XYLENE POWER LTD.

ELECTRICITY METERING

By C. Rhodes

OBJECTIVE:
The objective of this web page is to identify the general electricity metering methodology necessary for full implementation of a distributed power system in Ontario. It is shown that the Smart Meters presently being installed should be replaced by Smarter Meters that separately record transmitted and received energy registered during each measurement time interval.

DEFINITIONS:
Let Er = total energy received by a customer from the grid since meter installation;
Let Et = total energy transmitted by the customer to the grid since meter installation;
Let T = time;
Let Era = value of Er at time T = Ta;
Let Erb = value of Er at time T = Tb;
Let Eta = value of Et at time T = Ta;
Let Etb = value of Et at time T = Tb;

During measurement time interval (Tb - Ta) the received energy is (Erb - Era).

During measurement time interval (Tb - Ta) the transmitted energy is (Etb - Eta).

During measurement time interval (Tb - Ta) the net absorbed energy is:
[(Erb - Era) - (Etb - Eta)].

SMART METER:
A normal residential Smart Meter registers net absorbed energy (Er - Et). At the end of each measurement time interval the Smart Meter records the values of (Er - Et) and T. The difference between two successive recorded values is:
(Er - Et)b - (Er - Et)a = [(Erb - Etb) - (Era - Eta)] = [(Erb - Era) - (Etb - Eta)] = net absorbed energy during the measurement time interval.

SMARTER METER:
In order to permit directional energy calculations (required to calculate the power factor and to use different rates for received and transmitted power) the individual values of (Erb - Era) and (Etb - Eta) are required. A Smarter Meter registers Er and Et in separate registers using electronic signal processing. At the end of each measurement time interval the Smarter Meter records the values of Er, Et and T. The differences between successive recorded values are:
(Erb - Era) and (Etb - Eta)
A meter with this capability is also known as an interval directional kWh meter. Note that the net absorbed energy during a measurement time interval can be calculated by performing the subtraction:
[(Erb - Era) - (Etb - Eta)].

GENERAL METERING ARRANGEMENT:
Each grid customer (generator or load) is fitted with an interval directional kWh meter, also known as a Smarter Meter. This meter allows the grid customer to be a generator, a load or alternately both. This meter records interval cumulative energy data suitable for billing and provides optically isolated output signals suitable for local power monitoring and control.

SYSTEM DESCRIPTION:
A distributed power transmission / distribution system can be viewed as a collection of transmission / distribution subsystems. Each subsystem consists of an assembly of passive components such as wires, transformers, switches, fuses, capacitors and inductors that interconnect energy sources and energy sinks. Generators and loads are both transmission/distribution system customers. All energy entering or leaving each transmission / distribution subsystem is metered using directional power meters. Directional power metering is also used at points where different transmission / distribution subsystems interconnect. At such interconnection points each subsystem is a customer of the other.

At any instant in time T on each phase energy is either being received by the customer from the grid or is being transmitted by the customer to the grid. The customer's cumulative received energy is Er. The customer's cumulative transmitted energy is Et.

An interval directional kWh meter stores the cumulative Er, Et and T values at the end of each measurement time interval. Measurement time intervals are typically chosen to be in the range 5 minutes to 1 hour. The stored data is later transferred to a central computer for analysis and billing purposes.

SINGLE PHASE ELECTRICITY METER OPERATION:
Physics shows that instantaneous power Px guided by a phase x of a power transmission circuit is given by:
Px = Vx Ix
where:
Vx = instantaneous voltage
and
Ix = instantaneous current
An element of energy dEx is given by:
dEx = Px dT
where dT is an element of time.

North American AC power systems operate at 60 Hz = 60 cycles per second. It can be shown that for most practical purposes energy calculations are sufficiently accurate with respect to harmonic content if power metering responds up to the 30th harmonic of 60 Hz. Harmonic response is important because harmonics cause heat losses in the transmission/distribution system. The sampling theorm requires that for each multiplication element:
dT = (1 cycle / (2 X 30 samples)) X (1 second / 60 cycles)
= (1/3600) second / sample.
Hence a modern electricity meter should sample voltages and currents on each phase and calculate instantaneous power Px at least 3600 times per second. An instantaneous power calculation for one phase requires a 16 bit X 16 bit signed multiplication and a subsequent 32 bit addition with carry to a cumulative total.

In an AC power network Vx and Ix have approximately sinusoidal wave forms. The voltage and current both alternate positive and negative. However, due to reactance (usually primarily due to inductance related to motors and transformers), there is a phase shift between the voltage and current waveforms. Hence these waveforms do not cross zero at the same time. As a result, for some of the power samples the voltage is positive when the current is negative or vice versa, and the calculated value of Px is negative making the calculated value of dEx negative. A negative value of dEx corresponds to transmitted energy whereas a positive value of dEx corresponds to received energy.

A direction sensitive kwh meter separately cumulates and stores positive and negative dEx values. The total of all of the registered positive dEx values is Er, where Er is the cumulative received energy. The total of all of the registered negative dEx values is -Et, where Et is the cumulative transmitted energy. Note that Er and Et are both positive numbers.

THREE PHASE METERING:
As shown in the section titled Electricity-Three Phase Metering a three phase direction sensitive kWh meter requires two multiplication elements for an isolated delta fed customer and requires three multiplication elements for a wye fed customer in order to accurately calculate power P. It is important that all of the current and voltage samples occur simultaneously in all of the multiplication elements and that the sampling period be constant. After a sample each multiplication element outputs a signed value. If this value is positive it is added to the Er register. If this value is negative its sign is reversed and it is added to the Et register. The cumulative Er values, the cumulative Et values and the time are stored at the end of each measurement time interval.

The net energy absorbed by a wye fed three phase customer from the grid in element of time dT is given by:
dE = (dErx + dEry + dErz) - (dEtx + dEty + dEtz)
= dEr - dEt
where x, y, z designate the three phases.

DATA INTERPRETATION:
The net energy absorbed by a customer from the grid between time T = Ta and time T = Tb is given by:
[(Erb - Era) - (Etb - Eta)]
and the average power absorbed by the customer between time T = Ta and time T = Tb is given by:
P = [(Erb - Era) - (Etb - Eta)] / [Tb - Ta].

If the load is an ideal reactance and if [Tb-Ta] >>> (1/60) second:
(Erb - Era) ~ (Etb - Eta).
In this case during every cycle energy flows alternately in and out of the customer, but the net energy absorbed by the customer is zero. However, energy is continuously propagating through the transmission system, which still must be funded. Similarly, if there is a behind the meter wind generator, in a net metering system the net absorbed energy:
[(Erb - Era) - (Etb - Eta)]
may be zero but the transmission/distribution system still must be funded. To address this funding issue an electricity utility should allocate transmission/distribution costs to a grid customer in proportion to the absolute value of the net energy absorbed by the customer during a measurement interval divided by the power factor during that measurement interval, where the power factor is the fractional efficiency of transmission/distribution system usage. It is shown in the section titled Electricity Power Factor that this methodology results in a significant electricity bill for reactive loads.

DATA PROCESSING:
The values of Er, Et and T that were recorded at the end of each measurement interval are transferred to a remote computer where the quantities:
(Erb-Era), (Etb-Eta), [Tb-Ta], {[(Erb-Era)-(Etb-Eta)]/[Tb-Ta]} and [(Etb-Eta)/(Erb-Era)]
are calculated for each measurement interval. These quantities are required for electricity billing.

This web page last updated July 1, 2009.