Solid State Electricity Metrology

1.0 - Power 101 What is Electrical Energy ? Kinetic Energy of the generator or Chemical Energy of the cell is converted into Electrical Energy which flows through the circuit and is converted back into Light, Heat, and kinetic Energy. Energy flows from source to load

1.0 - Power 101 What is Electrical Energy ?

1.0 - Power 101 Electrical Energy in a dc circuit Total Energy (E) is equal to integral of p(t) over time

1.0 - Power 101 Electrical Energy in a dc circuit Total Energy Vs Time The slope of this graph is the product of v and i. E increases over time. The slope represents the rate of Energy flow.

Power is equal to the rate of flow of Electrical Energy What is Electrical Power? Electrical Power is the rate of flow of Electrical Energy in a circuit. The unit of power is the watt and is defined as joules per second. Therefore we can see that power is a rate expression Power is equal to the rate of flow of Electrical Energy

1.0 - Power 101 Energy - Power Relationship

1.0 - Power 101 What is Electrical Power? Power can also be defined as the time average of the instantaneous power p(t). This is equivalent to

1.0 - Power 101 Electrical Energy in an ac circuit where: V = rms voltage I = rms current

1.0 - Power 101 Total Electrical Energy in an ac circuit

1.0 - Power 101 Electrical Energy in an ac circuit Energy increases with time The rate of energy flow is not constant as in the dc case For a pure resistive load the rate of energy flow is > = 0

1.0 - Power 101 Electrical Power in an ac circuit time average over an integral number of line cycles (kT) where: k = integer T = period of v(t) P is often referred to as Active or Real Power in ac systems NOTE: The Real Power (P) calculated over an integral number of line cycles is equal to the steady state component (dc) of the instantaneous power signal p(t)

1.0 - Power 101 Energy = Power x time Electrical Energy in an ac circuit Energy flow in an ac circuit over an integral number of line cycles: averages to zero Energy = Power x time

1.0 - Power 101 Watts, VARS and VA Unfortunately practical loads are not purely resistive…………... E.g., the windings of an electrical motor contain a significant amount of Inductive Reactance as well as resistance

1.0 - Power 101 Pp(t) Pq(t)

1.0 - Power 101 P = VI cosq …active power…watts Q = VI sinq …reactive power…VARS S = VI …apparent power …VA

1.0 - Power 101 Why do we need to measure VARS & VA ? Cost to distribute Energy is higher when the load is reactive………. If V is constant and the load is reactive (current leads or lags V), then more current (I) must be transmitted in order to deliver a fixed amount of Electrical Energy (Watts). More current means more losses and higher transmission costs!

FUNCTIONAL BLOCK DIAGRAM 2.0 - AD775x Theory of Operation See page 1 of AN-545 FUNCTIONAL BLOCK DIAGRAM

2.1 - Theory of Operation See page 1 of AN-545 Analog Signals on Channel 1 and Channel 2 are digitized by the two ADCs These signals (Current and Voltage) are multiplied in a digital multiplier Multiplication generates an INSTANTANEOUS POWER SIGNAL The REAL POWER is extracted from the INSTANTANEOUS POWER by an LPF REAL POWER is converted to a FREQUENCY by the DIGITAL-TO- FREQUENCY Converters

2.1 - Theory of Operation See page 2 of AN-545 Non unity Power Factor Active Energy Calculation REAL POWER is still equal to the dc component of the INSTANTANEOUS POWER when PF <> 1

2.1 - Theory of Operation See page 2 of AN-545 Nonsinusoidal / Harmonic Active Energy Calculation Where: Total Harmonic Power is equal to the sum of the Real Power for each harmonic component !

2.1 - Theory of Operation See page 3 of AN-545 Digital-to-Frequency Conversion FOUT - High frequency output for meter calibration F1, F2 - Low frequency outputs for direct drive of counter FOUT has frequency ripple due to 2w instantaneous power signal. The ripple is removed by averaging the output frequency!

2.1 - Theory of Operation AD7755 typical watt-hour implementation