How To Calculate Overvoltages And Interference Voltages

Transcription

1 Calculation of overvoltages an interference voltages When installing telecom or computer systems close to heavy current equipment or traction power supplies, careful thought has to be given to the possibility of overvoltages or interference voltages that coul be cause by power lines or system frequency phenomena. The coupling that is possible between the interfering an affecte lines is usually of an electrical an/or magnetic nature. Analysis of galvanic, capacitive an inuctive coupling, plus the calculation of possible overvoltages an interference voltages, helps inustrial operators to make their electrical installations safe an immune to such phenomena. E lectrical apparatus an systems manufacture an/or sol within the European Union require certification that shows that they conform to EU requirements. Before a prouct is allowe to carry the CE marking proving conformity, it has to satisfy a number of conitions. EU irectives exist for the certification. The first one the irective for machines has been vali since January, 995. The secon is the EMC irective, which went into force as regars CE marking on January, 996. The thir irective, which eals with the electrical safety of lowvoltage apparatus, will become effective with regar to CE marking on January, 997. All electrical an electronic equipment, systems an installations intene for the European market have to meet the requirements lai own in the relevant EMC irectives. In recent years, interference voltages have been the cause of numerous isturbances in airport control towers an rail traffic control centers. In view of the potential anger of such interference, it is clearly essential for equipment to satisfy at least the minimum requirements of the pertinent EU irectives. Overvoltages that coul occur in installations site close to power lines an traction power supply systems have to be calculate in avance of their occurrence to ensure the require level of electrical safety an electromagnetic compatibility (EMC). The overvoltages occurring as a result of capacitive, resistive an inuctive coupling are calculate separately an the resultant overvoltage obtaine by vectorial aition of the iniviual values. Limits for the permissible overvoltages Overvoltages that occur on control or communications cables are not allowe to iminish safety (protection against electric shock must be ensure), impair the installation or interfere with its operation. The conitions regaring protection against electric shock are fulfille in Sween through compliance with the following limits specifie for telecom, signal an control cables: r. Sten Bena ABB Inustrial Systems AB U rms 50 V; t s U rms 430 V; 0.5 < t < s U rms 650 V; t 0.5 s The permitte limits with regar to equipment protection are specific to the particular apparatus an as such are a component of its esign. Permitte values for unisturbe operation also epen on the esign of the apparatus an how it is run. Telecommunications systems present a special problem, since they work with very low voltages an in a wie frequency ban. The permitte limits for telephone lines are efine by so-calle psophometric values. Psophometric coefficients take account of the way in which frequencies affect the human ear. The psophometric total voltage U p is given by the following relationship: U = p Σ( pu) p f f 800 () In the above equation, U f is the voltage for the frequency f, p f the psophometric weighting factor for f, an p 800 the psophometric weighting factor for the frequency 800 Hz. Telephone calls are transmitte within a frequency ban lying between 300 an 3,400 Hz. The permitte psophometric limits for telephone lines are 30 mv for the common moe voltage (CMV) an 0.5 mv for the normal moe voltage (NMV). The calculation of the psophometric normal moe voltage epens on the connecte equipment. If the circuit configuration is not known, it will not be possible to etermine NMV. In, the psophometric weighting factor accoring to CCITT is shown by the re curve, the weighting factor use in the USA by the blue curve. The ifference between the two curves is minimal. Galvanic coupling A galvanic coupling is establishe when two circuits have a common coupling impeance. A typical case is shown in. U X ZC = UG Z + Z G L () In practice, the common coupling impe- 34 ABB Review 8/996

2 0 ln πεl RR (3) p Psophometric weighting factor p accoring to the CCITT (re), an the US equivalent (blue) f Frequency ance Z C is mae up of the resistance an reactance an has a much lower value than the sum of the impeances Z G an Z L (Z C << Z G + Z L ) Hz f Capacitive coupling The consequences of capacitive coupling are greatest in analyses of high-frequency conitions. A lack of knowlege of their effect or inattention to the problem uring the installation of equipment can lea to serious isturbances occurring later. It is therefore immensely important to unerstan this kin of coupling an to be able to calculate the coupling conitions on the basis of the coupling impeance. The capacitance between two conucting components epens on the value of their charge an on the potential ifference. When calculating the capacitance, only the potential ifferences are consiere. When analyzing the relationships between two conuctors, two infinitely long cyliners are assume for the purpose of calculation. Capacitance between two parallel conuctors If ε is the ielectric constant an the two raii R an R are both much smaller than the istance between the conuctors 3, the capacitance is given by: With ientical thin conuctors having the same cross-sectional area (R = R = R), the capacitance is: πεl (4) ln ( / R) Capacitance between concentric conuctors The capacitance between two cyliners 4 is given by the relationship: πεl (5) ln ( R / R ) Capacitance between two conuctors lai above the earth The easiest way to calculate the capacitive coupling in such a case is to analyze two mirror-inverte conuctors 5. The formula use to calculate the capacitance C between two conuctors lai above the earth 6 is as follows: πεl (6) ln ( / R) This is ientical to eqn (4). If the conuctor raii are given by R an R, an their height above the earth by h an h, respectively, 5 then: h h ln R R πεl ( h + h) ln ( h h ) + (7) Galvanic coupling via a common impeance Z c Capacitance between two parallel conuctors 3 Capacitance between concentric conuctors 4 istance between conuctors R Conuctor raius U Voltage h istance to U = const Z G Z L U = const Z C R U R R U R Z U X h h ABB Review 8/996 35

3 tors, if any, are insulate from one another. I is the worst-case current in the interfering h r r h h p p r pk r p k k h k line an k a reuction factor use to take account of cable sheaths an conuctors lying in close proximity. If the connecte equipment is sensitive to frequencies lying above the funamental frequency, the harmonic currents in the power line have to be calculate. Such a calculation r p r pk k is very complex an yiels unreliable results. Measurement of the inuce EMF is therefore recommene. General analysis carrie out with the help of mirror-inverte conuctors (, an p, k ) h r istance between conuctors istance between conuctors an earth istance between mirror-inverte conuctors Common moe voltages prouce by inuctive means Common moe voltages prouce inuctively require special attention uring the calculation of overvoltages an interference voltages cause by power frequency phenomena. The overvoltages an interference voltages cause by capacitive coupling to live conuctors, on the other han, can be neglecte at least when the cables are shiele. In aition to the capacitive coupling to live conuctors, resistive coupling also occurs. The preominant case here is the coupling cause by the earthing resistance of the transformer substation (increase earth potential). The inuce electromotive force (EMF) is given by: E = ω MI k (8) In this relationship E is the inuce EMF in the conuctor of the control cable in V, ω (= πf, f in Hz) is the angular frequency an M is the mutual inuctance in H between the interfering conuctor an the control cable. It is assume that the cables sheaths an the ajacent metallic conuc- 5 The current in the interfering circuit The interfering an the affecte circuit consist of one or more conuctors, with the earth acting as the return conuctor. (The case in which the earth oes not act as the return conuctor will be ealt with later.) When consiering a high-voltage threephase AC power line, this applies only to the zero-sequence component of the current. The positive- an negative-sequence components o not return via the earth, an their consequences are minor ue to the relatively small istance between the outer conuctors. As a rule, I is use to esignate the sum of the zero-sequence currents (= 3I 0 ) proviing the control cable oes not lie immeiately next to the power line. If it oes lie in close proximity to the line, ifferent inuctions for each outer conuctor must be reckone with when sensitive equipment has been installe. Two conuctors locate at the same height above the earth 6 Table : Approximate values for the resistivity ρ Soil type ρ in Ωm h istance between conuctors istance between conuctors an earth Carbon, mineral layer 3 Light clay, alluvion 5 0 Chalk, marl, clay without alluvion 0 00 Quartz, limestone, sanstone, clay slate 00,000 Rocks, slate, granite, pebbles,000 0,000 h 36 ABB Review 8/996

4 mh/km α 7 5 mh/km ρ = 0.5 Ωm m 8 Mutual inuctance as a function of α 7 Mutual inuctance/length istance between interfering an affecte line α See eqn 0 5 mh/km Mutual inuctance as a function of at 50 Hz ρ Mutual inuctance/length istance between interfering an affecte line Soil resistivity ρ = 50 Ωm m Mutual inuctance as a function of for 6 /3 Hz 9 9 It is assume that the zero-sequence currents occurring at various fault locations in the installation being consiere are known. Often, calculations have to be carrie out for several fault locations in orer to etermine the maximum EMF. Mutual inuctance Assuming that the earth is homogeneous an that the interfering an the affecte line run parallel to each other, the mutual inuctance will be: M = l = 0 7 ln + 0.6ρ 06 f (9) l In this equation, M is the mutual inuctance in H, the quotient of the mutual inuctance/length in H/m (also a function of α), l the length of the parallel run, an the istance between the interfering an the affecte line in m. α = ωµ / 0 ρ (0) In eqn (0), ω is the angular frequency (= πf, f in Hz), µ 0 (= 4π 0 7 ) the permeability in empty space in H/m an ρ the soil resistivity in Ωm. The quantity is a complex number. As a rule, its phase angle is of no interest an the absolute value is sufficient for the calculation. The mutual inuctance is epenent upon the soil resistivity, measurements of which have been carrie out over a number of years. Where there are no values of any practical use available, a mean value can be use. (For most of Sween, for example, a value of 500 Ωm may be use. An exception is Scania in southern Sween, where the mean value is 00 Ωm). Approximate values for the soil resistivity are given in Table. In ensely populate areas, a large part of the return current flows through the pipes an other metallic conuctors which are usually burie in the earth. This factor can be taken into account by using a lower, fictitious value for the soil resistivity. Useful support for the calculations is provie by iagrams showing the mutual inuctance as a function of α 7 or for ifferent values of soil resistivity (for 50 Hz 8 an 6 3 Hz 9 ). If is not constant over the total length of the control cable (eg, the istance to the interfering line fluctuates), the run has to be broken own into sub-sections an separate calculations performe for each. The partial inuctances are afterwars summate. The values for are calculate uner the assumption that the interfering line is infinitely long. If it is too short in comparison with /α, the actual value for the coupling can be consierably lower than. In prac- ABB Review 8/996 37

5 tice, the same formula is also use for short lines; however, this gives a value for which is too high. Special conitions in transformer substations When an earth-line gri an other metallic conuctors are burie in the earth, the major part of the return current will flow through the earthing network. Here, too, the starting point is, although it has to be multiplie by a reuction factor which epens on the istance between the interfering an the affecte line. The value of correspons to approximately the value of the mutual inuctance when it is assume that the return current flows in a plane at a epth of /α below the earth s surface. This assumption is largely true for substations with a burie earth-line gri. Measurements carrie out in substations have shown that for a value for α of 0.05m (corresponing to ρ = 0.5 Ωm), the mutual inuctance will agree closely with the measure values at 50 Hz. Since more comprehensive measurement results are not available, it is recommene that the curve ifferent railway electrification systems Reuction factor k = in arrangement c Catenary 3 Sectioning point Booster transformer 4 Return line a b c 4 8 for ρ = 0.5 Ωm be use, as for calculations In a traction power supply system the for substations with an earth-line gri. When the interfering an the affecte line lie at ifferent heights, the actual istance between the lines can be use for the calculation since this will assure a sufficient accuracy for. current flows via the contact (catenary) line to the locomotive, the return current flowing through the tracks an earth. To reuce the current flowing through the earth 0, socalle booster transformers with a transformation ratio of : are use. The purpose of these transformers is to force the return Reuction factors Efforts are mae in many installations to reuce the inuce voltages. The reuction factor achieve by appropriate measures on the interfering line is esignate k, the factor corresponing to the measures taken for the control cable k. In general, the istance between the interfering line an the control cable is so large that the mutual influence of k an k can be neglecte. The resultant reuction factor is then the prouct k k. Proviing the equivalent resistance of their earth electroes is low an the conuctivity in the connecting link is goo, a goo reuction is achieve with top earth lines in substations. However, in many cases the equivalent resistance is so high that for current to flow through the tracks or return line. A return line hanging between the masts at about the same height as the contact line prouces the best results. The combination of return line an booster transformer gives a value for k of between 0.4 an 0.5. The conitions are ifferent when power an control cables are lai together with a protective earth line. The influence of interference voltages on the control cable is suppresse by: Proviing shieling, plus armour for the control cable when necessary Shieling other control cables in the same run Running protective conuctors close to the control cable safety reasons a value of k = has to be assume The reuction factor k is then calculate for the calculations. using the following metho: assuming that the shiel or the metal sheath is groune at 0 both ens, an possibly at other locations, a current with the following value passes through them: 3 I El = ( r + jωl ) l + R j () In this equation, E (= k I ) is the electrical fiel strength in V/m in the earth along the length of the control cable (isregaring the reactions cause by the currents in the control cables an in their protective conuctors), r the quotient given by iviing the equivalent resistance of the sheath circuit by its length (in Ω/m), L the quotient given by the inuctance of the sheath circuit ivie by the length (in H/m), R j the summate resistance at the earthing locations in Ω an l the length of the control cable in m. The current I causes an electrical fiel strength on the insie of the sheath, between it an the conuctor, equal to I Z k, in which Z k is the quotient of the transfer im- 38 ABB Review 8/996

6 Power an control cables lai in the same cable uct a b c Protective earth line Control cable Parallel three-wire cable or groups of single-conuctor cables lai closely together in triangular configuration peance of the sheath an the length (in Ω/m). At low frequencies this quotient is approximately equal to the quotient of the C resistance an the length, ie Z k r k. Neglecting R j, k has the value: k ZI k = = E r Zk + jωl () Here, r is the equivalent resistance of the sheath uner AC conitions. At power system frequency r is approximately equal to the C resistance of the sheath, this being calculate from the cross-sectional area an the resistivity of the shiel an metal sheath. For cables which have no armour mae of flat steel wire, L is given by the following formula: L = µ 0 π ln 4 α (3) In this formula is the iameter of the shiel or of the metal sheath in m. As the logarithmic relationship shows, the equivalent inuctance epens only to a relatively small egree on α an on the fluctuations in cable iameter. For control cables with normal imensions, the following approximation can be use for the calculation: L =.5 mh/km for ρ 500 Ωm L =.0 mh/km for ρ 00 Ωm L =.6 mh/km for ρ 0.5 Ωm (transformer substations) a c b In the case of shiele, plastic-insulate control cables of types EKFR, r is much greater than ω L, with the result that a reuction factor of k is obtaine. With cables of type EKFR, EKLR an FKLR, the k values lie between 0.87 an 0.99 for 50 Hz, ρ = 00 Ωm an L = mh/km. Goo k values are obtaine when several shiele control cables are run together. At power system frequency, a close approximation of k is given by: k Here, r tot is the quotient of the resultant C resistance an the length in Ω/m when all the shiels are connecte in parallel. L is then given (in µh/m) by: L (5) In this equation, b m is the mean geometric istance between the control cables in the run in m an m the mean geometric iameter of the cable shiels in m. Example Control cable, type EKFR 4.5 mm mm A shiel m b m L rtot (4) rtot + jω( L L) µ 0 m b = π ln = 7.5 mm, r k =.8 Ω/km = 9.5 mm = 00 mm m =.6 mh/km (transformer substation) L = 0.46 mh/km The reuction factor k changes with the number of cables. For example, for one cable it is 0.99, an for 0 cables 0.3. The value of k calculate using eqn 4 is also vali for non-shiele cables in the same run. The conuctors in the control cables can be inclue in the calculation of r tot proviing they are groune at both cable ens. In aition, any number of protective earth lines can be taken into account which are in the same cable run. In the case of heavy-uty protective earth lines (eg, with a cross-sectional area A Cu = 5 mm ), the effect of the line inuctance is restricte. k L /L is therefore vali for iniviual control cables run together with such a PE line. When a protective earth line having a iameter of about 0 mm is lai at a istance of 50 mm from the control cable, k 0.3. If the control cable has armour mae of flat steel wire, the inuctance of the sheath will be increase consierably. ue to the permeability of steel, the reuction factor epens on the fiel strength of the earth along the length of the control cable. When more than one cable are run together, it shoul be note that the reuction ue to the flat steel wire armour is vali only for those conuctors which are enclose by the armour. A better value for the reuction factor k is obtaine when a heavy-uty protective earth line ( 0. m) is lai next to the control cable. If an even larger reuction is require, a special esign will be necessary, for example with an increase amount of steel in the armour an improve conuctivity for the shieling. Power cable an control cable in the same cable uct When calculating the inuce voltages for control cables which are lai in the same uct as power cables, it is not possible to assign inepenent reuction factors to the ifferent cable sheaths. When the cables are lai as shown in, however, a simple metho of calculation can be use uner the given conitions. The following prerequisites apply: Cable sheaths an protective earth lines are connecte together an to the earth at least at each en of the cable. The fault occurs close to the far en of the power cable (worst case). The influence of flat steel wire armour aroun the power cables is neglecte (the steel is magnetically saturate in the event of short-circuit currents). In cases of multiple power cables, the istance between each power cable an the control cable is assume to be approximately the same. ABB Review 8/996 39

7 r r r r Configuration with two-wire lines The protective earth line is locate close to the control cable ( 0. m). The best safety factor is obtaine in this way. The inuce voltage is then: E = p 3 I r k k l (6) In this formula I is the sum of the zero-sequence currents in A an r p is the quotient obtaine by iviing the equivalent resistance by the length of the metal sheath or shieling of the power cable (alternatively, the parallel-connecte cable sheaths or shiels) in Ω/m. k is the reuction factor for the flat steel wire armour of the control cable. k is etermine by first calculating the fiel strength, given by I r p k 3, the value for k then being taken from the corresponing iagrams [6] (Sweish version). If the control cable has no flat steel wire armour, a value of is use for k. k 3 is a reuction factor which epens on the istance between the control cable an the power cables, the cross-sectional area A 3 of the protective earth line an the shieling of the control cable. If A 3 = 00 mm an = 0.5 m, a value of approximately 0.5 can be use for k 3. l is the length of the parallel run in m. Mutual inuctance between two two-wire lines In the configuration shown in the earth oes not serve as the return conuctor. In the first circuit, represents the conuctor an the return conuctor; the same is true for the secon circuit. The lines have the length l. Proviing the length of the lines is much greater than the istance between the conuctors, it is possible to neglect the connections at the beginning an en of the circuit (blue lines in ). Given these conitions, the mutual inuctance will be: M = M + M + M + M l r r M = ln π r r µ 0 (7) (8) Here, M is the mutual inuctance in H, l the length of the parallel lines in m, µ 0 (= 4π 0 7 ) the permeability in H/m, an r, r, r an r the istances in m. The mutual inuctance M can have either a positive or a negative value. In the configuration shown in, M has a positive value. This means that the currents given in the respective lines have to have the currents inuce as a result of the mutual inuctance M ae to them. In the event of the actual operating current having an opposite polarity to the assume current, the mutual inuctance M will be negative. The inuce voltage in circuit is calculate as follows: E = IωM (9) Summing up As of January, 996, all electrical an electronic components having a irect function, plus apparatus, systems an installations, have to conform to the European Union EMC irective referre to earlier, ie, the proucts must be constructe in a way that ensures that they neither cause excessive interference nor are unuly affecte by electromagnetic isturbance. The manatory CE marking shows conformance with all relevant irectives. These minimal requirements, however, o not guarantee interference-free performance of highly complex installations site close to traction power supplies an power transmission lines. In such cases, it is necessary to etermine the overvoltages in the cables in orer to ensure both electrical safety an electromagnetic compatibility. ABB Inustry an rives has been applying such regulations to its proucts for a long time. Electrical an electronic components with a irect function, as well as apparatus, systems an installations from ABB satisfy, as a minimum, the requirements set own in the new legislation. An where ABB consiers it expeient, the company even employs its own, more rigorous regulations. In view of this, oler ABB apparatus, systems an installations are also esigne to satisfy at least the requirements set own in the EMC irective. ABB has its own in-house EMC test facility in which the appropriate measurements can be carrie out. Although it is use primarily to test new ABB equipment an systems, the facility may also be mae available to other equipment venors. References [] S. Bena: The role of interference-free electronics in process automation. ABB Review /9, [] S. Bena: The new EMC stanars of the European Community. ABB Review /9, [3] S. Bena: Earthing an boning in large installations. ABB Review 5/94, 9. [4] S. Bena: Existing EMC stanars review an experience. ABB Review 5/95, [5] S. Bena: Earthing, grouning an shieling of process control an communication circuits. ABB Review 0/95, [6] S. Bena: Interference-free electronics. ISBN / ABB Report No. 3BSE R000 (Sweish version: 3BSE R000). Author s aress r. Sten Bena ABB Inustrial Systems AB S-767 Västerås Sween Fax: ABB Review 8/996