referring firstly to fig1 the relay comprises a master apparatus 1 , and a number of slave apparatus 3 , situated at the other ends of a multi - ended electrical feeder 5 , only one such slave apparatus 3 being shown in the figure for simplicity , each apparatus being under the control of one or more microprocessor - based control means 27 or 29 . referring now also to fig5 the master apparatus includes sampling means 31 which samples current signals at its end of the feeder 5 at time intervals t m1 , t m2 etc . which are defined by a free - running clock incorporated within the master apparatus as indicated in fig5 . the slave apparatus 3 includes sampling means 35 which samples current signals at its end of the feeder at time intervals t s1 , t s2 which also need not be identical but are defined by an independent free - running clock 37 incorporated within the slave apparatus , the sampling times at the master and slave ends of the feeder not necessarily being coincident . the sampling times may even be at slightly different frequencies . the sampled current signals at each end of the feeder are converted in analog to digital converter means 39 and 41 respectively to digital signals representing the instantaneous values of the three phase currents and the neutral current at the end , and may contain unwanted d . c . offset , harmonics , and high frequency components . the master and slave apparatus thus contain means for filtering the data , and preprocessing it to a form suitable for the calculation of the magnitudes of differential and bias currents as further described hereafter . at required times , for example after the time interval t m1 , a polling means 43 in the master apparatus 1 sends a polling message ( see block 10 in fig3 ) down a digital data communication channel indicated as 7 to the slave apparatus 3 ( see block 12 in fig4 ). this polling message contains a time tag corresponding to t m1 , and command and status information . the slave apparatus 3 includes return means 45 which responds to the polling message ( see block 14 in fig4 ) by returning a data message to the master apparatus ( see block 16 in fig3 ), containing the polling time tag t m1 , the time between the most recent slave apparatus sampling and the arrival of the polling message , the most recently filtered current data sampled by the slave apparatus , and other status information . using the send - off time of the polling message , and the arrival time of the slave data message , a transit time detector means 47 in the master apparatus is then able to calculate the communication channel delay time , and to time align the slave data to the master data in a synchronizing means 49 using a vector transformation technique as described hereafter . the master apparatus then operates a relay means 51 to protect the feeder when the difference between the time aligned current values at the two ends of the feeder 5 exceeds a predetermined value , as detected by a comparison means 53 . the one - cycle window fourier signal processing method is used to filter and preprocess the current signals measured at each end of the feeder . the algorithm for this method can be expressed as : ## equ1 ## where n is the number of samples measured per cycle of the current signal in the feeder ; i n is the instantaneous value of the current signal measured at time t n i s is the fourier sine integral of the current signal ; and i c is the fourier cosine integral of the current signal . can be shown to be i sin ( wt + wt θ ) where θ is a phase angle , then it can be shown that : as the phase angle θ is related to the time reference of the data window , i s and i c are not static , but are sinusoidal quantities . the phasor i =( i s + ji c ) thus represents a vector rotating in an anticlockwise direction on the complex plane at the angular frequency w , from which the magnitude of the current signal i may be extrapolated . assuming the master apparatus decides to send a polling message to the slave apparatus at time t a after data sampling at t m1 , the polling means 43 of the master apparatus will take some time t b to send out the whole polling message . if the transmit channel propagation delay time is t p1 , then the end of the polling message will have arrived at the slave apparatus at time ( t m1 + t a + t b + t p1 ). the returned data message , containing the polling time tag t m1 , the time between the slave sampling t s2 and the arrival of the polling message t sd , the filtered i s , i c data last produced by the slave apparatus at time t s2 , and other status information will have arrived back at the master apparatus at time t m * where t c is the processing time the slave apparatus takes before it starts to send off the data message ; t d is the time the communication interface of the slave apparatus takes to send out the whole data message ; and if it is assumed that the trensmit and receive channels have the same propagation delay time , i . e . t p1 = t p2 , as t a , t b , t c and t d are all known quantities , then the channel propagation delay time t p may be calculated ( see block 18 in fig3 ) from : after estimating the value of t p , the master apparatus is then able to identify the sampling time , t s * of the received slave data ( see block 20 in fig3 ) from the expression : after identifying t s * , the slave data may then be time aligned with the master data ( see block 22 in fig3 ). as can be seen in fig1 in the particular relay being described by way of example , t s * happens to be equal to t s2 . the master aparatus should identify , therefore , that the slave data are sampled at a time between t m2 and t m3 , so that the slave data must be aligned to these times . alignment to both these times is required , as this allows differential protection comparison to take place ( see block 24 in fig3 ) on every data sample of the master apparatus , while requiring the slave apparatus to be polled for data only once every two data samples , so reducing the data bandwidth requirement . using a look - up table , the parameters ( a + jb ) required to perform a phase shift on ( i s + ji c ) for the slave data , corresponding to the time ( t m3 - t s * ) may be obtained . the phasor value of the slave current i s3 at time t m3 may then be calculated from : ## equ2 ## the value of the slave current at time t m2 can be obtained likewise by rotating i s3 backward by a fixed angle corresponding to the sampling time period . referring now also to fig2 if i a , i b , i c , . . . are the current signals measured at ends a , b , c . . . of the protected feeder , then the differential current , i diff , and the through current i through are defined as : as indicated in fig2 a percentage biased differential protection characteristic is used for the relay , the tripping criteria being : i th is the minimum differential current value for trip protection . the microprocessor incorporated in the master apparatus then calculates | i diff |, | i a |, | i b | . . . from the corresponding vector components i s , i c using a linear approximation technique to perform the equivalent of the equality ## equ3 ## so as to determine from the monitored values of current after they have been time aligned whether to operate the relay to protect the feeder . the microprocessor may be self manipulating to vary the threshold and through current settings to produce an adaptive relay characteristic for improved sensitivity and stability . in one particular relay in accordance with the invention adopting the iso // ccitt &# 39 ; s high level data link control communication protocol , for the data message , the information field will suitably contain the polling time tag ( 1 byte ), the slave sampling delay time t sd ( 1 byte ), i s and i c of the phase and neutral current signals ( 16 bytes ), and status information ( 1 byte ). the whole message frame , would therefore be 25 bytes long , have a protocal efficiency of 76 %, and take about 3 . 75 ms to transmit through a single 64 kbps data channel . it will , therefore be possible to share the communication link with other signalling and telecommunication equipment . as only one data message needs to be transmitted for each two data samples , a suitable sampling rate would be 8 samples per cycle of the mains supply , the resulting average relay operating time being about 26 ms for 50h z operation . it will be appreciated however that this performance represents a balance of operating speed , and communication requirement and does not represent the limit of the relay . typically the relay will have sampling rates of between 400 to 800 per second , these relatively low sampling rates enables the use of low cost electronic components in the relay . faster operating times may be achieved by using wider bandwidth channels , whilst slower , more economical channels may be used for applications which do not required phase selection . it will be appreciated that any form of data communication channel may be used in a relay in accordance with the invention , such as fibre optic links , or conventional communication lines with adequate bandwidth . as the relay is microprocessor based however , a particular advantage of a relay in accordance with the invention is that it is easily adapted to work with different communication equipment by minor changes in the interfacing hardware . it will also be appreciated that as the channel delay time t p is calculated for each data poll , any changes on the communication channel are monitored , this being particularly important where the communication time is part of a switched telecommunication network . it will also be appreciated that as the time tag t m1 is incorporated in both the polling message and the data message , the time tag may be used by means 55 ( see fig5 ) to perform the function of a random number check on the communication and processing facilities of the relay . it will also be appreciated that whilst in the particular relay described herebefore by way of example there is a master apparatus , and a number of slave apparatus , the invention is equally applicable to master - master arrangements in which the relay can both send a poll message and respond to a polling message at the same time . whilst such a master - master arrangement may be applicable in a two - ended feeder system generally horewver , master - slave arrangements in multi - ended systems are advantageous as they lower the communication and processing requirements . it will also be appreciated that each master or slave apparatus may , in itself include a means for back - up protection of the feeder . thus in the event of the failure of the communication channel , or communication equipment , the protective equipment at the ends of the feeder may be given the option of staying idle or operating under a stand - alone mode as a form of back - up protection . for example the protection equipment may operate as an overcurrent protection relay based on the local i s , i c values measured .