MCP3909RD-3PH1 Microchip Technology, MCP3909RD-3PH1 Datasheet - Page 84

• Manufacturer Part Number: MCP3909RD-3PH1
• Description: REF DESIGN MCP3909 3PH ENGY MTR
• Manufacturer: Microchip Technology

Specifications of MCP3909RD-3PH1

• Main Purpose: Power Management, Energy/Power Meter
• Embedded: No
• Utilized Ic / Part: MCP3909, PIC18F2520, PIC18F4550
• Primary Attributes: 3-Ph, 220 VAC, In Case, LCD, USB, GUI
• Secondary Attributes: Opto-Isolated Interface for Safety
• Operating Voltage: 220 V
• Operating Current: 5 A
• Description/function: Energy Meter
• For Use With/related Products: MCP3909
• Lead Free Status / RoHS Status: Not applicable / Not applicable

MCP3909 / dsPIC33F 3-Phase Energy Meter Reference Design
C.4
DS51723A-page 84
MEASURING THE VOLTAGE/CURRENT RMS VALUE AND POWER USING
QUASI-SYNCHRONOUS SAMPLING ALGORITHM
From Equation C-11, a periodic voltage can be expressed as:
EQUATION C-25:
So the voltage fundamental and the voltage of each harmonic can be expressed as:
EQUATION C-26:
From Equation C-25, the fundamental voltage and voltage of each harmonic can also
be expressed as:
EQUATION C-27:
Where:
EQUATION C-28:
EQUATION C-29:
The voltage RMS value of each harmonic, then can be expressed as shown in
Equation C-31 with its initial phase angle shown in Equation C-29.
EQUATION C-30:
U t ( )
U
=
k
t ( )
U a0
---------- -
2
U
U
=
+
k
k
t ( )
u
k
=
∑
ak
∞
=
u
=
ck
1
------ - u
cos
ϕ
1
(
2
u ak
uk
u
=
⋅
(
ck
k
=
cos
sin
ck
⋅
u
ω
=
atan
ak
(
(
k
⋅
k
2
t
⋅
⋅
)
ω
+
u
--------------------------- -
ω
u
-------
u
+
ak
⋅
u
ak
bk
⋅
t
u
bk
2
)
t
k
+
+
+
2
2
sin
u bk
u
ϕ
bk
(
uk
k
sin
2
)
⋅
ω
(
k
© 2009 Microchip Technology Inc.
⋅
⋅
t
ω
)
⋅
t
)
)