AN939 Datasheet, PDF (2/18 Pages) Microchip Technology – Designing Energy Meters with the PIC16F873A

AN939
To get an accurate picture of power consumption for an
AC system, we need to make frequent measurements,
preferably many times that of the supply frequency. In
this application, we use a sampling rate of 400 Hz,
which provides 8 samples per full cycle of the line
frequency (for AC supply frequency of 50 Hz). For a
sampling rate F_s, we get N samples in N/F_s seconds. By
multiplying this expression for time by average power,
we obtain an expression for energy consumed in terms
of wattseconds (the second expression in Equation 1).
From here, we can use simple math to calculate
kilowatthours.
Of course, it is difficult for a microcontroller to make
direct measurements when the supply voltage is
coming straight off the mains: say, 230V at up to 50A.
This makes it necessary to indirectly measure line
voltage and current at a level consistent with a micro-
controller, then rescale these measurements to arrive
at the original value. The best way to do this is to
reduce the voltage to a level and dynamic range that is
compatible with digital circuitry. (Measuring current
here is essentially the same as measuring voltage, in
that we will use a transducer that generates a voltage
proportional to the load current.) The actual voltage
and current readings can then be derived.
For this application, the derived voltage reading, Vd, is
related to the actual instantaneous line voltage Vi by
the expression, V_d = V_i K_d/K_v or V_i = V_d K_v/K_d, where K_d
is the digitization constant for the ADC in this applica-
tion and K_v is the voltage proportionality constant for
the circuit design. For this particular application, K_d is
204.6, the digital value from the ADC that represents
1V. K_v is the factor by which the input line voltage is
reduced by a voltage divider; in our design, it is 300.
Similarly, the derived current reading, I_d, is related to I_i
by the expression, I_d = I_i K_d/K_i or I_i = I_d K_i/K_d, where K_i
is the current proportionality constant specific to this
design; it is calculated by dividing the CT turn ratio by
the product of the current amplifier gain and the input
burden resistance. For this application, based on a
5000-turn CT, the value of K_i works out to be
approximately 8.7. K_d is the same as before.
Note:
The calculation of K_i when using a shunt is
somewhat different. The actual circuit
design for current measurement, and the
design considerations for using a shunt,
are discussed in more detail in “Hardware
Design”, starting on page 10.
By substituting the attenuated values of V_d and I_d for
the V_i and I_i in the original power measurement
equation, we get an expression that relates the con-
sumed power directly to the indirect voltage and current
measurements, as shown in Equation 2.
EQUATION 2:
CALCULATING CONSUMED
ENERGY FROM INDIRECT
MEASUREMENTS
Σ^{⎛ N}
⎞
Energy Consumed
(wattseconds) ⁼
⎜
⎝
k
=
1^{Vdk •}
I_dk^⎟⎠
•
(K_v
•
K_i)
F_s • K_d2
We could accumulate a running total indefinitely and
directly interpret it for energy consumed over time. How-
ever, it’s more practical to accumulate up to some fixed
amount, then increment a counter to indicate energy
consumption. For our application, we will accumulate
10 Wh (0.01 kWh) before incrementing the counter. This
value represents the resolution limit of the meter. It is
equivalent to 36,000 wattseconds (10 Wh x 60 x 60); this
means that we increment the counter every time that the
right side of Equation 2 reaches 36,000.
We can also rearrange Equation 2 to define the power
consumed entirely in terms of V_d and I_d. Since we have
already defined F_s, K_v, K_i and K_d in constant terms, we
can give the whole quotient on the right side of the
equation a constant value, D (Equation 3).
EQUATION 3: REDEFINING POWER IN
TERMS OF V_d AND I_d ONLY
When 0.01 kWh is consumed:
Σ^N
k = 1^{Vdk • Idk}
=
3600 • F_s • K_d2
K_v • K_i
=D
In simple terms, any time that the accumulated sum of
the voltage and current products equals or exceeds D,
we increment the kWh counter. We also save any
remainder in excess of D to be used in the next round
of accumulation.
Note that anything which might influence the value of
the constants may also affect the value of D and
requires changes to the amplifier design. This includes
the use of a shunt instead of a CT, or even changing the
CT turn ratio, both of which may change K_i.
DS00939A-page 2
© 2005 Microchip Technology Inc.