8-12 L30 Line Current Differential System GE Multilin8.1 OVERVIEW 8 THEORY OF OPERATION8Depending on the 87L settings, channel asymmetry (the difference in the transmitting and receiving paths channel delay)cannot be higher than 1 to 1.5 ms if channel asymmetry compensation is not used. However, if the relay detects asymmetryhigher than 1.5 ms, the 87L DIFF CH ASYM DET FlexLogic™ operand is set high and the event and target are raised (if theyare enabled in the CURRENT DIFFERENTIAL menu) to provide an indication about potential danger.8.1.16 ONLINE ESTIMATE OF MEASUREMENT ERRORSGE's adaptive elliptical restraint characteristic is a good approximation to the cumulative effects of various sources of errorin determining phasors. Sources of error include power system noise, transients, inaccuracy in line charging current com-putation, current sensor gain, phase and saturation error, clock error, and asynchronous sampling. Errors that can be con-trolled are driven to zero by the system. For errors that cannot be controlled, all relays compute and sum the error for eachsource of error for each phase. The relay computes the error caused by power system noise, CT saturation, harmonics,and transients. These errors arise because power system currents are not always exactly sinusoidal. The intensity of theseerrors varies with time; for example, growing during fault conditions, switching operations, or load variations. The systemtreats these errors as a Gaussian distribution in the real and in the imaginary part of each phasor, with a standard deviationthat is estimated from the sum of the squares of the differences between the data samples and the sine function that isused to fit them. This error has a spectrum of frequencies. Current transformer saturation is included with noise and tran-sient error. The error for noise, harmonics, transients, and current transformer saturation is computed as follows. First, thesum of the squares of the errors in the data samples is computed from the sum of squares information for the presentphaselet:(EQ 8.28)Then fundamental magnitude is computed as follows for the same phaselet:(EQ 8.29)Finally, the local adaptive restraint term is computed as follows, for each local current:(EQ 8.30)Another source of the measurement errors is clock synchronization error, resulting in a clock uncertainty term. The L30algorithm accounts for two terms of synchronization error corresponding to:• Raw clock deviation computed from time stamps. There are several effects that cause it to not track exactly. First, theping-pong algorithm inherently produces slightly different estimates of clock deviation at each terminal. Second,because the transmission of time stamps is spread out over several packets, the clock deviation estimate is not up todate with other information it is combined with. Channel asymmetry also contributes to this term. The clock deviationcomputation is indicated in equation 8.15 as θi. If 2 channels are used, clock deviation is computed for both channelsand then average of absolute values is computed. If GPS compensation is used, then GPS clock compensation is sub-tracted from the clock deviation.• Startup error. This term is used to estimate the initial startup transient of PFLLs. During startup conditions, a decayingexponential is computed to simulate envelope of the error during startupThe clock uncertainty is expressed as:(EQ 8.31)Eventually, the local clock error is computed as:(EQ 8.32)The local squared adaptive restraint is computed from all local current sources (1 to 4) and is obtained as follows:(EQ 8.33)SumSquares 1_A k( )4N---- i1_f_A k p–( )( )2p 0=N 2⁄ 1–=I1_MAG_A I1_RE_A( )2 I1_IM_A( )2+=I1_ADA_A( )2 4N---- SumSquares 1_A k( ) I1_MAG_A( )2–( )=clock_unc clock_dev start_up_error+=CLOCK Aclock_unc( )29---------------------------------- ILOC_RE_A( )2 ILOC_IM_A( )2+( )⋅=ILOC_ADA_A( )2 18 I1_ADA_A( )2 I2_ADA_A( )2 I3_ADA_A( )2 I4_ADA_A( )2 Iq_ADA_A( )2 CLOCK A+ + + + +( )⋅=
