3.1. Fundamentals About the Contribution of IBRs to Faults in the Grid
IBRs can be grid-following, needing a phase-locked loop (PLL) to track the grid frequency and voltage angle, or grid-forming, whose frequency is controlled to help in the power system control. There are very many options for designing IBR control, and the IBR behavior for faults in the power system is strongly dependent on the particular control designs. IBR control rapidly limits the currents during short circuits in the grid to avoid damages in the power electronics (IBR currents are often limited to around 1.2 times the rated current, unlike contributions from synchronous generators, which are in the order of 5 to 10 times the rated current), and the IBR control also drives the angles of those currents. Some IBRs always inject only positive-sequence currents, even during asymmetrical faults in the grid. Nowadays, grid codes [107,108,109] tend to impose some constraints on IBR control designs. For example, the injection of reactive currents and negative-sequence currents, proportional to the change of positive- and negative-sequence voltages, respectively, has been imposed in some grid codes; such IBR contributions to fault currents should be useful to improve the behavior of distance protection, but there are still many installed IBRs without these features. In summary, the IBR behavior for faults in the grid cannot be generalized because it depends on the IBR control. On the other hand, IBRs by themselves do not inject zero-sequence currents into the grid, but the generation plants must have grounding paths (typically through transformers with delta/wye connections), offering a constant zero-sequence impedance in their equivalent network. That is, the zero-sequence contribution from IBRs to faults in the grid is predictable, unlike the negative-sequence contribution, which is typically unpredictable.
An illustrative example of a grid-following inverter is shown in Figure 2. The PWM voltage waveshape is not sinusoidal, but the output filter and the step-up transformers provide enough impedance to connect these sources to the strong sinusoidal source voltage of the grid. The fundamental component (or first harmonic) of the PWM voltage waveshape can be seen as an equivalent voltage source (EPWM-1h). This approach is useful to obtain similarities with the traditional phasor analysis of electric power systems. The IBR control can perform very fast changes of EPWM-1h (in module and/or angle), which are not attainable in a synchronous generation (where internal electromotive forces change slowly). Due to this, the fact of obtaining very fast changes of EPWM-1h has being related to the term “low inertia”, as a simplified way to describe this IBR behavior.
In the case of grid-following inverters, the PLL can fail in determining the grid frequency during faults and, consequently, the voltage waveshapes can be synthetized at a frequency different from the grid frequency. Thus, the waveshapes of IBR currents during faults in the grid can have erratic behavior regarding their modules, angles and fundamental frequencies.
3.2. Fundamentals About Distance Protection
Distance protections are based on apparent impedances; their characteristics are usually shown in the R-X plane and can have diverse shapes (mho, quadrilateral, polygonal, etc.). These protective functions use measurements of voltages and currents at relay locations. Almost all the distance protections currently in service are in microprocessor-based relays; therefore, the voltages and currents are sampled several times for each cycle, and their phasor magnitudes and angles are computed using algorithms that integrate the sampled values in a sampling window (e.g., using the last cycle of the sample). Consequently, each transition from a given condition to another one (e.g., from a steady state pre-fault condition to a fault condition) implies a transient behavior of apparent impedances seen by distance protection.
Apparent impedances should be internally computed by distance protections according to the phase(s) involved in the fault; otherwise, the apparent impedance of a non- faulted loop could cause the wrong operation of distance functions. Due to this fact, a faulted-phase detection element (or algorithm) is usually necessary for distance protection. Unfortunately, information concerning this element is not always clearly given by relay manufacturers. Nowadays, faulted-phase detection elements based on magnitudes of currents do not seem to be in use. Two types of conditions for the faulted-phase detection algorithms, reported by relay manufacturers, are shown in Figure 3 (Figure 3a, based on angles between negative- and positive-sequence currents [110]; Figure 3b, based on angles between negative- and zero-sequence currents [111]). Notice that both algorithms need the negative-sequence currents.
Negative-sequence quantities have also been very useful for determining the fault directionality of unbalanced faults. Figure 4 helpfully explains this point, showing only the negative-sequence networks for the sake of simplicity. Z2M and Z2N are negative-sequence source impedances at both line ends; Z1L is the positive-sequence impedance for the total line length, Z1X is the positive-sequence impedance between the relay and the fault point and Z1Y is the positive-sequence impedance between the fault point and the remote line end (i.e., Z1L = Z1X + Z1Y); Z2I is the negative-sequence equivalent impedance that represents the additional interconnections between buses M and N (i.e., in meshed networks, substations at both line ends are also usually interconnected by other paths, at the same voltage level and/or at a different voltage level, and the net effect can be summarized by equivalent impedances); V2R and I2R are the negative-sequence voltage and current at the location of the analyzed relay. Figure 4a shows the case of forward faults (in the protected line, for the sake of simplicity). Considering that the phases of I2R and I2M are similar to each other (as tends to happen for systems with only synchronous generation), the quotient V2R/I2R is an inductive impedance with a negative sign (if Z2I tends to infinite, I2R is equal to I2M and V2R/I2R is −Z2M). Figure 4b shows the case of reverse faults (in the busbar of relay location, for the sake of simplicity). The quotient V2R/I2R is an inductive impedance (if Z2I tends to infinite, then I2R is equal to I2N and V2R/I2R is Z1L + Z2N). Having different signs in the result of V2R/I2R is key for this directional detection method. The assumption of Z2I tending to infinite is not the general case, but it is very useful to show the tendency in a much simpler way (Z2I is included in this explanation for the sake of rigorousness, but it is often omitted in the literature regarding distance protection in order to show simpler deductions).
The effect of fault resistances on the apparent impedance seen by distance protection is influenced by the current from the remote line end. Figure 5 shows the case of three-phase faults, for the sake of simplicity. Z1M and Z1N are positive-sequence source impedances at both line ends; Z1I is the positive-sequence impedance that represents the additional interconnections between buses M and N (i.e., similar to Z2I, previously described for the case of the negative-sequence network), V1R and I1R are the positive-sequence voltage and current at the location of the analyzed relay; EM and EN are the source voltages behind the impedances for buses M and N, respectively. Considering that the apparent impedance (Zapp) is simply V1R/I1R, Equation (1) can be easily obtained by the application of Kirchhoff’s law. This equation indicates that the effect of fault resistance is amplified and phase-shifted due to the influence of I1Y/I1R. The mathematical analysis of asymmetrical faults is conceptually similar but slightly more complex [112]. However, there are diverse polarization methods for ground faults [113] from different manufacturers of real-life distance protections, and this fact implies that the apparent impedances seen by distance protections are dependent on the relay model. In general, the effect of fault resistance on the apparent impedance seen by the distance protection depends on the pre-fault load flow [112,113] (which determines the values of EM and EN, and the circuit solution under fault conditions depends on EM and EN).
Memory- and cross-polarized distance functions are usually applied to avoid wrong directional detection for faults very near to the relay location. These polarization methods are often applied with offset mho characteristics; in these cases, the offset impedance (ZOF) is not a relay setting and it can be seen as a quantity dependent on the fault direction. Figure 6a shows that ZOF is in the third quadrant for forward faults, whereas Figure 6b shows that ZOF is in the first quadrant for reverse faults [114,115,116,117] (ZR is the reach setting of the distance protection). The value of ZOF for forward faults is dependent on different variables [115]. For the sake of simplicity, ZOF for forward faults is often roughly approximated to −ZM (ZM is the source impedance at the relay location); that is, the offset mho characteristic expansion can be very large if ZM corresponds to a weak infeed.
In general, there are diverse polarization methods for distance functions. For the purpose of this article, it is worth mentioning that negative- and zero-sequence currents have, for a long time, been utilized for the reactance reach line of quadrilateral characteristics [126]. Nowadays, this type of method has been utilized by different manufacturers (e.g., [110,127,128]).
Faults very near to one line end tend to be in zone 2 of the distance protection of the other line end. To avoid the zone 2 delay, the distance protection is usually complemented by communication-assisted trip logics, for instance, permissive underreach transfer trip (PUTT), permissive overreach transfer trip (POTT) and directional comparison unblocking (DCUB). Weak infeed logic, in conjunction with echo logic, is available to avoid the non-operation of the communication-assisted trip logic if one line end has a weak source. The communication-assisted trip logic coexists with the noncommunication-based trips of distance protection zones; thus, a loss of communication does not imply the total loss of distance protection.
The analysis of distance protection has many details. For the purpose of this article, two additional details must be mentioned as follows:
- (a)
- The source-to-line impedance ratio (SIR) is a simplified parameter that has often been utilized to describe some features of distance relays. Although there are different possible ways to describe SIR, if Z1I is neglected (as shown in Figure 5), the SIR for three-phase bolted faults at the remote line end is simply Z1M/Z1L. For instance, a high SIR can imply that the voltage at the relay location is very low for faults at the remote line end and, consequently, substantial errors in the voltage measurement can be expected.
- (b)
- Transmission voltages are often measured with the help of capacitive voltage transformers (CVTs), which consist of a capacitive voltage divider with an inductance at the low-voltage side and ferro-resonance suppression circuits. CVT transient behavior should be considered for the proper setting of distance protections [132].
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Juan David Hernández-Santafé www.mdpi.com
