DIRECTIONAL RELAY

RELATED APPLICATION

[0001] This application is related to US provisional patent application serial no. 62/326,371 filed on April 22, 2016. The contents of this US provisional application are incorporated by reference herein.

FIELD OF DISCLOSURE

[0002] The present disclosure relates generally to methods and apparatus used in electrical power grids, and in particular, methods and apparatus for detecting faults in electrical power grids and inside generation units.

BACKGROUND

[0003] Traditional electrical power transmission and distribution systems typically have centralized power generation mechanisms (e.g., a coal, nuclear, or hydro power plant) which generate electricity and distribute the electricity to locations where it will be consumed. These systems are commonly referred to as a "power grid".

[0004] In a traditional power grid, the method of generating alternating current electricity is the three-phase method where, under balanced conditions, three conductors each carry an alternating current of the same frequency and voltage amplitude relative to a common reference but with a phase difference of one third the period. Power grids may have fault detection relays to detect faults in the power transmission and distribution systems.

[0005] Apart from the centralized power generation mechanisms, distributed sources of electricity may supplement the power of, or operate independent from, a power grid. Electrical power systems including such distributed electricity generation units are commonly referred to as "microgrids".

[0006] As explained below, using traditional fault detection relays in microgrid systems may not function correctly to detect faults. There is thus a need for improved methods and apparatus for detecting faults in electrical power grids with distributed generation units.

SUMMARY OF DISCLOSURE

[0007] In a first aspect, a control system for a relay in a power grid is provided in an

embodiment. The control system comprises: a first module to receive and store voltage and current data relating to a directional element in a power circuit in the power grid; a second module to calculate a negative-sequence impedance associated with the directional element using the voltage and current data; and a third module to determine whether an asymmetric fault is present at the directional element, based on an evaluation of the negative-sequence impedance.

[0008] In the control system, the superimposed negative-sequence impedance may be calculated by;

wherein Z _s ~ may be the superimposed negative-sequence impedance at the directional element; V may be a negative-sequence voltage at the directional element; V _m ~ may be a memorized negative-sequence voltage previously taken at the directional element; / ^" may be a negative- sequence current at the directional element; and \ _m ^' may be a memorized negative-sequence current previously taken at the directional element. In the control system, V _m ~ and f _m may be taken from measurements from a one prior cycle at the directional element.

[0009] In the control system, the third module may further compare a magnitude of the negative-sequence impedance against current values at the directional element to determine whether the asymmetric fault is present.

[0010] In the control system, the asymmetric fault may be either a forward fault or a reverse fault.

[0011] In the control system, wherein the directional element may be a relay.

[0012] The control system may further comprises a fourth module to selectively control the relay based on whether the third module determined that either the forward fault or the reverse fault is present.

[0013] In the control system the power grid may be a microgrid.

[0014] In a second aspect, another control system for a relay in a power grid is provided. This control system comprises: a first module to receive and store voltage and current data relating to a directional element in a power circuit in the power grid; a second module to calculate a superimposed positive-sequence impedance for the directional element using the voltage and current data; and a third module to determine whether a symmetric fault is present at the directional element, based on an evaluation of a magnitude of the superimposed positive- sequence impedance. [0015] In the control system the superimposed positive-sequence impedance may be is calculated by:

wherein Z ⁺ _s may be the superimposed positive-sequence impedance at the directional element; V ^* may be a positive-sequence voltage at the directional element; V _m * may be a memorized positive-sequence voltage at the directional element; /* may be a positive-sequence current at the directional element; and l _m * may be a memorized positive-sequence current at the directional element.

[0016] In the control system V _m * and l _m * may be taken from measurements from one prior cycle at the directional element.

[0017] In the control system, the third module may further compare the magnitude of the positive-sequence impedance against a threshold to determine whether the symmetric fault is present.

[0018] In the control system, the third module may further evaluate a torque angle of current at the directional element to determine whether the symmetric fault is present. As well, the third module may further still evaluate a change in the torque angle over a period of time to determine whether the symmetric fault is present. Alternatively, the third module may further still evaluate a change in the positive-sequence current over a period of time to determine whether the symmetric fault is present.

[0019] In another aspect, a processor-implemented method to control a relay in a power grid is provided. The method comprises: receiving and storing voltage and current data relating to a directional element in a power circuit in the power grid; calculating a negative-sequence impedance associated with the directional element using the voltage and current data; and determining whether an asymmetric fault is present at the directional element based on an evaluation of the negative-sequence impedance.

[0020] In the method, calculating the superimposed negative-sequence impedance may utilizes a formula:

wherein Z _s ^' may be the superimposed negative-sequence impedance at the directional element; V may be a negative-sequence voltage at the directional element; V _m ^~ may be a memorized negative-sequence voltage taken at the directional element from a one prior cycle; / ^" may be a negative-sequence current at the directional element; and F _m may be a memorized negative- sequence current taken at the directional element from the one prior cycle.

[0021] For the method, determining whether the asymmetric fault is present may further comprise comparing a magnitude of the negative-sequence impedance against current values at the directional element to evaluate whether the asymmetric fault is present.

[0022] In still another aspect, a processor-implemented method to control a relay in a power grid is provided. This method comprises: receiving and storing voltage and current data relating to a directional element in a power circuit in the power grid; calculating a superimposed positive- sequence impedance for the directional element using the voltage and current data; and determining whether a symmetric fault is present at the directional element, based on an evaluation of a magnitude of the superimposed positive-sequence impedance.

[0023] In the method, calculating the superimposed positive-sequence impedance may utilize a formula:

V*— v ⁺

z: = -—

i ⁺ - r

wherein Z _s ^* may be the superimposed positive-sequence impedance at the directional element; \Anay be a positive-sequence voltage at the directional element; V _m * may be a memorized positive-sequence voltage taken at the directional element from a one prior cycle; /Viay be a positive-sequence current at the directional element; and „ may be a memorized positive- sequence current taken at the directional element from the one prior cycle.

[0024] In other aspects, the above aspects may be incorporated into a fault detection system and / or a fault detection method for a relay.

[0025] In other aspects, various combinations and sub-combinations of the above aspects are provided.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Non-limiting examples of various embodiments of presented in this disclosure will next be described in relation to the drawings, in which:

[0027] FIG. 1 is a schematic diagram and the main parameters of a three-phase, three- wire microgrid test system, in accordance with at least one embodiment; [0028] FiGs. 2A-2B are exemplary waveform diagrams illustrating the voltage and current phases of a phase to phase fault detected in a microgrid, in accordance with at least one embodiment;

[0029] FIG. 3A is a diagram illustrating an exemplary operation of a traditional negative- sequence directional element for a reverse asymmetric phase to phase fault in the presence of a distributed generation power source, in accordance with at least one embodiment;

[0030] FIG. 3B is a diagram illustrating an exemplary operation of a traditional negative- sequence directional element for a reverse asymmetric phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment;

[0031] FIG. 4A is a diagram illustrating an exemplary operation of a traditional negative- sequence directional element for a reverse asymmetric phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment;

[0032] FIG. 4B is a diagram illustrating an exemplary operation of a traditional negative- sequence directional element for a reverse asymmetric phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment;

[0033] FIG. 5A is a diagram illustrating an exemplary operation of a traditional positive- sequence directional element for a symmetric fault in the presence of a distributed generation power source, in accordance with at least one embodiment;

[0034] FIG. 5B is a diagram illustrating the measurement of positive-sequence powers during the symmetric fault of FIG. 5A, in accordance with at least one embodiment;

[0035] FIG. 5C is a diagram illustrating an exemplary operation of a traditional positive- sequence directional element for a symmetric fault in the presence of a conventional power generation source, in accordance with at least one embodiment; [0036] FIG. 6A is a diagram illustrating the measurement of positive-sequence powers during a reverse phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment;

[0037] FIG. 6B is a diagram illustrating an exemplary operation of a traditional positive- sequence directional element for the reverse phase to ground fault of FIG. 6A, in accordance with at least one embodiment;

[0038] FIG. 6C is a diagram illustrating an exemplary operation of a traditional negative- sequence directional element for a reverse phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment;

[0039] FIG. 7A is a diagram illustrating an exemplary operation of a traditional phase directional element for a phase to phase fault in the presence of a distributed generation power source, in accordance with at least one embodiment;

[0040] FIG. 7B is a diagram illustrating an exemplary operation of a traditional phase directional element for a phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment;

[0041] FIG. 8 is an exemplary configuration of a system representing different

distributed generation types along a feeder, in accordance with at least one embodiment;

[0042] FIGs. 9A-9D are exemplary diagrams showing the direction and magnitude of

negative-sequence impedance values under various fdult conditions in the exemplary system of FIG. 8, in accordance with at least on embodiment;

[0043] FIG. 10 is an exemplary diagram showing impedance characteristics for forward and reverse fault detection of a negative-sequence impedance-based directional element, in accordance with at least one embodiment;

[0044] FIG. 11 is an exemplary logic diagram for identifying the direction of symmetrical faults, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to phase fault in the presence of a distributed generation power source, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to ground fault in the presence of a conventional power source, in accordance with at least one embodiment;

is a diagram illustrating an exemplary operation of a directional element for a reverse phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for a reverse phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment; is a diagram illustrating an exemplary operation of a directional element for the phase to phase fault of FIGs. 7A-7B in the presence of a distributed generation power source, in accordance with at least one embodiment;

is a diagram illustrating an exemplary operation of a directional element for the phase to phase fault of FIGs. 7A-7B in the presence of a conventional power generation source, in accordance with at least one embodiment;

is a diagram illustrating an exemplary operation of a directional element for a reverse symmetric fault and a close-in balanced forward fault in the presence of a distributed generation power source, in accordance with at least one embodiment; [0054] FIG. 17 is a table illustrating an example where unbalanced loads were used in the exemplary system of FIG. 1 to compare the operation of a traditional directional element with a directional element, in accordance with at least one embodiment;

[0055J FIG. 18A is a diagram illustrating an exemplary operation of a traditional directional element in the unbalanced system of FIG. 17 for a phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment; and

[0056] FIG. 18B is a diagram illustrating an exemplary operation of a directional element used in the exemplary system of FIG. 1 for the phase to ground fault of FIG, 18A, in accordance with at least one embodiment.

DETAILED DESCRIPTION

[0057] The description which follows and the embodiments described therein are provided by way of illustration of an example or examples of particular embodiments of the principles of the present disclosure. These examples are provided for the purposes of explanation and not limitation of those principles and of the disclosure. In the description which follows, like parts are marked throughout the specification and the drawings with the same respective reference numerals.

[0058] In one broad aspect, the present embodiments relate to improved methods and apparatus for detecting faults in electrical power grids with distributed generation units. Among other things, the present disclosure describes a different directional element that may be incorporated into a pilot relaying scheme with a minimal bandwidth requirement. As discussed below, one aspect of the disclosed directional element may be based on the magnitude and angle of superimposed sequence impedances, and may provide improved performance in fault detection in microgrids with distributed generation units.

[0059] Generally, deficiencies of current fault protection mechanisms may limit possible microgrid configurations to simple topologies or may lead to erection of microgrids that harbor risks of hidden relay failures. Some challenges of a reliable microgrid protection system may include the following points.

[0060] First, microgrids are supposed to be capable of switching between the grid-connected and islanded modes on a regular basis. Fault signals may be radically different in these two states, requiring automated detection of the system's operating mode and applying appropriate protection settings or even schemes.

[0061] Second, for a conventional power system, protection of generation and transmission systems may typically be more elaborate due to, for example: a) the more complicated operating scenarios and configurations of these systems, and/or b) the possibility of large-scale blackouts stemming from protection failures in such parts of the grid. Since the generation and transmission roles are embedded inside the distribution system in the microgrid context, microgrids may also be vulnerable to protection failures. However, unlike bulk generation and transmission systems, the size of a microgrid is expected to be relatively small, thereby limiting the amount of resources available for investment in the protection system. As a result, microgrid designers typically use simple and inexpensive relays for protection purposes.

[0062] Third, microgrid designs potentially permit integration of more renewable energy sources in the form of distributed generation (DG). Depending on the technology involved, the magnitude and waveform of fault currents of DG units may differ from those flowing from conventional synchronous generators (SGs), which are what commercially available relays are designed to operate with. The wide diversity of fault signal properties in a microgrid may make protection in such a system challenging.

[0063] Some existing methods have attempted to meet the first challenge noted above for microgrids of being able to switch between grid-connected and islanded modes by providing a pilot relaying scheme with directional elements at the end of each protection zone. This approach identifies an in-zone fault if a forward fault is declared by all of the directional overcurrent relays (DOCRs) or distance relays associated with a protection zone. Minimal bandwidth is required to link the relays, limiting the cost of communication and thereby somewhat taking the second challenge of having limited resources for investment into protection mechanisms into account.

[0064] This approach may have worked for conventional power systems. However, since small fault currents are one of the main protection problems posed by electronically-coupled DGs and this approach does not take into account such small fault currents when identifying faults, the capability of this scheme may not be able to tackle the third challenge handling the different magnitude faults arising from microgrids.

[0065] In addition to their inclusion in DOCRs, directional elements may be used to supervise distance relays, making these elements a material part of the above-noted pilot scheme. Even if this pilot scheme is not deployed to protect a microgrid, DOCRs may still be an integral part of either the primary or the backup protection of any system with bi-directional fault currents, including microgrids and active distribution networks. Despite the inclusion of directional elements in these systems, the performance of traditional directional elements to protect a microgrid with high penetration of DG units is not well understood.

[0066] The present disclosure describes directional and overcurrent features of DOCRs for microgrids that may include electronically-coupled DGs and induction-machine-based DGs (IMDGs), for example, as may be used in methods employed by commercial relays. To illustrate behaviours of methods of the embodiments of this disclosure, a test system is described below in relation to FIG. 1. Several exemplary scenarios are discussed in relation to FIGs. 2A - 7B to unveil several likely scenarios that impact existing DOCRs. An exemplary embodiment of the disclosure related to a directional element based on the superimposed sequence impedances is discussed in relation to FIGs. 8-11. A discussion of performance of the disclosed directional element in some exemplary scenarios is provided below in relation to FIGs. 12A-18B.

[0067] While the illustrative embodiments discussed herein primarily relate to microgrids, it will be understood by persons skilled in the art that discussed issues described herein may occur in any electric grid with wind and/or solar sources (and not just microgrids). Also, it will be appreciated that the directional element discussed herein is not limited in applicability to microgrids, but instead, may be used to any electric grid with any type of generation unit (whether distributed or centralized).

EXEMPLARY SYSTEM FOR ILLUSTRATIVE PURPOSES

[0068] Referring to FIG. 1 , shown there generally as 100 is a schematic diagram and the main parameters of a three-phase, three-wire microgrid test system, in accordance with at least one embodiment. FIG. 1 depicts a schematic diagram and the main parameters of a three-phase, three-wire 34.5 kV, 60 Hz microgrid test system. The main grid is represented by a three-phase voltage source with the short-circuit capacity of 900 MVA. The microgrid can include a combination of the following DG units:

DG1 : a 10.75 MVA, 4.16 kV synchronous generator (SG) based unit at bus B3.

DG2: a 7.5 MVA (or 5 MVA), 4.16 kV electronically-coupled unit at bus B7 (or bus B4), e.g., solar-photovoltaic (PV) or Type-4 wind generation unit. DG3: a 7.5 MVA (or 5 VA), 4.16 kV induction machine-based unit at bus B7 (or bus B4). This unit can represent Type-1 wind turbines and Type-3 wind turbines when their crowbar circuit is activated after a fault.

[0069] Two scenarios, i.e., (i) DG1 , 5 MW-DG2 and 7.5 MW-DG2 and (ii) DG1 , 5 MW-DG3 and 7.5 MW-DG3 are considered. DG1 is normally open in the grid-connected mode, and can supply the microgrid's total load in the autonomous mode together with the other DGs.

10070] As used herein, the terminology Rij denotes the relay next to bus / looking toward bus /. R43 and R76 are shown as examples in FIG. 1.

DIRECTIONAL FEATURE OF DOCRS

A. Negative-Sequence Directional Element

[0071] This section describes operation of a negative-sequence directional element, denoted by 67NEG (using references from FIG. 1 ), during unbalanced faults. 67NEG element is a main fault direction identifier of relays (such as R76), and performs logical operations relating to the relay based on evaluating impedance, phase and current values detected at related components. For example, one evaluation is based on: =V-rcos( -V--( r ₊ Zr)) _{{Equatjon 1 }} where + and - superscripts denote positive and negative sequence quantities, and Z is the impedance of the component to be protected. The argument of the cosine term is referred to as the torque angle. A positive T indicates a forward fault. The logic of Equation 1 may also be implemented based on the negative-sequence impedance. 67NEG is a logic module that is associated with R76 of FIG. 1.

[0072] Proper fault direction identification of 67NEG element in the presence of electronically- coupled DG units requires that the pattern of negative-sequence quantities of the unit agrees with that of a conventional SG-based source. An SG may be conventionally modeled by a single impedance in the negative-sequence circuit for fault studies. Therefore, the negative-sequence current may be determined by the fault loop impedance and the negative-sequence voltage generated by the fault. An e!ectronicaily-coupled DG, however, often operates as a current- controlled source for which the current magnitude and angle are regulated by the control system of an associated interface voltage-sourced converter (VSC).

[0073] A generic VSC current control may include feedforward compensation of the VSC filter's grid-side voltage, V _g , at the outputs of the controllers. The voltage feedforward signal may (i) enhance the d- and g-axis controls, and (ii) improve the VSC's transient performance. Thus, the voltage on the converter-side of the filter, ½, may contain the disturbances of V _g , including its imbalance. Therefore, the difference between V _g and V _t , i.e., the voltage across the filter, determines the VSC's output current and resembles an almost idea! sinusoid regardless of the severity of the grid voltage distortions.

[0074] For example, consider a solid phase C to phase A (CA) fault at f=2 s on bus B6 of the system of FIG. 1 when bus B7 is connected to the 7.5 MW-DG2 in the islanded mode.

[0075] Referring to FIG. 2A and 2B, shown there generally as 200 and 201 respectively are exemplary waveform diagrams illustrating the voltage and current phases of a phase to phase fault detected in a microgrid, in accordance with at least one embodiment. Specifically, FIG. 2A illustrates the severely unbalanced voltage at the low-voltage (LV) side of DG2 transformer. Since the fundamental frequency component of V, is unbalanced and because of the voltage feedforward, the VSC current in FIG. 2B remains fairly balanced and increases by about 20% following the fault inception. The negative-sequence current is only 2% of the positive-sequence current, while that of the voltage is 99%. Such negligible negative-sequence current in the event of a highly unbalanced voltage condition would not be observed in a conventional SG unit.

[0076] For reliable operation when the system is unbalanced, 67NEG element is normally deasserted when the Γ / ratio falls below a threshold. Therefore, the small negative-sequence current of DG2, at best, deactivates the 67NEG unit of R67 for the above fault. Meanwhile, if the threshold of Γ / Γ for the 67NEG unit is set to 2% (which may be a viable setting and may not be considered to be unreasonably low for this perfectly balanced system), then the relay may determine the fault direction spuriously. This is because a generic current control loop of DG2 does not regulate the negative-sequence current and the angle of this small component does not follow a certain pattern.

[0077] Referring to FIG. 3A, shown there generally as 300 is a diagram illustrating an exemplary operation of a traditional negative-sequence directional element for an asymmetric phase to phase fault in the presence of a distributed generation power source, in accordance with at least one embodiment. As shown, the negative-sequence torque angle of R67 for this fault is within the [-90°,+9G°] range 310a for most of the fault time interval, causing a positive T and erroneous detection of the forward fault.

[0078] In contrast, referring to FIG. 3B, shown there generally as 301 is a diagram illustrating an exemplary operation of a traditional negative-sequence directional element for an asymmetric phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 3B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 3A (e.g., a fault a bus B6, which is in the reverse direction to relay R67), except that FIG. 3B illustrates conditions under a conventional power generation source instead of a distributed generation power source. In the illustrated model, it can be seen that in a conventional power context, the negative sequence torque angle is outside of the [-90°, +90°] range 310b, and as expected, reverse fault is correctly detected.

[0079] It is noted that even if a 67NEG element is set to a high Γ / trigger threshold, the high threshold may not provide the desired behaviour of the 67NEG elements of the relays in the vicinity of electronically-coupled DGs not being activated and letting other directional elements identify the fault direction. This is because the unconventional fault behavior of electronically- coupled DGs may also adversely affect the operation of 67NEG units that are not in close proximity of an electronically-coupled DG and their negative-sequence currents are not necessarily small.

[0080] Referring to FIG. 4A, shown there generally as 400 is a diagram illustrating an exemplary operation of a traditional negative-sequence directional element for an asymmetric phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment. Referring simultaneously to the exemplary schematic of FIG. 1, consider a bolted phase A to ground (AG) fault at bus B2 of the architecture of FIG. 1 , for which R15 should detect a reverse fault and prevent undesired tripping of the lower feeder associated with buses B1, B5, B6 and B7. While R15 is not shown in FIG. 1, its location can be understood therein using the naming convention introduced for elements in FIG. 1. The negative-sequence current measured by R15 consists primarily of the negative-sequence current that flows to the loads through the feeder. The positive-sequence current of neither DG2 nor the load is large, so the negative-sequence current of the loads may readily cause Γ/t to exceed even a large threshold value and activate R15's 67NEG unit. Since the patterns of the DG unit loads' negative-sequence currents and voltages are not the same as those of the conventional SG- based units, based on which Equation 1 has been derived, the 67NEG element may either malfunction or be unduly restrained if the operating point is close to the zero torque angle.

[0081] The Γ /Γ ratio for the above AG fault is approximately 22%, which is above a 10% recommended threshold, so the 67NEG element is activated. As shown in FIG. 4A, the 4.Γ of R15 is displayed as being fixed at roughly 88.5° once the post-fault transients die out, which is close to reaching the [-90°, +90°] range 410a for indicating a forward fault. Thus, if the 67NEG element is allowed to operate around the zero torque angle, R15 may falsely detect a forward fault. If a forward fault is not detected, the 67NEG unit is de-asserted, and the fault direction is identified using other directional elements.

[0082] It is worth noting that the angles between the DG loads' negative-sequence currents and voltages are almost unaffected by the line impedance angle. For the system shown in the architecture of FIG. 1 , the line impedance angle is approximately 68.2° under normal operating circumstances. However, in the case of the fault shown in FIG. 4A, there is a larger line impedance angle, and the torque angle in FIG. 4A becomes even smaller for the same fault condition. This is another indication that the logic behind Equation 1 is not suitable when electronically-coupled DGs are involved. Moreover, the following sections show that even a slight load imbalance can potentially force 4-F further into the forward zone 410a of FIG. 4A, thereby potentially aggravating the incorrect nature of 67NEG element's response.

[0083] In contrast, referring to FIG. 4B, shown there generally as 401 is a diagram illustrating an exemplary operation of a traditional negative-sequence directional element for a reverse asymmetric phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 4B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 4A (e.g., a fault a bus B2, which is in the reverse direction to relay R 5), except that FIG. 4B illustrates conditions under a conventional power generation source instead of a distributed generation power source. In the illustrated model, it can be seen that in a conventional power context, the negative sequence torque angle is outside of the forward fault indication [-90°, +90°] range 410b, and as expected, a reverse fault is correctly detected.

[0084] In some scenarios, the 67NEG element also may be influenced by a separate relay unit in the presence of electronically-coupled DGs. For example, consider a scenario in which the system measurements are not available, i.e., when the secondary side of a voltage transformer (VT) is disconnected due to either a blown potential fuse or a loose connection. A relay should detect the so-called !oss-of-voltage (LOV), trigger an alarm, and apply extra measures to supervise voltage-controlled units, including directional elements, until the voitage is restored. However, the relays can potentially misinterpret the unconventional fault currents and voltages in the presence of electronically-coupled DGs for LOV conditions.

[0085] Some traditional LOV detection logic for conventional power systems may be based upon large negative-sequence voltages accompanied by an insignificant negative-sequence current; e.g., the DG2 fault scenario illustrated in FIG. 2A and 2B discussed above. Some other traditional relays may declare an LOV condition if a voltage drop coincides with no change in the total current, or in the sequence currents. This may be another likely scenario for false LOV detection in the presence of electronically-coupled DGs.

[0086] In these scenarios, if the LOV detection logic does not evaluate zero-sequence currents and voltages, the relays proximate to electronically-coupled DGs may incorrectly raise the LOV flag during ground faults. Under a phase fault and in an ungrounded distribution system, the LOV detection methods that evaluate zero-sequence quantities may also give false alarms. Many traditional relays may either set the directional elements to default forward, or deassert the directional units upon detection of a LOV condition. Thus, for example, under the faults discussed above in relation to FIGs. 3A and 4A respectively, R15 and R67 may maloperate.

[0087] Since the angle of the positive-sequence voltage remains constant during LOV and fault conditions, a strategy for supervising directional elements during LOV conditions is to use a positive-sequence directional element, as discussed in the following subsection.

[0088] The discussion above has generally been in the context of a conventional 67NEG operating in the context of electronically coupled DGs (e.g., solar units and Type IV wind turbines). However, for DGs that are not electronically coupled, it is noted that the problems noted above with the 67NEG in relation to FIGs. 3A and 4A may not be as pronounced. For example, this may be the case in systems that include DGs that are Type I wind turbines (which include induction machines without electronic coupling). Also, this may also be the case for systems including DGs that are Type III wind turbines, in which the grid interface of the induction machine is composed partially of electronic components and the effects on a conventional 67NEG noted above may be less pronounced if the crowbar circuit of the turbine is activated during the fault. While this may suggest that replacing the electronically coupled DGs with IMDGs may ameliorate some of the shortcomings of a conventional 67NEG noted above, as discussed in greater below, the use of IMDGs may itself be associated with various problems.

B. Positive-Sequence Directional Element

[0089] This section describes operation of the memory-polarized positive-sequence directional element, denoted by 67POS. This element is used to identify the fault direction when negative- sequence quantities are either not present or not reliable, e.g., during balanced faults and LOV events. 67POS element is a main fault direction identifier of relays (such as R76), and performs logical operations relating to the relay based on evaluating impedance, phase and current values detected at related components. For example, one evaluation is based on the torque relation: _{(Equation 2)} where a positive V indicates a forward fault. There may also be Impedance-based versions of 67POS element. The sensitivity and security of 67POS element for conventional systems may be affected by large load angles and fault resistances. The issues explored in this section, however, do not overlap with those issues, as the following discussion deals with bolted faults and small load angles (the load angle along the feeders does not exceed 1 °). 67POS is a logic module that is associated with R76 of FIG. 1.

1) Electronically-Coupled DGs:

[0090] Referring to FIG. 5A, shown there generally as 500 is a diagram illustrating an exemplary operation of a traditional positive-sequence directional element for a symmetric fault in the presence of a distributed generation power source, in accordance with at least one embodiment. In the context of the exemplary configuration of FIG. 1 , consider a bolted balanced fault being placed at bus B6 when the system operates in the grid-connected mode and bus B4 is connected to the 5 MW-DG2 operating at one third of its rated capacity. In this example scenario, the symmetric fault is a three-phase line to line to line (L-L-L) fault, but the results may not be materially different if this was a line to line to line to ground (L-L-L-G) fault. The fault direction would be reverse for R12 and the upper feeder that connects buses B1 to B4 should not trip. However, FIG. 5A depicts that the angle of 7 ^* is 61.5° after the initial fault transients, thereby putting it into the forward fault [-90°,+90°] range 510a for detecting a forward fault and causing undesired disconnection of the upper feeder.

[0091] Referring to FIG. 5B, shown there generally as 501 is a diagram illustrating the measurement of positive-sequence powers during the symmetric fault of FIG. 5A, in accordance with at least one embodiment. Referring simultaneously to FIG. 1 , and continuing on with the same example, since the 5 MW DG2 connected to bus B4 is considered to be generating one third of its nominal power, the majority of the load connected across the upper feeder would be supplied by the main substation prior to the fault. This may result in the positive active and reactive powers at R12's location shown in F!G. 5B. While R12 is not shown in FIG. 1 , its location can be understood therein using the naming convention introduced for elements in FIG. 1. [0092] After the fault inception, the positive-sequence power measured by R12 decreases due to the reduced voltage and the absence of a source along the upper feeder that contributes a large fault current. The reduction in the active power is larger since a part of the loads' active power at buses B2 and B3 is supplied by the local 5 MW DG2, operating at unity power factor (PF). However, the active power of R12 is close to zero and the reactive power remains positive. Using the sample data points shown in FIG. 5B at t=2095.99, the angle of the positive- sequence complex power, which is substantially the same as the phase difference between the positive-sequence voltage and current, is 129.8°. With the line impedance angle begin at 68.2°, the angle becomes 61.5°, so as to cause a positive torque and thus false identification of a forward fault as noted with respect to FIG. 5A.

[0093] In contrast to a conventional SG-based unit, the fault current contribution of the 5 MW DG2 unit is not appreciably larger than the load currents and does not dominate the current measured by R12. Also, the phase differences between fault voltages and currents along the upper lateral may not be determined by the fault loop impedance, but rather by the power relations between the sources and loads. As a result, the logic behind existing 67POS elements may be rendered inapplicable to the systems with electronically-coupled DGs. For a

conventional system, 4- is independent of Z\ In contrast, if the line impedance angle was larger than 68.2" for the above fault, the power relations still remains almost identical, resulting in the same phase difference between V ^* and Γ, but smaller 4-T ^* .

[0094] Referring to FIG. 5C, shown there generally as 502 is a diagram illustrating an exemplary operation of a traditional positive-sequence directional element for a symmetric fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 5C illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 5A {e.g., a fault at bus B6, which is in the reverse direction to relay R12), except that FIG. 5B illustrates conditions under a conventional power generation source instead of a distributed generation power source. In the illustrated model, it can be seen that in a conventional power context, the positive sequence torque angle is outside of the forward fault indication [-90°,+90°] range 510c and, as expected, a reverse fault is correctly detected.

2) IMDGs:

[0095] Referring to FIG. 6A, shown there generally as 600 is a diagram illustrating the measurement of positive-sequence powers during a reverse phase to ground fault in the presence of an induction-machine-based distributed generation power source, in accordance with at least one embodiment. IMDGs (e.g., wind source induction generators or squirrel-cage induction generators), whose fault currents are large enough to dominate the load currents, also can cause misoperation of a traditional 67POS element. Referring again to the exemplary schematic of FIG. 1, consider the operation of R67 for a reverse AG fault at bus B6 when the 7.5 MW-DG3 (in this example, an IMDG) supplies its nominal power at bus B7. Once the fault occurs, the IMDG generates both active and reactive powers in the positive-sequence circuit. These are illustrated in FIG. 6A.

[0096] Referring to FIG. 6B, shown there generally as 601 is a diagram illustrating an exemplary operation of a traditional positive-sequence directional element for the reverse phase to ground fault of FIG. 6A, in accordance with at least one embodiment. Continuing on with the same example discussed with respect to FIG. 6A, the resultant phase lead of the fault current over the voltage along with the relatively large magnitude of the IMDG short-circuit current approximates to the SGs' fault behavior. Therefore, the angle of T for R67, as plotted in FIG. 6B, correctly indicates the fault's reverse direction after the fault inception.

[0097] However, after the initial few cycles of the fault, the voltage drop partially demagnetizes the induction machines, causing reactive power consumption by the DG3 and a decaying pattern for the corresponding current magnitude. In addition, the reactive power supplied by the PF correction capacitors of the IMDG is reduced due to the voltage drop. Therefore, the IMDG starts to absorb reactive power after a certain time, which is dictated by the fault severity.

Meanwhile, active power is still generated by the IMDG since it is not fully demagnetized.

Therefore, the phase lead of V ^* over I ^* falls in the center of the second quadrant for R67. Given the feeder's 68.2° impedance angle, the positive-sequence torque angle passes below 90° into the forward zone 610b, in less than 0.3 s after the fault inception. Thus, the torque becomes positive and the 67POS unit falsely detects a forward fault. More severe faults result in faster demagnetization of the IMDG and less reactive power injection by the capacitors, leading to a faster reversal of the relay's initial correct decision.

[0098] In contrast, referring to FIG. 6C, shown there generally as 602 is a diagram illustrating an exemplary operation of a traditional negative-sequence directional element for a reverse phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 6C illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 6B (e.g., a fault a bus B6, which is in the reverse direction to relay R67), except that FIG. 6C illustrates conditions under a conventional power generation source instead of a distributed generation power source. Although FIG. 6C shows the torque angle of a negative-sequence directional element as opposed to the positive-sequence as was shown in FIG. 6B, FIG. 6C still illustrates the operation of the directional element under similar conditions because the torque angles of the positive - and negative - sequence directional elements for this type of fault and for conventional sources are similar. In the illustrated model, it can be seen that in a conventional power context, the negative sequence torque angle is outside of the forward fault indication [-90°, +90°] range 610c and, as expected, a reverse fault is correctly detected.

C. Phase Directional Element

[0099] This section discusses operation of a phase directional element, denoted by 67PH. Despite inaccuracy in the presence of zero-sequence-dominated fault currents, the 67PH element with quadrature connection may be still used in certain environments and may operate based on:

(zi _A +ZZ ⁺ )+90") (Equation 3) (ζΐ _Β +ΖΖ ⁺ )+9θή (Equation 4)

T _c = V _AB I _c cos(zV _AB - ^• (z/ _c +ZZ ⁺ )+90"j (Equation 5) where a positive torque indicates a forward fault. Phase quantities are composed of the sequence components, which were shown unreliable for fault direction identification in the previous subsections. Consequently, the 67PH element also cannot be relied upon to detect the fault direction for a system that incorporates electronically-coupled DGs and/or IMDGs.

[0100] Referring to FIG. 7A, shown there generally as 700 is a diagram illustrating an exemplary operation of a traditional phase directional element for a phase to phase fault in the presence of a distributed generation power source, in accordance with at least one

embodiment. Referring again simultaneously to the exemplary schematic of FIG. 1, consider a bolted phase B to phase C (BC) fault at bus B6, when the 5 MW-DG2 generates half of its rated power at bus B4. As illustrated, FIG. 7A shows the torque angles of the 67PH elements of R12, for which the fault is in the reverse direction. As can be seen, two of the angles are situated inside the [-90°,+90°3 forward zone range 710a, causing incorrect positive torques and forward fault detection. The other angle is relatively close to the zero torque line, even though the fault is bolted. [0101] In contrast, referring to FIG. 7B, shown there generally as 701 is a diagram illustrating an exemplary operation of a traditional phase directional element for a phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 7B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 7A (e.g., a fault a bus B6, which is in the reverse direction to relay R12), except that FIG. 7B illustrates conditions under a conventional power generation source instead of a distributed generation power source. In the illustrated model, it can be seen that in a conventional power context, the angle of the phase torques measured by relay R12 for the faulty phases (i.e., phases B and C for the example bolted phase B to phase C fault) is correctly outside the forward fault indication [-90°, +90°] range 710b.

[0102] There are two distinctions between the described malfunction of 67PH elements and other malfunctions known in the art. Some other known malfunctions include sources with significant zero-sequence current contribution, while the fault discussed here relates to a phase to phase fault that does not involve the ground path. In addition, some other known

malfunctions, the three 67PH elements disagree on the fault direction; however, for a system with electronically-coupled DG units, all three 67PH elements may agree on a wrong fault direction, if the system is slightly unbalanced, given the narrow margin between 4.7c and the zero torque angle in FIG. 7A. Similar unreliable responses by 67PH elements are observed in systems that include IMDGs.

[0103] Although a zero-sequence directional element is used in some relays, they may not identify the fault direction during phase-to-phase and balanced faults. Also, they may be prone to misoperation if the system includes parallel lines with zero-sequence mutual coupling.

Moreover, they may not be helpful in ungrounded distribution systems.

NEGATIVE-SEQUENCE IMPEDANCE-BASED DIRECTIONAL ELEMENT

[0104] Since the fault current depends on the control systems of DG units and the microgrid's operating mode, an existing approach has attempted to apply a pilot protection scheme with directional relays at the end of each feeder using the existing directional elements. However, this approach may not be reliable in the presence of electronically-coupled DGs and IMDGs, as discussed above. An embodiment provides a directional element that may be deployed in a directional relay, where the directional element's performance is isolated from unconventional fault properties of DG units. As part of an embodiment, measurement, receiving of

measurements, storage, and evaluation of various electrical characteristics (voltage, impedance, phase, etc.) relating to one or more selected location(s) in the power circuit in a microgrid (see for example FIG. 1) are conducted. The measurement of the various electrical characteristics may be conducted using devices, circuit, and techniques known in the art. The receiving of measurement, storage and evaluation of the various electrical characteristics may be conducted using hardware and / or software components. The results of the evaluations of the electrical characteristics may be used to indicate certain fault conditions and may be used to selectively control one or more devices, such as directional elements and relays, according to embodiments described herein. Control system(s) for a directional element of an embodiment implement corresponding control signals selectively controlling operation of a relay that is enabled to identify a fault direction in view of the results. The control systems may be comprised of one or more modules that implement one or more of the measurement, storage, and evaluation of selected electrical characteristics of the associated grid and the control functions. The modules may be implemented in any combination of hardware and / or software

components.

A. Asymmetrical Faults

[0105] Despite problems of existing 67NEG elements in the presence of electronically-coupled DGs, for an embodiment the negative-sequence quantities may still be useful in identifying a direction of an asymmetrical fault. As discussed below, the negative-sequence impedance may be used to identify the fault direction. However, an embodiment may implement certain differences as compared with existing impedance-based 67NEG elements in terms of impedance measurement and a criterion applied to identify the fault direction. These distinctions may allow the fault behavior of DG units to not impact the relay operation. The superimposed negative-sequence impedance is calculated by:

(Equation 6)

where

s and m subscripts denote superimposed and memorized quantities;

V is a negative-sequence voltage at the location;

V _m is an earlier negative-sequence voltage at the location;

/ ^" is a negative-sequence current at the location; and

l ^~ _m is an earlier negative-sequence current at the location. In one embodiment, the earlier voltage and current readings are memorized signals of one cycle prior to activation of a disturbance detector, which may be implemented in a directional relay (e.g. R _A B) or a related control system for the directional element of an embodiment. In view of the potentially low negative-sequence fault currents, the use of superimposed quantities may help to provide correct operation under unbalanced conditions. It will be appreciated that for other embodiments, impedance calculations may be made based on other cycle times (e.g. more than one cycle) for earlier negative-sequence voltage and current readings.

[0106] Referring to FIG. 8, shown there generally as 800 is an exemplary configuration of a system representing different distributed generation types along a feeder, in accordance with at least one embodiment. To derive appropriate zones inside the negative-sequence impedance plane to differentiate between forward and reverse faults, consider relay R _AB in FIG. 8, which may include a directional element of an embodiment. R _A8 and / or its associated directional element may include a control system comprising control circuits and logic (implemented in any combination of hardware and/or software elements) that selectively control the relay's activation, according to an embodiment. The control circuits and logic may include a disturbance detector. The control circuits and logic may be implemented remotely from R _AE . FIG 8 shows a

combination of the electronically-coupled DG (shown as ECDG), load, and I DG at bus B that may represent different load and DG conditions along a feeder. In the negative-sequence circuit, IMDGs and SGs may behave almost similarly, so the IMDG may be used to represent the SG as well.

[0107] In discussing various example faults in the exemplary configuration of FIG. 8, reference is also be made to FIGs. 9A-9D, which, shown generally as 900, 901 , 902, and 903 respectively are exemplary diagrams showing both direction and magnitude of negative-sequence impedance values under various fault conditions in the exemplary system of FIG. 8, in accordance with at least one embodiment.

[0108] Referring again to FIG. 8, for a reverse fault at F _{1 T} Z _S ^' may be situated inside one of the three regions, depending on the status of switches Si to S ₃ . When S ₂ and S ₃ are open and the electronically-coupled DG is the only component connected to bus B, the earlier-discussed feedforward compensation of the grid voltage in the electronically-coupled DG's control system may make the magnitude of Z~ _S for an Fi fault excessively large, up to a level not observed in the conventional systems for any fault condition. However, since the angle of the small negative- sequence current of the electronically-coupled DG is not regulated by its controllers, may fall in any of the four quadrants. Therefore, the region for Z _S ~ may be located in the shaded area of FIG. 9A, which is outside the circular area that is symmetrical about the origin. The radius of this circle, , is large, as it is inversely related to the maximum negative-sequence current of the electronically-coupled DG.

[0109] If the load is also connected to bus B for the Fi fault and S ₃ remains the only open switch, then fault-caused voltage imbalance also may result in negative-sequence current flow of the load. Given the load's high impedance, particularly at the distribution voltage level, this current may not be substantial; nevertheless, it may be sufficiently large to overshadow contributions from the electronically-coupled DG in the negative-sequence circuit. Thus, as illustrated in FIG. 9B, the magnitude of Z _S ^' falls in the shaded region in FIG. 9B, which shape is similar to the load zones defined for the distance relays' load encroachment logic. The default value assigned to the load angle a in FIG. 9B by a commercial distance relay is normally approximately 20° to 45° and may be increased to approximately 70° by the user. However, in exemplary embodiments discussed herein, when Z _S ^' does not approach this region during a forward fauit for RAB, a rnay be conservatively set to be approximately 70°. The minimum distance between the load region and the origin along the R axis, / _2l may be automatically set according to maximum loading conditions. This may be determined based on the relay's rated current plus a safety margin (e.g. approximately between 10 and 20%) to factor in potential overloads.

[0110] Now suppose all three switches at bus B are closed and the R _AB measurements also include the contribution of the IMDG for fault F-i . The comparatively larger fault current of the IMDG may dominate the electronically-coupled DG and the load currents in the negative- sequence circuit, resulting in a smaller Z _S ~ calculated by R _AB - Furthermore, being represented by a mainly inductive impedance in the negative-sequence domain, the IMDG makes Z~ _S close to the feeder impedance angle. Thus, the reverse zone of an existing impedance-based 67NEG characteristic, shaded in FIG. 9C, is where Z~ _S lies.

[0111] For a forward F ₂ fault in FIG. 8, the relatively large current of the system on the left side of R _A B and the mainly inductive impedance of the fault loop make Z _S ^' small and inside the third quadrant of the impedance plane in the highlighted region of FIG. 9D. Since h is inversely related to electronically-coupled DG's negative-sequence current, the radius of the shaded area in FIG. 9D is large enough to cover Z during forward faults. Extra allowance is made in FIG. 9D by slightly tilting the zone boundaries beyond the R and axes.

[0112] Referring to FIG. 10, shown there generally as 1000 is an exemplary diagram of impedance characteristics for forward and reverse fault detection of a negative-sequence impedance-based directional element, in accordance with at least one embodiment. Considering FIGs. 9A-9D together, it can be seen that the three shaded Z ^' _s regions of FIGs. 9A, 9B, and 9C for reverse faults substantially do not overlap with the∑l region of FIG. 9D for the forward fault. Therefore, when taken together, the impedance plane of FIG. 10 may be divided into two zones for R _AB to distinguish between forward and reverse asymmetrical faults. Notably, at least one or more of the following characteristics of performance of an embodiment shown in FIG. 10 is distinctive over an existing impedance-based 67NEG element:

1) The embodiments utilize superimposed impedance, while existing elements utilizes total fault signals;

2) The embodiments evaluate impedance magnitude and compare the magnitude with

settings for Ι and k of the relay (which are parameters that may be set in a design for the directional element or when the relay is installed), whereas existing elements may not inspect the impedance magnitude; and

3) For the embodiments, the fourth quadrant is mainly inside the reverse zone of FIG. 10, which is unlike existing elements.

[0113] As will be understood by persons skilled in the art, for R _BA , the zone labels of FIG. 10 may be switched to achieve similarly correct outcomes. Also, similar to existing impedance- based directional elements, the forward zone shown in FIG. 10 may be offset vertically to help ensure correct operation for different impedance levels for the generation units and protected components.

B. Symmetrical Faults

[0114] Referring back to FIG. 8, in an exemplary scenario when the IMDG is not in service and switches St and S ₂ are closed, R _AB may identify the direction of a symmetrical fault based on a superimposed positive-sequence impedance, defined by

(Equation 7).

[0115] For an open S ₃ , the positive-sequence voltage of R _AB exhibits a significant decline during the reverse fault since there is no voltage source on the right side of R _AB . For the current, in contrast, the change is small and around the load-level current, leading to a large magnitude for Zj. If a reverse symmetrical fault involves a high resistance, the voltage decline becomes insignificant. However, not only is a high fault resistance unlikely for symmetrical short-circuits, it also may cause a very small increase in the electronically-coupled DG current. Thus, \Z \ (i.e., the absolute value of the positive-sequence impedance) may remain large during reverse faults, irrespective of the fault resistance. For the forward balanced F ₂ short-circuit, in contrast, \Z ^* _S \ may take a relatively small value due to the elevated fault current contribution of the system to the left of R _AB .

[0116] Meanwhile, a small \Z ^* _S \ may be obtained during a reverse fault, if S ₃ connects the IMDG to bus B. For such a case, the initial response of a conventional 67POS element can correctly identify the fault direction. The previously-discussed misoperation of the 67POS element due to the IMDGs' fault behavior occurs several cycles after the beginning of the fault when the IMDG current decays and 4 T ^* experiences a slow transition, in a manner similar to the curve shown in FIG. 6B. As such, assertion of a 67POS element may be made contingent upon a high rise of the fault current or a fast variation of T within a one-cycle interval before the element picks up.

[0117] Referring simultaneously to FIG. 11 , shown there generally as 1100 is an exemplary logic diagram for identifying the direction of symmetrical faults, in accordance with at least one embodiment. The logic diagram of FIG. 11 shows a Boolean circuit using impedance, current and phase data from the system to implement a method by which R _AB may identify the direction of symmetrical faults. Briefly, a reverse fault condition may be signalled when either of the following two conditions is satisfied:

1) The magnitude of \Z _S ^* \ exceeds a defined threshold;

or

2) T indicates a reverse fault direction;

and either

i) -Γ indicates a too-fast variation within a time frame; or

ii) The fault current \Γ | indicates a too-fast variation within a time frame.

(The time frame may be a one-cycle interval for either i) or ii) ).

The threshold used to compared \Z _S ⁺ \ may be defined according to results obtained for forward faults that cause maximum voltage and minimum current variations. For example, close-in bolted forward faults, when the system to the left of R _AB is weak, typically lead to the highest \Z ^* _S \ and so may be used to set the threshold. The insignificant fault current of the electronically- coupled DG may enable use of the threshold to determine the fault direction if the IMDG is not connected to bus B. If an IMDG is in service, a conventional 67POS element that is supervised by the change of the fault current and 4. determines the fault direction. The setting K in FIG. 11 is selected such that the fault trigger for an embodiment is robust against noise and other non-fault transients. In identifying reverse fault conditions, other embodiments may include other conditions that those noted in FIG. 11 , may include weighting schemes for one or more conditions or may not include one or more of the conditions in FIG. 11. It will be appreciated that an embodiment may implement the logic diagram shown in FIG. 11 in discrete components, an application specific integrated circuit, in a software implementation when digital values for the inputs are provided, or in other known hardware or software implementation techniques.

EXEMPLARY EVALUATION DATA OF A DIRECTIONAL ELEMENT

[0118] Having discussed various embodiments of a directional element described herein, this section examines how embodiments may perform in various fault conditions of the microgrid discussed above with respect to FIG. 1. The studies include various fault and relay locations, fault resistances and electronically-coupled DG's PFs and are carried out for both autonomous and grid-connected modes. The speed of the directional element of an embodiment depends on the length of the window used for phasor measurement-normally one or a half cycle of the power frequency. This speed may be adequate even for instantaneous overcurrent relays.

A, Asymmetrical Faults

[01 9] Referring to FIG. 12A, shown there generally as 1200 is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to phase fault in the presence of a distributed generation power source, in accordance with at least one

embodiment. As shown, FIG. 12A illustrates Z _s ^~ measured by R67 for the fault conditions discussed above in relation to FIGs. 2A, 2B, 3A, and 3B (e.g., a fault at bus B6, which is in the reverse direction for R67). Referring simultaneously again to FIG. 1 , since there is no load at bus B7, l ₂ is equal to /·, for R67. The negative-sequence component of the 7.5 MW-DG2 current was examined for a variety of faults and did not exceed 11 A under transient conditions.

Therefore, considering a safety factor of approximately 30% plus and assuming a maximum 15 A negative-sequence current for the DG2, k may be set to approximately 1328 Ω. Since the DG2 is the only component connected to the lower feeder after R67, the operating point should lie outside the central circular area shown in FIG. 10A. Hence, Z ^~ _s is safely out of the shaded forward zone in FIG. 12A and the directional element of an embodiment correctly detects a reverse fault. The fluctuation of Z _s ^~ shown in FIG. 12A occurs since the angle of the small negative-sequence current of the DG2 is not regulated by the control system. [0120] Referring to FIG. 12B, shown there generally as 1201 is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to phase fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 12B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 12A (e.g., a fault a bus B6, which is in the reverse direction to relay R67), except that FIG. 12B illustrates conditions under a conventional power generation source instead of a distributed generation power source. As illustrated, the superimposed negative sequence impedance measured by R67 still functions correctly to be outside the forward zone, so as to detect a reverse fault.

[0121] Referring to FIG. 13A, shown there generally as 1300 is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to ground fault in the presence of a distributed generation power source, in accordance with at least one

embodiment. As shown, FIG. 13A illustrates Z ^~ _s measured by R15 for the fault conditions discussed above in relation to FIGs. 4A and 4B (e.g., a fault at bus B2, which is in the reverse direction for R15). Referring simultaneously again to FIG. 1 , the maximum 121 A load current passes through R15 when the 7.5 MW DG2 of bus B7 does not inject power and all of the loads connected to the lower feeder are supplied by other sources. Considering a security margin of approximately 25% for overloads, / ₂ may be set to approximately 132 Ω. Only the load and the 7.5 MW DG2 are connected to the lower feeder after R15 for the fault at bus B2. Therefore, as shown in 13A, Z _s ^~ is situated in the load region of the impedance plane, detecting a reverse fault and avoiding erroneous tripping on the lower feeder.

[0122] Referring to FIG. 13B, shown there generally as 1301 is a diagram illustrating an exemplary operation of a directional element for an asymmetric phase to ground fault in the presence of a conventional power source, in accordance with at least one embodiment. FIG. 13B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 13A (e.g., a fault a bus B2, which is in the reverse direction to relay R15), except that FIG. 13B illustrates conditions under a conventional power generation source instead of a distributed generation power source. As illustrated, the superimposed negative sequence impedance measured by R15 still functions correctly to be outside the forward zone, so as to detect a reverse fault.

[0123] Referring to FiG. 14A, shown there generally as 1 00 is a diagram illustrating an exemplary operation of a directional element for a reversed phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment. As shown, FIG. 14A illustrates Z _s ^' measured by R67 for the fault conditions discussed above in relation to FIGs. 6A, 6B, and 6C (e.g., in the context of FIG. 1 , a fault at bus B6, which is in the reverse direction for R67). Since an IMDG is represented by a single impedance in the negative-sequence domain, the superimposed negative-sequence impedance does not vary after the fault. Hence, unlike the positive-sequence torque angle that switches regions during the fault discussed above in relation to FIG. 6B, Z _s ^' remains substantially constant. In addition, as discussed above in relation to FIG. 9C, Z _s ^~ is located inside the first quadrant, which is outside the forward zone in FIG. 14A, and therefore the lower feeder is not tripped.

[0124] Referring to FIG. 14B, shown there generally as 1401 is a diagram illustrating an exemplary operation of a directional element for a reverse phase to ground fault in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 14B illustrates the operation of the system architecture of FIG. 1 under the same fault conditions as was discussed for FIG. 14A (e.g., a fault a bus B6, which is in the reverse direction to relay R67), except that FIG. 14B illustrates conditions under a conventional power generation source instead of a distributed generation power source. As illustrated, the superimposed negative sequence impedance measured by R67 still functions correctly to be outside the forward zone, so as to detect a reverse fault.

[0125] Referring FIG. 15A, shown there generally as 1500 is a diagram illustrating an exemplary operation of a directional element for the phase to phase fault of FIG. 7 in the presence of a distributed generation power source, in accordance with at least one

embodiment. As discussed above in relation to FIG. 7 and FIG. 1 , the fault condition in that scenario was at bus B6, which is in the reverse direction to relay R12. As shown in FIG. 15A, the superimposed negative sequence impedance measured by R12 using a directional element of an embodiment functions correctly and is outside the forward zone, so as to detect a reverse fault.

[0126] Referring to FIG. 15B, shown there generally as 1501 is a diagram illustrating an exemplary operation of a directional element for the phase to phase fault of FIG. 7 in the presence of a conventional power generation source, in accordance with at least one embodiment. FIG. 15B appears similar to FIG. 15A, indicating that the superimposed negative sequence impedance measured by R12 similarly functions correctly for conventional power sources, so as to be outside the forward zone and detect a reverse fault. B. Symmetrical Faults

[0127] Referring to FIG. 16, shown there generally as 1600 is a diagram illustrating an exemplary operation of a directional element for a reverse symmetric fault and a close-in balanced forward fault in the presence of a distributed generation power source, in accordance with at least one embodiment. As discussed above, in a directional element of an embodiment, the logic shown in FIG. 11 may be used to detect the direction of symmetric faults in power systems having distributed generation units.

[0128] To illustrate how such logic may be used, reference again is made to the symmetric fault conditions discussed above in relation to FIGs. 5A-5C (e.g., in the exemplary system

architecture of FIG. 1, a symmetric fault at bus B6, which is in the reverse direction for relay R12). The results obtained for the weakest grid and closest bolted forward fault may be used to set the threshold of \Z _S ^* \ for relay R12. As illustrated in FIG. 16, the dashed line represents \Z ^* _S \ measured by R12 for a close-in forward symmetrical fault when the impedance of the 115 kV source at the substation is increased to 500 Ω. This is may not be a practical source impedance and may result in a voltage drop of approximately 17% (or more) across the system, but may represent a conservative worst case scenario.

[0129] As shown in FIG. 16, \Zt\ of R12 for the symmetric fault discussed in relation to FIGs. 5A-5C is also plotted by a solid line and is safely above the maximum possible \Z _S ^* \ for a forward fault. Therefore, referring simultaneously to FIG. 11 , the upper input of the right-most OR gate is high and detects a reverse fault and prevents tripping of R12.

C. Unbalanced Microgrid

[0130] Referring to FIG. 17, shown there generally as 1700 is a table illustrating an example where unbalanced loads were used in the exemplary system of FIG. 1 to compare the operation of an existing directional element with a directional element, in accordance with at least one embodiment. Since the negative-sequence component of fault currents in systems with electronically-coupled DGs are very small, the negative-sequence current of unbalanced loads can impact protection schemes that rely on sequence currents, including a directional element. To compare the operation of the conventional directional element with a directional element discussed herein, the loads of the system in FIG. 1 may be changed to those shown in the table of FIG. 17.

[0131] Referring to FIG. 18A, shown there generally as 1800 is a diagram illustrating an exemplary operation of a traditional directional element in the unbalanced system of FIG. 17 for a phase to ground fault in the presence of a distributed generation power source, in accordance with at least one embodiment. In an exemplary scenario, an AG fault may be placed at bus B4 when the 7.5 MW-DG2 operates at 60% of its nominal power at bus B7. The superimposed negative-sequence current of R15 is 0.011 kA and is only half of the negative-sequence current caused by the load imbalance. Hence, despite the 133.7° negative-sequence torque angle for the superimposed quantities, the 21.1° torque angle, for the load's negative-sequence voltage and current, makes the total torque angle of a conventional 67NEG element 78.7°, shown as being in the forward fault [-90°,+90°] range 1810a. Therefore, R15 may falsely detect a forward fault.

[0132] In contrast, referring to FIG. 18B, shown there generally as 1801 is a diagram illustrating an exemplary operation of a directional element used in the exemplary system of FIG. 1 for the phase to ground fault of FIG. 18A, in accordance with at least one embodiment. In such system, Z ^' s used by a directional element of an embodiment results in an indication in the reverse zone, within the load region that had been illustrated earlier in relation to FIG. 9B.

[0133] For simplicity and clarity of illustration, where considered appropriate, reference numerals may have been repeated among the FIGs. to indicate corresponding or analogous elements or steps. In addition, numerous specific details have been set forth in order to provide a thorough understanding of the exemplary embodiments described herein. However, it will be understood by those of ordinary skill in the art that the embodiments described herein may be practiced without these specific details, in other instances, certain steps, signals, protocols, software, hardware, networking infrastructure, circuits, structures, techniques, well-known methods, procedures, and components have not been described or shown in detail in order not to obscure the embodiments generally described herein.

[0134] Furthermore, this description is not to be considered as limiting the scope of the embodiments described herein in any way. It should be understood that the detailed description, while indicating specific embodiments, are given by way of illustration only, since various changes and modifications within the scope of the disclosure will become apparent to those skilled in the art from this detailed description.

[0135] It will be appreciated that embodiments relating to circuits, algorithms, calculations, processes, methods, calculations, devices, modules, networks, and systems of this disclosure may be implemented in a combination of any of electronic circuits, hardware, firmware, software, or applications. [0136] Firmware, software, applications, and modules may be provided in executable software code that is stored in a physical storage device and executed on a processor of a device.

Embodiments may be implemented in one or more computer programs executing on one or more programmable computing devices including at least one processor, a data storage device (including in some cases volatile and non-volatile memory and/or data storage elements), at least one communications interface (e.g., a network interface card for wired or wireless network communications), at least one input device, and at least one output device.

[0137] Embodiments, control circuits, logic, computing devices, and methods as described herein may also be implemented as a transitory or non-transitory computer-readable storage medium configured with software code, wherein the storage medium so configured causes a computing device to operate in a specific and predefined manner to perform at least some of the functions as described herein. The medium may be provided in various forms, including one or more diskettes, compact disks, tapes, memory devices, wireline transmissions, satellite transmissions, Internet transmission or downloadings, magnetic and electronic storage media, digital and analog signals, and the like. The software code's useable instructions may also be in various forms, including compiled, non-compiled, bytecode, or other forms in which the instructions may be interpreted or translated. Software code is applied to input data to perform functions described herein and generate calculations, output signals, and output information. The calculations, output signals, and output information may be provided to one or more output devices.

[0138] The algorithms, methods, calculations, and processes described herein may be executed in different order(s). Interrupt routines may be used. Data may be stored in volatile and non-voiatile devices described herein and may be updated by the hardware, firmware and/or software. It will further be appreciated that all processes, algorithms, steps etc. as described herein may be conducted in a single entity. For example calculations for equations and processes described herein may be provided in the device itself. Such calculations may be conducted by one or more modules in the device. The disclosure as such provides a method of operating a device and / or a method for a function operating on the device. Alternatively, such calculations may be conducted in an off-site location (e.g. a design laboratory) and the resulting circuits and calculations can be provided to the device.

[0139] Any circuit may be implemented in whole or in part through a combination of analog and / or digital components. In a circuit, an element may be connected to another element either directly or through another circuit. When a first element is identified as being connected to another element, that first element itself may be considered to be a "circuit".

[0140] Where a component (e.g. an assembly, device, circuit, etc.) is referred to above, unless otherwise indicated, reference to that component should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the disclosure.

[0141] Additional aspects and advantages of embodiments discussed in this disclosure will be apparent in view of the preceding description.

[0142] All references, publications, and patent applications mentioned or identified in this specification are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually incorporated by reference.

[0143] While the foregoing disclosure has been described in some detail for purposes of clarity and understanding, such disclosure is provided by way of example only. It will be appreciated by one skilled in the art, from a reading of the disclosure that various changes in form and detail of these exemplary embodiments may be made without departing from the scope of the disclosure. For example, it should be understood that acts and the order of the acts performed in the processing described herein may be altered, modified and/or augmented (whether or not such steps are described in the claims, figures or otherwise in any sequential numbered or lettered manner) yet still achieve the desired outcome. While processes or blocks are presented in a given order, alternative examples may perform routines having steps, or employ systems having blocks, in a different order, and some processes or blocks may be deleted, moved, added, subdivided, combined, and/or modified to provide alternatives or sub-combinations. Each of these processes or blocks may be implemented in a variety of different ways. Also, while processes or blocks are at times shown as being performed in series, these processes or blocks may instead be performed in parallel, or may be performed at different times.

[0144] In this disclosure, where a threshold or measured value is provided as an approximate value (for example, when the threshold is qualified with the word "about"), a range of values will be understood to be valid for that value. For example, for a threshold stated as an approximate value, a range of about 25% larger and 25% smaller than the stated value may be used.

Thresholds, values, measurements and dimensions of features are illustrative of embodiments and are not limiting unless noted. Further, as an example, a "sufficient" match with a given threshold may be a value that is within the provided threshold, having regard to the approximate value applicable to the threshold and the understood range of values (over and under) that may be applied for that threshold.

[0145] As used herein, the wording "and/or" is intended to represent an inclusive-or. That is, "X and/or Y" is intended to mean X or Y or both. Moreover, "X, Y, and/or Z" is intended to mean X or Y or Z or any combination thereof.

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