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By C. Rhodes, P.Eng., Ph.D.

An electricity meter is an instrument that measures the cumulative amount of electrical energy that flows past a certain point in an electric circuit. Single phase residential and small commercial electricity meters are usually located outside the premises so that they are readily accessible to electricity utility personnel without requiring access to the interior of the premises. The maximum power sensed by such in-line single phase meters is usualy less than 40 kW.

In a larger commercial-industrial premises a bulk three phase electricity meter is usually installed on the load side of the main electrical service disconnect switch. If the building contains tenants or condominium suites each suite may have its own submeter. That submeter should be installed on the load side of the disconnect breaker dedicated to that suite. For electrical safety reasons the distribution breaker panel and the associated metering equipment should be located in the same electical room or electrical closet.

A simple electricity meter registers the net amount of electrical energy that flows through that meter. A more complex meter separately registers the amount of electrical energy that flows from the grid to the load and the amount of electrical energy that flows from the load to the grid. A smart meter records in memory the cumulative registered data values every 15 minutes and then transmits these data values to the electricity utility. There may be some preprocessing of this data. Electricity meters vary in quality in terms of accuracy at the 60 Hz fundamental, accuracy in harmonic response and other features. Some electricity meters calculate and display the instantaneous power and/or instantaneous kVA. This feature is useful in local peak load control. Some electricity meters provide features that support remote load control by the electricity utility. Local display features vary from meter to meter. In Canada electricity meters used for revenue metering are expected to be accurate to +/- 0.1% for resistive loads varing from 10% to 100% of meter full scale. There may be small amounts of permitted additional error due to instrument transformers, phase angle and harmonics.

The objective of this web page is to identify the electricity metering methodology necessary for future electricity metering in Ontario. The Smart Electricity Meters presently in use in Ontario record cumulative net absorbed kWh, date and time at the end of each measurement interval. These meters should be gradually replaced by Smarter Meters that record cumulative incident energy (KVAh), cumulative net absorbed energy (kWh), date and time and control flag status at the end of each 15 minute measurement interval. One of the control flags should respond to a control signal from the IESO and prevents updating of the peak kVA measurement when surplus non-fossil electrical kWh are available. The other flag indicates a reset of the peak kW or peak kVA register.

To comprehend the material on this web page it is helpful to remember that electricity is actually incident and reflected flows of electromagnetic energy quanta known as photons. The electric and magnetic fields are strongest close to the conductors. In basic electromagnetic field theory the Poynting Vector (E X B) indicates the direction of energy propagation where E is the instantaneous local electric field and B is the instantaneous local magnetic field. If the current I changes sign then the sign of B changes. If the sign of B changes without a corresponding change in sign of E then the sign of the cross product (E X B) changes and hence the direction of energy propagation reverses. Under these circumstances there is reflected electromagnetic field energy that propagates in the opposite direction to the intended direction of energy transmission.

In general every party connected to the grid alternately sources and sinks energy during a cycle period due to the non-zero phase angle between the voltage and current. Thus, most electricity consumers are both energy receivers and energy transmitters. The net energy absorbed, as indicated by an induction type kWh meter, is the difference between the energy received and the energy transmitted. However, with non-fossil electricity generation the net energy absorbed is a poor indication of the shared electricity system resources used. For example, if a customer has behind the meter wind and/or solar generation without energy storage, his net energy absorbed may be close to zero but he may still use a significant fraction of the shared electricity system resources. The electricity metering and cost allocation system should be fair to all parties including the metered customer, the Local Distribution Company (LDC) and the other electricity system customers.

The electricity meter on each connection to the grid should separately register and display the cumulative incident energy (kVAh) and the cumulative absorbed energy (kWh). These separate registers are required to monitor cumulative energy transfers and to properly allocate generation/transmission/distribution costs. The acquired data should be stored at the end of each 15 minute measurement interval for subsequent remote reading and processing. The concept of net metering is fundamentally flawed because it does not fairly allocate shared electricity system costs among electricity system customers. Much of the market value of electricity lies in instantaneous availability of power on demand, not in the inherent value of the delivered energy. This issue is poorly reflected in the present Ontario retail electricity rate structure.

Let Ei = cumulative total energy incident on a load customer from the grid since meter installation expressed in kVAh;
Let Er = cumulative total energy reflected by the load customer back into the grid since meter installation expressed in kVAh;
Let T = time;
Let Eia = value of Ei at time T = Ta;
Let Eib = value of Ei at time T = Tb;
Let Era = value of Er at time T = Ta;
Let Erb = value of Er at time T = Tb;

During measurement time interval (Tb - Ta) the incident energy is:
(Eib - Eia)
and is expressed in kVAh

During measurement time interval (Tb - Ta) the reflected energy is:
(Erb - Era)
and is expressed in kVAh

During measurement time interval (Tb - Ta) the net absorbed energy is:
[(Eib - Eia) - (Erb - Era)]
and is expressed in kWh.

During measurement time interval (Tb - Ta) the average incident power is:
(Eib - Eia) / (Tb - Ta)
and is expressed in kVA.

During measurement time interval (Tb - Ta) the average absorbed power is:
[(Eib - Eia) - (Erb - Era)] / (Tb - Ta)
and is expressed in kW.

For electricity cost allocation purposes a billing period should be divided into 15 minute = 0.25 hour intervals so typically:
(Tb - Ta) = 0.25 hour

In order to fairly allocate electricity system costs to customers it is necessary to record both Ei and (Ei - Er) at the end of each 15 minute interval. That is the basic purpose of the electricity metering system. This data is stored and is later centrally analysed for billing purposes.

However, it is also necessary to provide each customer feedback as to how his electricity load is performing and how he should change his behavior to minimize his electricity cost. Hence part of the electricity cost allocation algorithm should be implemented in the electricity meter and should drive a local display. Typically this local display will as a minimum show cumulative absorbed energy:
(Ei - Er)
in kWh, present incident power:
[(Eib - Eia) / (Tb - Ta)]
in kVA and sliding average peak incident power in kVA registered thus far during the billing period. At times when interruptible electricity is available the sliding average peak incident power registration mechanism should be bypassed.

In principle it is possible to operate a comparable billing system without displaying the sliding average peak power or the sliding average peak power used for billing purposes. However, then the administrative burden on the distribution utility increases.

If the load is an ideal reactance and if:
0.25 hour = [Tb-Ta] >>> (1/60) second:
(Eib - Eia) ~ (Erb - Era).
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, dissipating heat, the costs of which must be funded. Similarly, if there is a behind the meter wind generator, in a net metering system the net absorbed energy:
[(Eib - Eia) - (Erb - Era)]
may be zero but the transmission/distribution system still must be funded. To address this funding issue a non-fossil fuelled electricity utility should allocate standard electricity service costs to a grid customer in proportion to the peak value of:
(Eib - Eia) / (Tb - Ta)
This cost allocation methodology results in a significant electricity cost penalty for reactive loads.

In a non-fossil electricity system the variable cost is zero and the cost per billing period of serving a particular customer is proportional to the peak value of [(Eib - Eia) / (Tb - Ta)] which is the peak kVA during that billing period.

The marginal extra cost of providing a non-fossil interruptible electricity service should be met from revenue proportional to the number of absorbed kWh.

The electricity rate structure and metering should provide a financial incentive for all parties connected to the grid to do all necessary to achieve high power quality and high transmission / distribution utilization efficiency without reliance on complex and difficult to enforce regulations.

Efficient use of the transmission / distribution system should be financially rewarded. The transmission / distribution system operates most efficiently when each connected party transfers power to or from the transmission / distribution system at a constant rate with unity power factor.

One of the properties of a balanced 3 phase resistive load is that its power drain from the grid is constant. Hence for such a load the instantaneous power is equal to the average power. This is the most efficient way of coupling to the grid and should attract the lowest transmission/distribution charges per kWh of energy transferred.

Inefficient use of the transmission / distribution system should be financially penalized. If a customer presents a reactive impedance or harmonic distortion to the grid then that customer should be allocated a larger fraction of the transmission/distribution costs.

The higher the fluctuations in power transfer rate, the less efficiently the transmission / distribution system is utilized. If a customer presents a resistive impedance to the grid that varies over a 24 hour period that customer should be charged more for distribution than is a customer that consumes the same amount of energy at a constant energy transfer rate.

The metering technology used should be able to resolve power harmonics up to at least the 30th harmonic of the power line frequency in order to measure significant harmonics generated by power inverters. These harmonics cause heat losses in the transmission/distribution system.

The aforementioned grid connection issues should be addressed through the use of peak kVA metering. Consideration should be given to making each billing period one week or two weeks instead of one month to better incent use of customer owned energy storage. The issue is that customers generally do not have redundant equipment so that when the energy storage equipment is out of service for maintenance the customer is heavily financially penalized. The financial consequences of occasional random equipment failures would be much smaller if the billing period was one week or two weeks instead of one month.

One of the practical problems in Ontario is that much of the electricity system is owned by the government. For political reasons the government chooses to transfer part of the electricity cost burden from one customer class to another customer class or to the taxpayers. The government also imposes other system constraints that have no basis in science or engineering. This governmental intervention cancels many of the electricity system benefits that would otherwise be available via sophisticated electricity metering.

A basic electricity transmission line consists of two parallel isolated wires that are relatively closely spaced. These wires connect a generator to a load. At any point along these wires at any instant in time the current in one wire is I and the current in the other wire is - I, so the sum of the two currents is zero. At that point and at that time the voltage between the wires is V. At that point and at that time the rate of energy propagation past that point is power P where:
P = (V I)

Note that depending upon the instantaneous values of V and I, P can be instantaneously either positive or negative. Positve P corresponds to energy propagating toward the load known as incident energy, negative P corresponds to energy propagating away from the load known as reflected energy. The problem with reflected energy is that absent high efficiency phase shifting equipment owned by the utility it is usually dissipated as heat. Thus electricity loads should be designed to minimize emission of reflected energy.

In the special case of a generator the design objective is to maximize energy propagation away from the generator (reflected energy sourced by the generator) and minimize energy propagation toward the generator (incident energy absorbed by the generator) which if dissipated in the generator becomes heat.

Over time (T - To) the net energy that flows past a point toward a load is:
Integral from T = To to T = T of:
V I dT

This integral can be broken into two parts, incident energy Ei plus reflected energy (- Er). The incident energy Ei corresponds to integration over time of positive values of (V I). The reflected energy (- Er) corresponds to integration over time of negative values of (V I).
Note that Er is positive. Hence:
(Ei - Er)
= Integral from T = To to T = T of:
(Pi - Pr) dT
= Integral from T = To to T = T of:
V I dT

Now assume that whenever the product (V I) is negative its sign is switched. Hence:
(Ei + Er)
= Integral from T = To to T = T of:
|V I| dT

Ei = [(Ei - Er) + (Ei + Er)] / 2
= [Integral from T = To to T = T of:
V I dT] / 2
+ [Integral from T = To to T = T of:
|V I| dT] / 2
= [Integral from T = To to T = T of:
{(V I) + |V I|} dT] / 2

Note that when (V I) is negative this integrand is zero.

If the measurement point is located near the transmission line termination at the load the energy Ei is energy from the generator which is incident upon the load and energy Er is energy reflected off the load that is usually dissipated as heat in the transmission/distribution network. The energy absorbed by the load is;
(Ei - Er)
= Integral from T = To to T = T of:
V I dT

Thus (Ei - Er) in kWh can be obtained by cumulating the signed (V I) products at a constant sampling rate. Note that (Ei - Er) is the quantity measured by an induction type kWh meter.

However, the incident energy is:
Ei = [Integral from T = To to T = T of:
{(V I) + |V I|} dT] / 2

The units of incident energy Ei are kVAh.

Thus kVAh can be obtained by cumulating the positive (V I) product values at a constant sampling rate.

The fractional loss of energy due to reflection off the transmission line termination is known as the power factor PF which is given by:
PF = (Ei - Er) / Ei

Note that this definition of Power Factor PF is general and is true for any frequency or wave form. Similarly the aforementioned expressions for (Ei - Er) and Ei are also completely general.

Now consider the special case where the voltage and current of the incident power are sinusoidal and in phase with each opther. Then for the incident power waveform:
V = Vo Sin(W T)
and a current I given by:
I = Io Sin(W T)

Then the instantaneous incident power Pi is:
Pi = (V I)
= Vo Io [Sin(W T)]^2
and the incident energy Ei is given by:
Ei = Integral from T = To to T = T of:
Vo Io [Sin(W T)]^2 dT

For (T - To) >> (2 Pi / W):
Ei = [(Vo Io / 2) (T - To)]
which has units of kVAh. The quantity:
(Vo Io / 2)
has units of kVA.

Now assume that the load is reactive so that at the load:
V = Vo Sin(W T)
I = Io Sin[(W T) + Phi]
= Io Sin(W T) cos(Phi) + Io cos(W T) sin(Phi)

(Ei - Er)
= Integral from T = To to T = T of:
V I dT
= Integral from T = To to T = T of:
Vo Io {[Sin(W T)]^2 cos(Phi) + Sin(W T) cos(W T) sin(Phi)} dT

For (T - To) >> (2 Pi / W):
(Ei - Er) = [(Vo Io / 2)(T - To) cos(Phi)]

Thus the power factor PF is given by:
Pf = (Ei - Er) / Ei
= [(Vo Io / 2)(T - To) cos(Phi)] / [(Vo Io / 2) (T - To)]
= cos(Phi)

This is the familiar definition of power factor for sinusoidal waveforms.

Unless there is nearby power factor correction equipment reflected power is dissipated as heat in the transmission/distribution network. If there is power factor correction equipment that equipment should be located on the load side of the electricity meter so that the customer financially benefits from the power factor correction equipment.

Recall that the incident energy provided by the generation is Ei while the energy dissipated in the load is (Ei - Er). However, for network cost allocation the energy that is consumed due to the presence of the load is Ei plus the transmission losses relating to delivery of Ei.

Recall that for sinusoidal wave forms:
Ei = [(Vo Io / 2) (T - To)]
Ei / (T- To) = (Vo Io / 2)
which is known as the kVA.

An electricity system usually operates with a Vo ~ constant. The value of Io generally varies with time. However, the electricity system must be built to meet the maximum value of:
Io = Iom.
Hence the cost of electricity system capacity is proportional to (Vo Iom) / 2 which is known as the customer's peak kVA.

For standard electricity service billing purposes it is necessary to record Ei while for interruptible electricity service billing purposes it is necessary to record (Ei - Er). Thus for each meter interval the meter should record both Ei and (Ei - Er). If at any time during a metering interval the IESO enables Interruptible Power at this premises, it is also necessary to set an IESO flag for this metering interval. The quantities Ei and (Ei - Er) are each 5 bytes long, the peak kVA requires 2 bytes, the flags require 1 byte, the interval counter for date/time calculation requires 2 bytes, and 1 byte is required for memory error checking so the meter needs at least:
2976 intervals per month X 16 bytes per interval = 47,616 bytes / month of memory. Allowing for possible meter reading problems which could extend up to a year the meter should have:
12 months X 47,616 bytes / month = 571,392 bytes of non-volitile read-write data memory.

Failure to separately record incident energy (Eib - Eia) and net absorbed energy [(Eib - Eia) - (Erb - Era)] for each measurement time interval leads to electricity rates that do not provide proper cost signals and proper financial incentives to either distributed generators or load customers.

The reflected energy (Erb - Era) in an interval can be calculated from:
[(Erb - Era)] = [(Eib - Eia)] - [(Eib - Eia) - (Erb - Era)]

The registers that store Ei and (Ei - Er) values must be non-volatile against power failures and must have sufficient bytes that these registers will not roll over during the working life of the electricity meter. Provision of one redundant byte per measurement interval allows use of a checksum for memory and communication error checking.

Legal metrology presently requires that a Smart Meter locally display the current value of (Ei - Er). Apart from being legally required this local display is helpful for: confirming meter accuracy, local electricity load measurements and resolving clerical billing errors relating to which meter and which instrument transformers are associated with which customer. When a Smarter Meter is used the meter should also locally display the current value of Ei.

To assist with local power system diagnostics it may be helpful if each electricity meter can display the RMS 3 - phase voltages Va, Vb, Vc and the RMS 3 - phase currents Ia, Ib, Ic.

A normal residential Smart Meter registers and locally displays cumulative net absorbed energy (Ei - Er). Note that (Ei - Er) is a signed quantity. At the end of each measurement time interval the Smart Meter records the values of (Ei - Er) and time T. The difference between two successive recorded values at times Ta and Tb is:
(Ei - Er)b - (Ei - Er)a
= [(Eib - Erb) - (Eia - Era)]
= [(Eib - Eia) - (Erb - Era)]
= net absorbed energy during the measurement time interval (Tb - Ta).

In order to permit directional energy calculations, as required to calculate the power factor PF, where:
PF = [(Eib - Erb) - (Eia - Era)] / [Eib - Eia]
the individual values of Ei and (Ei - Er) are required. A Smarter Meter stores Ei and (Ei - Er) in separate registers and locally displays current values of:
kVA = (Eib - Eia) / (Tb - Ta)
kW = [(Ei - Er)b - (Ei - Er)a] / (Tb - Ta).

At the end of each measurement interval the Smarter Meter records the values of Ei, (Ei - Er) and T. Note that (Ei - Er) is a signed quantity. The differences between successive recorded values at times Ta and Tb are:
(Eib - Eia) and [(Eib - Eia) - (Erb - Era)].
A meter with this capability is known as a directional interval meter. Note that the net absorbed energy in kWh during measurement time interval (Tb - Ta) is:
[(Eib - Eia) - (Erb - Era)].

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

A power system can be viewed as a collection of local distribution subsystems interconnected via a common transmission system. Each local distribution system 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 may be either transmission system customers or distribution system customers. All energy entering or leaving each distribution subsystem is metered using directional power meters. 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 incident energy on that phase is Ei. The customer's cumulative reflected energy on that phase is Er.

An interval directional kWh meter stores the cumulative Ei, Ei - Er and T values at the end of each measurement time interval. Measurement time intervals are typically 15 minutes. The stored data is later transferred to a central computer for analysis and billing purposes.

North American AC power systems operate at a fundamental frequency of 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 systems. 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 signed 32 bit addition with carry to a cumulative total.

In an AC power network V and I 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:
P = (V I)
is negative making the calculated value of dE negative. For a load customer a negative value of dE corresponds to reflected energy whereas a positive value of dE corresponds to incident energy.

A direction sensitive kWh meter separately cumulates and stores Ei and (Ei - Er) values where Ei is the cumulative incident energy. and (Ei - Er) is the cumulative absorbed energy. Note that Ei and Er are both positive numbers.

Note that for a generator the "reflected energy" is actually mechanical energy that powers the generator. For a generator the "incident energy" is energy absorbed from the grid.

As shown on the web page 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 total power Pt. It is important that on each phase the current and voltage samples occur simultaneously and that the sampling period is constant. After a sample each multiplication element outputs a signed (V I) value. This signed (V I) value is added to the (Ei - Er) cumulation register. If this signed (V I) value is positive it is added to the Ei cumulation register.

The net energy absorbed by a wye fed three phase customer from the grid in element of time dT is given by:
dE = (dEix - dErx) + d(Eiy - dEry) + d(Eiz - dErz)
= d(Ei - Er)

where x, y, z designate the three phases.

The values of Ei and (Ei - Er) and time T are stored at the end of each measurement time interval.

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

The potential weak links in a peak kVA based electricity rate are unauthorized bypass of the sliding average kVA calculation or unauthorized reset of the peak kVA register. To prevent these events happening every time the kVA calculation is bypassed or the maximum kVA register is reset a flag is set in recorded data and the status of that flag for that measurement interval is later compared to the known status of the IESO control signal for that interval. If a bypass flag is set in any interval when a IESO interruptible power enable signal was not transmitted or if a reset flag occurs at any time other than the end of a billing period then unauthorized tampering with the metering equipment is occurring. In that event the electricity bill should be calculated by detailed analysis of the kVAh and kWh energy profiles using IESO supplied data rather than flag data from the meter. A checksum should be used to detect any tampering with the meter software.

This web page last updated May 3, 2020.

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