Patent Description:
Measuring power requires monitoring both voltage and current in a circuit. For measuring the power consumed or generated by appliances, this typically requires making direct electrical contact with a household mains supply and inserting a power meter between the supply and the load or appliance. This is a straightforward and effective way to measure power and there are many devices on the market that can be used to measure power in this way. However, there are several drawbacks to this approach. For example, an electrician may be required to install the power meter depending on the appliance, and the power meter must be placed in-line with the load circuit which may make the installation more complex. Also, the power meter circuit can be relatively complex, since it needs to measure both voltage and current. Furthermore, there is an added cost due to the need for components such as a current transformer, Rogowski coil or shunt resistor for current measurement. The publication titled '<NPL>) and patent <CIT> disclose the use of noncontact sensors for monitoring power usage in power cables and other devices. The sensors use magnetic field sensing elements. Calibration methods are used to derive a relationship between the measured magnetic fields and the power in the cables.

It is desired to address or ameliorate one or more shortcomings or disadvantages associated with prior energy monitoring devices, or to at least provide a useful alternative thereto.

The invention relates to a method of measuring power delivered by a cable, the method comprising:.

Additional features of the method are proposed in the appended dependent claims.

Embodiments are described in further detail below, by way of example and with reference to the accompanying drawings, in which:.

Described embodiments generally relate to energy monitoring. In particular, described embodiments are directed to systems, methods and devices for measuring energy consumption and generation.

Magnetometers are commonly used to measure current flowing through a conductor by detecting the induced magnetic field around the conductor. Applying this approach to measure current in a home environment has several drawbacks. Firstly, typical electrical wiring in the home contains two conductors (active and neutral) which have equal and opposing current flows which tend to cancel the magnetic field. Secondly, separating the active and neutral conductors in a power cord, multi-core cable or conduit in order to make a measurement on a single conductor is not practical. To overcome these difficulties, the present system uses the residual magnetic field generated by a current flowing through a conductor pair to obtain a measure of the current flowing through the conductors.

<FIG> shows an energy monitoring system <NUM> having a number of appliances <NUM>, sensor devices <NUM>, a smart meter <NUM>, an energy monitoring system <NUM>, a server system <NUM> and a number of external devices <NUM>. Appliances <NUM> may include household appliances such as refrigerators, televisions, washers, dryers, air conditioners and heaters, as well as energy generation devices such as solar panel systems. In some embodiments, appliances <NUM> may be powered by an AC mains voltage, which may be around <NUM>, <NUM>, or another frequency in some embodiments. It is to be understood that any specific examples in this document that refer to a specific AC mains frequency, such as <NUM>, are not limited to that frequency, and that that frequency is only used as an illustrative example. According to some embodiments, the appliances may be powered by another AC signal, such as a signal from a solar power system or a generator. For the purposes of this document, the term "mains power" will be used to describe grid power as well as these alternative AC power sources. Each appliance <NUM> may be associated with a sensor device <NUM>, which may be used to measure the electrical power used and/or generated by appliance <NUM>. Sensor devices <NUM> are described in further detail below, with reference to <FIG>.

Sensor devices <NUM> communicate with a server system <NUM>. Server system <NUM> may include one or more servers, databases, and/or processing devices in communication over a network. In some embodiments, server system <NUM> may be a cloud computing system, such as the Intelligent. li cloud computing system.

Smart meter <NUM> may be an electronic meter that monitors, records and communicates the consumption and generation of electrical energy in relation to a particular premises, household, building or area. Smart meter <NUM> may sample instantaneous power usage at a rate of around once every <NUM> to <NUM> seconds in some embodiments. Smart meter <NUM> may be in communication with an energy monitoring device <NUM>, which may be a Power VU Gateway device by DiUS Computing Pty Ltd in some embodiments. Server system <NUM> may make data available for presentation purposes through external devices <NUM>, which may include desktop computers, laptop computers, smart phones, tablets, and/or other computing devices.

System <NUM> may be configured to monitor energy consumed and generated by appliances <NUM>, and to make this information available through externals devices <NUM>, based on energy levels determined by data produced by sensor devices <NUM> and smart meter <NUM>. The data may be processed by a transformation engine within server system <NUM> to produce accurate power and energy data.

The energy data derived from sensor devices <NUM> and energy monitoring device <NUM> may include instantaneous or live power (measured in Watts), energy consumption (measured in kWhr), and energy consumption and generation for homes with solar (measured in kWhr) including gross solar energy, net energy and household energy consumption.

According to some embodiments, server system <NUM> may be configured to calibrate the output of sensor <NUM>, and thereby provide accurate power measurements at an appliance level. This is unlike traditional voltage and current sensors, where power consumption or generation is measured directly. Instead, server system <NUM> may leverage billing grade data from smart meter <NUM> by correlating the measurement from sensor device <NUM> with the measurement from smart meter <NUM>. Energy monitoring system <NUM> may poll smart meter <NUM> at regular intervals, buffer the data and push the data to server system <NUM> at regular intervals. Server system <NUM> may combine this data with data from sensor device <NUM> to provide an accurate power measurement.

<FIG> shows a sensor device <NUM> in more detail. Sensor device <NUM> may be configured to determine a measurement corresponding to the AC current which is flowing through a standard two or three conductor AC cable electrically connected to an appliance <NUM> by measuring the residual magnetic field produced by the cable. The measurement determined by sensor device <NUM> can then be used along with data from smart meter <NUM> to calculate the current and power transferred through the cable. Sensor device <NUM> may include a magnetometer <NUM>, a power supply <NUM>, a communications module <NUM>, a processor <NUM> and memory <NUM>.

Sensor <NUM> may be configured to be clamped around the outer insulation of the power cord or AC cable of an appliance <NUM>. This attachment method means that the operation of sensor device <NUM> does not rely on making electrical contact with the household supply, making the operation of sensor device <NUM> safer than the operation of typical power sensing devices. This further makes sensor device <NUM> easy to install, as it does not require the AC cable to be spliced or even disconnected, as would be required if a current transformer or in-line power meters were to be used. This makes it possible to deploy sensor device <NUM> on AC cables which cannot be physically interfered with, such as those of electric ovens, large air conditioners or solar installations.

Magnetometer <NUM> may be configured to measure the magnetic field produced by the power cord or cable around which sensor device <NUM> is clamped. Magnetometer <NUM> may communicate this data to processor <NUM>. Sensor device <NUM> may be powered by a power supply <NUM>, which may include at least one battery in some embodiments. According to some embodiments, sensor device <NUM> may be configured to be able to be battery-powered for extended periods of time, such as for <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM> or more months. This makes it possible to deploy sensor device <NUM> in locations where no ready source of mains power is available, such as in outdoor areas near a solar inverter, for example. Communications module <NUM> may receive data from processor <NUM>, and communicate data to and/or receive data from one or more external server networks, which may include server system <NUM> in some embodiments.

Processor <NUM> may include one or more data processors for executing instructions, and may include one or more of a microcontroller-based platform, a suitable integrated circuit, and one or more application-specific integrated circuits (ASIC's). Processor <NUM> may include an arithmetic logic unit (ALU) for mathematical and/or logical execution of instructions, such operations performed on the data stored in internal registers of processor <NUM>.

Processor <NUM> may have access to memory <NUM>. Memory <NUM> may include one or more memory storage locations, which may be in the form of ROM, RAM, flash, or other memory types. Memory <NUM> may store program code <NUM>, which may be executable by processor <NUM> to cause processor <NUM> to communicate with magnetometer <NUM> and communications module <NUM>, and perform functions as described with further detail below.

When a current flows through a conductor, a circular magnetic field is induced in the plane perpendicular to the conductor. The strength of this magnetic field is proportional to the amount of current flowing, and diminishes linearly with distance from the conductor. For an AC current, the field reverses direction at the same time as the current reverses direction. Thus, measuring the strength of the reversing magnetic field provides a means to measure the amount of current.

This is the principle behind the common Current Transformer ("CT Clamp"), which completely encircles one conductor with a magnetically conductive material. This in effect integrates the magnetic field across the path of the encirclement, and as a result a total magnetic field is induced in the clamp that is directly proportional to the current in the conductor, independent of the relative location of CT Clamp and conductor. For AC conductors, this magnetic field can be measured by winding a (secondary) conductor around the magnetically conductive material, creating a transformer. For standard AC sources, the current induced in this secondary winding is directly proportional to the current flowing through the original conductor.

However, because the strength of field in the CT Clamp is independent of the location of the conductor relative to the clamp, encircling two conductors carrying equal but opposite current (as is the case in a standard AC cable) results in two equal but opposite magnetic fields being induced, which exactly cancel each other out. The resulting net field is zero. For this reason, CT Clamps can only be used when access to a single conductor is possible.

In common two or three conductor AC cables, individually insulated conductors for Active ("A"), Neutral ("N") and optionally Earth ("E") are placed next to each other, and encased in a second layer of insulator, which provides both additional insulation and structural integrity to the cable. <FIG> shows a cross-section <NUM> of a typical two conductor cable <NUM> having an Active conductor <NUM> and a Neutral conductor <NUM>, and <FIG> shows a cross-section <NUM> of a typical three conductor cable <NUM> having an Active conductor <NUM>, a Neutral conductor <NUM> and an Earth conductor <NUM>.

During normal operation, the current in Active conductors <NUM>/<NUM> and Neutral conductors <NUM>/<NUM> are equal but opposite in direction. Any current in Earth conductor <NUM> is generally a sign of a dangerous malfunction, and in modern installations will trigger a Residual Current Device ("RCD"). Based on this, it is reasonable to assume zero current through Earth Conductor <NUM>.

While integrating the magnetic field along a path encircling both Active conductor <NUM>/<NUM> and Neutral conductor <NUM>/<NUM> will always result in a net field of zero, this does not mean that the sum of magnetic fields from the two conductors is zero in any given place. <FIG> is a cross section <NUM> illustrating the Active field <NUM> for two-conductor cable <NUM>, and <FIG> is a cross section <NUM> illustrating the Neutral field <NUM> for two-conductor cable <NUM>. Comparing <FIG>, it is apparent that field <NUM> is not the exact opposite of field <NUM>, due to the difference in the position of Active conductor <NUM> to Neutral conductor <NUM> in cable <NUM>. This is further illustrated in <FIG>, which shows a cross section <NUM> illustrating the residual field <NUM> of the addition of Active field <NUM> with Neutral field <NUM>, and <FIG>, which shows a cross section <NUM> illustrating the residual field <NUM> of the addition of an Active field with a Neutral field of three-conductor cable <NUM>.

A significant residual field <NUM>/<NUM> exists at the surface of cables <NUM> and <NUM>, which rapidly diminishes with distance away from cables <NUM> and <NUM>, roughly proportional to the square of the distance away from the cable <NUM>/<NUM>. While the direction and exact strength of residual field <NUM>/<NUM> at any point on the surface of cable <NUM>/<NUM> is dependent on the relative geometry of that point and conductors <NUM>/<NUM> and <NUM>/<NUM>, there are in fact no points in which residual field <NUM>/<NUM> is zero, or even vanishingly small. Thus, a direct measurement in any particular single point on or near the surface of cable <NUM>/<NUM> will observe a significant residual field <NUM>/<NUM>. The strength of residual field <NUM>/<NUM> is proportional to the amount of current flowing through conductors <NUM>/<NUM> and <NUM>/<NUM>, even though the proportionality factor and the direction of field <NUM>/<NUM> vary from point to point.

Recent advances in micro-electromechanical systems (MEMS) and hall effect magnetic sensor technology, driven by the inclusion of magnetometers in commodity smart phones, have resulted in high performance, low cost miniaturized magnetometers becoming readily available. Sensor device <NUM> includes such a magnetometer <NUM>, configured to be positioned directly adjacent to the cable <NUM>/<NUM> in which current is to be measured when sensor device <NUM> is clamped to the cable. As detailed above, in that location, magnetometer <NUM> will experience a residual magnetic field <NUM>/<NUM> in the plane perpendicular to cable <NUM>/<NUM>. Given a mains AC cable, this field will oscillate at the mains frequency (e.g. <NUM> in Australia), and will be proportional in strength to the current flowing through the cable.

In the following examples, a mains frequency of <NUM> will be assumed, but it is understood that the mains frequency may vary in some cases, and may be <NUM> or another frequency. The calculations described can easily be adjusted to account for an alternative frequency other than <NUM> if required.

Magnetometer <NUM> will also be affected by the Earth's magnetic field, and possibly by magnetic fields from permanent magnets (e.g. from magnetic toys, or from motors) and electromagnets (e.g. from speakers or magnetic door locks) in the vicinity of magnetometer <NUM>. In most cases, these additional fields would not oscillate at or near the mains frequency.

Commodity magnetometers typically measure in three axes. For the purpose of sensor device <NUM>, magnetometer <NUM> is arranged to be positioned so that the magnetic field is measured along the longitudinal axis of the cable, and along the plane perpendicular to the longitudinal axis of the cable.

For a purely resistive load, connected to a pure sine wave mains voltage, the current through the load is described by a perfect sine wave, at the same frequency as (and in phase with) the mains voltage. Based on this, for a mains frequency of <NUM>, it would be sufficient to sample the magnetic field at no less than <NUM> to determine the strength of the oscillating field.

However, many modern loads are far from being purely resistive. The prime example are switch mode power supplies, which tend to draw close to zero current through most of each period of AC voltage, and just short, large surges near the voltage peaks. In the frequency domain, this results in very significant current components at the odd harmonics (e.g. for a mains frequency of <NUM>, the odd harmonics are at <NUM>, <NUM>, etc.). In order to resolve and discount these higher-frequency components, a much higher rate of sampling is required.

MEMS magnetometers are readily available which can support sample rates of <NUM> to <NUM> samples/second. This corresponds to <NUM> to <NUM> samples per period, which is not quite sufficient to resolve the harmonics from common switch mode supplies. As a result, the observed field at <NUM> varies somewhat depending on the phase alignment between sample points and the mains period.

This is illustrated in <FIG> and <FIG>. <FIG> shows a graph <NUM> of a signal <NUM> with sample points <NUM>, sampled at a rate of <NUM> samples per period. <FIG> shows a graph <NUM> of signal <NUM> with sample points <NUM>, also sampled at a rate of <NUM> samples per period, but with a different alignment of the signal with the sampling rate. Comparing <FIG> with <FIG>, it is apparent that the sampling alignment of <FIG> does not capture the maximum and minimum values of signal <NUM>.

Since the current in an appliance cable <NUM>/<NUM> is generally periodic, sampling across multiple mains periods allows gathering more samples, and, given suitably chosen sample times, allows an effective increase in the effective temporal resolution. <FIG> shows a graph <NUM> of signal <NUM> with sample points <NUM>, when taking <NUM> samples during <NUM> periods, or sampling at a rate of <NUM> samples per period. <FIG> shows a graph <NUM> of signal <NUM> with sample points <NUM>, also sampling at a rate of <NUM> samples per period, showing the resulting effective sampling resolution.

Sensor device <NUM> may sample for around <NUM> periods (i.e. <NUM>) in some embodiments, taking around <NUM> samples (i.e. at <NUM>, and at <NUM> effective). This resolves sufficiently high harmonics such that the aliasing from the remaining ones is below the noise floor. In some embodiments, a different sampling duration may be used, such as <NUM>, <NUM>, <NUM>, <NUM>, <NUM> or <NUM> periods, for example. In some embodiments, the sampling time for sensor device <NUM> may be selected to ensure a good isolation for the magnetic field <NUM>/<NUM> from DC or other frequencies, but short enough that the actual mains frequency varying a fraction of a percent (as often occurs) will not cause problems.

According to some embodiments, sensor device <NUM> may sample data at intervals of around <NUM> seconds. In some embodiments, sensor device <NUM> may sample data at intervals of around <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM> or <NUM> seconds.

Sensor device <NUM> may be active for a particular time per sampling period. For example, sensor device <NUM> may operate for periods of approximately <NUM>, which may include time for sensor device <NUM> starting up, sampling, processing and communicating the sampled data. The active time for sensor device <NUM> may be dependent on both the sampling time, and the hardware of sensor device <NUM>. In some embodiments, sensor device <NUM> may operate for periods of approximately <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM> or <NUM>.

The strength of the <NUM> residual magnetic field (i.e. the magnitude of the corresponding Fourier coefficient) is directly proportional to the amount of current in the cable. The conversion factor, however, depends on the (unknown) physical arrangement of the two wires relative to the magnetometer. As long as the arrangement stays the same, the factor stays the same - hence the need to fixate the cable in the sensor.

<FIG> shows a flowchart of steps taken to calculate a measure of the strength of the oscillating magnetic field based on the data measured by magnetometer <NUM>. In some embodiments, each of the method steps may be performed by processor <NUM>. In some alternative embodiments, sensor device <NUM> may send measured data to server system <NUM> via communications module <NUM> to perform one or more of the method steps. In some embodiments, some or all of the processing steps may be performed by an external device in communication with sensor device <NUM>.

At step <NUM>, sensor device <NUM> samples the magnetic field <NUM>/<NUM> of a cable <NUM>/<NUM> of an appliance <NUM>. In order to obtain a measure for the magnitude of AC current in a cable <NUM>/<NUM>, at step <NUM> the samples measured by sensor device <NUM> are multiplied with a complex AC mains signal, which may be a <NUM> signal in some embodiments, and the results summed at step <NUM>. As described below, in some embodiments step <NUM> may involve a number of separate complex sums, being the sums of separate subsets of the signal samples multiplied with the complex signal. This gives either a single, complex sum, or a number of separate complex sums. The magnitude of the sums represents the size of the oscillating-at-mains-frequency magnetic field <NUM>/<NUM> observed by magnetometer <NUM>, and its angle represents the phase difference between the start of sampling and the start of the mains period.

Given a sample duration of <NUM>, and a sample rate of slightly over <NUM> samples per second, for example, this results in a filter which is sufficiently discerning to suppress most non-mains-related magnetic fields, yet sufficiently relaxed to not be significantly affected by changes in mains frequency in the plus or minus one percent range.

Steps <NUM> to <NUM> may be sufficient when the current through cable <NUM>/<NUM> of appliance <NUM> is periodic, which may be true in most circumstances. However, when an appliance <NUM> is first connected or switched on, a single short, sharp spike of inrush current may be observed. For example, this switching may occur periodically with a fridge motor that turns on and off to keep the fridge at a particular temperature. Also, non-mains-related magnetic interference, such as the magnetic field induced by the very high but very short-lived current in a photographic flash, might also be spiky in nature.

In order to prevent the effect of such one-time spikes in the magnetic field from influencing the value reported for the AC mains signal oscillating field strength, samples taken by sensor device <NUM> may optionally be split into a number of separate groups, and steps <NUM> and <NUM> may be done independently for each group by processor <NUM> or server system <NUM>. In some embodiments, the samples may be split into <NUM>, <NUM>, <NUM><NUM>, <NUM>, <NUM>, <NUM>, <NUM>, or <NUM> groups, for example. At optional step <NUM>, the median of the separate magnitudes of each group of the complex sums may be determined, being the median of the calculated field strengths. This is done by taking the magnitude of the complex sums, giving one field strength estimate for each complex sum. At optional step <NUM>, any sums with a magnitude more than around <NUM>% different from this median are excluded, and the remaining sums are averaged to at optional step <NUM>. In some embodiments the threshold percentage for excluding the sums may be around <NUM>%, <NUM>%, <NUM>% or <NUM>%. Finally, at step <NUM>, the final measure of the strength of the oscillating magnetic field is estimated, based on the magnitude of the average calculated at step <NUM>.

As mentioned above, commodity magnetometers provide separate measurements in three axes, "X", "Y" and "Z". Of these three axes, one is substantially parallel to cable <NUM>/<NUM>, and thus experiences only a negligible amount, if any, of magnetic field <NUM>/<NUM> induced in the plane perpendicular to conductors <NUM>/<NUM>/<NUM>/<NUM>. While conductors <NUM>/<NUM>/<NUM>/<NUM> in cable <NUM>/<NUM> may be slightly twisted, and the plane in which they induce magnetic field <NUM>/<NUM> may therefore not be exactly perpendicular to the direction of cable <NUM>/<NUM>, the effect is small enough to be safely ignored. The direction of magnetic field <NUM>/<NUM> in the plane spanned by the other two axes, however, is dependent on the orientation and distance of the two current-carrying conductors <NUM>/<NUM> and <NUM>/<NUM> inside cable <NUM>/<NUM> relative to magnetometer <NUM>. However, these measurements are generally unknown and not practically measurable. Thus, the sampling described with reference to the method of <FIG> is performed separately for each of the two axes, and the resulting measures for the strength of the oscillating magnetic field <NUM>/<NUM> are then vector-added to provide an ultimate, single magnitude of the strength of magnetic field <NUM>/<NUM>.

The single number obtained by the method of <FIG> is an indication of the strength of the oscillating-at-mains-frequency residual magnetic field <NUM>/<NUM> that surrounds cable <NUM>/<NUM> of appliance <NUM>. Except for minor noise-floor effects, it is directly proportional to the amount of AC current that flows through cable <NUM>/<NUM> to or from appliance <NUM>.

The factor of proportionality, however, depends on the distance of magnetometer <NUM> from the current-carrying conductors <NUM>/<NUM> and <NUM>/<NUM>, the distance between conductors <NUM>/<NUM> and <NUM>/<NUM>, the presence or absence, and the geometry of, materials in the vicinity that influence the shape of magnetic field <NUM>/<NUM>, and the sensitivity of magnetometer <NUM>, which may vary from one magnetometer to the next. While it is difficult to calculate the proportionality factor, this factor remains constant as long as the geometry of sensor device <NUM> and cable <NUM>/<NUM> remain unchanged. The proportionality factor can therefore be determined by calibration against external power generation and consumption information.

Generally, consumers are not interested in the amount of current that passes through cable <NUM>/<NUM>, but rather in the amount of power that is delivered through cable <NUM>/<NUM>, for which they get charged, or possibly paid. Assuming that current and voltage are in phase, and assuming that the line voltage is nominal, converting current to power is straightforward. However, neither of these assumptions necessarily holds true in the real world. The power transferred through cable <NUM>/<NUM> may have a significant reactive part when the voltage and current are out of phase, and line voltage can depend heavily on how far from the closest transformer a consumer is located.

Fortunately, for a given appliance <NUM> in a given household, both line voltage and fraction of power that is reactive tend to vary very little. Thus, if the calibration mentioned above is made against external information that measures active power, rather than current, then these complicating influences get transparently included in the proportionality factor. One suitable source of such external information is smart meter <NUM>, which does measure active power.

As described above, the values of the measured magnetic field <NUM>/<NUM> returned by sensor device <NUM> are proportional to the current through cable <NUM>/<NUM> to which sensor device <NUM> is attached, but the proportionality factor differs for different sensor device <NUM> installations, due to varying geometries and also due to sensitivity variations. Thus, on its own, sensor device <NUM> can provide accurate relative information, such as the current through a cable at a time T1 being r times as much as the current through that cable at time T0. However, sensor device <NUM> cannot provide absolute information as to the number of Amperes flowing through the cable at any given time. To obtain the latter information from sensor device <NUM>, a proportionality factor needs to be determined, based on calibration against some sort of external information for which the absolute magnitude is known. According to some embodiments, the proportionality factor may be calculated based on independently measured reference data related to the power delivered by cable <NUM>/<NUM>.

At any given time, the value S reported by sensor device <NUM> is a direct reflection of the AC mains signal component of the current flowing through the cable. i.e. For an AC mains signal of <NUM>: <MAT> where p is the proportionality factor, or equivalently, with q being <NUM>/p: <MAT>.

If at any time, the absolute value of I<NUM> is known, determining p and q is trivial.

In order to reduce the influence of noise, and improve accuracy, one would typically use several known values Ii<NUM> and their corresponding sensor readings Si at various times Ti. This would be done using trivial linear regression, minimizing the error term: <MAT>.

However, such calibration requires a direct measurement of the current through the cable, which as described above, may be undesirable or infeasible.

In general, real world users are merely interested in the active component of the power (i.e. the one that shows up on their electricity bill), ignoring the reactive component which has no financial consequences to them. Of course, current and active power are closely related: <MAT> where V is the line voltage, and cos ϕ is the power factor, resulting from a phase angle of ϕ between current and voltage. Substituting Equation <NUM> into Equation <NUM> yields: <MAT>.

For most specific applications, V and ϕ are near enough to constant to be treated as such without introducing significant error. Line voltage V depends mainly on the voltage drop between the household and the transformer which converts the distribution network's high voltage to line voltage, and thus tends to stay close to constant for any particular household. The phase angle ϕ, which indicates to what degree a particular load deviates from being purely resistive towards being either inductive or capacitive, is a characteristic of the load of an appliance <NUM>, and thus tends to not change unless the load is changed. However, this assumption is somewhat invalid for appliances <NUM> which can operate in a number of modes. For example, a washing machine using a motor to rotate its drum would tend to be somewhat inductive, while the same washing machine using its heating element to heat up water would be purely resistive.

Assuming a constant V and ϕ, we can define Q = q * V * cos ϕ and get <MAT>.

Equation <NUM> matches the form of Equation <NUM>, and thus Q can be obtained in analogous manner, as long as PA is known at one or more times. This may be considerably easier to achieve than knowledge of I<NUM>, because smart meter <NUM> can measure PA. So if it is possible to ensure that the appliance <NUM> for which Q is to be determined is the only appliance <NUM> connected to smart meter <NUM>, the existing smart meter <NUM> can be used to calculate Q. Modern electricity meters may provide the value of PA either on a display or via a network connection, allowing for direct application of Equation <NUM>. Others may only provide a running total E of energy consumed, i.e. the integral of PA over time. For such meters, Equation <NUM> needs to be integrated: <MAT>.

In Equation <NUM>, <MAT> is the metered energy consumption between times T<NUM> and T<NUM>, which is equivalent to E(T<NUM>) - E(T<NUM>). Because sensor device <NUM> may be configured to measure at discrete times ti with ti+<NUM> = ti + Δt, <MAT> is approximated by <MAT>. Thus: <MAT>.

From this, Q can be easily obtained given the required observations. Again, if more than one set of observations is available, simple linear regression can be used to minimise the influence of noise and improve accuracy.

Determining Q using the smart meter <NUM> requires the user to isolate the appliance <NUM> to which sensor device <NUM> is attached, to temporarily disconnect all other appliances <NUM> from smart meter <NUM>. This requires considerable effort, and can be highly disruptive. Thus, while theoretically appealing, it is not practical in reality. Modern smart meters <NUM> provide frequently updated measurements of the overall household's active power <MAT>. Those measurements are often reported via a local wireless network, which may be a ZigBee network in some embodiments. At any given time t, this overall power is the sum of a large number N of individual loads: <MAT>.

If load <NUM> is the appliance <NUM> to which sensor device <NUM> is attached, then by substituting in Equation <NUM>, we get: <MAT>.

Here, <MAT> is the compensated power, being the overall household's power use at time t minus an estimation of the power used by an appliance <NUM> that is being measured by sensor device <NUM>, or sensor-equipped load number <NUM>. This estimation is obtained using g as the proportionality factor between S(t) and <MAT>. Evaluating Equation <NUM> at different times t<NUM> and t<NUM> gives: <MAT>.

Here, D(t1, t2, g) is the change in <MAT> between times t1 and t2.

If <MAT> and <MAT> are independent, then it can easily be seen that the expectation value <MAT> is minimized for g = Q.

In general, the loads for appliances <NUM> are not independent for arbitrary choices of t<NUM>, t<NUM>. For example, the power consumed by a TV may be strongly correlated to the power consumed by the lighting of the room the TV is located in, as both are more likely to be used in the evenings on weekdays when people get home from work, for example. Also, the expectation value cannot be directly calculated, but must be estimated by examining |D(t<NUM>, t<NUM>, g)| for a number of given times.

In practice, however, by choosing a large number of pairs (t<NUM>, t<NUM>) with t<NUM> and t<NUM> close together, and by observing changes over short time frames only, the loads of appliances <NUM> are close enough to independent such that minimising the estimate of A(g) tends to yield a g that is an excellent approximation for the unknown, desired calibration factor Q.

Straightforwardly implementing the method described above occasionally results in wildly inaccurate estimates. Particularly for loads which change very rarely, and for which thus S(t<NUM>) - S(t<NUM>) is near zero for most (t<NUM>, t<NUM>) with t<NUM> and t<NUM> close together, there is a significant risk of the minimum of A(g) being due to a random correlation of the sensor noise present in S and some large change(s) in one of the loads <NUM>. Similarly, an actual change in <MAT> and the corresponding change in S may by chance coincide with a large change in another load, and the minimum of A(g) may again be dominated by such random coincidence, masking the effect of the other, less prominent changes in <MAT>.

For practical use, the general process described above of choosing a proportionality factor estimate in such a way as to minimise the variation that remains in <MAT> using that factor is used. However, a number of changes can be made to the process to increase robustness and minimise the influence of noise.

Instead of measurements taken at only two times t<NUM> and t<NUM>, a larger number M of (consecutive) samples of the measurement of sensor device <NUM> can be used for each individual calculation. For example, M = <NUM> sensor samples may be used in some embodiments. Alternatively, M =<NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>,<NUM>, <NUM>, or another number of sensor samples may be used. Consequently, instead of calculating the absolute difference between <MAT> (t<NUM>) and <MAT> (t<NUM>), the standard deviation <MAT> of values in M-sized tuples <MAT> (ti) for i = <NUM>. M and the ti being consecutive, can be used.

Minimization of A(g) with respect to g relies on the term (S(t<NUM>) -S(t<NUM>)) * (Q - g), or rather, the equivalent terms when using a larger number of samples. If the load of the monitored appliance does not change during the time covered by those samples, then ideally all the S(ti) would be exactly the same, and the term would be zero, regardless of g. In reality, the sensor's measurements S are noisy, and thus these terms would make a contribution to the equivalent of A(g) which is dependent on g, but which is not a reflection of any actual relationship between <MAT> and S.

For this reason, an estimate of the sensor's noise level σsensor is made. Then for each tuple considered above, the observed standard deviation σsamples of the corresponding sensor samples is compared with σsensor. Only tuples for which the σsensor exceeds σsamples by at least a factor F are used in the calculation of the equivalent of A(g). According to some embodiments, this factor is F = <NUM>. In some embodiments, this factor may be F = <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, or another factor. This limits the observations used to estimate the proportionality factor Q to those times during which <MAT> actually changed, and thus S(t<NUM>) -S(t<NUM>) is meaningfully related to <MAT>. It excludes times during which <MAT> and during which S(t<NUM>) -S(tl) is thus largely or exclusively determined by random sensor noise.

According to Equation <NUM>, <MAT>. This means that any sensor noise present in S will also be present in <MAT>, and that the level at which it is present depends on g. However, g can be chosen such as to minimise the overall variation in <MAT>, based on the argument that the correct g, i.e. g = Q, will result in the best removal of <MAT> from <MAT>. The variable amount of sensor noise, completely unrelated to the relationship between <MAT> and S, that presents in <MAT> and thus in <MAT> interferes with this argument.

Given the known level of sensor noise σsensor as described above, it is possible to attempt to compensate for its contribution to <MAT>: <MAT> where <MAT> for x ≥ <NUM> and zero otherwise.

Selecting g to minimize the straightforward sum of the <MAT> for all selected tuples can occasionally result in an erroneous choice, when a change in S by chance coincides with a large change in another, unrelated load, and thus in <MAT>. A particular g may remove that coincidental large change from <MAT>, and thus reduce the corresponding <MAT> and consequently the sum by a large amount. That amount may be larger than the amount realisable by correctly choosing g and thus removing all genuine changes of <MAT> from <MAT>.

In order to reduce the influence of individual large changes, and to instead bias the selection towards consistency across all tuples, the <MAT> are not summed up directly, but instead rather their k-th root. According to some embodiments, this value may be k = <NUM>. According to some embodiments, this value may be k = <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, or another value.

<FIG> summarises the steps required to estimate g of Q, by minimising the result A with respect to g. In some embodiments, sensor device <NUM> and energy monitoring device <NUM> may send measured data to server system <NUM> via communications module <NUM>, and server system <NUM> may perform one or more of the method steps.

At step <NUM>, A is set to equal <NUM>. At step <NUM>, the noise level σsensor of sensor device <NUM> is calculated. At step <NUM>, t is iterated over each of the samples from sensor device <NUM> to be considered. At step <NUM>, σsamples is calculated over a short period of time starting at t, σsamples being the observed standard deviation of M for all samples starting at t. At step <NUM>, if σsamples is smaller than F * σsensor, that sample is ignored, t is increased, and the method moves back to step <NUM>. Otherwise, the method proceeds to step <NUM>. At step <NUM>, <MAT> is calculated according to the given proportionality factor, over a short period of time starting at t, <MAT> being the household power compensated for the estimate of <MAT> for the corresponding sample times, being the active power of the appliance <NUM> to which sensor device <NUM> is attached. This will depend on g. At step <NUM>, <MAT> is calculated, being the observed standard deviation in <MAT> from step <NUM>. At step <NUM>, <MAT> is calculated, being the remaining variation in <MAT> after accounting for added sensor noise from sensor device <NUM>. At step <NUM>, <MAT> is added to A. At step <NUM>, t is incremented and the method is repeated from step <NUM>.

The method described with relation to <FIG> can be performed by an exhaustive search of all values considered for g. However, A(g) is generally a smooth function with a single, well defined minimum, allowing the use of a variety of much faster standard methods for finding that minimum.

The method described with relation to <FIG> depends on the monitored load of appliance <NUM> changing at distinct times between discrete and significantly different power levels. This dependency is fulfilled for almost all common appliances. However, it is not necessarily fulfilled for the "load" presented if appliance <NUM> is a photovoltaic solar system. The output of such a system changes continuously. Also, while on partly cloudy days, significant changes can occur over very short time scales, no such significant changes may be present in the data available for calibration.

The continuous changes in solar generation make it possible to derive useful information regarding the proportionality factor Q not merely from a few select sample times of interest, as outlined above, but from all sample times collected during daylight hours. Because all other appliances <NUM> in a household tend to stay at discrete power levels for extended periods of time, for most of those sample times, the only change to <MAT> is attributable to the solar generation. Thus, the factor g is chosen so as to maximise the number of times that, after compensating for the estimated solar generation, a zero change is observed.

Similar to the previous approach, <MAT> (t) is defined as the household power use as reported by the smart meter <NUM>, and <MAT> is defined as the power use after compensating for the estimate of the solar system's contribution. <MAT> (t) obviously depends on g. Also, as before, the noise level σsensor of sensor device <NUM> is estimated. In addition, the noise level σmeter of smart meter <NUM> is estimated.

For each pair of consecutive samples in <MAT> (t), the likelihood is calculated that the observed difference represents a zero change in a hypothetical, noiseless version of <MAT> (t). As both the noise from sensor device <NUM> and the noise from smart meter <NUM> are considered to be normal distributed, and they are considered to be independent, that likelihood can be modelled by a normal distribution centred around zero, and with a standard deviation σcombined of <MAT> and thus the likelihood measure l(t), as <MAT>.

Because a large number of sample times can be used for the estimation, and because for most of those times, the measure l(t) is expected to be fairly large, no explicit biasing towards consistency, as described above for the method described with respect to <FIG> is necessary. In fact, the opposite is beneficial - the l(t) can be weighted according to the corresponding differences in <MAT>, emphasising the influence of sample times where large differences were observed, and where a successful compensation thus requires a very accurate value of g. The result of this weighting is called L(t): <MAT>.

The value chosen for g is simply the one that maximises <MAT>.

Modern solar power inverters typically have fairly large capacitances in their output stages. This capacitance presents a purely capacitive load to the household grid, resulting in significant current that is <NUM>° out of phase with the voltage V, and thus a significant reactive power component. And unlike in the common appliance case discussed above with relation to <FIG>, the ratio of reactive power to active power (and thus the phase angle ϕ and ultimately the power factor cos ϕ) are not even remotely constant for a solar power inverter.

The observed sensor reading S is <MAT> where SR is the sensor response to the current <NUM>° out of phase, and SA is the sensor response to the in-phase current, i.e. ultimately to active power.

The magnitude SR can be estimated because just after sunset, and just before sunrise it is known that SA = <NUM>. Therefore, SR can be observed directly as SR = S at those times. Furthermore, because the capacitance is constant, SR is also constant throughout the day. Thus, once SR has been observed, SA can easily be calculated as <MAT> where <MAT> is defined as above.

Equation <NUM> for SA has a large derivative for S near SR. Given that S(t) is a noisy sensor reading, which in the ideal, noiseless case would have value SR at sunrise and sunset, this large derivative can result in severe amplification of the noise from sensor device <NUM>. However, in practice, there are very few times t when SA(t) is non-zero, yet small enough that <MAT> is near SR. Consequently, this noise amplification can reasonably be avoided by treating all values S(t) ≈ SR as if they were exactly SR, and thus the in-phase component as zero. In the current implementation, this is done whenever S(t) ≤ SR + <NUM> * σsensor.

Additionally, it is known that sA(t) ≠ <NUM> only during daylight hours. This ultimately yields <MAT>.

The SA(t) so calculated are then used instead of S(t) for the algorithms described above, as well as for calculating the solar power production reported to the user.

In the embodiments described above with respect to <FIG> and <FIG>, the phase of the measured current I<NUM> relative to the phase of the mains voltage V was not calculated. While a complex result was obtained as the output from the <NUM> isolation, the phase of this result is random, because the timing of the samples taken by sensor device <NUM> is randomly aligned to the voltage's phase. However, according to some embodiments, it may be desirable to know the phase φcurrent of the measured current I<NUM> relative to the AC voltage V, being whether the current I<NUM> rises and falls at the same time as the voltage V, or if not, how much earlier or later.

Measurements of the magnitude and phase of the current I<NUM> can be combined into a complex number, represented by a point in a two-dimensional coordinate system. The magnitude determines how far away from the origin the point is, and the phase determines in what direction it is located. When the current is in-phase, i.e. rises and falls at the same time as voltage, then the point will be on the horizontal axis, also called the "real" axis. If it is out-of-phase, the point will be at a certain angle to the horizontal axis, with some vertical, or "imaginary" component. The "real" component of AC current results in "active power", i.e. actual energy transfer, which can perform actual work and which consumers are charged for. The "imaginary" component results in "reactive power", which is merely shifting energy back and forth, without converting it into work, and generally without the consumer having to pay for it.

As long as the phase of the current for a monitored appliance <NUM> stays constant, applying a single proportionality factor p to translate the observed magnitude of the magnetic field S (and thus the observed current I<NUM>) into an active power value is valid and straightforward. Unfortunately, for many real world appliances <NUM>, the phase φcurrent does not stay constant. For example, when running its motor, a washing machine presents significant reactive power, but while heating the water, it consumes purely active power. Similarly, the compressors used in self-defrosting fridges present significantly reactive power, yet during the regular defrost cycle, the load is almost purely active. With no information from sensor device <NUM> to discern between those distinct consumption modes, any single proportionality factor p may provide an inaccurate result at least some of the time.

One particular example of an appliance <NUM> where phase φcurrent is important is for solar inverter systems. Solar inverter systems typically have a large output capacitor. This capacitor presents a significant reactive load to the grid, regardless of the presence or absence of solar generation. Thus, the current observed in a cable <NUM>/<NUM> connecting a solar inverter system to the grid is a combination of a near-fixed reactive component and a highly-variable active component. Although the magnitude of the reactive component of the current can be estimated (as described above with reference to <FIG>), the operation required for removing the reactive component from the measured combined signal leads to strong noise amplification when the active component is small. Also, the method as described above with respect to <FIG> assumes a constant reactive component.

Though the actual variations in the reactive component may be quite small, they experience the same amplification when the active component is small. Furthermore, estimation (and removal) of the reactive component is made more difficult because many inverters disconnect their output stage, either fully or partially, during times of darkness. This is especially problematic in systems using several micro-inverters in parallel, as each inverter is likely to disconnect at a different time, and thus at any time, the observed reactive load may be representative of an arbitrary number of inverter output stages.

The measurements from the magnetometer <NUM> in sensor device <NUM> naturally contain a certain amount of noise. This noise is also present in the calculated <NUM> component of the magnetic field S, and results in repeated measurements forming a circular point cloud around the point representing the actual complex value in the complex coordinate system. This noise level is generally small compared to the signal resulting from the operation of an appliance <NUM>, and thus over time, the occasions during which it results in increased magnitude will balance out with occasions during which it results in a decreased magnitude. In visual terms, the average distance from the coordinate system's origin to the points in a circular point cloud with its centre far away from the origin well approximates the distance from the origin to that centre.

However, when there is little or no current I<NUM> through cable <NUM>/<NUM>, the actual complex signal describing the magnitude and phase of the current I<NUM> is close to the origin, and the point cloud centred around it envelops the origin. In that case, the average magnitude of points in the point cloud is significantly larger than its centre's magnitude.

What this means is that, for small or zero signals, when observing only the amplitude of the measurements S, the signal will be lost in the noise, and cannot be recovered through averaging the observations over time. In particular, a zero signal (i.e. the appliance is inactive, no current flowing) would result in a series of small positive reported magnetic magnitudes, which translate into a series of small positive power consumptions.

This is problematic for appliances <NUM> that have a low duty cycle, as even the small erroneous power draw, when reported over the extended periods of inactivity, can become highly significant compared to the power consumed during the comparatively short active times of appliance <NUM>. For this reason, according to some embodiments sensor device <NUM> may be configured to report a zero magnitude whenever the measured magnetic field magnitude S is small enough to be merely an artefact of noise.

That strategy is appropriate for appliances <NUM> which do indeed have zero power draw during periods of inactivity. However, many modern devices have non-zero standby current, and this so-called standby or vampire power accounts for up to <NUM> percent of total domestic power consumption. Thus, such devices also being reported as consuming zero power while inactive may be undesirable in some cases.

To overcome this, some embodiments relate to an alternative sensor device <NUM>, as shown in <FIG>. Sensor device may include a magnetometer <NUM>, power supply <NUM>, and communications module <NUM>, which may be similar or identical to parts <NUM>, <NUM> and <NUM> of sensor device <NUM>. Sensor device <NUM> may be configured to calculate the phase φcurrent as well as the magnitude of current I<NUM>. To do so, sensor device <NUM> may make use of the alternating electrostatic field that exists near any conductor carrying AC voltage. According to some embodiments, sensor device <NUM> may comprise a comparatively large conductive plane <NUM>, connected to an extremely high impedance input, on its processor <NUM>. Conductive plane <NUM> may be a sheet, plate or panel made of copper or another conductive material, such as aluminium or silver.

Conductive plane <NUM> may be of a relatively large size, and according to some embodiments the size of conductive plane <NUM> may be limited by the size of the housing of sensor device <NUM>. In some embodiments, conductive plane <NUM> may be positioned outside of sensor device <NUM> and may be bigger than the housing of sensor device <NUM>. According to some embodiments, conductive plane <NUM> may be around <NUM> by <NUM> in size. According to some embodiments, conductive plane <NUM> may be between <NUM> and <NUM> in width, where width is the dimension running latitudinally across cable <NUM>/<NUM>. According to some embodiments, conductive plane <NUM> may be between <NUM> and <NUM> in width. According to some embodiments, conductive plane <NUM> may be between <NUM> and <NUM> in length, where length is the dimension running longitudinally along cable <NUM>/<NUM>. According to some embodiments, conductive plane <NUM> may be between <NUM> and <NUM> in length.

Processor <NUM> may comprise a comparator <NUM> and memory <NUM>, the memory storing program code <NUM>, executable by processor <NUM> to perform the functions as described. When sensor device <NUM> is attached to a cable <NUM>/<NUM>, conductive plane <NUM> may be configured to be in close vicinity to the conductors <NUM>/<NUM> and <NUM>/<NUM> in the cable <NUM>/<NUM>, resulting in capacitive coupling between the potential of conductive plane <NUM> and the potentials of conductors <NUM>/<NUM> and <NUM>/<NUM>. According to some embodiments, the distance between conductive plane <NUM> and conductors <NUM>/<NUM> and <NUM>/<NUM> may be as close as possible, and may be limited by the insulation on cable <NUM>/<NUM>, the thickness of the casing or housing of sensor device <NUM>, and the diameter of the conduit in which cable <NUM>/<NUM> is enclosed. According to some embodiments, , the distance between conductive plane <NUM> and conductors <NUM>/<NUM> and <NUM>/<NUM> may be less than <NUM>. According to some embodiments, , the distance between conductive plane <NUM> and conductors <NUM>/<NUM> and <NUM>/<NUM> may be less than <NUM>. According to some embodiments, , the distance between conductive plane <NUM> and conductors <NUM>/<NUM> and <NUM>/<NUM> may be less than <NUM>.

The potential of Active conductor <NUM>/<NUM>, relative to Earth <NUM>, changes at the frequency of the AC mains voltage, being <NUM>, for example, whereas the potential of Neutral conductor <NUM>/<NUM> (and optionally the Earth <NUM>) does not change. Thus, the potential of conductive plane <NUM>, which is capacitively coupled to all two (or three) conductors, will change at <NUM> as well.

Sensor device <NUM> is shown in more detail in <FIG>, which illustrated the physical relationship between sensor device <NUM>, processor <NUM>, and conductive plane <NUM>. Conductive plane <NUM> is positioned in close proximity to cable <NUM>/<NUM>, and is connected to processor <NUM> through a wire <NUM> connected to a pin of processor <NUM>.

The input impedance R of processor <NUM> and the capacitance C between conductive plane <NUM> of sensor device <NUM> and the cable's conductors <NUM>/<NUM> and <NUM>/<NUM> form an RC circuit. Because the capacitance C is very small, this RC circuit results in a phase shift Δφ despite the very large R. This means that its potential changes in sync with, but not exactly at the same time as, the potential of Active conductor <NUM>/<NUM>. The amount of phase shift depends on R and C, both of which are largely fixed for a fixed physical arrangement of sensor device <NUM> and cable <NUM>/<NUM>. Thus, while the phase Δφ shift will vary between installations, for each installation it will stay largely constant.

In processor <NUM>, the analogue signal from conductive plane 1570is connected to a comparator <NUM>, translating the analogue signal into a digital on/off signal. A standard software or hardware phase-locked loop (PLL) implementation is then applied separately to both the on-off and off-on transitions. The maxima and minima of the signal are then located at the midway points between the PLL-predicted transition points. Also, as a side effect, the PLLs track the mains frequency.

Unlike sensor device <NUM>, sensor device <NUM> is configured to synchronise to the voltage phase repeatedly, and is also able to adjust its sampling rate to match variations in the period ω of the mains supply. Because of this, sensor device <NUM> can apply a more sophisticated sampling strategy.

According to some embodiments, sensor device <NUM>, as described above with reference to <FIG>, for example, may achieve extended battery life by running processor <NUM> at a very low duty cycle, only spending about <NUM> milliseconds sampling once every <NUM> seconds. However, sensor device <NUM> may be configured to constantly perform the software PLLs for voltage phase tracking, and also spread out sampling, thus requiring processor <NUM> to manage magnetometer <NUM> every four seconds. To nonetheless increase battery lifetime of sensor device <NUM>, a separate, high-power processor <NUM> may be for communication, while processor <NUM> may be a low-power processor used to manage magnetometer <NUM>. Processor <NUM> may comprise memory <NUM> storing program code <NUM>, executable by processor <NUM> to perform the communication functions.

Referring to <FIG>, t method for determining magnitude and phase of a measurement is described. According to some embodiments, each measurement may consist of <NUM> pairs of sample sets with <NUM> samples per set. Different numbers of pairs and samples-per-set are possible. According to some embodiments, the factors <NUM>, <NUM>, and <NUM> may appear in the number of pairs and the number of samples per set, providing resilience against aliasing due to <NUM>rd, <NUM>th and <NUM>th order harmonics in the measured current. For example, <NUM> pairs of <NUM> x <NUM> samples per set, <NUM> pairs of <NUM> x <NUM> samples per set, or <NUM> pairs of <NUM> x <NUM> samples per set, as well as other combinations of <NUM>, <NUM> and <NUM>, could be used. According to some embodiments, the set size may be selected based on the supported rate of the magnetometer <NUM> used. Within each set, the samples may be spaced at exactly <MAT>. The two sets making up each pair may be timed to start exactly <MAT> apart. This means the two sets are taken at corresponding points in the cycle, <NUM>° apart, providing for optimal rejection of constant magnetic field components, as well as aliasing artefacts due to high-order odd harmonics.

Each pair of sample sets is synchronised to start at a specific offset from the PLL-predicted maximum of the voltage phase tracking, as described below with reference to steps <NUM> and <NUM>. This offset increases by <MAT> from pair to pair, providing for an effective sampling frequency of <NUM> samples per period (being <NUM> pairs of sample sets making up <NUM> sample sets, each set having <NUM> samples), preventing aliasing from 3rd, 5th and 7th order harmonics.

As described below with reference to steps <NUM> to <NUM>, sensor device <NUM> is configured to take a plurality of samples. Because sensor device <NUM> can synchronise to the voltage potential phase repeatedly, the pairs of sample sets need not be taken in quick succession. In fact, spacing them out allows the PLLs to refine their locking in between. Also, as each pair of sample sets is an independent measurement, taking them at distinct points through an overall measurement period provides a level of averaging. For this reason, according to some embodiments sensor device <NUM> may space the pairs around four seconds apart. According to some embodiments, a different time period may be used, such as <NUM> second, <NUM> seconds, <NUM> seconds, <NUM> seconds or <NUM> seconds, for example. If frequent full samples were desired, this time period may be further decreased to tens or hundreds of milliseconds, depending on the time required to re-synchronise to the voltage phase in each cycle. However, more samples increase the power consumption of sensor device <NUM>, and may decrease battery life.

Because the current sampling performed by sensor device <NUM> is synchronised to the voltage phase of the mains power, the phase information in the result of the <NUM> isolation is meaningful. Consequently, sensor device <NUM> may be configured to upload both magnitude and phase information to server system <NUM>, as described below with reference to step <NUM>. According to some embodiments, the separate results corresponding to the three axes of magnetometer <NUM> are not combined on sensor device <NUM>, but are instead separately uploaded to server system for processing by an external device <NUM> or in the cloud.

As outlined above, sensor device <NUM> may be configured to return separate complex measurements Sx, Sy and Sz, corresponding to the x, y and z axes of magnetometer <NUM>. Each of these measurements is a combination of the effect of the current corresponding to the complex power P<NUM> on that axis, and a noise term: <MAT>.

Given a set of complex weights ωx, ωy and ωz, a simple over-determined equation system, easily solved for P<NUM> according to least squared error, can be obtained by zeroing the noise terms. However, the different axes of magnetometers <NUM> exhibit different levels of noise σx, σy, and σz, so a better system to solve is <MAT>.

To determine the weights ωx, ωy and ωz, an additional complex variable r is temporarily introduced: <MAT>.

This introduces two additional degrees of freedom, meaning that the νx, νy and νz merely need to determine the relative phase and magnitude of the weights ω, without providing absolute values for either.

It is noted that while the phase of the magnetic field resulting from the current through cable <NUM>/<NUM> should be the same in each axis of magnetometer <NUM>, commodity magnetometers actually take a three-axes sample by sampling the three axes in sequence, i.e. at slightly different times. For this reason, the phases as observed through a commodity magnetometer may differ slightly.

Given a set of S(t) at a number of times ti, and a set of chosen νx, νy and νz, solving the over-determined equation system <MAT> for J at each ti provides a set of J(ti) (. In turn, given a set of S(t) at times ti as well as a corresponding set of J(t), the over-determined <MAT> can be solved for νx; νy and νz can be calculated in a corresponding manner.

Starting with νx = <NUM>, νx = <NUM> and νz = <NUM>, iterating equations <NUM> and <NUM> will provide successive, eventually converging sets of J and ν. Given equations <NUM>, <NUM> and <NUM>, it can be seen that <MAT>.

To determine r, it is expressed as the product of a real value ra, and a unity-magnitude complex value rp, encapsulating the amplitude and phase of r, respectively.

For appliances <NUM> that are active solar inverter systems, P<NUM> ( t ) is a combination of a variable active component, corresponding to the power produced by the solar panels, and a constant reactive component resulting from the capacitance in the output stage.

To determine rp , the J(t) are sorted by amplitude, and J<NUM> calculated as the average of the top quartile, as well as J<NUM> as the average of the second-top quartile. rp is then chosen such that <MAT>.

Once rp has been determined, ra can be determined by applying the algorithm above with respect to <FIG> and <FIG>, taking Re ( r p * J ( t ) ) as S(t) in equations <NUM> onwards.

For appliances <NUM> that are not solar inverter systems, no a-priori knowledge exists regarding the active and reactive components of the current. Thus, the rp cannot be calculated in a way similar to that in the previous section.

Instead, the algorithm from equation <NUM> onwards as described above with respect to <FIG> and <FIG> is applied repeatedly. We define B(rp, ra ) as the A (g) that results from applying that algorithm with Re ( rp * J ( t ) ) as the real-valued sensor samples and g = ra as the proportionality factor. The chosen values for ra and rp are those that minimise B(rp, ra ). As before, while these can be determined by exhaustive search, B(rp, ra ) is generally a smooth function, and thus much faster minimisation methods can be applied.

Once νx, νy and νz as well as r = ra * rp have been determined, the final weights can easily be determined by applying equation <NUM>: <MAT> <MAT> <MAT>.

These weights describe the strength of electromagnetic coupling between the current through cable <NUM>/<NUM> and the three axes of magnetometer <NUM>, as well as the phase shift experienced by the voltage phase tracking, and thus indirectly the strength of the electrostatic coupling between the cable's conductors <NUM>/<NUM> and <NUM>/<NUM> and the phase tracking's conductive plane <NUM>. The weights are determined by the physical circumstances of the installation of sensor device <NUM>, and as long as those circumstances are unchanged, remain constant. Thus, the weights need to be recalculated whenever sensor device <NUM> is moved, whether intentionally or inadvertently. Once calculated, the weights can be used to transform future magnetic measurements into complex power values P<NUM> for presentation to the user. Typically, only the active power, Re(P<NUM>) will be presented.

The method for determining the magnitude and phase of measurement as described above is further illustrated at <FIG>. At step <NUM>, a PLL is synchronised with the known AC frequency of the appliance <NUM>. At step <NUM>, the calculated AC phase offset is waited for, to ensure the measurements are taken in synchronisation with the AC mains signal. At step <NUM>, the predetermined number of readings are taken, during one period of the AC mains cycle. At step <NUM>, a further half a period is allowed to elapse, to produce a phase offset of <NUM>° between the measurement and the AC mains signal. At step <NUM>, the predetermined number of readings are taken again, during one further period of the AC mains cycle.

At step <NUM>, sensor device <NUM> determines whether or not the predetermined number of iterations has been reached. If not, the method iterates back to step <NUM>. If the predetermined number of iterations has been reached, the measurements taken by sensor device <NUM> are combined into complex measurements at step <NUM>. Subsequently, at step <NUM>, the determined magnitude and phase of the measurements are stored on sensor device <NUM>, and/or uploaded to server system <NUM>.

The embodiments described above relate to a situation in which authoritative whole-house measurements are available on demand. However, in many cases the authoritative whole-house measurements are only available as interval aggregates, as opposed to frequent instantaneous demand measurements. Determining the proportionality factor for sensor device <NUM>/<NUM> where only interval aggregate measurements are available requires a different approach. <FIG> relates to a method for calculating the proportionality factor that draws on the understanding that there is a minimum base load below which the whole-house consumption would not go were it not for the solar installation (or other generation facility).

As an initial step <NUM> the sensor data generated by sensor device <NUM>/<NUM> is integrated into intervals matching those of the authoritative reference, e.g. <NUM> minute intervals where the authoritative reference generates aggregate data every <NUM> minutes. These intervals are then matched with the corresponding authoritative intervals at step <NUM>. According to some embodiments, these intervals may be <NUM> minutes, <NUM> minutes, <NUM> minutes, or another time period.

The process of estimating the proportionality factor for sensor device <NUM>/<NUM> effectively takes place in a Cartesian plane <NUM>, as illustrated in <FIG>, which is generated at step <NUM>. The (now aggregated) sensor data is used on the X-axis <NUM>, with the reference data on the Y-axis <NUM>. In the case of multiple generation sources, additional axes would be needed.

The factor being sought can be represented by the line <NUM> which keeps all points <NUM> on or above it, while maximising the area underneath it. In a perfect system without noise and outliers this would be most straight forward. Reality however requires compensation for these, and this is the driver for the chosen iterative algorithm described below with further reference to <FIG>.

The iterative algorithm comprises several parts:.

At step <NUM>, given the limited data set being operated upon, finding f(x) = ax + b may be performed using an exhaustive left-to-right search, evaluating candidate lines <NUM> iteratively. Many optimisations are possible, such as observing that to compare the areas under two candidate lines A and B, fA(xmin) + fA(xmax) can be compared to fB(xmin) + fB(xmax). This comparison will be referred to as the "area under A and B comparison".

At step <NUM>, to avoid the situation where line <NUM> pivots around a single (likely outlying) data point <NUM>, a weighted system is used. Each point <NUM> is given an initial weight based on the sensor value output by sensor device <NUM>/<NUM>. This is done since higher readings are considered more influential, and as such outliers there would be more detrimental if kept around. Other weighting methods may also be suitable.

For each candidate line <NUM>, the two end points are weighed off against each other, and the "heavier" one disregarded. The kept point gains the weight of the disregarded point. In many cases this weighting results in a see-saw effect, and is very effective at eliminating outliers in an appropriate manner. After each disregard of a potential outlier, a new optimal f(x) = ax + b is calculated.

While the disregarded points PDi may include outliers, many "good" data points will also be disregarded during the application of step <NUM>. Rather than fully disregarding the data point in each pass, a small but noticeable improvement to the end result can be seen if the disregarded data point is allowed to influence the finding of the next candidate line. As such, at step <NUM>, rather than solely working to optimise the area, the following algorithm is used to slightly bias comparisons between two possible choices of lines towards candidate lines similar to those already observed: <MAT>.

In equation <NUM> above, (minx, maxy) refers to a point above the very left of the point cloud <NUM>. Thus, moving the left side of a candidate line <NUM> up will move it closer to this point. (maxx,maxy) is a similar point above the very right of the point cloud <NUM>. Moving the right side of a candidate line <NUM> up will move it closer to this point. Reducing the combined distance between line <NUM> and those two points (minx, maxy) and (maxx,maxy) implements the area under A and B comparison as referred to above.

PD<NUM>, PD<NUM> etc. are points from the bottom of the point cloud <NUM> which were disregarded previously, in step <NUM>.

The terms cmpA and cmpB are used to calculate the combined distance of candidate lines A and B to all of the points given above. As outlined above, the rationale for looking to reduce the distance between a candidate line <NUM> and points (minx, maxy) and (maxx,maxy) is to implement the comparison at step <NUM>. The rationale for trying to reduce the distance between candidate line <NUM> and PD0, PD1 etc. is to implement step <NUM>.

The estimated factor tends to oscillate from pass to pass, even during the later passes. To avoid the distorting effect of picking only the last calculated factor, at step <NUM> the estimated factor from each pass is kept. An averaging or smoothing function is then applied to determine the final factor. The chosen function can be, for example, a plain average, or application of a normal distribution probability based on previously established noise levels in the data of sensor device <NUM>/<NUM>, or even an evaluating, exhaustive search near a for the optimal match against the data points produced by sensor device <NUM>/<NUM>.

At step <NUM>, the method checks whether a threshold has been reached. If not, the method moves back to step <NUM> and generates a new line <NUM> based on the new set of data points, such that the algorithm is applied in several passes, refining the line in each pass as outliers are disregarded. The number of passes required is somewhat flexible, and depends on several factors such as signal noise, time differences between the sensor data and reference data edges, and likelihood of outliers in the observations. According to some embodiments, the threshold is related to a total weight of the disregarded data points compared to the total weight of all of the data points in the point cloud.

Empirically, stopping after a predetermined percentage, which may be around <NUM>%, of the combined weight of all samples has been disregarded, yields consistently good estimates. Alternatively, according to some embodiments, the threshold may be set based on the number of samples that have been disregarded. Once the threshold is reached, the method moves to step <NUM>. To avoid the distorting effect of picking only the last calculated factor, at step <NUM> the estimated factors from all passes are combined, using an averaging or smoothing function to determine the final factor. An averaging or smoothing function is then applied to determine the final factor. The chosen function can be, for example, a plain average, or application of a normal distribution probability based on previously established noise levels in the data of sensor device <NUM>/<NUM>, or even an evaluating, exhaustive search near the factors from all passes for the optimal match against the data points produced by sensor device <NUM>/<NUM>.

The algorithm operates in terms of line <NUM> represented by f(x) = ax + b, where the proportionality factor produced is the term a, while b is the perceived base load.

Claim 1:
A method of measuring power delivered by a cable, the method comprising:
receiving data related to a residual magnetic field produced by the cable;
determining a proportionality factor relating the received data to the power delivered by comparing the residual magnetic field data to independently measured reference data related to the power delivered by the cable; and
based on the proportionality factor, determining the power delivered by the cable;
wherein the cable comprises two or three conductors, and characterized in that the physical arrangement of the conductors is unknown; and
wherein the independently measured reference data is aggregate data, being the sum of data related to power consumption through the cable and power consumption unrelated to power consumption through the cable.