t dt is a constant, and
thus ip*(t)=Ip
View Correction for Evaluating an SPSAPF HCD
Similarly, a view correction for evaluating an SPSAPF
HCD is obtained as follows from the view correction for
evaluating an SPSAPF RHCD: When iL(t) changes periodically,
the precondition for (1) is satisfied. Therefore, both
*  (2 / )T i t( ) sin( )t dt and I T i tqL( )cos( )t dt
are constants, and thus il*(t)=Ip
T
IpL
dal. Under ideal conditions, id'(t)=id
*  (2 / )
*sin(ωt)+Iq
(t) and id
T
*cos(ωt) is sinusoi(t)=ih
is(t)=iL(t)-id'(t)=iL(t)-ih*(t)=i1*(t)
from Fig. 1, Kirchhoff's current
law, and (1). Consequently, the essential function of the
SPSAPF to make is
tion of the HCD is to detect ih
(t) sinusoidal is implemented, and the func*(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 is. As a result,
when iL
(t) changes periodically, it is correct that the higher
the detection accuracy of the HCD is, the more effective the
HCD is.
When iL
(t) changes non-periodically, the precondition for
*  (2 / )T i t
T
*(t); hence,
track Ip
* slowly and smoothly. These insights are called a view
correction for evaluating an SPSAPF RHCD.
```

# Instrumentation & Measurement Magazine 25-5

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