Banestrømforsyning/Prosjektering og bygging/Kraftsystem/Vedlegg/Kompatibilitetsstudie steg 1-7 (Informativt)
When introducing a new power system component, e.g. a converter substation or a contact line system, electrical system compatibility must be ensured. According to the European standard NEK EN 50388:2012, this is a new element in the rail system and a compatibility study has to be carried out regarding harmonics and dynamic effects.
The overall intention of the process is to ensure compatibility between the new element and the existing and planned future infrastructure and rolling stock. The present document aims to very briefly and generically describe the existing infrastructure, rolling stock and operation conditions in the system together with the acceptance criteria for the new element. That is step 2-7 in the float diagram for the compatibility check in NEK EN 50388:2012 Figure 2. As a guideline, the description for each step is repeated for the corresponding chapter in this document.
- 1 Plan for compatibility check
- 2 Characterisation of infrastructure
- 3 Characterisation of existing rolling stock
- 4 Characterisation of existing operation conditions
- 5 Characterisation of overall rail system/network
- 6 Theoretical analysis of overall rail system/network
- 7 Acceptance criteria for new element
- 8 References
1 Plan for compatibility check
The plan for a specific compatibility check when introducing a new element in an existing railway system defines the scope of the analysis, and the precise tasks and responsibilities. The plan shall be agreed between all involved parties. This includes nomination of the organization in charge of the compatibility study.
1.1 Scope of the analysis
The scope of the work is the introduction of the new element in the power system. The amount of work to be done depends on the risk of the integration of this new element:
- If the integration is, based on earlier experiences, without any risk, this shall be documented in the plan which then is the only step in the process in this case.
- For new technology, new technical solutions or other new conditions, however, where the experience is limited the analysis shall be performed more thoroughly. In this case it is recommended that the process starts with a presentation and exchange of information about both the existing rail system and the new element between the involved parties in order to identify possible need for more description or detailing or more precisely defining the requirements. This document consequently may be updated.
EN50388:2005 explicitly describes compatibility with existing rail system. In order to be prepared for future, the study to be performed shall also include information about future as far as it is known.
1.2 Tasks and responsibilities
The involved bodies or parties with the corresponding roles in the process are as described in the table below.
|the owner of existing infrastructure||Bane NOR||Infrastructure manager|
|the operator(s) of existing traffic||Train operators||Operator/owner of rolling stock|
|the purchaser/owner of the new element||Bane NOR|
|the manufacturer of the new element||Supplier of the new element|
The organisation in charge of the compatibility study is: To be decided by the project
If nothing else is decided, each body has the responsibility for the corresponding steps in the compatibility process as described in EN 50388:2012 Table 6.
1.3 Time schedule
As a part of the plan for the compatibility check a rough time schedule shall be made in order to coordinate the different activities.
2 Characterisation of infrastructure
Characteristics of the existing power supply system, information relevant to the compatibility with vehicles (see EN 50388:2012 Table D1), normal feeding arrangements, emergency feeding arrangements.
2.1 ESC datasheet
Generic information about the Norwegian electrical infrastructure and existing rolling stock according to the ESC (electrical system compatibility) data base is given in JBV document Supplementary information and regulations#Onboard power supply and control systems Appendix d. A summary of this information according to EN 50388:2012 table D.1 is given below and the following sections.
|Attribute||Unit||Oslo Area||Rest of Norway||Comment|
|Typical available power of the source (interpreted as ONE source)||MW||10-20
2 sec (+75%)
|Typical power of one train||MW||3-7-14||3-7-14|
|Length of the route supplied by one source in normal operating conditions||Km||5
|Possible presence of compensation filters in the substation||Y/N||Y||Y|
|Tuned frequency of the filter (resonance frequency of the filter) ||Hz||50
|Filter quality factor (corresponding to above)||210
|Impedance of source, fundamental frequency (high voltage grid, transformer)||Ohm||-
|Resonance frequency of 16,7-Hz high voltage transmission network||Hz||Not known||Not known||Min |
|Resonance frequency of the electrified section of the route 15000V-16,7 Hz||Hz||Not known||200 local / 500 global
450 local / 800 global
|Resonance frequency of the electrified section of the route 2*15000V-16,7 Hz||Hz||Not known||140-200 local / global
350 local / 450 global
Notes to the table:
- 1 When substations are connected in parallel (which they in normal operation are in Norway), this length is half of the distance between two consecutive substations.
- 2 May become 120 km with outage of one power substation
Figur 1 shows a sketch of the existing electrical power supply infrastructure with electrified lines and power substations.
2.3 Power substations
At present there is directly feeding into the overhead contact line network:
- 7 converter stations equipped with static converter units, e.g., both with PWM (pulse-with modulation) and MMC (modular multilevel converter) technology inverters on the single-phase side.
- 24 converter stations equipped with synchronous-synchronous rotary converter units
- 1 small hydro power station
- 3 separate transformer substations
- 2 combined converter stations with synchronous-synchronous rotary converter units and transformer substations
Each substation is equipped with 1 to 3, with 2 as typical, number for units. Future plan is to collect more converter units in less converter stations resulting in a longer distance between them, which can be possible due to an autotransformer system (see below).
Rotary and some static converter stations take regenerated power while some static converter stations are not equipped for reverse power direction. The latter either push it forward by changing the output voltage angle or burn transients in heating resistors.
All the existing static converters have DC link filters, which aim to reduce the DC link voltage ripple. All of the converter DC links have the following DC link components:
- DC-link capacitor of various capacitance
- 33 1/3 Hz (2 nd harmonic)
- High-pass filter with variable component values.
Some converters also have filters with the following tuned frequencies:
- 66 2/3 Hz (4 th harmonic)
- 100 Hz (6 th harmonic)
- 133 1/3 Hz (8 th harmonic)
2.4 Transmission and distribution systems
The following distribution systems exist:
- 1*15-kV overhead contact line system with and without booster transformers (BT) and return conductors. Most of the network is single-track line a small part is double-track line.
- 2*15-kV overhead contact line system and autotransformer (AT) system. Is planned for the most of the network, both single- and double track lines.
- Double track railway line may have separate overhead contact line system for each track or interconnected overhead contact line system for the two tracks together.
Generic parameters for feeding sections are given below. For more detailed information about distribution system concepts (in Norwegian only), see
- Electrical designs of overhead contact line systems
- Switching designs for overhead contact line systems
|1*15 kV system||2*15 kV system|
|Resistance||0.16…0.23 Ohm/km||0.03...0.07. Ohm/km|
|Inductance||1.7…2.2 mH/km||0.47...0.57 mH/km|
|Capacitance||9…17 nF/km||10…18 nF/km (phase-earth)|
|Length of feeding section||20…80…90 km||120 km|
|Length of cables||0…5 km||0…12…40 km|
|Transformer||BT if present every 3rd km||AT every 10th km|
The numbers for capacitance in the table are not calculated for the Norwegian systems specifically, but taken from the generic numbers in TS503238-2:2010 Annex B.
The influence of the cable position has been checked for the variants, where the whole cable is concentrated in the middle of the line, concentrated on one line end or distributed evenly along the line. It turns out that the position and splitting of the cable has no effect on the damping and frequency of the lowest resonance. The differences show at higher frequencies, but no additional resonances occur. Only the total length of the cables is relevant for the frequency range up to 500 Hz.
The following transmission systems exist:
- 2*15-kV high voltage transmission system on the Ofoten line
- 2*27-kV high voltage transmission system for a limited extension west of Oslo.
2.5 Coupling posts
Coupling posts normally exist between power substations having more than 50 km distance in between.
2.6 Switching posts
Switching post exists on some junctions where three or more lines meet, but not all.
2.7 Series and shunt capacitors
From former times, series and shunt capacitors were used for improving the overhead contact line voltage level. Some of the series capacitors of -7.35 Ohm at fundamental frequency are still in operation. The only shunt capacitor of 4 MVAr at Oslo S is currently disconnected.
2.8 Neutral sections
Neutral sections (a.c. phase separation sections) are arranged at
- some power substations – normally unenergised and floating
- some switching posts – normally unenergised and floating
- all coupling posts – normally energised if network is interconnected, otherwise unenergised and floating
- all series capacitances – normally unenergised and floating
At unenergised and floating sections a train shall decrease its traction power to zero and disconnect the main circuit breaker before passing.
Train depots where several trains may be parked at low load with pulsing converters exist at several places. A general rule may be that the larger the city is the more trains may be parked. Several larger depots in the Inter City area around Oslo are planned.
Figur 2 shows an estimation of the number of 110 m vehicle units for different planned depots i the network versus the estimated maximum corresponding 15-kV source impedance during reduced feeding situation. Reduced feeding by disconnecting lines is regularly done in order to maintain the railway lines when low or no traffic.
Further compatilbility considerations and power supply mitigations may be necessary if depots having high input admittance is planned depending on actual vehicle characteristics.
2.10 Special circumstances and experiences
The following experiences have been made regarding the existing and planned infrastructure:
- The rotary converters shows a poorly damped resonance frequency at 1.5-2.0 Hz and can easily together with improperly tuned rolling stock or static frequency converters turn instable. The measured step response from a load rejection of a Q38 (5.8 MVA) rotary converter is shown in Figur 3. The corresponding dq-frequency responces are shown in Figur 4. Typical damping ratio of the 1.6 Hz oscillation mode is 3 %. Furthermore, a SimuLink simulation model reflecting this characteristic is available on request for manufacturers of new elements.
- The excitation control loop of the rotary converters has a limited bandwith and hence the responces to changes in the system, e.g. load changes, may result in a temporary voltage output deviation. Figur 3 shows the increase in voltage due to a fast load decrease. Opposite decrease in voltage is experienced on fast load increase.
- The distance between the power substations are commonly long (typically 80 km for existing 1*15-kV system and 120 km for planned 2*15-kV system)
- The planned 2*15-kV system may include a large amount of cables in order to pass the high amount of tunnels and cuttings. This reduces the electrical resonance frequency of the electrified sections. Figur 5 shows the calculated network admittance for a 120 km long feeding section with AT system. The share of cables are increased from 0 to 8.3, 25 and 50 % and the lowest resonance frequency is decreased from 430 to 275, 185 and 140 Hz respectively. In some areas having large share of tunnels with AT feeders cabled the lowest resonance freuqency is calculated to be around 100 Hz under some operational conditions.
- The earth resistivity is high in comparison to most of the rest of the Europe. This has a direct effect on traction power supply design to avoid disturbing other electrical systems.
- Three static converter stations (in Oslo Area) shows active behaviour regarding electrical resonance instability (arg(Y(f))<-90 or arg(Y(f))>90 degrees) in the range f<200 Hz. For details, se .
For more details about feeding arrangements, see #Characterisation of existing operation conditions.
3 Characterisation of existing rolling stock
Characterisation of existing rolling stock operating in the network, information relevant to the compatibility with the power supply system information (see EN50388:2005 Table D.3).
3.1 Existing electrical vehicles
The following vehicles has today acceptance for traffic in the Norwegian national rail network. Passive filters refer to HV-filters or filters on a separate winding of the transformer, not filters on the DC-link in case of an inverter vehicle. Vehicles may in addition have capacitive cables on the roof. Active behaviour refers to if the control system compensates for harmonics in the traction current in order to draw a sinusoidal current.
Number of vehicles in operations is given for the total amount in Norway and Sweden. It does not necessarily mean that all vehicles are operating at the same place and time.
Multiple operation refers to the numbers of vehicles that can be operated together given by number for normal operation and number for special situation in brackets. This is valid for Norway only.
All inverter vehicles may use regenerative braking and are able to control reactive power consumption and production independently of the active power.
3.2 Electric locomotives
|Operator||Vehicle (no of vehicles in op. in brackets.)||Type||Cont. power at wheel||Multiple operation|
|CargoNet AS, Hector Rail AB, CargoLink AS, Peterson Rail AB, GreenCargoAB||CE119/BR241/BR 185.2 (20-50) (DB BR185.2)||Inverter||5.6 MW||Up to 2|
|Unknown||El 13 (5)||Tap changer||2.6 MW||No|
|CargoNet AS||El 14 (30)||Tap changer||5.1 MW||No|
|Hector Rail AB||El 15 / BR 161 (5)||Tap changer, diode rectifier||5.4 MW||Up to 2|
|CargoNet AS, TKAB, TGOJ||El 16 (15)||Thyristor rectifier||4.4 MW||Up to 2|
|NSB AS||El 17 (9)||Inverter||3 MW||Up to 2|
|NSB AS||El 18 (22)||Inverter||5.4 MW||Up to 2|
|SJ AB, Green Cargo AB, TÅGAB, TGOJ||Rc 1 to Rc 7 (356)||Thyristor rectifier||3.6 MW||Up to 2 (Possibly up to 3 on Ofotbanen)|
|Green Cargo AB||Rm (6)||Thyristor rectifier||3.6 MW||Up to 2 (Possibly up to 3 on Ofotbanen)|
|LKAB||IORE (2*13=26)||Inverter||10.8 MW||No|
|LKAB||Dm 3 (19)||Tap changer||7.2 MW||No|
|LKAB, TKAB||Da (5)||Tap changer||1.8 MW||No|
|Railion AS||EG3100 (13)||Inverter||6.5 MW||No|
3.3 Electric multiple units
|Operator||Vehicle (no of vehicles in op. in brackets.)||Type||Cont. power at wheel||Multiple operation|
|Unknown||Class 68 (3)||Tap changer||0.6 MW||Up to 2|
|NSB AS||Class 69 a-g (77)||Phase angle control||1.2 MW||Up to 2 (3)|
|NSB AS||Class 70 (16)||Inverter||1.7 MW||Up to 2|
|Flytoget AS||Class 71 (16)||Inverter||3.5 MW||Up to 2 (3)|
|NSB AS||Class 72 (36)||Inverter||2.5 MW||Up to 2|
|NSB AS||Class 73 (20)||Inverter||2.6 MW||Up to 2 (3)|
|NSB AS||Class 74/75 (50)||Inverter||4.5 MW||Up to 2 (3)|
|SJ AB||X2 (43)||Inverter||3.3 MW||No|
|SJ AB and regional operators||X50-54 (50)||Inverter||1.6 MW||No|
3.4 Special circumstances and experiences
EN 50388:2012 table D.3 describes the different types of traction units generically, mainly in terms of impedances, conducted interference harmonics and stability from the point of view of the traction power supply.
However the following experiences have been made regarding the existing rolling stock in the system:
- El16 and Rc/Rm and Cl 69 consist of half-controlled thyristor brigdes which makes the total harmonic distortion of its line current very large. This represents a danger for exciting electrical resonances in the system to over voltages.
- El16 and Rc/Rm locomotives are equipped with large passive input filter (~0.6 MVAr at fundamental frequency and nominal voltage) for improving power factor. These filters significantly lower the electrical resonance frequency in the traction power system, but appears well damped. The value is reduced to 10 % when parked.
- El18 was formerly known for an efficient adhesion control that repetitively changed the locomotives power demand from the power supply. Experience shows still some power demand changes that excite the rotary converters to oscillations at their eigenfrequency.
- Cl 72 has several times been a part of heavy low-frequency oscillations and instability in the network that has become a major concern. This type of vehicle is currently the “back bone” of the mass transit in the area of Stavanger.
- Cl 73 has been observed as a part of low-frequency oscillations and instability in the network.
- Cl 74/75 has a high possible power/current ramp, up to 9 MW/s and 500 A/s per train set (vehicle) which multiplies with multiple operation.
- It cannot be expected that the existing rolling stock follows the required reduction of maximum power as function of low line voltage as described in EN50388:2012 clause 7.2.
- Several excisting electrical rail vehicles are found show active behaviour regarding electrical resonance instability (-90>arg(Y(f))>90) for frequencies above fl=87 Hz. For details, see . One vehicle has active 100 Hz anticontroll. Several types are active below 200-300 Hz and one type in the range of 950...1600 Hz. Expected negative damping from measurement is shown in Figur 6 for
- "old vehicles", e.g. manufactured before electrical resonance instability was discovered and hence are not compliant with today's input admittance criterion.
- "newer vehicles", e.g. manufactured after electrical resonance instability was discoverend, but still not fully compliant with today's input admittance criterion.
3.5 Future vehicles
Future vehicles are declared compatible with the electrical infrastructure and existing rolling stock according to the national Norwegian rules for rail vehicles published by Norwegian Rail Authority together with the Supplementary information and regulations.
4 Characterisation of existing operation conditions
Information about the operation of the existing system: number of trains in service, typical timetables, normal feeding arrangements, emergency feeding arrangements.
4.1 Power supply operation
Normal feeding arrangement:
- Interconnected operation via the overhead contact line in general
- Section of the network and island operation of one or several converter stations a common operating mode due to e.g. maintenance work both on the track and on the catenary. That means that single-side feeding of trains in a distance of approximately 60 km must be expected.
- The number of converter units operating in each converter station is adapted to the daily varying power demand from the train traffic.
Abnormal feeding arrangements are covered by the worst figures (respective min and max values) in Table 1. That is emergency feeding
- Outage of one complete substation resulting in distance between the remaining up to 160 km today’s 1*15 kV system and 240 km in planned 2*15 kV system (AT).
4.2 Train traffic
The traffic varies largely from sparse time tables for the long distance lines (0.7 trains/hour and 13 trains/day to 3,8 trains/hour and 70 trains/day in each direction) to the dense Oslo area (1,1 trains/hour and 19 trains/day to 24 trains/hour and 459 trains/day). Graphical timetable for all lines is available on internet at . All trains must be expected to be electric. Future plans are to increase the train traffic considerably, both freight and passenger traffic.
4.3 Electric vehicles
Several of the rolling stock listed in #Characterisation of existing rolling stock must be expected to operate in multiple configurations. The vehicle with highest power must be expected three times Cl74/75 with a rating of 14 MW at measured on current collector.
5 Characterisation of overall rail system/network
This is the combination of the information from steps 2, 3 and 4. It may be necessary to define different scenarios.
The rail system is characterised by:
- A large amount of thyristor controlled vehicles with high total harmonic distortion of the traction current resulting in high total harmonic distortion of the overhead contact line voltage and correspondingly high crest voltages. That is THDu may exceed 30 % and crest voltage up to 33 kV . Note however that these measurements are done in Sweden and that such conditions are not yet reported in Norway to any extent.
- Large electrical rating of the vehicles compared to common rating of one converter unit – their ratings may be in the same range
- Long single-track distance between the power substations when operated interconnected
- Frequent sectioning of the overhead contact line and then reduced or lost interconnection of between the power substations, i.e. single-side feeding of trains.
- Possible island operation of power substations resulting in the converter station and the vehicles operation directly connected in a one-to-one relation.
- The sectioning of the overhead contact line and island operation and relative rating of power substations compared to the operating trains increases the frequency of intervention of the substations current or power limiting function in order to prevent overload.
- Generally weak power supply (long lines, sectioning and so on) compared to the electric power demand from the trains results in automatic power limitation in the trains being a normal operating condition, e.g. limiting of power consumption when the line voltage decreases and limiting regenerated power when the voltage increase outside given limits. In order to increase the transmission capacity of the system before reaching these voltage limits, inverter vehicles may produce or consume reactive power, respectively. In some cases this reactive power consumption may be significant.
- Rotary converters with a poorly damped resonance frequency at 1.6 Hz
- Static converter stations that may not take regenerated power
- Large amount of cables for planned 2*15-kV system (AT) results in a generally low electrical resonance frequency
- Existing vehicles having capacitive filters that clearly lowers the electrical resonance frequency of the total power supply system
- Existing vehicles that do not comply with today’s compatibility requirement regarding stability (both electrical resonance instability and low-frequency instability)
- Some single-phase filters in existing static frequency converters apparently have a low damping.
- Detailed information about what electrical loading that must be expected in the network is given in Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Dimensjonering/Påregnelig belastning.
6 Theoretical analysis of overall rail system/network
Investigation of compatibility aspects for different scenarios. In a first step: confirm compatibility of the existing system. In a second step: test potential new element, check what characteristics they need to fulfil to maintain compatibility of the system.
6.1 Compatibility of existing system
The existing and expected future rail system shows the following signs of poor compatibility:
- Low-frequency instability and heavy power oscillations between the existing rotary converters and rolling stock
- Some observations of a rotating and static converter station oscillating together in close to no-load, though with a very small amplitude.
- Some static converter stations do not take power in reverse direction (by design)
- Future rail system in the line is expected to include a considerable amount of cables which have the impact of lowering the frequency of electrical resonances in the system. The lines are today trafficked by electric vehicles that are not passive above 90 Hz. The situation is expected to be worse when trains with large passive input filters are on the line. Then the lowest resonance frequency of the system may be below 90 Hz in some cases.
- The distances between the converter stations on the line are long, especially in abnormal situations
- The high total harmonic distortion of the line voltage may result in increased harmonic loading of the power substations compared to the total harmonic distortion of the load current only (e.g. by the “vacuum cleaner effect”).
6.2 Needed characteristics of the new element
Based on this, the requirements for the new element must as far as possible being passive or damping for any oscillations in order to be compatible with existing infrastructure and rolling stock under the given operation situations. Furthermore, the new element should not lower the already low electrical resonances in the system.
In general, the design of active converters and their control must be robust and generic. The needed operating conditions are:
- All possible load situations, that is in load (in both directions and in power limitation) and no-load with rapid changes between them
- As a standalone converter and located together with other static or rotary converters
- In interconnection to other converters via overhead contact line 1*15 kV and autotransformer system 2*15 kV and in island operation (alone in a network)
7 Acceptance criteria for new element
The results from the theoretical investigations in step 6 are the particular acceptance criteria for new element. The particular acceptance criteria must be understandable and measurable when designing and testing a new element. In future, these criteria shall be set up for all networks in identical form.
The following specific requirements have been generally identified:
- Contineously over voltage emission: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Generelt -> b) Kontinuerlig overspenning
- Short-term over voltage emission: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Generelt -> c) Kortvarig overspenning
- THDi immunity: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Dimmensjonering/Påregnelige påkjenninger -> g) THDi
- THDu immunity: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Dimmensjonering/Påregnelige påkjenninger -> h) THDu
- Low-frequency oscillations: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Lavfrekvent stabilitet -> a) Demping av resonanser
- Low-frequency oscillation immunity: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Dimmensjonering/Påregnelige påkjenninger -> i) Lavfrekvente pendlinger
- Dynamics immunity: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Dimmensjonering/Påregnelige påkjenninger -> j) Dynamiske hendelser
- Electrical resonance instability activity/passivity: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Elektrisk resonansustabilitet -> c) Aktivt frekvensområde
- Lowest electrical resonance frequency including rolling stock: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Elektrisk resonansustabilitet -> a) Laveste resonansfrekvens med rullende materiell
- Lowest electrical resonance frequency excluding rolling stock: Banestrømforsyning/Prosjektering og bygging/Kraftsystem#Overharmoniske og dynamiske fenomener/Elektrisk resonansustabilitet -> b) Laveste resonansfrekvens uten rullende materiell
Note that other or more specific acceptance criteria may have to be developed for the specific case depending on the new elements intended use and applied technology and technical solutions. For example, additional requirements valid for converter stations are given in Banestrømforsyning/Prosjektering og bygging/Matestasjoner#Overharmoniske og dynamiske fenomener.
- “201202 Single phase filters in static converters.odt” from Øyvind Stensby, undated but received by email 2012-02-27. The information in the document is based on plant documentation for the existing static converter units.
- Steinar Danielsen, A simulation study of the output impedance in the rotating reference frame. Jernbaneverket document EB.800100-00 dated 2010-09-01. May be available on request.
- Banestrømforsyning Autotransformatorsystem, Overspenninger pga. overharmoniske og elektrisk resonansustabilitet, Rapport, Bane NOR document EB.800502-000 dated 2017-02-21. May be available on request.
- Målte frekvensresponser for elektrisk resonansstabilitet - Måleresultater, Jernbaneverket document EB.800501-000. May be available on request.
- Målte frekvensresponser for elektrisk resonansstabilitet - Måleresultater, Jernbaneverket document EB.800501-000. May be available on request.
- Steinar Danielsen, Electric Traction Power System Stability – Low-frequency interaction between rail vehicles and a rotary frequency converter. PhD thesis at the Norwegian University of Science and Technology 2010. May be downloaded from http://ntnu.diva-portal.org/smash/record.jsf?searchId=1&pid=diva2:319110
- Markus Meyer, AT system stability analysis, JBV document EB.800110-000-004, Emkamatik document 05-0089, version 3 dated 2006-01-19
- Stefan Menth, AT system model structure and frequency responces, JBV document EB.800110-000-003, Emkamatik document 05-0088, version 1 dated 2005-10-31
- Markus Meyer, AT system stability analysis for Sørlandsbanen:Resonance and stability calculation. JBV document EB.800041-000, Emkamatik document 06-0129, version 3 dated 2006-08-23
- Markus Meyer, AT system stability analysis for Sørlandsbanen: Structure of calculation models. JBV document EB.800042-000, Emkamatik document 06-0123, version 1 dated 2006-04-13
- Markus Meyer, Compatibility study for static converter Stavanger. Emkamatik document 11-0380 dated 2011-11-29.