Patent ID: 12237668

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following discussion of the embodiments of the disclosure directed to a system and method for estimating fault current using a sliding observation window that is shorter than one cycle is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses.

FIG.1is a schematic type diagram of an electrical power distribution network10including an electrical substation12that steps down high voltage power on a high voltage power line (not shown) to medium voltage power, such as 12.47 kV, provided on a substation bus14. A three-phase feeder16is connected to the bus14and a recloser18is provided proximate to the connection point between the feeder16and the bus14. The recloser18is intended to represent any reclosing or fault interrupting device suitable for the purposes described herein.FIG.2is a simplified block diagram of a representative example of the recloser18, and includes a vacuum interrupter20for opening and closing the recloser18to allow or prevent current flow therethrough on the feeder16, sensors22for measuring the current and/or voltage of the power signal propagating on the feeder16, a controller24for processing the measurement signals and controlling the position of the vacuum interrupter20, and a transceiver26for transmitting data and messages to a control facility (not shown) and/or to other reclosers and components in the network10.

The network10includes single-phase lateral lines30coupled to the feeder16usually at a utility pole32and a secondary service lines34coupled to each lateral line30usually at a utility pole36, where a lateral fuse38is provided at the connection point between each lateral line30and the feeder16and a primary fuse40is provided at the connection point between each lateral line30and each service line34. A distribution transformer42is provided at the beginning of each service line34that steps down the voltage from the medium voltage to a low voltage to be provided to loads44, such as homes.

This disclosure proposes a current estimator and an overcurrent detection and protection algorithm operating, for example, in the controller24that is similar to the traditional 1-cycle DFT current estimation method that may use the time derivative of the current waveform or the current waveform. The estimator uses a parametric method, which means that the observed waveform is modeled, and the parameters of the model are estimated that best fit the model to the observed waveform. The algorithm uses a sliding observation window that is shorter than one cycle, such as ¼-cycle, which may cause the estimator to produce larger overshoots, such as greater than 10%. The amount of overshoot depends on the validity of simplifying assumptions, such as a large X/R ratio, where the X/R ratio is the ratio of total inductive impedance X (that comes from that net inductance L) to the total resistive impedance R along the fault path, and may thus trigger false fault detections at current levels lower than the predetermined pickup level. In order to reduce the false detections, the detection algorithm employs two mechanisms, namely, a time-delay qualifier and a no-delay threshold that are described in detail below. It is noted that the time-delay mechanism described herein is not used for purposes of coordination in the context of this disclosure, which typically use delays in protection, but for security reasons, to reduce the probability of false detections.

Assuming that the current in a conductor is i(t), and using the standard model of a fault, the instantaneous current is modeled as:

i⁡(t)=2⁢Irms·cos⁡(2⁢π⁢ft+θ)+AD⁢C·e-tT+N⁡(t),(1)
where f is the system frequency (50 Hz or 60 Hz), √{square root over (2)}Irmscos(2πft+θ) is the system power current,

AD⁢C·e-tT
is the decaying DC component and N(t) represents other nuisance components such as harmonics, switching or other transients, and sensor noise. In general, noise is produced by active components such as A/D converters, amplifier stages in the conditioning circuits, filters and other electronic components. The constant T is the decaying time constant dependent on the X/R ratio of the circuit during the fault. It is assumed at this point that the system frequency f is known a priori. The frequency is assumed to be stable at the system frequency or is tracked independently by an external algorithm.

If the sensors22do not directly measure the current waveform itself, but the time derivative of the current, then the observed waveform di/dt (t) has a form of:

di/dt⁡(t)=2⁢πf·2⁢Irms·sin⁡(2⁢π⁢ft+θ)-AD⁢CT·e-tT+N′(t).(2)

Note that after differentiation, the form of equation (2) is the same as equation (1) except for the scaling factors, and the nuisance term N(t) is differentiated into N′(t). During a fault, it is reasonable to assume that the nuisance parameter N(t) or N′(t) is negligibly small because the current magnitude is very large. In documenting and illustrating the algorithm in the discussion below, the time derivative of the current waveform is used, but the process applies equally to the waveforms that are the current itself.

The proposed algorithm estimates the model parameters by processing sampled waveform data, sampled at frequency Fsand denoted from this point onward as xk≙x(tk), where tk=k/Fs, using a moving window containing N samples. It achieves fast fault detection by operating with a sampling window that is shorter than one full cycle, such as 4 cycle. For a window that is a fraction of one cycle, it is assumed that the amount of decay in one such processing window is negligibly small. In general, this assumption holds well for large X/R ratios, and worsens as X/R ratios decrease. Much like the effect of decay is considered negligibly small, so is the effect of the average DC offset within the processing window. Taking these assumptions into consideration, it is clear that the simplified model obtains an approximation to the true waveform, which is denoted as x(k). Using the definitions introduced above, the final model has the form:
{tilde over (x)}(k)=Acos(2πFk)+Bsin(2πFk),  (3)
where the model has two unknown parameters, namely, amplitudes A and B of the cos(⋅) and sin(⋅) components.

Digital frequency F is defined as the ratio of the system frequency and the sampling frequency as F=f/Fs. Once these two components are known, the desired quantities can be computed as:

Irms=1/2⁢2⁢π⁢f⁢A2+B2,(4)θ=tan-1(B/A).(5)

The model in equation (4) can be represented as an N component vector because the moving observation window has N samples, and can thus be written in the matrix-vector form {tilde over (x)}=A{right arrow over (p)}. Vector {right arrow over (p)} is a two-component vector such that p1=A and p2=B. Since the model is an approximation to the true observation xk, the relationship between xkand {tilde over (x)}(k) can be written as xk={tilde over (x)}(k)+ε(k), where ε(k) represents the unknown errors between the measurement and the model at instance tk. In vector notation, and using the definition for {tilde over (x)}(k) from above, the relationship becomes:
{right arrow over (X)}=A{right arrow over (p)}+{right arrow over (ε)},(6)
where the quantities A and {right arrow over (x)} are:

x→"\[Rule]"=[xkxk+1⋮xk+N-2xk+N-1],(7)A=[cos⁡(2⁢π⁢ftk)sin⁡(2⁢π⁢ftk)cos⁢(2⁢π⁢ftk+1)sin⁡(2⁢π⁢ftk+1)⋮⋮cos⁢(2⁢π⁢ftk+N-2)sin⁡(2⁢π⁢ftk+N-2)cos⁢(2⁢π⁢ftk+N-1)sin⁡(2⁢π⁢ftk+N-1)].(8)

From the definition above it follows that xkis the earliest sample in the current window, and xk+N-1is the most recent sample in the window. The optimal vector {right arrow over (p*)} is solved to minimize the total error between {right arrow over (x)} and {tilde over (x)} as:

p*→=minp→"\[Rule]"∑k=0N-1⁢❘"\[LeftBracketingBar]"ε⁡(k)❘"\[RightBracketingBar]"2.(9)

This formulation is a least-squares problem for which the classic solution is {right arrow over (p*)}=(ATA)−1AT{right arrow over (x)}. This solution is easily implemented with a microprocessor in a digital relay. To simplify the implementation, the matrix [(ATA)−1AT] can be precomputed, processed and stored using timestamps

tk,tk+1,tk+2,…,tk+N-2,tk+N-1=0,1Fs,2Fs,…,N-2Fs,N-1Fs.

The time-delay qualifier referred to above is an integrator of time that works with a prescribed delay, and starts integrating when the current estimator first detects a current magnitude that crosses a predefined pickup level. This process of detection can be described using a rotating disk analogy that spins in one direction (positive, clockwise) when the current estimator is above the pickup level, and the other direction (negative, counterclockwise) when the current estimator is below the pickup level. The disk starts spinning from a reset zero position when the current estimator reaches the pickup level the first time, and detects a fault when current estimator reaches a predefined position governed by the predefined delay period.

FIG.3is a graph with time on the horizontal axis and current magnitude on the vertical axis showing a fault scenario and illustrating the time-delay qualifier discussed above. Waveform50is fault current, curve52is the RMS current estimate from the current estimator and line54is the pickup level that identifies when the vacuum interrupter20should open because of the fault current. In one example, the current estimator samples the current 128 times per current cycle and estimates the fault current in a manner so that it overshoots the pickup level a couple of times before settling below the pickup level. Thus, since the actual RMS fault current did not exceed the pickup level, the vacuum interrupter20should not be triggered open. However, for the traditional system, the vacuum interrupter20would be triggered open when the current estimator estimated the current above the pickup level during the first overshoot.

FIG.4illustrates a timing disk60positioned at an initial or vertical reset position that occurs before the fault current is detected. The current estimator as described above first estimates the fault current to go above the pickup level at a 0.3-cycle point at point56. Instead of detecting a fault and opening the vacuum interrupter20as soon as the current estimate reaches the pickup level at the point56, the fault detection algorithm starts integrating time while the current estimate is above the pickup level. As the detection algorithm integrates time when the current estimate is above the pickup level, the disk60rotates in a clockwise or positive direction, as shown inFIG.4. Since the current estimate goes above the pickup level at the start, the disk60starts rotating in the positive direction from the reset zero position. If the current estimate goes below the pickup level, such as at point58, the detection algorithm subtracts time from the already accumulated time while the current estimate is below the pickup level. This is illustrated inFIG.5where the disk60is shown rotating in a counter-clockwise or negative direction from a point where some time has been accumulated from the current estimate being above the pickup level. When the current estimator drops below the pickup level, the disk60spins in the negative direction, but it stops if it reaches the reset zero position. A certain time accumulation threshold value is used for each system that provides a point where the estimate of the fault current indicates that the actual fault current is above the pickup level, which is illustrated by line62. This functionality can be implemented in software using an integrator.

Additionally, a no-delay threshold line64is provided at the maximum overshoot level above the pickup level, which is a parameter specified as a percentage above the pickup level, for example, in the range of 1%-100%. If the current estimator estimates the fault current to be above the no-delay threshold, a fault is detected instantaneously because this level could not be reached by overshoot from the current level that is below the pickup level. Using the no-delay threshold mechanism speeds up the detection process in cases when the true current level is much higher than the pickup level.

The foregoing discussion discloses and describes merely exemplary embodiments of the present disclosure. One skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes, modifications and variations can be made therein without departing from the spirit and scope of the disclosure as defined in the following claims.