Surge protection device and system

Abstract

The present invention discloses a surge protection device and system, comprising: an impedance device, a voltage-limiting surge protector and a switch-type surge protector; the impedance device is connected in parallel with the voltage-limiting surge protector, and the parallel branch of the impedance device and the voltage-limiting surge protector is connected in series with the switch-type surge protector to form a discharge channel for lightning impulse current; wherein the series branch of the impedance device and the switch-type surge protector forms a discharge channel for freewheeling current. The surge protection device and system of the present invention can effectively improve the multiple pulse tolerance capability and avoid arc extinguishing failure.

Description

Technical Field

[0001] The present invention relates to the technical field of overvoltage protection, and in particular to a surge protection device and system. Background Art

[0002] A surge protection device is an overvoltage protection device connected to electronic equipment or low-voltage power distribution systems. It is mainly used to discharge surge currents caused by lightning current, lightning induction and switching operations, and limit the amplitude of overvoltage, thereby preventing surge currents from damaging other equipment in the circuit.

[0003] In order to improve the surge current discharge capability of the surge protection device, it is usually necessary to test the surge protection device installed between the LPZ0 (Lightning Protection Zone, LPZ for short) and the LPZ1 zone using a simulated lightning impulse current (impact current waveform is 10 / 350us) in accordance with the IEC 61643-11 standard or the GB / T 18802.1 standard. The lightning impulse current has the characteristics of long waveform time and high energy, which requires the surge protection device to have a strong charge transfer capability in order to effectively protect the equipment in the circuit.

[0004] In order to meet the above test requirements, existing surge protection devices include the following two types:

[0005] (1) Multi-pipe varistor parallel type surge protection device: Due to the limitation of manufacturing process, it is difficult to produce a larger varistor, and the current carrying capacity of the varistor is directly related to its own size. Therefore, the current carrying capacity of a single varistor is generally in the range of 10 to 100kA (the impulse current waveform is 8 / 20us). In order to meet the test of lightning impulse current Iimp = 12.5kA (10 / 350us), at least 4 varistors of 20kA (8 / 20us) are required to be connected in parallel. However, because the varistor is a semiconductor device, when the energy of the lightning impulse current is too large, the varistor is easily broken down due to overheating, and the surge protection device has the problem of poor multiple pulse tolerance.

[0006] (2) Single gap + arc extinguishing device type surge protection device: This surge protection device uses a single gap to discharge lightning impulse current. When the power frequency continuous current is caused, the arc is limited by the arc extinguishing device to cut off the continuous current. This surge protection device has a strong ability to discharge lightning impulse current, but due to the existence of a blind spot for continuous current interruption, when the continuous current generated by the protected system is large enough (usually in the kiloampere level), the arc is easily sent to the arc extinguishing device by electromagnetic force or the gas generated by the thermal corrosion of the insulating material by the current. However, when the continuous current is hundreds of amperes or tens of amperes, the arc is not easily sent to the arc extinguishing device, which will lead to arc extinguishing failure.

[0007] In summary, existing surge protection devices have the problems of poor multiple pulse tolerance and low arc extinguishing reliability. Summary of the invention

[0008] In view of the above problems, a surge protection device and system of the present invention can effectively improve the multiple pulse tolerance capability and avoid arc extinguishing failure.

[0009] In order to solve the above technical problems, a surge protection device of the present invention includes: an impedance device, a voltage-limiting surge protector and a switch-type surge protector; the impedance device is connected in parallel with the voltage-limiting surge protector, and the parallel branch of the impedance device and the voltage-limiting surge protector is connected in series with the switch-type surge protector to form a discharge channel for lightning impulse current; wherein the series branch of the impedance device and the switch-type surge protector forms a discharge channel for follow-on current.

[0010] As an improvement of the above scheme, the surge protection device also includes: a thermal protector connected to the series branch where the switch-type surge protector is located; the thermal protector is activated when the temperature reaches a preset temperature threshold, cutting off the connection with the series branch where the switch-type surge protector is located.

[0011] As an improvement of the above solution, the thermal protector includes a temperature fuse, a resettable thermostat, a thermal disconnector, a bimetallic thermal circuit breaker, a mechanical thermal disconnect mechanism or a low melting point alloy disconnector.

[0012] As an improvement of the above solution, the low-melting-point alloy disconnector comprises an elastic metal sheet, one end of which is welded to the switch-type surge protector by means of a low-temperature alloy.

[0013] As an improvement of the above solution, the impedance device includes a resistor or a series branch consisting of the resistor and an inductor.

[0014] As an improvement of the above solution, the voltage-limiting surge protector includes a varistor or a suppression diode; the switch-type surge protector includes a gas discharge tube, a semiconductor discharge tube or a discharge gap.

[0015] As an improvement of the above solution, the discharge gap includes a graphite discharge gap, an insulating tube and two copper electrodes; wherein,

[0016] The graphite discharge gap includes two graphite electrodes, a polytetrafluoroethylene annular film disposed between the two graphite electrodes, and an insulating ring sleeved on each graphite electrode;

[0017] Both ends of the insulating tube are provided with internal threads;

[0018] The outer walls of the two copper electrodes are provided with external threads;

[0019] The graphite discharge gap is sleeved in the insulating tube, and the external threaded parts of the two copper electrodes are screwed into the two ends of the insulating tube to achieve assembly.

[0020] As an improvement of the above scheme, the switch-type surge protector includes n discharge gaps and n-1 capacitors, and the n discharge gaps are connected in sequence to the voltage-limiting surge protector; the first ends of the n-1 capacitors are respectively connected to the second end of the voltage-limiting surge protector, and the second ends of the n-1 capacitors are respectively connected one-to-one to the second ends of the 1st discharge gap to the n-1th discharge gap among the n discharge gaps; wherein n≥2, and n is an integer.

[0021] To solve the above technical problems, the present invention also provides a surge protection system, comprising: m surge protection devices of any one of the above types and m-1 capacitors; the m surge protection devices are connected in series in sequence, and the m-1 capacitors are respectively connected in parallel with the switch-type surge protectors in the 1st to m-1th surge protection devices among the m surge protection devices; wherein m≥2, and m is an integer.

[0022] A surge protection device and system provided by the present invention have the following beneficial effects: an impedance device is connected in parallel with a voltage-limiting surge protector, and a parallel branch of the impedance device and the voltage-limiting surge protector is connected in series with a switch-type surge protector to form a discharge channel for a lightning impulse current (or surge current); when a lightning impulse current occurs, since the current of the lightning impulse current is relatively small, the lightning impulse current is discharged through the series branch of the impedance device and the switch-type surge protector; when the lightning impulse current gradually increases, the voltage across the impedance device gradually increases, and when the voltage across the impedance device exceeds the action voltage of the voltage-limiting surge protector, the voltage-limiting surge protector shunts part of the lightning impulse current, and the lightning impulse current is discharged through the impedance device, the voltage-limiting surge protector and the switch-type surge protector. Since the impedance device can share all the lightning impulse current when the lightning impulse current occurs, and the voltage at both ends of the impedance device exceeds the action voltage of the voltage-limiting surge protector, the voltage-limiting surge protector shares part of the lightning impulse current, the surge protection device can effectively reduce the lightning impulse current load of the voltage-limiting surge protector and improve the multiple pulse tolerance of the surge protection device; at the same time, the voltage-limiting surge protector can limit the overvoltage caused by the lightning impulse current to a lower level, so that the lightning impulse current can be effectively discharged. Furthermore, in the surge protection device, the impedance device also forms a discharge channel for the follow-up current with the switch-type surge protector. When the power frequency follow-up current occurs, the impedance device can limit the follow-up current value to a lower current value range, and then when the power frequency follow-up current still has the follow-up current after the first current zero point, the switch-type surge protector can safely cut off the follow-up current, so that the surge protection device has a reliable follow-up current blocking capability and can effectively extinguish the arc. In addition, the surge protection device adopts a limiting surge protector and a switching surge protector to achieve the protection performance and safety performance that can only be achieved by multiple varistors in the existing surge protection device, which greatly reduces the volume of the surge protection device and saves the manufacturing cost of the surge protection device. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a structural schematic diagram of an embodiment of a surge protection device of the present invention.

[0024] Figure 2 It is a structural schematic diagram of another embodiment of a surge protection device of the present invention.

[0025] Figure 3 It is a structural schematic diagram of a connection mode of a thermal protector in a surge protection device of the present invention.

[0026] Figure 4 It is a structural schematic diagram of another connection method of a thermal protector in a surge protection device of the present invention.

[0027] Figure 5 It is a structural schematic diagram of another embodiment of a surge protection device of the present invention.

[0028] Figure 6 It is a schematic structural diagram of a surge protection device of the present invention having two discharge gaps and one capacitor C1.

[0029] Figure 7 It is a schematic diagram of the structure of the surge protection device of the present invention having n discharge gaps and n-1 capacitors C1.

[0030] Figure 8 It is a structural schematic diagram of an embodiment of a surge protection system of the present invention.

[0031] Fig. 9 It is a structural schematic diagram of an embodiment of a discharge gap in a surge protection device of the present invention. DETAILED DESCRIPTION

[0032] Many specific details are described in the following description to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from the description, and those skilled in the art can make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0033] The technical solution of the present invention is clearly and completely described below in conjunction with specific embodiments and drawings.

[0034] Please see attached Figure 1 , is a schematic structural diagram of an embodiment of a surge protection device of the present invention.

[0035] The surge protection device comprises: an impedance device SI, a voltage-limiting surge protector PMOV and a switch-type surge protector SG; the impedance device SI is connected in parallel with the voltage-limiting surge protector PMOV, and a parallel branch of the impedance device SI and the voltage-limiting surge protector PMOV is connected in series with the switch-type surge protector SG to form a discharge channel for lightning impulse current; wherein the series branch of the impedance device SI and the switch-type surge protector SG forms a discharge channel for freewheeling current.

[0036] In the present invention, the surge protection device has a T1 end and a T2 end, both of which are made of copper sheets. When the surge protection device is tested using a lightning surge waveform, the lightning surge waveform flows into the surge protection device from the T1 end, and the surge protection device discharges the lightning impulse current and the follow-on current to the outside from the T2 end.

[0037] In the specific implementation process, the surge protection device is suitable for single-phase system, single-phase branch line system, multi-phase system and any circuit that requires lightning surge protection. For example, the surge protection device can be connected between L-PE and N-PE of a single-phase system, or between L-PE, N-PE and LN, or between L1-L2, L2-L3, L1-L3, L1-PE, L2-PE, L3-PE and N-PE of a three-phase system, or between L1-PE, L2-PE, L3-PE and N-PE of a multi-phase system, where L is the phase line / live line, N is the neutral line / zero line, and PE is the protection line / ground line.

[0038] Compared with the prior art, in the surge protection device of the present invention, the impedance device SI is connected in parallel with the voltage-limiting surge protector PMOV, and the parallel branch of the impedance device SI and the voltage-limiting surge protector PMOV is connected in series with the switch-type surge protector SG to form a discharge channel for the lightning impulse current (or surge current); when the lightning impulse current occurs, since the current of the lightning impulse current is small, the lightning impulse current is discharged through the series branch of the impedance device SI and the switch-type surge protector SG; when the lightning impulse current gradually increases, the voltage across the impedance device SI gradually increases, and when the voltage across the impedance device SI exceeds the action voltage of the voltage-limiting surge protector PMOV, the voltage-limiting surge protector PMOV shunts part of the lightning impulse current, and the lightning impulse current is discharged through the impedance device SI, the voltage-limiting surge protector PMOV and the switch-type surge protector SG. Since the impedance device SI can share all the lightning impulse current when the lightning impulse current occurs, and the voltage-limiting surge protector PMOV only shares part of the lightning impulse current when the voltage across the impedance device SI exceeds the operating voltage of the voltage-limiting surge protector PMOV, the surge protection device can effectively reduce the lightning impulse current load of the voltage-limiting surge protector PMOV and improve the multiple pulse tolerance capability of the surge protection device; at the same time, the voltage-limiting surge protector PMOV can limit the overvoltage caused by the lightning impulse current to a lower level, so that the lightning impulse current can be effectively discharged. Furthermore, in the surge protection device, the impedance device SI also forms a discharge channel for the freewheeling current with the switch-type surge protector SG. When the power frequency freewheeling current occurs, the impedance device SI can limit the freewheeling current value to a lower current value range. Then, when the power frequency freewheeling current still has a freewheeling current after the first current zero point, the switch-type surge protector SG can safely cut off the freewheeling current, so that the surge protection device has a reliable freewheeling current blocking capability and can effectively extinguish the arc. In addition, the surge protection device uses a limiting surge protector PMOV and a switch-type surge protector SG to achieve the protection performance and safety performance that can only be achieved by multiple varistors in the existing surge protection device, which greatly reduces the volume of the surge protection device and saves the manufacturing cost of the surge protection device.

[0039] Optionally, in the surge protection device, the voltage-limiting surge protector PMOV includes a varistor or a suppression diode; the switching surge protector SG includes a gas discharge tube, a semiconductor discharge tube or a discharge gap; the impedance device SI includes a resistor or a series branch consisting of a resistor and an inductor, and the impedance device SI can also be a structural device with a certain resistance value, for example, a spiral conductor with inductance and resistance value formed by mechanical processing; a resistor of a certain shape wound by a metal wire with a higher resistivity, etc.

[0040] Next, the structure of the surge protection device is described by taking the voltage-limiting surge protector PMOV as a varistor PMOV1, the switching surge protector SG as a graphite discharge gap SG1, and the impedance device SI as a series branch composed of a resistor R and an inductor L as an example.

[0041] like Figure 2 FIG. 1 is a schematic structural diagram of another embodiment of a surge protection device of the present invention.

[0042] In this embodiment, the size of the varistor PMOV1 is 34mm×34mm, the nominal varistor voltage is 300V, and the surge withstand capability is 40kA (8 / 20us); the graphite discharge gap SG1 is a 0.4mm air gap formed by two graphite electrodes. The resistor R and the inductor L are wound with 6J20 type resistance wire, wherein the resistivity of the resistance wire is 1.4Ω·m, the resistance value of the resistor R is about 1Ω, and the inductance value of the inductor L is about 1.1μH.

[0043] In this embodiment, the series branch formed by the resistor R and the inductor L is connected in parallel with the varistor PMOV1 to form a discharge channel for the lightning impulse current, and serves as a freewheeling path in the first half wave of the power frequency freewheeling that may be caused by the lightning impulse current; the series branch formed by the resistor R and the inductor L is connected in parallel with the graphite discharge gap SG1, and the series branch formed by the resistor R and the inductor L is used to limit the current value of the freewheeling current of the graphite discharge gap SG1, and forms a discharge channel for the freewheeling current with the graphite discharge gap SG1.

[0044] See also Figure 3 , is a structural schematic diagram of a connection method of a thermal protector in a surge protection device of the present invention.

[0045] In order to improve the safety of the surge protection device, the surge protection device also includes: a thermal protector TP connected to the series branch where the switch-type surge protector SG is located; the thermal protector TP is activated when the temperature reaches a preset temperature threshold, and cuts off the connection with the series branch where the switch-type surge protector SG is located.

[0046] like Figure 3 and Figure 4 As shown, in this embodiment, the thermal protector TP can be connected between the switch type surge protector SG and the T2 terminal, or can be connected between the parallel branch formed by the impedance device SI and the voltage limiting type surge protector and the switch type surge protector SG. When the temperature of the thermal protector reaches a preset temperature threshold, the thermal protector TP is activated to cut off the connection with the switch type surge protector SG, so that the surge protection device is in a safe failure state, avoiding secondary fire disasters caused by damage or burning of the surge protection device due to excessive temperature.

[0047] Optionally, the thermal protector TP includes a temperature fuse, a resettable thermostat, a thermal disconnector, a bimetallic thermal circuit breaker, a mechanical thermal disconnect mechanism or a low melting point alloy disconnector. The structure of the surge protection device is described below by taking the thermal protector as a temperature fuse as an example.

[0048] like Figure 5 FIG. 1 is a schematic structural diagram of another embodiment of a surge protection device of the present invention.

[0049] In the surge protection device, the thermal protector is a temperature fuse TP1, the rated operating temperature of the temperature fuse TP1 is 125°C, the actual fusing temperature is 121°C±3°C, the rated current is 30A, and the surge withstand capacity is 40kA (8 / 20us); the impedance device is a resistor R. When the temperature of the temperature fuse TP1 reaches its fusing temperature, the temperature fuse TP1 is actuated to cut off the connection with the graphite discharge gap SG1, so that the surge protection device is in a safe failure state.

[0050] Optionally, the low melting point alloy disconnector in the thermal protector comprises an elastic metal sheet, which is stamped from 0.5 thick phosphor bronze and has a width of 10 mm. The elastic metal sheet is welded to the switch type surge protector through a low temperature alloy, wherein the melting point of the low temperature alloy is 145°C ± 3°C. When the low temperature alloy melts, the elastic metal sheet bounces off the switch type surge protector.

[0051] In order to improve the continuous current breaking capability of the switch type surge protector, the switch type surge protector can be composed of two or more switch type surge protectors.

[0052] Next, taking the switch type surge protector as the discharge gap and the limiting type surge protector as the varistor as an example, combined with the attached Figure 6 and attached Figure 7 This structure will be described in detail.

[0053] Please see attached Figure 6 and attached Figure 7The switch-type surge protector includes n discharge gaps SG2 and n-1 capacitors C1, the n discharge gaps SG2 are connected to the varistor PMOV1 in sequence; the first ends of the n-1 capacitors C1 are respectively connected to the second ends of the varistor PMOV1, and the second ends of the n-1 capacitors C2 are respectively connected one-to-one to the second ends of the first discharge gap to the n-1th discharge gap among the n discharge gaps SG2; wherein n≥2, and n is an integer.

[0054] In this embodiment, n discharge gaps SG2 in the switch-type surge protector are connected in sequence with the varistor PMOV1 to form a lightning impulse current discharge channel, and serve as a freewheeling path in the first half-wave in which the lightning impulse current may cause power frequency freewheeling; the n discharge gaps SG2 and the resistor R form a freewheeling current discharge channel; wherein the first ends of the n-1 capacitors C1 are respectively connected to the second ends of the varistor PMOV1, and the second ends of the n-1 capacitors C1 are respectively connected one-to-one with the second ends of the first discharge gap to the n-1th discharge gap, so that the surge pulse voltage formed by the lightning surge waveform can be coupled, and each discharge gap SG2 in the n discharge gaps SG2 can be triggered at the same time, thereby improving the freewheeling breaking triggering capability of the n discharge gaps SG2 in the switch-type surge protector.

[0055] In this embodiment, the discharge gap SG2 can use a gas discharge tube with a diameter of 12 mm, a height of 6 mm, a DC breakdown voltage of 600 V, a surge withstand capability of 20 kA (8 / 20 us), and a follow current breaking capability of 50 A at 255 V; the capacitor C1 uses an ordinary ceramic chip capacitor with a capacitance of 1000 pf and a rated withstand voltage of 2000 V.

[0056] Please see attached Figure 8 The present invention also provides a surge protection system, which comprises: m surge protection devices of any one of the above and m-1 capacitors C2; the m surge protection devices are connected in series in sequence, and the m-1 capacitors C2 are respectively connected in parallel with the switch-type surge protectors in the first to m-1th surge protection devices among the m surge protection devices; wherein m≥2, and m is an integer. The impedance device in each surge protection device is a series branch of a resistor R and an inductor L in series, the voltage-limiting surge protector is a varistor PMOV1, and the switch-type surge protector is a discharge gap SG2.

[0057] In this embodiment, m surge protection devices are connected in series in sequence, which can reduce the resistance value of the impedance device in each surge protection device, reduce the lightning impulse current load of the voltage-limiting surge protector in each surge protection device, and achieve the reduction of the lightning impulse current load and the segmented discharge of the follow-on current, so that the surge protection system has stronger stability, while achieving the reduction of the lightning impulse current load of the limiting surge protector and reliable arc extinguishing; and, the m-1 capacitors C2 are used to couple the surge pulse voltage formed by the lightning surge waveform, which can trigger the switch-type surge protector in the m surge protection devices, thereby improving the follow-on current breaking triggering capability of the switch-type surge protector.

[0058] In the above embodiments of the present invention, Fig. 9 As shown, the discharge gap of the present invention includes a graphite discharge gap, an insulating tube 21 and two copper electrodes 31; wherein the graphite discharge gap includes two graphite electrodes 11, a polytetrafluoroethylene annular film 12 arranged between the two graphite electrodes 11, and an insulating ring (not shown in the figure) sleeved on each graphite electrode 11; both ends of the insulating tube 21 are provided with internal threads; the outer walls of the two copper electrodes 31 are provided with external threads; the graphite discharge gap is sleeved in the insulating tube 21, and the external threaded parts of the two copper electrodes 31 are screwed into the two ends of the insulating tube 21 to achieve assembly. In this embodiment, each graphite electrode 11 has a diameter of 18 mm and a thickness of 2 mm; the thickness of the polytetrafluoroethylene annular film 12 is 0.4 mm, the outer diameter is 20 mm, and the inner diameter is 15 mm; the outer diameter of the insulating ring is 20.5 mm, the inner diameter is 18.2 mm, and the thickness is 1.8 mm, and the function of the insulating ring is to facilitate assembly; the inner diameter of the insulating tube 21 is 20.6 mm and the length is 10 mm; the diameter of each copper electrode 31 is 20 mm and the thickness is 3 mm, and the copper electrode is exposed about 0.2 mm after being screwed into the insulating tube.

[0059] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Therefore, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A surge protection system, characterized in that: include: m surge protection devices and m-1 capacitors; The m surge protection devices are connected in series in sequence, and the m-1 capacitors are respectively connected in parallel with the switch-type surge protection devices in the 1st to the m-1th surge protection devices among the m surge protection devices; wherein m≥2, and m is an integer; The surge protection device includes: an impedance device, a voltage-limiting surge protector and a switch-type surge protector; the impedance device is connected in parallel with the voltage-limiting surge protector, and the parallel branch of the impedance device and the voltage-limiting surge protector is connected in series with the switch-type surge protector to form a discharge channel for lightning impulse current; wherein the series branch of the impedance device and the switch-type surge protector forms a discharge channel for freewheeling current; the impedance device includes a resistor R and an inductor L connected in series with each other, the resistance value of the resistor R is 1Ω, and the inductance value of the inductor L is 1.1μH.

2. The surge protection system according to claim 1, characterized in that: Also includes: A thermal protector connected to the series branch where the switch type surge protector is located; the thermal protector is activated when the temperature reaches a preset temperature threshold, and cuts off the connection with the series branch where the switch type surge protector is located.

3. The surge protection system according to claim 2, characterized in that: The thermal protector includes a temperature fuse, a resettable thermostat, a thermal disconnector, a bimetallic thermal circuit breaker, a mechanical thermal disconnect mechanism or a low melting point alloy disconnector.

4. The surge protection system according to claim 3, characterized in that: The low melting point alloy disconnector comprises an elastic metal sheet, one end of which is welded on the switch type surge protector by means of a low temperature alloy.

5. The surge protection system according to claim 1, characterized in that: The impedance device includes a resistor or a series branch formed by the resistor and an inductor.

6. The surge protection system according to claim 1, characterized in that: The voltage-limiting surge protector includes a varistor or a suppression diode; the switch-type surge protector includes a gas discharge tube, a semiconductor discharge tube or a discharge gap.

7. The surge protection system according to claim 6, characterized in that: The discharge gap comprises a graphite discharge gap, an insulating tube and two copper electrodes; wherein, The graphite discharge gap includes two graphite electrodes, a polytetrafluoroethylene annular film disposed between the two graphite electrodes, and an insulating ring sleeved on each graphite electrode; Both ends of the insulating tube are provided with internal threads; The outer walls of the two copper electrodes are provided with external threads; The graphite discharge gap is sleeved in the insulating tube, and the external threaded parts of the two copper electrodes are screwed into the two ends of the insulating tube to achieve assembly.

8. The surge protection system according to claim 1, wherein: The switch type surge protector comprises n discharge gaps and n-1 capacitors, the n discharge gaps are connected in sequence with the voltage limiting type surge protector; the first ends of the n-1 capacitors are respectively connected to the second ends of the voltage limiting type surge protector, and the second ends of the n-1 capacitors are respectively connected one-to-one with the second ends of the first discharge gap to the n-1th discharge gap among the n discharge gaps; wherein n≥2, and n is an integer.

Images