The invention relates to an electricity meter, in particularly an electricity meter for measuring electricity consumption in polyphasic electricity systems, including high-precision meters for measuring electricity consumption of a user in an electricity supply network in connection with payment to the electricity provider for consumed electric energy.

BACKGROUND OF THE INVENTION

In an electricity distribution network supplying energy to a number of consumers, the electric energy provider needs to be able to measure the electric energy consumed by or delivered to the individual consumers. Each consumer has an electricity meter installed measuring the electric energy delivered to the connection point of the consumer.

The electrical network is usually divided in two levels, a transmission network level and a distribution network level. The transmission network is operated at high voltages above 60kV and the distribution network is operated below 60kV. Most consumers are connected to the distribution network at voltage below lOkV; the majority are in fact connected at low voltages below 1000V.

In the transmission network, the grid, i.e. cables, transformers generators etc. are well defined with known impedances, allowing the Transmission System Operator (TSO) to simulate load flows based on known parameters. Whereas, when looking at the distribution network often only parameters of main

components are known. This makes it more difficult for the Distribution System Operator (DSO) to predict overload and system stability. When it comes to overload and faults, it is important to know the short circuit currents (SC- currents), which may occur during a fault.

Today, SC-currents are determined by calculations with input data from

transformer-, radial- and service wire impedances. Alternatively, impedances for calculating SC-currents may be measured with special equipment installed near or at the point of supply. In the first instance, the SC-currents are based on theoretical measures only and the actual SC-currents may differ in case of incorrect input data. In the second instance, expensive and specialized equipment have to be installed and manual operated which is labor- and cost intensive and only provides momentary impedance data. Electricity meters of the prior art, have the drawback that they only provide the DSO with information about voltages, currents, and power consumption at the point of use. An object of the present invention is to provide a cost-effective electricity meter providing additional information about impedances of the electricity distribution network as seen by the electricity meter. SUMMARY OF THE INVENTION

According to a first aspect of the present invention there is provided an electricity meter for measuring electricity consumption in an electricity distribution network with three phases, in which the electricity meter comprises a measuring circuit for measuring voltages and currents for each of the three phases, so as to calculate the electric energy for each phase supplied from the electricity distribution network; an impedance learning algorithm unit arranged to estimate an impedance value seen at the electricity meter, wherein the impedance learning algorithm unit is arranged to, - calculate zero sequence components and negative sequence components, including zero- and negative sequence voltages and currents, of the three phases, based on the measured voltages and currents, estimate a zero sequence impedance, based on a ratio between changes in the zero sequence voltage and changes in the zero sequence current, and - estimate a negative sequence impedance, based on a ratio between changes in the negative sequence voltage and changes in the negative sequence current.

An advantage of the first aspect is that the electricity meter provides the impedance seen at the electricity meter, based on values already measured by it. Further, as electricity meters are permanently installed in the distributions grid, information about impedances in the distributions grid are continuously obtained.

In one embodiment, the impedance learning algorithm unit may be arranged to estimate the negative sequence impedance and the zero sequence impedance by using Least Square algorithms, especially minimum Least Square algorithms. An advantage in this regard is that the impedance is estimated by the ratio of two summations.

Furthermore, the impedance learning algorithm unit may be arranged to

approximate the zero sequence impedance by an auto-regressive (AR) process comprising a first forgetting factor, and to approximate the negative sequence impedance by another auto-regressive (AR) process comprising a second forgetting factor. An advantage of this implementation is that it minimizes the use of data memory in the electricity meter.

In another embodiment, the first- and second forgetting factors may be dynamical factors depending on the ratio of the changes in the sequence current to a summarized current change. An advantage of this embodiment is that the system is less sensitive to voltage noise from the grid.

Additionally, the summarized current change may be limited by a maximum measured current value of the electricity meter whereby small current changes has less weight than larger current changes.

Further, the electricity meter may include a low pass filter, arranged to filter out higher harmonics of the measured voltages and currents. By filtering out higher harmonics, the higher harmonics of negative sequence or positive sequence will have less effect on the impedance estimation. In one embodiment, the voltage changes and current changes of the

measurements are measured over a time interval of 5 to 30 seconds.

Alternatively, the time interval may be 0,1-1 seconds or 15-30 milliseconds.

The electricity meter may also comprise a communication module arranged to transmit the impedance value to a data collector. By transmitting impedance values from a plurality of electricity meters installed in a distributions grid, information about impedances in the distributions grid are collected and can be used in a model of the distributions grid.

According to a second aspect of the present invention there is provided a method for estimating grid impedance in a distribution network with three phases, the method comprising the steps of: measuring voltages and currents for each of the three phases, so to calculate the electric energy for each phase supplied from the electricity

distribution network; estimating an impedance value of the electrical grid by an impedance learning algorithm, wherein the impedance learning algorithm comprises: calculating zero sequence components and negative sequence components, including zero- and negative sequence voltages and currents, of the three phases, based on measured voltages and currents, estimating a zero sequence impedance, based on a ratio between changes in the zero sequence voltage, and changes in the zero sequence current, and estimating a negative sequence impedance, based on a ratio between changes in the negative sequence voltage and changes in the negative sequence current.

According to a third aspect of the present invention there is provided a system including a plurality of electricity meters as described above, each being arranged for measuring electricity data of a supplied utility and a data collector for collecting the electricity data, including impedance values, the electricity meters and the data collector being arranged as data nodes in a communication network; wherein the electricity data, including impedance values, are being used to form a network model of the electricity distribution network of the plurality of electricity meters; the network model of the electricity distribution network, providing information about the electricity distribution network; and a distribution system operator operates the system according to the network model. It is appreciated that any sub aspect mentioned in connection with the first aspect may in any way be combined with any of the sub aspects of the second and third aspect.

BRIEF DESCRIPTION OF DRAWINGS In the following, the invention will be described in more details by referring to embodiments illustrated in the accompanying drawings, of which :

Fig ure 1 shows a block diagram of an electricity meter,

Fig ure 2 shows details of a measurement circuit of an electricity meter,

Fig ure 3 shows a classical system representation of a sing le installation along a distribution line,

Fig ure 4 shows a symmetrical system eq uivalent,

Figure 5 illustrates a system comprising a plurality of consumption meters and a data collector.

DETAILED DESCRIPTION

Referring to Fig . 1, an electricity meter 2 includ ing an impedance learning algorithm (ILA) is illustrated . By including the ILA in the meter, impedances of the grid as seen by the meter can be continuously estimated thereby allowing for example continuously estimation of short circuit currents (SC-currents) . This allows Distribution System Operators (DSOs) to monitor the condition of the low voltage (LV) d istribution g rid, without installation of add itional equipment. By this, action can be taken by the DSO if the estimated impedances do not comply with the theoretical or former estimated impedances. Chang ing impedances could for example be a symptom of bad connections that may cause melt down or, in case of a broken neutral wire, an overvoltage situation with extensive damages to follow. The purpose of the ILA is to estimate the impedance in front of the electricity meter, i.e. the impedance of the distribution grid between substations and the terminals (LI, L2, L3) of the meter.

Electrical impedance is the measure of the complex ratio of the voltage to the current in an alternating current (AC) circuit. The impedance therefore has two orthogonal vectors, where resistance forms the real part of complex impedance, and reactance forms the imaginary part of complex impedance.

The electrical grid comprises a plurality of consumers, distribution lines and generators or sources, all of which changes over time. The impedance of the grid as seen from each electricity meter therefore changes every time the

configuration of the grid changes. Changes can be very small, when small loads and sub systems are connected, or large when larger loads and sub systems are connected . In a simple system, impedance is the resistance and reactance between the meter and the source, i.e. a generator, and the impedance measured at the electricity meter is the impedance seen by the meter from the terminals to the power source. However, in reality every single component of the electrical grid contributes to the impedance thus affecting the impedance seen by the meter. Therefore, the impedance estimated by the ILA is denoted the impedance value of the electrical grid as seen by the electricity meter. In respect of SC-current, the measures maximum SC-current and minimum SC- current are of primary interest. The maximum SC-current determines the required grade of switching equipment at the point of supply and the minimum SC-current is used to calculate the energy deposing in cables in case of a critical short circuit failure between a live line and the neutral conductor. Improper dimensioning of the former, may cause explosion or fire in protection equipment during short circuit, whereas improper dimensioning of the latter, may cause cables to melt down before the fuses blow in case of a short circuit event. In Fig . 1, a block diagram illustrates the main elements of an electricity meter according to the invention . The electricity meter includes a microcontroller unit (Legal MCU), which handles the data processing of measured current and voltage values in order to sum the consumed power. The microcontroller unit also includes or is configured to execute the impedance learning algorithm, as will be further described in the following . The electricity meter measures voltages and currents for each of the three electrical phases (LI, L2, L3), to determine the total electricity consumption on the three phases. The neutral connection is denoted N and only the current measurement circuit for phase one (LI) is shown in detail, but the measurement circuits for phases L2 and L3 comprise identical features. The current signal is measured through a shunt resistor and send to an electronic processing unit (EPU). Further, a switch operated by a control block is included to open or close the measurement circuit thereby controlling the current flow through the shunt. The electronic processing unit is galvanically isolated from the microcontroller unit and fed by a power supply circuit. As is readily understood by the skilled person, the present invention is not limited to embodiments where the current is measured using a shunt resistor. Other types of measurement circuits may also be implemented, such as measurement circuits including current transformers or Hall effect circuits.

The power supply includes a switch mode power supply (SM Power supply), connected to the electrical phases via a preregulator including of a rectifier circuit. The electricity meter further includes a communication module (RF function) and two antenna elements for communication of measurements and data such as estimated impedance values. The communication module is coupled to the calculating circuit in such a way that the measurements and any other data can be sent wirelessly through a wireless network to a data collector.

Fig. 2 shows the separate measuring circuits for each of the three phases (LI, L2, L3) configured to measure and calculate energy consumption and adapted to communicate the result, via an optocoupler, to a calculation circuit. The

calculation circuit sums up the consumption data for each of the phases (LI, L2, L3) and calculates a total energy consumption. The separate measuring circuits are directly coupled to the three phases (LI, L2, L3) to measure the voltage of each phases. As the measuring circuits determine the current based on the shunt resistor principle, they are coupled directly to the voltage potential of each phase. Therefore, galvanic separation is provided between the power supply for each of the measurement circuits. For this purpose, the transformer T has separate secondary windings galvanically separated from each other for power supply of each of the measuring circuits. Furthermore, calculating circuits, additional circuits and feedback (optocoupler) for the switch mode circuit in the switch mode voltage supply are supplied with voltage from an additional secondary winding of the transformer T. This secondary winding being galvanically separated from the secondary windings for the supply to the measuring circuits.

The primary winding of the transformer T is charged with energy from a coupled switch mode circuit operating with a switch frequency of preferably 100 kHz or more. As may be seen, the switch mode circuit is connected to the primary winding of the transformer, and the primary winding is connected to the different phases (LI, L2, L3) via diodes in a way allowing the switch mode circuits and the calculating circuits to be supplied when only a potential is present on one of the three phases (LI, L2, L3).

The electrical voltages and currents measured at the electricity meter contains all the harmonics present in the network, only limited by the bandwidth of the measurement system. Measuring electrical power, higher harmonics should be included, as they are also obtained by the consumer. On the other hand, higher harmonics such as 5 ^th , 7 ^th 11 ^th and 13 ^th may be seen as disturbances when using the voltages and currents to estimate other values, such as impedances. Low pass filtering of the signals may therefore be advantageous. Such filtering can be achieved with analogue filters prior to measurement. However, if only one set of measurements are used, i.e. the same set of measurements are used for both calculating power consumption and for estimating impedances, the power measurements lack the contribution from the higher harmonics. Therefore, digital filtering may be preferred and in one embodiment, voltage and current signals are digitally low pass filtered prior to impedance estimation.

The impedances in a distribution grid can be described by symmetrical

components, i.e. the positive sequence impedance^), the negative sequence impedance (Z ₂ ) and the zero sequence impedance (Z ₀ ), known to the skilled person. By the nature of symmetrical components, the positive-, negative- and zero sequences does not affect each other and may be estimated independently. Additionally, the positive and negative sequence impedances in transformers and distribution systems are mainly equals. By this, is possible to estimate the positive sequence impedance by the negative sequence impedance, which is advantageous as the negative sequence component is easier to estimate than the positive sequence component.

Referring back to the higher harmonics, some of them belongs to negative sequence components, some to positive sequence components and some to the zero sequence components. Harmonics such as the 5 ^th and 11 ^th , which "rotate" in the opposite sequence as the fundamental, are negative sequence components. Harmonics such as the 7 ^th and 13 ^th , which "rotate" with the same sequence as the fundamental, are positive sequence components. Triplen harmonics (3 ^r and 9 ^th ) which do not "rotate" as they are in phase with each other are zero sequence components. In a symmetrical 3 phase system triplen harmonics are not present, but in systems where the loads in the households or the like often are single phase and often non-linear, the triplen will be present. An example of a non-linear single phase components is low energy fluorescent lights. The pattern of positive- zero-negative-positive continues indefinitely for all odd-numbered harmonics, but the higher the number of harmonic, the lower the content are present in the electrical grid . Harmonics comes from non-linear loads in the grid. The 5 ^th , 7 ^th , 11 ^th and 13 ^th harmonics often come from electrical machines, both generators and motors. The content of each of the harmonics differ and the level of 5 ^th harmonic is rarely the same as the level of 7 ^th harmonic. This means that the 5 ^th harmonics is added to the negative sequence components and the 7 ^th harmonics will be added to the positive sequence components. In electrical grids with high level of harmonic content and especially with a large difference between harmonics of positive sequence and harmonics of negative, the assumption that the negative and positive sequences are equal may become false. In such networks, low pass filtering of the signals may be beneficial to the accuracy of impedance

estimations.

In the following, the symmetrical components are explained further. Zero sequence components will be noted by the subfix-0 (zero), positive sequence components by the subfix-1 (one) and negative sequence components by the subfix-2. The traditional phase components related to the voltage and current measurements at the three phases will be denoted by subfix-a, -b and -c.

In the transform between normal and symmetrical components, the complex size operator a, denoting the 120-degree phase shift, is used : .271

a = e ^l 3 = cos(120°) + i sin(120°)

Using the below transformation matrix, T:

The relationship between normal/traditional components and symmetrical components are as follows:

Vabc — TV ₀₁₂ and Above the transformation to symmetrical components are shown for the voltage components, however the symmetrical current components are calculated using the same transformation matrix. The transformation of impedances into symmetrical components is as follows:

Zoi2 ⁼ T ¹ Z _ABC T For transmission lines with balanced impedances, the special case appears that the symmetrical impedance matrix is diagonal :

Referring to Fig. 3 a classical system representation of a single grid installation is shown. The installation includes a power generation unit (SYN GEN) along a distribution line having a three-phase output (E _a , Eb, E _c ) . The power generation unit is a synchronous generator (alternatively, it could be a Delta-wye coupled transformer). The installation is further characterized by a set of balanced line impedances (Z _a , Zb, Z _c ), some measures of unbalanced currents (la, lb, Ic) and voltages (V _a , Vb ,V _C ) to the installation at the end of the distribution line. These are the impedances an electricity meter sees in a simple electrical grid .

Fig . 4 shows a symmetrical system eq uivalent to the system of Figure 3, including a zero seq uence- a positive seq uence, and a negative seq uence network. The generator is changed to a symmetrical positive seq uence generator E _{l r} which drives the positive sequence current l through the positive seq uence line impedance Z and into an unbalanced load network (the end user's installation), which may distribute the current through the negative- or zero sequence impedances depending on the load configuration, especially in case of unbalanced loading .

As elucidated above, positive, negative and zero sequence currents (Io, Ii, I2) and voltages (Vo, Vi, V2) may be calculated based on the unbalanced currents (la, lb, Ic) and voltages (V _a , Vb ,V _C ) measured by the meter, accord ing to below

equations : V ₀₁₂ = T- ¹ ^

However, in the real world the precise magnitude of E will be unknown . Further, the degree of balance is not guaranteed but is assumed static for short time frames. The unbalanced nature of the power generator and g rid-induced disturbances are illustrated with sparks (Eo and E2) in the zero- and negative sequence networks shown in Fig . 4.

The zero seq uence-, positive sequence, and negative sequence networks can each be individually identified . To this end, we use the equation for voltage drop over the symmetrical impedance (Here shown only for the negative sequence network, but identical eq uations apply to the positive- and the zero sequence networks) :

To identify the symmetrical impedance the change in load current is monitored to identify what change in voltage measurement it causes. For this, we define a period at where E is assumed to be mainly static, such as a period of 5- 10 seconds. The value changes within this period is denoted by capital Delta, Δ and by rearrang ing, we get the following expression for the negative sequence :

„ E ₂ AV ₂ Assuming the injected voltage E ₂ to be mainly static, we get the following expression for the negative sequence impedance :

A similar simplified expression could be elucidated for the zero sequence network. However, as the positive sequence network includes the generator the injected voltage can only be assumed static for a very short period making it practically impossible to determine the positive sequence impedance based on above simplified expression . However, as the transmission line impedances are assumed balanced, the positive- and negative sequence networks have equal impedances and the positive seq uence impedance (zj may be estimated from the negative sequence impedance (Z ₂ ) . Based on the above we get the following :

AV ₂

To identify the zero sequence impedance (Z ₀ ) and the negative sequence impedance (Z ₂ ) . Minimum least square (MLS) techniq ues may be applied on time series of delta values, i .e. voltage changes and current changes. These time series might not be continuous time series but must be composed based on change in the load network.

In the following, further details of the impedance learning algorithm (ILA) will de described . The ILA starts by converting the voltage and current measurements for each time interval into the correspond ing zero- and negative seq uence

components :

Next, a load admittance for each phase is calculated :

and the level of change of the load admittance is determined : = Yabcin) - Yabcin - 1),

The level of change of the load admittance is included in the ILA to control which current and voltage changes to include in the impedance estimation. The level of change could be based on a simple threshold analysis of the phase admittances changes. Otherwise, the load admittances may be converted into symmetrical components and the decision to proceed may then depend on the change of current "injection" from the positive sequence system into the zero sequence- and negative sequence systems.

When a certain change in the load admittances has been achieved, e.g . 4.348mS equivalent to approx. 1A at 230V, the algorithm proceeds with the calculation of the deltas of the symmetrical voltage- and current components :

AV ₀₂ (n) = V ₀₂ (n) - V ₀₂ (n - l)

AI ₀₂ (n) = I ₀₂ (n) - I ₀₂ (n ~ Ό

The correlation between the time series of these deltas is determined by the symmetrical impedance matrix without the positive sequence component:

Z ₀ 0

o z ₂ _

-AV ₀₂ = Ζ ₀₂ Δ/ ₍ 02 and because the symmetrical impedance matrix Z ₀₂ is assumed diagonal, two independent systems, with respectively the zero- and negative sequence impedances as correlation constants, can be defined :

-AV ₀ = Z _Q AT _Q

-AV ₂ = Ζ ₂ ΑΪ ₂

Solving the two independent systems in a least squares sense is done by the following matrix manipulation (omitting the deltas, numbers and bars for simplicity) :

Z = -vi ^U Ql")- ¹ By the dimensionality of one for each sample, each system is defined by below equation showing that the impedance can be estimated as the ratio between two summations :

∑ \

In one embodiment of the ILA, the number of samples summarize could be infinite, provid ing an all-time best estimate of the impedance. However, to prevent numerical saturation and as the impedance may change slowly over time, due to reconfigurations of the g rid, it may be advantageous to limit the

summation to a certain interval (a), i .e. limit the summation to a predetermined number of samples :

The above definition of a limited summation could alternatively de defined by two moving average finite impulse response (FIR) filters of degree alpha (a) :

In an alternative embodiment, to save memory for storing current and voltage data in case of large intervals, the moving average MA(a) processes may be approximated by an auto-regressive (AR) processes with a forgetting factor (p), resulting in the below definition of the impedance (still omitting the deltas) : ^num 00

00 = —

¾ _er iOO

¾»W = (1 - p)Z _num 0i - 1) + ρν(η)Γ (η)

¾ _e „(n) = (1 - p)Z _den (n - 1) + pUOOI ²

In the above defined auto-regressive process, the forgetting factor (p) is a static number determining the weight of new sample-sets compared to the accumulated result of previous samples. In some implementations, this may be undesirable, as it gives small current changes, the same weight in the process as the larger current changes, thereby making the system more sensitive to voltage noise from the grid. To improve the performance of the ILA the forgetting factor may be defined as a dynamic factor based on the ratio of a present current change to a summarized current change up to a certain limit of current, as defined below:

|Δ/(η)|

pOO min(∑„|A/(n) | ; A) Here capital alpha (A) is an upper limit for summarizing current change stored in a memory of the electricity meter, e.g. 15kA (15,000 ampere). Based on the above the ILA may be defined by: ^num 00

00 = —

Znum i ) = (1 - p(n))Z _num (n - 1) + p(n)AV(n)M* (n),

Z _den (n) = (1 - p(ri))Z _den (n - 1) + p(n) \M(n) \ ²

The above algorithm for estimating impedance is run by the microcontroller unit based on measured currents and voltages to estimate both the zero sequence impedance (z ₀ ) and the negative sequence impedance (z ₂ ). The zero- and negative sequence impedances are thus estimated based on the ratio between Znum and Zden, being a ratio between a summation of changes in the voltage components and a summation of changes in the current components wherein both summations are continuously updated in an adjustable auto-regressive (AR) process.

As previously described, it is important to know the impedances of a distributed network to be able to modulate the network for simulation purposes. A valid model of the distribution network will allow the DSO to detect faults and contingency risks before they cause problems. In this regard, impedance values estimated by a single electricity meters may be of limited value, whereas the collection of impedance values from an entire population of electricity meters may provide the DSO with sufficient information to make a valid model of a distribution network. Being able to collect impedance value from individual electricity meter, each electricity meter being a node in the network model, thus may be

advantageous.

Referring to Fig. 5, a system including a plurality of electricity meters 2 as described above, is shown. Each meter is connected to the three phases (PI, P2, P3) of the electricity network and configured to measure currents and voltages associated with each phase. By processing the measured currents and voltages in a processor 21 (previously referred to as the microcontroller unit) of the electricity meter, meter data such as impedance, power consumption etc. is derived. The electricity meters thus estimates the impedance value seen at the measurement terminals of the meter (LI, L2, L3, and N). The electrical power measured at the meters 2 is supplied from a power plant 10, and send via a transmission network 11 to a substation 3, which sends the power through an electricity distribution network 12. Still referring to Fig. 5, the system further comprises a network of data collectors, here in the form of sub-collectors 7 and main collectors 8. The main collector is connected to a backend system 5 of the utility provider and the sub-collector is a concentrator unit arranged as a concentrator node to collect meter data from a group of consumption meters. The total network may advantageously be a radio network, however at least the network between the concentrators and the electricity meters are a radio network, whereas the link between the collectors and the backend system may be of any suitable type. The number of consumption meters in the system may range from a few hundreds to several thousands of meters connected in the network. Each of the electricity meters are thus wirelessly connected 9 to the data collectors thereby creating a communication network for transmitting estimated meter data, including impedance value to the data collectors. From the main collectors 8 the meter data is transmitted to a backend system 5 and stored in an associated server 6.

To ensure a network where all nodes (i.e. the consumption meters and other network devices) are connected to provide a communication path between each electricity meter and the main collector, a rather complex network may be created, in particular in residential areas. For example, a meter 2 may be connected to the main collector 8 via direct connection to the concentrator 7; such a meter may be referred to as a zero level meter. In a real large-scale network, a large number of high-level meters may also be found. Such networks may also be referred to as a multi-hop network. However, generally the network is a hybridized network based on a number of basic topologies, including but not limited to point-to-point, star, tree and mesh as the important topology types.

Furthermore, a valid network model as discussed above may allow the DSO to detect unexpected behaviour in the distribution network, such as tampering with the electricity meters, i.e. the local electricity network of the consumer, which is monitored by the electricity meter. To this end, the plurality of electricity meters of the system may provide impedance information to establish a network model. The network model is then used to simulate the distribution network, and thereby provide information about short circuit levels and load flow issues. Further, it can also be used to detect irregularities in the electrical power fed into the distribution network compared to the consumed power measured by the electricity meters. By combining current and voltage measurements with impedance estimations, more precise information about the specific location of the potential meter tampering may be achieved. In this regard, impedance value from single meters may be used to detect local grid issues such as cable degradation, which often leads to cable faults. Furthermore, the electricity meters may be equipped with a unit to receive GPS based time signals. Having a large number of nodes, i.e. meters, in the network model, each with an impedance value and a time stamp from the GPS signal, will furthermore allow the DSO to include phase values in the model and thereby get an even better model of the network. However, as meters with GPS unit are expensive, a good compromise may be a meter that can estimate impedance without a GPS time signal. In this regard, a system including a combination of electricity meters with GPS units and electricity meters without GPS units may be envisaged . The meters with GPS units may be installed at key nodes in the network, where it is important to receive precise phase values and the remaining nodes may be provided with meters for estimating impedance values without GPS units.