Switching Transients Application Example DIgSILENT PowerFactory * Abstract Therefore, transients have to be expected and are observed in the system during the change from the situation before to the situation after switching. Transients are abnormal patterns of current and voltage that have a limited duration. They frequently exceed the currents and voltages met during steady-state operation. In order to ensure a safe and reliable operation of the power system, electrical equipment has to be designed to withstand the stresses caused by transients. This example provides an introduction to switching transients. The application example contains various study cases for the investigation of electromagnetic transient (EMT) phenomena in such as transformer energistaion, overhead line energisation, fault and load switching as well as the analysis of transient recovery voltage in PowerFactory. The following topics and functionalities are discussed: Power System Modelling for Electromagnetic Transients, Electromag- The network model in Figure 1 is used to demonstrate netic Transients Simulation, Statistical Switching Anal- the use of PowerFactory for the analysis of switching transients. The network comprises parts of a meshed ysis. 400 kV transmission system and an underlying 110 kV sub-transmission system. 1 General Description The transmission system consists of five substations, a power plant and two large loads. The power plant is connected to the substation North via a 400 kV cable Switching operations in power systems are very com- system. The substations are interconnected by single mon and must not jeopardize the system’s reliability and double circuit overhead lines according to Figure and safety. Switching in power systems is necessary 1. for the following reasons and duties: The neighbouring network in the West is modelled by • Taking into or out of service some sections of the a voltage source with an equivalent short circuit power system, certain loads, or consumers. Typical ex- which acts as slack bus for the system. The transmisamples are: Energisation and de-energisation of sion system in the East is modelled by an equivalent overhead lines, cables and transformers, switch- load. Shunt reactors and capacitor banks are used for ing of shunt capacitor banks or shunt reactors. reactive power compensation. • Transferring the flow of energy from one circuit The 110 kV sub-transmission system comprises three to another, e.g. in a substation from one busbar substations which are connected to the Central subto another. station by overhead lines. Furthermore a wind farm • Isolating certain network components because is connected to the substation through a high voltage cable system. of maintenance or replacement. • Isolating faulted sections of the network in order to avoid damage and/or system instability. Examples are: terminal fault and short line faults. 2 Simulation Model Switching in electrical power systems re-configures the topology of an electrical network. It involves the The investigation of electromagnetic transients remaking and breaking of circuits and causes a distur- quires an accurate representation of relevant power system components. Depending on the transient bebance of the steady state energy flow. * DIgSILENT GmbH, Heinrich-Hertz-Str. 9, 72810 Gomaringen, Germany, www.digsilent.de DIgSILENT PowerFactory, r4594 1 Switching Transients Example ing analysed the network model should include: • Stray inductances and capacitances • Valid representation of the model for a frequency range which may vary from DC to several MHz • Electric arcing model The following subsections describe the models of the power system components of the transmission system • Non-linear saturation characteristics of induc- shown in Figure 1. tances • Distributed parameter line models 2 Generator GT-1 GT-2 0 C Bank ~ SG Power Plant 9 PP1 PP2 Load NE Central North-East Inactive Out of Calculation De-energised NPP-1 20 km Voltage Levels 400, kV 110, kV 33, kV 27, kV NPP-2 20 km North1 Load N Shunt Reactor 1 CE-1.1 25 km North2 West NC-1 100 km Load E-1 NC-2 100 km CE-1.2 25 km 0 WN 100 km East-1 Grid CE-2.1 30 km TR_C1 Load E-2 TR_C2 0 CE-2.2 30 km WC-1.1 100 km WC-1.2 100 km WC-2.1 100 km WC-2.2 100 km East-2 WC-1.3 100 km Wind Farm 8 WFT-1 WC-2.3 100 km WT 8 CE-3 12 km West 1 West 2 WF C4_1.1 C4_1.2 WFT-2 C1_1 C1_2 Figure 1: Single line diagram of the power system DIgSILENT PowerFactory, r4594 2 Switching Transients Example CCE-1-1 IS.R0.2 IS.R0.1 CB.R0 IS4.3 CNC-1_comp IS.R6.3 IS4.2 CB4 IS4.1 CE-1.1 25 km IS7.2 CB7 IS7.1 CE-1.2 25 km IS3.2 CB3 IS3.1 CE-2.2 30 km IS2.2 CB2 IS2.1 CE-2.1 30 km CB1 IS1.1 IS.R3.3 IS.R3.1 NC-2 100 km CB.R3 IS.R6.2 CB.R6 IS.R6.1 IS.R5.2 CB.R5 IS.R5.1 CNE-1 100 km IS.R3.2 CNE-2 100 km CCE-1-2 CNC1 IS.R5.3 IS7.3 IS.R1.3 IS6.3 CB.R4 CB.R1 IS.R1.1 IS6.1 IS.R4.2 IS.R4.3 TR_C2-MV TR_C2-HV WC-1.3 100 km CB.L2 IS3.3 TR_C1-MV TR_C1-HV CBS1 IS.L2.3 IS.L2.1 IS6.2 TR_C1 CBS2 CWC1_comp CB6 IS.L2.2 CWC1 TR_C2 IS.L3.2 CB.L3 IS2.3 IS5.1 CB5 IS5.2 CCE2-1 IS.R4.1 CCE2-2 IS.R1.2 Shunt Reactor IS.L3.1 IS5.3 CWC2 IS.L3.3 WC-2.3 100 km IS1.3 IS.L1.1 CB.L1 IS.L1.2 IS1.2 IS.L1.3 CE-3 12 km IS0.2 CB0 IS.L0.1 IS0.1 CB.L0 C1_1 C4_1.1 CCE-3 IS.L0.2 CWC-2_comp C4_1.2 C1_2 Figure 2: Detailed substation layout diagram of substation Central 2.1 Transmission Lines The transmission system contains the following overhead lines (OHL) and cable systems: • 400 kV double circuit OHL • 400 kV single circuit OHL • 400 kV double circuit cable system • 110 kV double circuit OHL • 110 kV single circuit cable system Both cables and overhead lines are modelled based on their geometry of the corresponding characteristics of conductors and insulation layers. Overhead Lines Overhead lines can be modelled based on their ge- Figure 3: 400 kV double circuit overhead line structure ometry and material characteristics of the conductors and earth return path in PowerFactory. The Y-values which are entered in PowerFactory corThe geometry is entered in PowerFactory using the respond to the average height of the conductor and X-Y coordinates of the phase conductors and ground ground wire along the line. The average height inwires as shown in Figure 3. The graph shows the ge- cludes the sag and is calculated as follows: ometry of the 400 kV and 110 kV double circuit overhead line being used in the network model (Figure 1). DIgSILENT PowerFactory, r4594 3 Switching Transients Example 2 βaverage = βtower − · πsag 3 Apart from the overhead line geometry the phase conductors and earth wires have to be defined. As input parameter the geometry of the corresponding conductor, its DC-resistance and bundling configuration has to be entered. The 400 kV overhead line is a bundled conductor type configuration and comprises 4 subconductors per phase. The 110 kV overhead lines are untransposed in this application example. Phase A Phase B Phase C upper middle lower upper The specific earth resistivity for the earth return path middle is assumed with 100 β¦π for all overhead lines which corresponds to a typical value [1]. Based on the lower above input parameters, PowerFactory calculates the impedance and admittance matrix for all phases of the Figure 4: Transposition of the 210 km long 400 kV OHL multiphase overhead line system. WC-1 and WC-2 The impedance and admittance matrix is then used to calculate the reduced impedance matrix, sequence impedances and corresponding distributed parameter High Voltage Cables line models which will be required for the switching The high voltage cables are modelled in a similar way. transients studies. The geometry of the single core cable and its correDepending on the frequency of the transient being in- sponding material characteristics are entered in Powvestigated, one of the following models will be used for erFactory. The following layers are included in the model of the single core cable: the EMT simulation: • Lumped parameter model • Conductor • Distributed parameter model with constant parameter (frequently known as Bergeron model) • Sheath • Distributed parameter model with frequency dependent parameter (frequently known as J. Marti model) • Insulation • Oversheath • Semiconducting layers Transposition The cross-section of the 400 kV single core cable is displayed in Figure 5. The geometry is entered by Due to the geometry of the overhead lines, the defining the thickness of each layer. Furthermore the impedances of each phase differ from each other. In resistivity, relative permittivity and permeability is enorder to mitigate unbalances in the system, overhead tered in PowerFactory. lines are usually transposed. In this example the transposition is modelled explicitly for the lines WC-1 and WC-2 between substation West and Central. The phasing is entered in the line coupling (ElmTow). Figure 4 shows the transposition of OHL WC-1 and WC-2. The other 400 kV overhead lines are transposed circuit wise in *.TypTow by selecting the option Transposition → Circuit Wise. By selecting this option the positive and zero sequence offdiagonal elements of the mutual sub-matrices between transposed circuits are eliminated. Figure 5: 400 kV single core cable DIgSILENT PowerFactory, r4594 4 Switching Transients Example The cables are layed directly in ground in flat formation with a distance of 0.7 m apart. Two cable systems connect the substation North with the Power Plant (see Figure 1). They are layed in parallel. The layout of the complete cable system is shown in Figure 6. The earth resistivity is assumed to be 100 β¦π. tion of the wind farm with the 110 kV terminal of the sub-transmission system. Saturation Model For simulating non-linear, electromagnetic transients such as the transformer energisation, the core saturation needs to be included in the model of the transformer. The saturation is defined in the transformer type. In this simulation model the magnetising branch of the 3winding transformer is placed at the start point. The magnetising branch of the 2 winding transformers is located between the primary and secondary side. Figure 6: 400 kV double circuit cable system laid in ground The non-linear flux-current relationship of the 2winding transformers is modelled using a polynomial approximation for the saturation curve. As an example As for overhead lines, internal routines calculate the for a saturation curve Figure 7 shown the magnetising impedance and admittance matrix of the cable system characteristic of the transformer WFT-1 in Figure 1. and all required parameters for steady state, dynamic The saturation characteristic of the 3-winding transand electromagnetic transient analysis. former is modelled based on open circuit measurement data. They are entered as RMS values (open cirLine Compensation cuit test). PowerFactory converted them internally to Shunt reactors are used for the compensation of the current-flux peak values to model the saturation charcharging current of the 400 kV cable system and the acteristic properly. 200 km single circuit and 210 km long double circuit overhead line connecting substation West and Cen- The residual flux of the transformer is taken into consideration using a parameter event. The residual flux tral. is entered in PowerFactory in the dq-frame. The transThey are connected directly to the line at its sending formation of the a-b-c fluxes in the dq-frame is docuand receiving end and are designed to compensate mented in the Technical Reference of the transformer. approximately 70 % of the charging current. Furthermore, hysteresis can be included in the transformer core model. 2.2 Transformers The network model comprises two-winding and threewinding transformers [6], [7]. Transformer Types 3-winding transformers (TR_C1 and TR_C2) are installed in substation Central connecting the 110 kV sub-transmission system to the 400 kV transmission system. The transformers have a rated power of 275 MVA. The vector group is YN0yn0d11. The substation PowerPlant in the North of the network includes a YNd5 1600 MVA transformer which connects the generator’s 27 kV terminal with the 400 kV terminal of the transmission grid. Figure 7: Saturation characteristic of transformer Furthermore two YNd5 50 MVA transformers are installed in the wind farm and connect the 33 kV substa- DIgSILENT PowerFactory, r4594 5 Switching Transients Example 2.3 Generator NPP-1 The synchronous machine of the power plant has a rated power of 1560 MVA and a nominal voltage of 27 kV. Switching transients will not be investigated in close vicinity of the generator. Therefore the model is not further described here. NNPS2_comp North 1 The wind farm has a rated power of 100 MVA and is represented by an aggregated wind turbine as shown in Figure 1. The wind turbine is a full-scale converter model. The converter is implemented in PowerFactory using a static generator element, which is configured to operate as a current controlled voltage source. The converter currents are controlled using a classical dq rotating reference system current controller in the EMT simulation. 2.4 NPP-2 NNPS1_comp NWN1 IS2.2 IS4.2 CB2 CB4 IS2.1 IS4.1 ISa.2 ISb.2 CBa CBb ISa.1 ISb.1 IS1.1 IS3.1 CB1 CB3 IS1.2 IS3.2 NNC2 Loads The loads are modelled as constant impedance loads. North 2 2.5 Substations WN NC The network model comprises 5 substations: • Substation West Figure 8: Substation North with 1 1/2 breaker method • Substation North The substation layout includes two-breaker and 1 1/2breaker configuration. The two-breaker configuration • Substation Power Plant is shown in Figure 2. In this case the circuit breaker, branch disconnector and instrumental transformers • Substation Wind Farm are duplicated in each branch. Busbar interchange All substations are modelled in detail as shown in Fig- and isolation of one busbar for maintenance is possiure 2 for substation Central. The substation models ble. One branch breaker can be taken out for maininclude busbars, circuit breakers (CB), disconnector tained at any time without interrupting operation. switches, surge arresters and shunt reactors for reacThe 1 1/2-breaker design is applied in Figure 8. Fewer tive power compensation. breakers are needed here for the same flexibility as Generally busbars, circuit breakers and disconnec- above. Isolation without interruption is possible. All tor switches are modelled as ideal elements without breakers are normally closed. Uninterrupted supply is impedances and as ideal switches. If required, bus- thus maintained even if one busbar fails. bars will be modelled as distributed parameters lines. Relevant stray inductances and capacitances of substation equipment (such as instrumental transformers) 2.5.1 Circuit Breakers will also be considered if necessary. Circuit breakers (CB) are modelled as ideal switches. Arcing models and models for re-ignition are available in PowerFactory but will not be considered in the study cases which are discussed in this example. • Substation Central For Transient Recovery Voltage (TRV) studies the DIgSILENT PowerFactory, r4594 6 Switching Transients Example breaker capability curve is modelled according to IEC 62271-100 with a 2-parameter or 4-parameter curve depending on the voltage level and circuit breaker rating. 2.5.2 Surge Arresters Surge arresters are used to protect electrical equipment in substations, such as transformers, circuit breakers and bushings, against the effects of overvoltages caused by incoming surges. Such overvoltages can be caused by a direct or nearby lightning strike and other electromagnetic transients such as e.g. switching operation in the power supply system. Surge arresters present a nonlinear resistor and are characterised by a highly non-linear U-I curve. During normal operating voltages surge arresters have an extremely high resistance and a relatively low resistance during transient overvoltages. Metal oxide arresters (MOA) are usually used for surge arresters and in most cases are connected from phase to ground. The charactersitic U-I curve of an surge arrester which is necessary for an EMT study is usually provided in the vendor datasheet and is entered in PowerFactory in tabular form. Figure 9: Surge arrester π − πΌ characteristic 2.5.3 Reactive Power Compensation For reactive power compensation a shunt reactor is installed in substation Central. The rated reactive power of the shunt reactor is 50 Mvar per step. The reactor is switchable and has 4 steps. Thus, the shunt reactor can consume a maximum of 200 Mvar. A capacitor bank is installed at the substation NorthEast with a rated reactive power of 50 Mvar per step. It is also switchable and has 10 steps. DIgSILENT PowerFactory, r4594 7 Switching Transients Example 3 Switching Transients be at its peak in steady state operation. However, due to the initial condition (Ψ equals zero) the flux starts at zero. As a result the curve of the flux Ψ is shifted by Switching in electrical power systems re-configures Ψπ upwards in the first cycle of the transient. Thus, the flux starts at zero and then reaches a maximum of the network topology for the following purposes: 2Ψπ in the first cycle as indicated in Figure 10 [1]. • Isolation and Earthing Taking into a account a residual flux of Ψπ in the iron • Busbar-Transfer Switching core, the curve is shifted upwards even further as indicated in Figure 10 and reaches a maximum peak • Load Switching values of Ψπ + 2Ψπ . The magnetization curve is now • Fault-Clearing operating in the saturated region and the relationship between the flux Ψπ and the current π are no longer The following switching transients are analysed in this governed by a linear relationship. This causes high application example: and distorted inrush currents as shown in the graph. • Transformer Energisation • Overhead Line Energisation ψ ψR + 2 ψm ψ, B 2 β ψm • Inductive Load Switching ψR • Fault-Current Interruption Switching H, i The transient phenomena following the above switching actions will result in abnormal patterns of current and voltage during the transient. The root causes of the abnormal currents and voltages are described in the following section. 3.1 u i Saturation For simulating electromagnetic transients such as transformer inrush currents or ferro-resonance, reactor / transformer core saturation needs to be included in the model of the transformer. The non-linear behaviour of a typical transformer iron core is shown in Figure 10 [1]. The solid lines represent the steady state voltage and flux and current relationship when no saturation occurs. The dashed lines represent the behaviour during a transient, when the core is being saturated (e.g. during transformer energisation). Figure 10: Saturation and inrush current 3.2 Travelling Waves When investigating transient and high-frequency steady-state phenomena, it is necessary to account for the distributed-parameter nature of conductors such as overhead lines, cables and in the case of high frequency transients, even of busbars. The magnetic flux Ψ, representing the time-integral of the voltage, lags in steady state the sinusoidal waveform of the voltage by 90β . Being still in the linear part of the saturation characteristic, the current is sinusoidal as well. Thus, the current is proportional to the voltage. Typically, for low frequency steady-state analysis, lines and cables are modelled using the well-known lumped parameter equivalent circuit, thus neglecting the distributed nature without loosing too much accuracy in the results. In reality, a current in a conductor having even a very short length, needs a certain time to travel from its sending end to the remote end [1]. When a completely demagnetised transformer is energised the flux Ψ in the iron core is zero at the instant of switching. The instantaneous voltage in Figure 10 is zero at this instance. Due to the 90β phase shift between the flux Ψ and the voltage, the flux ought to When an overhead line or cable is energised from the grid as shown in Figure 11, a voltage and current surge are injected into the line. Before the breaker is closed, the voltage at both ends of the line is zero. Upon breaker closing at the sending end of the line, DIgSILENT PowerFactory, r4594 8 Switching Transients Example the voltage changes instantaneously from zero to the supply voltage π’π . At the receiving end of the line, the voltage π’π is still zero since the surge needs a certain time to travel from the sending to the receiving end of the line. The surge propagates with the speed π£ along the line and arrives at the sending end of the line with a delay equal with the propagation time π . The propagation speed π£ is a function of the line inductance πΏ′ and capacitance πΆπΏ′′ . For a lossless line the propagation speed π£ is calculated by the following equation [1]: π’π π’π π’π π’π π’π π’π Figure 11: Voltage surge line energisation During the transient, the surge is travelling back and forward until damping and attenuation will eventually result in a steady state condition. At each electrical boundary the surge is reflected and refracted as The propagation time constant π is dependent on the indicated in Figure 11. Electrical boundaries arise propagation speed v and the line length when the surge impedance of the network components change, e.g. at an overhead line - cable tran√οΈ sition or at the open end of a line. π π = = π · πΏ′ · πΆ ′ π£ π£=√ 1 ′ πΏ · πΆ′ Figure 11 shows the voltage surge during the line energisation of an ideal single phase conductor for three time steps of the transient: π1 π2 π1 π2 • 1: Breaker is closed at the sending end • 2: Surge propagates from sending to receiving end π’1 π’π π2 > π1 : • 3: Reflected surge travels back to sending end Transient voltage and current surges are thus a function of time and location along the line. Distributed parameter line models are therefore required to analyse such phenomena. Depending on the transient being investigated, line models with constant or frequency dependent parameters are used in simulation models. π’π π’1 π’2 π’2 π1 π1 π2 ππ The constant distributed parameter model in PowerFactory is based on Bergeron’s method, which calculates the voltages and currents at one end of the line based on the voltage and current at the other end de- Figure 12: Travelling voltages and currents at surge layed in time. For further information refer to the tech- impedance jump location nical reference of the line models [4]. With the exception of lossless and distortion-less lines, the characteristic impedance ππΆ and the propagation constant πΎ are frequency dependent. To handle frequency-dependent parameters for overhead lines, PowerFactory uses the approach proposed by J.Marti [4]. For cable systems the Universal Line Model is available and offers a high accuracy and a phasedomain formulation [5]. DIgSILENT PowerFactory, r4594 The reflected and refracted voltage and current surge are a function of the incoming voltage and current waveform and the surge impedance on both sides of the boundary. For an ideal surge with a very steep rise / very short rise time, the reflected and refracted surges are calculated according to the following equations: 9 Switching Transients Example interruption must wait for the zero crossing of the current. Depending on the type of circuit-breaker, the device may not be ready to interrupt at the first occurring current zero after contact separation. 2 · π2 π’2 = π’1 π1 + π2 π + π1 π’π = 2 π1 + π2 For SF6 circuit breakers, it takes a certain minimum arcing time before the electric arc extinguishes in the circuit breaker because sufficient cooling pressure of the extinction medium must be available and sufficient contact distance must be reached. For vacuum circuit breakers sufficient contact distance has to be reached in order to extinguish the electric arc [2]. π1 2 · π1 = π2 π1 + π2 π − π2 ππ = 1 π1 + π2 Typical surge impedances for common power system components are: πΏπ • Overhead lines: 200 β¦ to 500 β¦ • Cable systems: 40 β¦ to 70 β¦ πΆπ π’π π’πΏ πΆπΏ πΏπΏ • Transformers: 1 πβ¦ to 10 πβ¦ 3.3 Transient Recovery Voltage (TRV) Figure 14: Frequency spectrum of load side oscillation Transient recovery voltages (TRV) arise both at fault interruption and load switching. In both cases a circuit breaker is switching off. The circuit breaker opening procedure is explained in Figure 13. The switching command is usually initiated automatically by a relay that detects a fault in the system or a switching command from the control center to trigger a change in the operation scenario of the network. Fault currents and inductive load currents (e.g. disconnection of shunt reactors) lag the voltage by around 90β . Thus, the instantaneous voltage at both sides of the breaker pole is at its peak when the current is interrupted at the current zero-crossing. Immediately after current interruption a transient voltThe tripping command activates the operating mech- age will oscillate on the load side and source side. anism and through its kinematic chain separates the Figure 14 shows the equivalent circuit of the load and contacts in the circuit-breaker. After a certain opening source side after the switching action. time, the circuit-breaker arcing contacts will open in all The source side voltage is composed of two compothree poles. nents, the power frequency voltage (e.g. 50 Hz) and the transient voltage oscillating between πΏπ and πΆπ . Breaker state The frequency of the transient part of the voltage is calculated by the following formula: 1 1 ππ = · √οΈ 2π πΏπ · πΆπ Switching command Contacts start to separate Arc extinction in last pole ο Current interruption Contacts fully separated arcing time The oscillation frequency of the voltage on the load side is defined by πΏπΏ and πΆπΏ and is a single frequency oscillation in case of linear inductive load. Total break time Figure 13: Circuit breaker operation switching off 1 1 ππ = · √οΈ 2π πΏπΏ · πΆπΏ Upon contact separation, an arc is formed in the in- The Transient Recovery Voltage (TRV) is the voltage terruption chamber of each pole. The actual current across the open circuit-breaker contacts which arises DIgSILENT PowerFactory, r4594 10 Switching Transients Example immediately after current interruption. It is the differπΏL = 1000 mH; πΆL = 2 πF ence between the voltage-to-earth at the source side π’π and load side π’πΏ : Figure 15 shows that the TRV starts from zero at current zero, makes an excursion to the momentary power-frequency voltage, overshoots in a damped π’TRV = π’π − π’πΏ oscillatory manner and continues to oscillate until a steady-state condition is reached. The frequency of The TRV always consists of at least two oscillatory the load side oscillation is ππΏ = 3558.8 π»π§ and of components, the source-side and load-side frequency the source side ππ = 73.9 π»π§. Important paramecomponent. Depending on the switching action (e.g. ters in a TRV study are the maximum transient recovshunt reactor switching, terminal fault, short line fault ery voltage π and the rate of rise of recovery voltπΆ interruption) the TRV contains multiple oscillation fre- age (RRRV). Both parameters are required for circuit quencies which superimpose. breaker design studies. The exemplary TRV for a single phase circuit is shown Current chopping may need be considered as well in in Figure 15 assuming the following values: the TRV study for some types of circuit breakers or switching transients. πΏS = 17 mH; πΆS = 273 πF 200,00 100,00 0,00 -100,00 -200,00 -300,00 0,00 2,00 Source: Phase Voltage SP in kV 4,00 6,00 8,00 [ms] 10,00 0,00 Load: Phase Voltage SP in kV 4,00 6,00 8,00 [ms] 10,00 200,00 100,00 0,00 -100,00 -200,00 -300,00 2,00 200,00 40,00 100,00 30,00 0,00 20,00 -100,00 10,00 -200,00 0,00 -300,00 0,00 2,00 Circuit Breaker: Voltage Difference in kV Source: Power Frequency Voltage 4,00 6,00 8,00 Circuit Breaker: Phase Current/Terminal i in A [ms] -10,00 10,00 Figure 15: Source side, load side and transient recovery voltage (TRV) DIgSILENT PowerFactory, r4594 11 Switching Transients Example 4 Study Cases Large loads are connected to substation North and North-East, each with a consumption of 1200 MW and a power factor of 0.9 and 0.98 respectively. For reacThe application example contains several study cases, tive power compensation the capacitor bank at substation North-East is supplying 400 Mvar (tap 8). The each of them being discussed further below: shunt reactor at substation Central is tapped to zero • “Steady State Load Flow Analysis”: Intro- and thus not consuming any active power. duction to the network model and components. Load flow calculation and analysis (see section The load flow calculation is configured with automatic 4.1); tap adjustment of transformers at substation Central • “Transformer Energisation”: Investigation of and at the wind farm. The load flow calculation will instantaneous inrush currents caused by the en- determine the active and reactive power flows for all ergisation of the wind farm transformer WF-1. branches, and the voltage magnitude and phase for all nodes. Executing the load flow results in the phase Peak currents and RMS voltage dip. Fourier voltages displayed in Figure 16. The voltage at subanalysis of the inrush currents (see section 4.2); station West is the reference voltage with an angle of • “Overhead Line Energisation”: Investigation 0 β and a symmetrical phase shift of 120 β for each of transient overvoltages occurring during the phase respectively. energisation of the 400 ππ overhead line WC-1. Determination of peak and duration of transient The external grid serves as slack and is supplying voltages and currents. Statistical switching tool 1900 MW for active power balancing and a reactive power of 60 Mvar. The voltages of all busbars in (see section 4.3); the transmission system and sub-transmission sys• “TRV Analysis of Shunt Reactor tem, are in the range of 0.99 to 1.03 π.π’. in the steady Switching off”: Analysis of the transient recov- state load flow calculation. The loading of lines and ery voltage (TRV) during shunt reactor open- transformers varies between 14 % and 50 %. ing. Circuit breaker design validation (see section 4.4); The steady state load flow calculation results are the • “TRV Analysis Terminal Fault”: Investigation basis for the calculation of the initial conditions and of the TRV following a terminal fault at substa- thus the starting point of the EMT simulation. tion Central. High voltage TRV modelling (see section 4.5); [deg] 4.1 Steady State Load Flow Analysis 6,00 5,00 4,00 3,00 The load flow calculation is based on algorithms for the unbalanced load flow taking into account unbalances resulting from imperfect line transposition of the multi-phase network and unsymmetrical loads and generation. The active power control in the load flow calculation is based on the dispatch of generators and loads. The difference between load and generation is balanced by the reference machine. 2,00 1,00 -240, -210, -180, -150, -120, -90,0 -60,0 -30,0 30,0 60,0 90,0 120, 150, 180, [kV] -1,00 -2,00 -3,00 -4,00 -5,00 -6,00 The external grid connected to substation West rep-7,00 resents the transmission system in the West is used -8,00 as reference machine (slack). It controls the voltage West 1: Line-Ground Voltage North 1: Line-Ground Voltage C4_1.1: Line-Ground Voltage to 1 p.u. at substation West. The power plant conNorth-East: Line-Ground Voltage nected to substation North is set to dispatch 750 MW. A station controller is used to regulate the voltage at Figure 16: Phase voltages of the transmission system the HV-side of the Power Plant to 1.02 p.u. The wind farm connected to the 110 kV sub-transmission system is set to dispatch 30 MW at a power factor of 0.95 overexcited. DIgSILENT PowerFactory, r4594 12 Switching Transients Example 4.2 Transformer Energisation This study case investigates the energisation of the wind farm transformer WF-1. Before energisation, the complete wind farm is disconnected. The 110 kV HV cable which connects the wind farm to the point of common coupling (PCC) at substation Central is already energised and in steady state. The wind farm transformer WF-1 is energised by closing the circuit breaker CB4. The residual flux in the transformer core is assumed to be zero at the time when the transformer is energised (ππ΄ (π‘0 ) = ππ΅ (π‘0 ) = ππΆ (π‘0 ) = 0). phase C results in a phase current of 2.97 π.π’. in the saturation curve corresponding to transformer WF-1. A Fast Fourier Transform (FFT) is used to investigate the inrush currents in order to quantify their harmonic content. The FFT is carried out with a 20 ms window and 64 samples, resulting in a sampling rate of 3200 Hz. Figure 18 shows the FFT of the inrush currents in the same plot. As can be seen, phase C contains a significant DC-component. This is because the flux in phase C starts at zero when the transformer is energised, thus resulting in a fluctuating flux between 0 π.π’. and 2 π.π’. (fluctuating around 1 π.π’.). The EMT simulation is initialised at π‘ = −100 ππ and the integration step size is set to π‘ = 100 ππ . The circuit breaker CB4 is closed at π‘ = 0 π . The simulation results are documented in Figure 17 and Figure 18. Following the switch event the flux in all three phases rises proportional to the source voltage at the HV side of the transformer with a 90β phase shift. The peak flux arises in phase C and is −1.68 π.π’. which corresponds to a flux of 339.6 π π . The energisation of the wind farm transformer causes a voltage drop at the grid connection point (Central substation). The RMS voltage during the energisation process is shown in Figure 18. Ahead of energisation the RMS voltage in all three phases is approximately 1.015 π.π’. The minimum RMS voltage during the energisation occurs in phase C and is 0.99 π.π’. which corresponds to a voltage dip of approximately 2.5 %. Usually grid code requirements limit the maximum alDuring the energisation, the fluxes in all three phases lowable RMS voltage dip to 2.0 %. Thus, countermeaexceed 1 p.u. and drive the transformer into satura- sures such as point on wave switching (π ππ ) would tion. The current-flux relationship is no longer linear have to be considered for the specific case. and results in high inrush currents which contain harEnergising both transformers instantaneously at π‘ = monic distortion as described in section 3.1. The non0 π results in a minimum voltage of 0.97 π.π’.. This will linear flux-current relationship can also be plotted in most likely not be acceptable with regard to the grid PowerFactory and is shown in Figure 17. The peak code. Taking residual flux into consideration will ininrush current on the HV side of the transformer arises crease the inrush currents and consequently the RMS in phase C and is 780 π΄. This is approximately 3 times voltage dip. the rated current of 262.4 π΄. Thus, a flux of 1.68 π.π’. in DIgSILENT PowerFactory, r4594 13 Switching Transients Example 2 3 3 [p.u.] [p.u.] [p.u.] Max. = 1,197 p.u. 1 2 0 1 1 -1 0 0 -2 -1 -1 -3 0 10 -2 20 30 40 [ms] 50 WF: Phase Voltage A WFT-1: Magnetising Flux A 2 Max. = 1,471 p.u. 0 10 -2 20 30 40 [ms] 50 WF: Phase Voltage B WFT-1: Magnetising Flux B Min. = -1,675 p.u. 0 4 800 3,00 [p.u.] [A] [p.u.] 2 400 0 0 10 20 30 40 [ms] 50 WF: Phase Voltage C WFT-1: Mag. Flux c C 2,00 1,00 -2 -400 -4 -800 -6 -1200 0,00 -1,00 0 10 20 30 40 [ms] 50 WFT-1: Magnetising Current, Phase a WFT-1: Magnetising Current, Phase b WFT-1: Magnetising Current, Phase c 0 10 20 30 40 [ms] 50 WFT-1: Phase Current A/HV-Side WFT-1: Phase Current B/HV-Side WFT-1: Phase Current C/HV-Side -2,00 -6 -4 -2 0 2 [p.u.] 4 Figure 17: Transformer HV side voltage, magnetic flux in the core, magnetizing current 1,03 [sec.V] 1,02 PCC\RMS Voltage: Phase A PCC\RMS Voltage: Phase B PCC\RMS Voltage: Phase C 1,01 1,00 0,99 0,98 0,0 100,0 200,0 300,0 400,0 [ms] 500,0 800,0 [A] 400,0 WFT-1: Phase Current A/HV-Side WFT-1: Phase Current B/HV-Side WFT-1: Phase Current C/HV-Side 0,0 -400,0 -800,0 -1200,0 0,0 100,0 200,0 300,0 400,0 [ms] 500,0 500,0 [A] 400,0 WFT-1: Phase A WFT-1: Phase B WFT-1: Phase C 300,0 200,0 100,0 0,0 0,000 50,00 100,0 150,0 200,0 [Hz] Figure 18: RMS voltage dip at PCC, Inrush currents and their harmonic distortion DIgSILENT PowerFactory, r4594 14 Switching Transients Example 4.3 Line Energisation The energisation of high voltage overhead lines and cable systems may cause considerable overvoltages. With increasing operating voltages of transmission systems, switching surge overvoltages determine the insulation design rather than lightning overvoltages. Transient overvoltages caused by internal line events such as line switching are one of the main problem in EHV and UHV systems with regard to insulation coordination and are discussed in this study case. These transients typically have durations ranging from a few tens to several thousands of ππ and belong to the category of slow front transients. They usually have complex waveforms with frequencies in the range of 100 Hz to several ππ»π§ superimposed on the power frequency. 4.3.1 Overhead Line 400 kV This study case investigates the energisation of the overhead line WC-1. Before the energisation, the line is disconnected from the grid and will be energised from the substation Central while the other end of the line remains disconnected. The initial condition before the energisation is based on the steady state load flow calculation as described in section ??. The surge arresters connected to the overhead line WC-1 are in service. The network topology is stored in the Operation Scenario Energisation 400 kV OHL WC-1 which is activated with the Study Case Overhead Line Energisation. Figure 19: Frequency dependent parameters of the line model for Mode 1 The EMT simulation is initialised at π‘ = −20 ππ and the integration step size is set to π‘ = 10 ππ . A switch event is defined to close all three phases of the high voltage circuit breaker CB.L2 simultaneously at π‘ = 0π as shown in Figure 20. After the breaker contacts are closed, transient voltage and current surges are injected and travel towards the receiving end at substation West with the propagation speed of approximately 300 π/ππ . For the purpose of this analysis a frequency dependent, distributed parameter line model is used for overhead line WC-1. The change of the line model compared to the base case is stored in the Variation Distributed Parameter WC. The modal transformation matrix is calculated at a frequency of 500 Hz. The minimum and maximum frequency for the approximation by rational functions of the propagation factor and the characteristic impedance are 0.01 Hz and 1 MHz respectively. The frequency dependent parameters of the overhead line model are displayed in Figure 19 for Mode 1. Figure 20: Energisation of OHL WC-1 at substation Central DIgSILENT PowerFactory, r4594 15 Switching Transients Example Max. =552,791 kV 600 300 0 -300 -600 -900 0 L2: Phase Voltage A in kV T1.6: Phase Voltage A in kV 4 8 12 16 [ms] 20 4 8 12 16 [ms] 20 8 12 16 [ms] 20 500 250 0 -250 Min. =-394,306 kV -500 -750 0 L2: Phase Voltage B in kV T1.6: Phase Voltage B in kV 500 250 0 -250 Min. =-410,437 kV -500 -750 0 L2: Phase Voltage C in kV T1.6: Phase Voltage C in kV 4 Figure 21: Transient phase-to-ground voltages at the sending and receiving end during the energisation of OHL WC-1 1200 [A] 800 WC-1.3: Phase Current A/Terminal j WC-1.2: Phase Current A/Terminal j WC-1.1: Phase Current A/Terminal j 400 0 -400 -800 0 300 600 900 1200 [us] 1500 1200 [A] 800 WC-1.3: Phase Current B/Terminal j WC-1.2: Phase Current B/Terminal j WC-1.1: Phase Current B/Terminal j 400 0 -400 -800 0 300 600 900 1200 [us] 1500 300 [A] 0 WC-1.3: Phase Current C/Terminal j WC-1.2: Phase Current C/Terminal j WC-1.1: Phase Current C/Terminal j -300 -600 -900 -1200 0 300 600 900 1200 [us] 1500 Figure 22: Transient phase currents during the energisation of OHL WC-1 DIgSILENT PowerFactory, r4594 16 Switching Transients Example Figure 21 shows the transient voltage at the sending and receiving end of overhead line WC-1 during the energisation process. The voltage surges are injected at the sending end of the overhead line and then duplicated and reflected at the receiving end (substation West). Then the surges travel back to substation Central. Due to attenuation, the magnitude of the wave decreases and the waveform is distorted, as it propagates along the line. The current and voltage wave shapes become dissimilar, though they were the same initially. The following maximum overvoltages arise during the energisation of overhead line WC-1: • Phase A: 516 kV • Phase B: 400 kV • Phase C: 420 kV the switch event) is varied randomly by ± 10 ππ . Furthermore, the scatter time corresponding to the mechanical delay of the closing time of each individual phase of the breaker is varied randomly by 0...1 ππ in each simulation. Figure 25 shows the maximum overvoltages for the π = 100 EMT simulations executed automatically by the statistical tool in PowerFactory. Figure 25 documents the maximum line-to-earth overvoltages at substation West resulting from each simulation executed during statistical analysis. The plot documents the overvoltages resulting from the energisation of overhead line WC-1 from substation Central for all three phases. As demonstrated, the overvoltages significantly depend on the breaker closing time and also the operation scenario, such as e.g. energisation from substation West or Central. For economic reasons the insulation design for self-restoring insulation is usually not based on the maximum prospective overvoltage of all investigated cases. Instead the design is based on a probabilistic approach to withstand only a certain percentage, e.g. 98%, of the prospective overvoltages which are calculated in a statistical analysis. Figure 22 shows the current surge along the line. In phase A a current surge of approximately 1080 A is injected into the line, in phase B the amplitude is 845 A and in phase C 267 A. The propagation time of the first line segment is approximately 234 ππ . Thus the injected current surge arrives at the first point of transposition only after 234 ππ which can be observed in Figure 22. The surge arrives at SS West (open end of overhead line WC-1) approximately 712 ππ after the According to the insulation coordination standard IEC 60071-2 first the maximum overvoltages are detercircuit breaker is closed. mined using EMT simulations. The maximum overThe overvoltages resulting from line energisation voltages are documented in Figure 25 and are based highly depend on the magnitude of the injected surge on the statistical analysis. As a next step, the repat the sending end of the line. The magnitude of the resentative overvoltage πππ is derived from the maxinjected surge depends mainly upon the voltage in- imum overvoltages. Secondly, the coordination withstantaneous value (point on the waveform) at which stand voltage πππ€ is calculated from the representathe circuit-breaker contacts close electrically. Since tive overvoltage using the coordination factor πΎπ , as the point on the waveform of the voltage depends on follows: the circuit breaker closing instant, statistical studies should usually be performed. As the circuit breaker πππ€ = πππ · πΎπ closing time is of random nature in reality, all potential breaker closing times and thus overvoltages should be The coordination factor πΎπ makes allowance for limevaluated. itations in the modelling, shape and duration of an The randomness of the circuit breaker closing time overvoltage. For the deterministic approach (non-self is modelled in PowerFactory by means of statistical restoring insulation) in the insulation coordination πΎπ analysis. The statistical analysis tool in PowerFactory is usually 1.0 . For a probabilistic approach it is based runs a number of π simulations. In each simulation on the statistical analysis. the breaker closing time is varied randomly within a defined range. Additionally, breaker pole scattering For that purpose, the risk of failure π (π ) is calcucan be included in the statistical analysis in order to lated based both on the probability distribution of the account for deviations in the closing time between the overvoltage π (π ) and the probability of the insulation strength π (π ) and is illustrated in Figure 23. three phases. An example of a statistical switching analysis is pro∫οΈ vided in this section. The overhead line WC-1 from π (π ) = π (π ) · π (π ) ππ the previous simulation is used for this purpose. For the statistical analysis, 100 simulations are run. For each simulation the breaker closing time (defined in Figure 23 shows the probability distribution of the DIgSILENT PowerFactory, r4594 17 Switching Transients Example overvoltages and the failure probability of the dielectric strength of the insulation. According to the figure, a voltage of 1.5 π.π’. is most likely. For that voltage the failure of the insulation is very small. Thus, the risk of failure R(U) is also relatively small. For higher voltages, e.g. 2 π.π’., the probability for overvoltages is smaller. However, the probability of insulation failure is much higher. Thus, the overall risk of failure is higher. For very high overvoltages the risk of insulation failure is significant. However, the probability of such high overvoltages is almost zero and thus the risk of failure is also nearly zero. Table 1: Statistical overvoltages for different bands around the mean π 1 f(U) 0,8 Probability in p.u. The insulation for self-restoring insulation, such as overhead lines, is usually designed for the 98 % percent value of the prospective voltage stresses. The statistical tool in PowerFactory determines the prospective overvoltage π for a defined probability π (π ) (e.g. 98%). The analysis is based on the π number of EMT simulations executed during the statistical analysis. In this example (π = 100 EMT simulations) the statistical results in Table 1 are obtained for energisation of overhead line WC-1 from the substation Central. P(U) R(U) 0,6 0,4 ππππ π (π ) π π’πππ₯ (π − π, π + π) 65.9 % 471 ππ 492 ππ (π − 2π, π + 2π) 95.5 % 471 ππ 548 ππ (π − 3π, π + 3π) 99.73 % 470 ππ 593 ππ 0,2 0 -3 -2 -1 0 1 2 3 4 Stress, e.g. voltage in p.u. The coordination withstand voltage πππ€ is chosen based on the 2 % probability and is equal to 564 ππ in this case. This means that only 2% of the simulated overvoltages exceed this value. Figure 23: Risk of failure π (π ) In the following insulation coordination study the required withstand voltage πππ€ is now determined based on the coordination withstand voltage πππ€ and The distribution of the breaker closing time and thus using the safety factor πΎπ and altitude correction facthe transient overvoltages π (π ) is usually a normal tor πΎπ : distribution. Consequently, a normal distribution function can be assumed for the breaker closing time and the resulting overvoltages: πππ€ = πππ€ · πΎπ · πΎπ 1 π’−π 2 1 √ · π− 2 ·( π ) π· 2·π Finally, the standard withstand voltage ππ€ is selected according to the tables in IEC 60071-1. In case the required withstand voltage πππ€ exceeds the desired The mean π of the distribution function and the stan- standard withstand voltage defined in IEC 60071-1, dard deviation π are determined using the statistical the prospective overvoltages can be reduced by additool in PowerFactory. The normal distribution function tional surge arresters, pre-insertion resistors or point is shown in Figure 24 and shows the probability versus on wave switching. standard deviation π in general. It should be noted that usually 1000 runs are recommended for a statistical switching study in order to en0,4 sure the statistical significance of the study. Probability overvoltages in p.u. π (π’) = 0,3 0,2 68.5 % 0,1 95.5 % 99.7 % 0 -4 -3 -2 -1 0 1 2 3 π 4 DIgSILENT PowerFactory, r4594 Figure 24: Probability distribution of switching overvoltages 18 overvoltages in kV Switching Transients Example 600 500 400 300 200 Phase A 100 Phase B Phase C 0 0 20 40 60 80 100 number of simulation n probability in % 100 Phase A 80 Phase B Phase C 60 40 20 0 350 400 450 500 550 600 voltage in kV Figure 25: Probability distribution of energisation overvoltages for OHL WC-1 TRV Analysis of Shunt Reactor the model in order to do the TRV analysis. Switching off For reactive power compensation a shunt reactor is installed at substation Central as shown in Figure 2. The shunt reactor is a three-phase five-leg core type with a rated reactive power of 200 Mvar. The reactor is switchable and has 4 steps. Thus, it is able to consume 0 π π£ππ, 50 π π£ππ, 100 π π£ππ, 150 π π£ππ and 200 π π£ππ. The reactor is connected directly to the 400 kV busbar via a 400 kV circuit breaker. In this study case the transient recovery voltage (TRV) is analysed when the shunt reactor in substation Central is switched off. Before disconnecting, the shunt reactor is operated at step 2, supplying the grid with 200 Mvar of reactive power. The reactor is then disconnected by opening the CB. The objective of this study case is to analyse the transients following the reactor drop out. For the purpose of this analysis the variation Detailed CB model shunt reactor is activated which contains a more detailed model of CB.R4 with a two parameter curve according to IEC 62271-100 to model the dielectric strength of the breaker during the transient. Furthermore, winding capacitances of the shunt reactor and additional stray capacitances are included in DIgSILENT PowerFactory, r4594 Figure 26 shows a simplified single line diagram of the most important components of the switching bay of the shunt reactor. The shunt reactor is tapped at step 1. The inductance of the reactor is 10.19 π». The capacitance on the source side of the CB corresponds to the lumped capacitances of the instrumental voltage and current transformers. They are assumed to be equal to 4 ππΉ . The capacitances on the shunt reactor side mainly represent the winding stray capacitances of the shunt reactor and are assumed to be equal to 1 ππΉ . 68.51 ππ» 4 ππΉ 1 ππΉ 10.19 π» 4.4 Figure 26: Equivalent circuit diagram showing the source inductance and stray capacitances of the shunt reactor bay The network impedance at the shunt reactor is calcu- 19 Switching Transients Example lated using the Frequency Sweep Calculation Tool in PowerFactory. The inductance is 68.51 ππ» at substation Central in case the shunt reactor is out of service. Based on the network capacitances and inductances the approximate oscillation frequency can be calculated as described in section 3.3. The load side oscillation frequency is approximately 1.58 kHz: ππ = parameters for the TRV envelope are based on the maximum peak voltages π’π and rate of rise of recovery voltage π π π π . In this example the following parameters are assumed for the breaker capability curve: • Peak TRV voltage π’πΆ : 787 ππ • Time to π’πΆ : 112 ππ 1 1 = 1.58 ππ»π§ · √οΈ 2π πΏπ · πΆπ Figure 28 shows the transient oscillation voltage on the shunt reactor side after disconnecting the device together with the phase currents through the circuit breaker connecting the reactor with substation Central. The first zero-crossing occurs in phase A after the circuit breaker is triggered by a simulation event. At π‘ = 0.607 ππ the current in phase A is zero and the breaker is opened. Then, 3.404 ππ later at π‘ = 4.011 ππ the current in phase C goes to zero and the ideal switch is opened for that phase. In phase B the switch is opened at π‘ = 7.314 ππ . Due to the 90β phase shift between the interrupted current and the supply voltage (inductive load), the voltage in each phase of the isolated shunt reactor is at its peak when the breaker contacts separate. Thus, the stray capacitances in each phase are charged with energy πΈπΆ when the current is interrupted. The stored energy πΈπΆ is: 1 πΈπΆ = · πΆ · π’2 2 The energy is now oscillating between the inductance and capacitance until the transient is damped out and Figure 27: Equivalent circuit of source and load side the load side voltage is zero. Figure 28 shows the transient oscillation on the load side. The peak value of the voltage is approximately 315 ππ and the fre- In the investigated case the maximum peak voltages quency corresponds to the resonant frequency of the and RRRV of the TRV are within the defined limits for circuit in Figure 26. Applying a Fast Fourier Trans- all three poles. The following results are obtained: former (FFT) to the load side transient voltage results • Phase A: π’π = 626 ππ ; π π π π = 2.57 ππ /ππ in the plot in Figure 27. The dominant frequency is between 1.8 kHz and 1.9 kHz as predicted by the sim• Phase B: π’π = 625 ππ ; π π π π = 2.47 ππ /ππ plified hand calculation. • Phase C: π’π = 627 ππ ; π π π π = 2.53 ππ /ππ Following the current interruption in each phase, the TRV, as described in section 3.3 arises across the The interruption of small inductive currents frequently breaker poles. The TRV for each phase is depicted results in current chopping and virtual current chopin Figure 29 together with the breaker capability curve ping which might lead to re-ignition and even multiple of the CB. According to IEC 62271-100 the TRV en- re-ignitions. Both effects can easily be included in the velope is defined by a two-parameter curve. The input breaker model used for this study. DIgSILENT PowerFactory, r4594 20 Switching Transients Example 600 [kV] 400 200 0 -200 -400 0 T1: Phase Voltage A T1: Phase Voltage B T1: Phase Voltage C 4 8 12 16 [ms] 20 8 12 16 [ms] 20 200 [A] 100 0 -100 -200 -300 0 4 CB phase A: Phase Current/Terminal i CB phase B: Phase Current/Terminal i CB phase C: Phase Current/Terminal i Figure 28: Load side oscillation voltagesand phase currents in the high voltage circuit breaker 1000 500 0 -500 -1000 -1500 0,0 2,5 CB phase A: Voltage Difference in kV TRV Limit Phase A T10: TRV_limit_neg TRV Limit Phase A T10: TRV_limit_pos 5,0 7,5 10,0 [ms] 12,5 0,0 2,5 CB phase B: Voltage Difference in kV TRV Limit Phase B T10: TRV_limit_neg TRV Limit Phase B T10: TRV_limit_pos 5,0 7,5 10,0 [ms] 12,5 0,0 2,5 CB phase C: Voltage Difference in kV TRV Limit Phase C T10: TRV_limit_neg TRV Limit Phase C T10: TRV_limit_pos 5,0 7,5 10,0 [ms] 12,5 1000 500 0 -500 -1000 -1500 1000 500 0 -500 -1000 -1500 Figure 29: Transient recovery voltage (TRV) and dielectric strength of circuit breaker DIgSILENT PowerFactory, r4594 21 Switching Transients Example CBS2 IS.L2.1 IS.L2.2 IS.L3.2 IS.L1.1 CB.L1 IS.L1.2 IS.L1.3 CWC-2_comp IS.L0.2 IS.L0.1 π£ 4·π Before the fault, the transmission system is in steady state as described in section ??.The short circuit is applied on the line side of the circuit breaker CB.L2 as depicted in Figure 30. To simulate the fault, a 3phase short circuit is triggered at π‘ = 0 π . After 50 ππ switch events are triggered to isolate the faulted part of the network. The following circuit breakers have to be opened: • CB.L2.1 (substation Central) • CB.W.1 (substation West) • CB.W.1 (substation West) The current in each circuit breaker is interrupted at the following current zero of each individual phase. The line is re-connected after clearing of the fault. However, the re-closure action of the line is not simulated in this study case since the investigation focuses on the TRV capability of the HV circuit breaker during the Terminal fault. The breaker capability curve is modelled according to the limits defined in IEC62271-100 for a voltage level of 420 kV. The relevant parameters for the envelope curve are listed in Table 2 and define a 4-parameter envelope. The envelope curve defines the maximum transient voltages which are allowed after the fault interruption across the breaker poles and represents the dielectric strength of the breaker. DIgSILENT PowerFactory, r4594 CB.L3 IS.L3.3 0,0 0,00 91,4 ππ = IS.L2.3 CB.L2 C4_1.1 CB.L0 0,0 0,00 91,4 The detailed breaker model is stored in the Variation TRV Analysis Terminal Fault which is activated with WC-2.3 the study case TRV Analysis Terminal Fault. Furthermore, all lines connected to the faulted terminal are modelled as distributed parameter lines. The frequency for travel-time estimation ππ is chosen based on the line lengt π and propagation time of each line according to the following equation: CWC1_comp CWC1 In this section the transient recovery voltage across the breaker poles of the circuit breaker CB.L2 in substation Central is analysed, following a terminal fault on the line side of the circuit breaker. For the purpose WC-1.3 of this analysis the CB.L2 is modelled by detailed circuit breaker model. The breakers include a model of the dielectric strength during the transient according to IEC 62271-100. CBS1 0,0 0,00 91,4 TRV Analysis Terminal Fault CWC2 4.5 C4_1.2 Figure 30: Fault location of terminal fault The limits in Table 2 correspond to the short-circuit duty tests T100, T60 and T30. The duty test T100 corresponds to a short circuit current equal to the short circuit rating of the CB. In the duty test T60 the short circuit current is only 60 % of the short circuit rating of the CB. Table 2: Parameters of TRV envelope of 420 kV circuit breakers; terminal faults (T) Curve π‘1 /ππ T100 π’1 /ππ 334 π‘2 /ππ 167 ππΆ /ππ 624 T60 334 11 669 666 T30 - - 687 137 668 Figure 31 shows the short circuit current flowing from substation Central to the fault location at the beginning of overhead line (OHL) WC-1.3. Initially the current through the circuit breaker is in steady state. At time π‘ = 0π the fault is initiated with zero fault impedance (π π ππ’ππ‘ = 0 β¦ and ππ ππ’ππ‘ = 0 β¦). The steady state load current changes into a significantly higher short circuit current in an oscillatory manner as shown in Figure 31. After a few ππ the short circuit current is nearly in steady state. At time 22 Switching Transients Example π‘ = 50 ππ a switch event triggers the CBs to open. The The maximum peak voltages π’π and rate of rise of reshort circuit current is then interrupted at the following covery voltage π π π π during the transient for the difcurrent zero (zero-crossing) in each phase. ferent phases are as follows : • Phase A: π’π = 529 ππ ; π π π π = 0.32 ππ /ππ During the short circuit the terminal voltage at substation Central drops from a peak line-to-earth voltage of 328.3 ππ to 0 ππ and afterwards returns approximately to its original value. The peak short circuit current through the circuit breaker connected to substation Central is 16.7 ππ΄. As described in section 3.3 a transient recovery voltage arises across the circuit breaker poles after the current is interrupted. The TRV appearing across the circuit breaker poles is the instantaneous values sum of the voltage from the source and the line side phaseto-earth voltage and is shown in Figure 32. The plot shows the TRV arising in phase A, B and C together with the breaker capability curve of the circuit breaker CB.L2. 30 • Phase B: π’π = 497 ππ ; π π π π = 0.24 ππ /ππ • Phase C: π’π = 489 ππ ; π π π π = 0.14 ππ /ππ The maximum withstand voltage of the CB for the T100 duty is 624 ππ and the maximum RRRV is 0.32 ππ /ππ . The transient recovery voltage (TRV) therefore does not exceed the limits defined in IEC62271-100. For this particular case a high voltage circuit breaker with a fault current ratio of 100% of its rated short circuit capability is sufficient for the application. Short Circuit Switch Event [kA] 20 10 0 -10 -20 600 0 IS.L2.3: Phase Current A/Terminal i IS.L2.3: Phase Current B/Terminal i IS.L2.3: Phase Current C/Terminal i 20 40 Short Circuit 60 80 [ms] 100 60 80 [ms] 100 Switch Event [kV] 300 0 -300 -600 -900 0 C4_1.1: Phase Voltage A C4_1.1: Phase Voltage B C4_1.1: Phase Voltage C 20 40 Figure 31: Short circuit current through the CB.L2 during the transient and voltage at substation Central DIgSILENT PowerFactory, r4594 23 Switching Transients Example 1000 500 0 -500 -1000 -1500 50 54 CB phase A(1): Voltage Difference in kV TRV Limit Phase A: TRV_limit_neg TRV Limit Phase A: TRV_limit_pos 58 62 66 [ms] 70 50 54 CB phase B(1): Voltage Difference in kV TRV Limit Phase B: TRV_limit_neg TRV Limit Phase B: TRV_limit_pos 58 62 66 [ms] 70 50 54 CB phase C(1): Voltage Difference in kV TRV Limit Phase C: TRV_limit_neg TRV Limit Phase C: TRV_limit_pos 58 62 66 [ms] 70 1200 800 400 0 -400 -800 1000 500 0 -500 -1000 -1500 Figure 32: Transient recovery voltage (TRV) and dielectric strength of circuit breaker References [1] Juan A. Martinez-Velasco: “Power System Transients: Parameter Determination”, CRC Press, 2009, ISBN 978-1420065299 [2] R. Smeets; L. Sluis; M. Kapetanoviae; D. Peelo; A. Janssen: “Switching in Electrical Transmission and Distribution Systems”, Wiley, 2014, ISBN 978-1118381359 [3] Allan Greenwood: “Electrical Transients in Power Systems”, Wiley-Interscience, 1991, ISBN 978-0471620587 [4] DIgSILENT PowerFactory Technical Reference Documentation “Overhead DIgSILENT PowerFactory, r4594 Line Models”, PowerFactory 2018, DIgSILENT GmbH, Gomaringen, Germany, 2018 [5] DIgSILENT PowerFactory Technical Reference Documentation “Cable System”, PowerFactory 2018, DIgSILENT GmbH, Gomaringen, Germany, 2018 [6] DIgSILENT PowerFactory Technical Reference Documentation “TwoWinding Transformer”, PowerFactory 2018, DIgSILENT GmbH, Gomaringen, Germany, 2018 [7] DIgSILENT PowerFactory Technical Reference Documentation “ThreeWinding Transformer”, PowerFactory 2018, DIgSILENT GmbH, Gomaringen, Germany, 2018 24