Degree project in
Potential of using Low Voltage Direct
Current in local distribution network to
improve the overall efficiency
Pierre Waeckerlé
Stockholm, Sweden 2011 Electric Power Systems
Master thesis report
KTH supervisor: KTH examiner:
Lars Abrahamsson Lennart Söder
Master student: Nexans supervisor:
Pierre Waeckerlé Lazhar Kebbabi
Abstract
This project reviews the potential of Low Voltage Direct Current (LVDC) to replace Low Voltage Alternative Current (LVAC) power in distribution grids. The study addresses three different problems: a comparative literature review on LVAC and LVDC systems, a study of the compatibility of the type of low voltage cables that are used in buildings with a future LVDC distribution grid and a technical comparison from transmission and conversion losses point of view.
The literature review provides an overview and explanations for the understanding of the problem. Then, a special review of ageing phenomena and implementation to the case study – low voltage building cables – concludes that there is a low risk of electrical ageing in existing Alternating Current (AC) cables when used in a Direct Current (DC) system.
Projektet studerar möjligheterna att ersätta LVAC med LVDC i distributionsnät. Studien behandlar tre olika frågor: en litteratustudie om LVAC- och LVDC-system, en studie av huruvida vanliga lågspänningskablar av den typ man har i byggnader kan användas i ett framtida LVDC-nät och en teknisk jämförelse av förlusterna i överföring och omvandling i LVDC- och LVAC-nät.
Litteraturstudien ger en översikt och förklaringar för att underlätta förståelsen för problemet. Sedan en särskild litteraturgenomgång av åldrandefenomen för likströms- och växelströmskablar för byggnader med låga spänningar och genomförandet av fallstudien – som drar slutsatsen att det är låg risk för elektriskt åldrande om man använder kablar avsedda för växelström i ett likströmssystem.
Aknowledgments
I would first like to thank Nexans for welcoming me at the NRC in Lyon. I
learned a lot of technical and non-technical things during those 6 months. I had
a very rewarding opportunity to learn a lot about cable manufacturing, even on
some matter that are out of my study scope but fed my curiosity.
Thank you to Lazhar Kebbabi and Arnaud Allais for their valuable technical
comments, guidance and critical review of my work all along that project.
A special thanks to the other interns, Yannis, Pierre-Marie and Jérémy for their
help. I would also like to thank the Nexans technicians that helped and/or
wel-comed me: Xavier, Jean-Michel, Olivier and Yann.
I also carried that project in connection with my supervisor Lars Abrahamsson
at the Electric Power Systems department at KTH. Thank you for the hints,
corrections and advices. Thank you also to Lennart Söder, my examiner, for the
critical, sensible and valuable comments on my work.
Abstract ii
Sammanfattning iii
Aknowledgments iv
List of figures viii
List of tables ix
Introduction 1
1 Literature review on LV systems 2
1.1 Conversion technologies . . . 2 1.1.1 From AC to DC . . . 3 1.1.1.1 Historical review . . . 3 1.1.1.2 Un-commanded rectification . . . 3 1.1.1.3 Commanded rectification . . . 4 1.1.2 From DC to AC . . . 5 1.1.2.1 Historical review . . . 5 1.1.2.2 Principles . . . 5 1.1.3 From DC to DC . . . 6 1.1.3.1 Historical review . . . 6 1.1.3.2 Linear converter . . . 6 1.1.3.3 Switched-mode converters . . . 6 1.1.4 From AC to AC . . . 7
1.1.5 Switched-mode power supply . . . 8
1.2 Appliances technology . . . 10 1.3 Protection systems . . . 11 1.3.1 Electrifying . . . 11 1.3.2 Grid fault . . . 11 1.3.3 AC protection systems . . . 12 1.3.4 DC protection systems . . . 13
1.4 DC and new trends . . . 13
1.4.1 Environmental concerns . . . 13
1.4.2 Improving the overall efficiency . . . 14
1.4.2.1 AC intrinsic losses . . . 14
1.4.2.2 Electronics . . . 14
1.4.2.3 Renewable sources . . . 15
1.4.3 Smart grids . . . 15
1.4.3.1 Grid ageing . . . 16
1.4.3.2 Grid topology evolution . . . 16
1.4.3.3 Micro-grids . . . 17
vi CONTENTS
2 Cable ageing in LVDC 18
2.1 Description of ageing phenomena . . . 18
2.2 Basic calculations of some ageing phenomena . . . 20
2.3 Conclusion of the chapter . . . 20
3 AC and DC comparison 22 3.1 AC versus DC in literature . . . 22
3.1.1 AC advantages . . . 22
3.1.2 DC advantages . . . 23
3.2 Cables under LVDC conditions . . . 24
3.2.1 Methodology . . . 24
3.2.2 Energy losses in cables . . . 24
3.2.3 Analytical calculations . . . 25
3.2.3.1 Simple skin effect model . . . 26
3.2.3.2 Skin and proximity effect coefficients . . . 27
3.2.3.3 Conclusion on the skin and proximity effects . . . 28
3.3 LVDC layouts . . . 30
3.3.1 Comparison generalities . . . 30
3.3.2 Transmissible power . . . 30
3.3.2.1 Household power grid . . . 32
3.3.2.2 Distribution power layout . . . 33
3.3.3 Results and analysis . . . 36
3.3.3.1 Household power grids . . . 36
3.3.3.2 Distribution power grids . . . 36
3.4 Energy consumption comparison . . . 40
3.4.1 Methodology . . . 40
3.4.2 Monte Carlo simulation theory . . . 40
3.4.3 Simulation model and hypothesis . . . 41
3.4.4 Energy consumption of appliances . . . 43
3.4.5 Simulation workflow . . . 44
3.4.6 Simulation results . . . 45
3.5 Conclusion of the chapter . . . 47
4 Conclusion 49 4.1 Discussion . . . 49
4.2 Future work . . . 50
A Ageing phenomena complements 51 A.1 Electric field calculation . . . 51
A.2 Electric field results . . . 51
B Analytical results 53 B.1 Skin depth calculation . . . 53
B.2 Skin and proximity coefficients . . . 55
C Monte Carlo complements 58
C.1 Stratified sampling theory . . . 58
C.2 Batch allocation method . . . 59
C.3 Appliances equipment rate . . . 60
C.4 Appliances usage description . . . 61
C.5 Appliances consumption . . . 62
C.6 Matlab scripts . . . 63
C.6.1 Main code program . . . 63
C.6.2 Household creation . . . 66
C.6.3 Household simulation . . . 67
C.6.4 Set of equipments . . . 68
C.6.5 Consumption patterns . . . 68
C.6.6 Consumption calculation . . . 69
C.6.7 Calculation stopping rule . . . 70
C.6.8 Batch allocation . . . 71
Glossary 73
List of Figures
1.1.1 Three different schemes of rectifiers . . . 3
1.1.2 Graph of the voltage rectification from three-phase system . . . 4
1.1.3 Power Wave Modulation example . . . 6
1.1.4 Dimmer for AC power modulation . . . 7
1.1.5 Appliances safety classes . . . 8
1.1.6 Switched-mode power supply principle . . . 9
1.4.1 Sales of ICT units . . . 15
1.4.2 Cumulated installed PV capacity . . . 16
2.1.1 Breakdown and degradation phenomena . . . 19
3.2.1 Geometry parameters of the cable section . . . 26
3.2.2 Conductor disposition . . . 28
3.2.3 Chart representation of ys+yp for 2 and 3 conductors configurations . . 29
3.3.1 Possible grid layouts at household scale . . . 31
3.3.2 Possible grid layouts at distribution scale . . . 31
3.3.3 A simple scheme of a load fed by a single-phase system . . . 32
3.3.4 Synthesis of the power limitation capacity . . . 37
3.3.5 Transmissible power versus load distance . . . 38
3.3.6 Transmissible power limitation change at constant section . . . 39
3.4.1 The layout of a basic Monte Carlo simulation . . . 40
3.4.2 Pure AC appliances power conversion . . . 43
3.4.3 Pure DC appliances power conversion . . . 44
3.4.4 Monte Carlo simulation workflow . . . 45
3.4.5 Simulation results . . . 48
A.1.1Parameters of a building cable . . . 51
B.1.1Skin effect impact on resistance . . . 54
1.1.1 IGBT conversion losses . . . 5
1.2.1 Main appliances . . . 11
3.4.1 Household types . . . 41
3.4.2 Description of the usage of each appliance, extract . . . 42
3.4.3 Summary of the conversion efficiencies [1] . . . 44
3.4.4 Yearly consumption by type of household . . . 46
3.4.5 Yearly consumption difference for each household type . . . 46
A.2.1Values of electric field . . . 52
B.1.1Skin depth . . . 53
B.2.1Skin and proximity coefficients, 2 conductors . . . 55
B.2.2Skin and proximity coefficients, 3 conductors – trefoil . . . 55
B.2.3Skin and proximity coefficients, 3 conductors – flat . . . 56
B.3.1Transmissible power . . . 57
C.3.1Appliance equipment rate by type of household . . . 60
C.4.1Usage description of each appliance by household type . . . 61
Introduction
The project was initiated by Nexans to explore the potential of DC distribution networks. As a cable manufacturer Nexans produces a wide variety of cables from building cables to High Voltage Direct Current (HVDC) submarine cables. Within Nexans, the project was conducted by the Nexans Research Center of Lyon in the MV/HV unit.
The potential of DC in the power system is the subject of many papers. But the outcomes of each study are related to the initial assumptions of each study. The thesis was to provide an insight to Nexans on the subject.
The project was divided in three objectives: a) a state of the art on Low Voltage (LV) networks, with the idea to compile useful knowledge for the understanding, assessment and comparison of LVAC and LVDC grids, b) a losses comparison between LVAC and LVDC to provide comparative figures resulting from verified calculations about trans-mission and conversion losses, c) cable capabilities is the last concern dealing with the capability of existing LVAC cables to sustain LVDC stress.
Literature review on Low Voltage
distri-bution systems
In 1879, the American scientist and inventor, Thomas Edison, patented an incandescent electric lamp [3]. But T. Edison also tried to design a complete power distribution scheme so to make electric lighting competitive with gas systems [3]. In 1880s lighting appliances used electric arcs, Edison designed a DC grid [3]. The first DC grids build by Edison appeared in 1882 (Holborn Viaduct, London, England – temporary installation) and 1884 (Pearl Street Station, New York City, USA – permanent) [3].
The Edison DC system used LVDC. As the raise of the voltage level was not eco-nomically competitive in the 1880s, the served loads were only found in dense area. The copper needed to carry the power at 110V was costly and the line losses limited the size of the systems down to around 2 miles [3].
That issue was solved with AC systems. According to Michael Faraday’s law, the change of a magnetic field with time will induce a current in a nearby wire. By nature, the AC power creates a varying magnetic field. Using two inductors winded up around the same magnetic circuit, the voltage can be stepped up and down. The first AC power system was demonstrated in 1881 by Lucien Gaulard and John Gibbs [3]. The early transformers were improved over history by many inventors and engineers. Among those improvements, the contribution of Nikola Tesla is significant. In 1887, he filled 7 patents on the matter of polyphase AC motors, power transmission, generators, transformers and lighting.
The combined use of three-phase AC for transmission and distribution and single-phase AC for end-use proved to be a very efficient system [4]. The AC solution, backed by George Westinghouse, opposed with the Edison DC solution in what is commonly named The War of Currents starting 1888 [3]. The AC system won that “War” because it succeeded in installing power lines over always increasing distances. The increase of the distance was made possible thanks to the increasing voltage of High Voltage (HV) power lines.
AC power has been the power distribution power form ever since. But the arrival of home electronics by the end the of the 20th century reintroduced DC in an increasing number of appliances.
1.1
Conversion technologies
1.1 Conversion technologies 3
1.1.1
From AC to DC
1.1.1.1 Historical review
The first AC to DC conversion used electromechanical means as the power electronics did not exist. It means coupling an AC motor – converting the AC power into rotational energy – with a DC generator – converting rotational energy into DC power. Due to the complexity of the motor-generator set, the technology is inefficient, expensive and requires intensive maintenance [3].
Power electronics made the rectification an economically feasible technique, first using plasma technology. For HVDC transmissions, mercury arc valves were used. The mercury arc rectifier is based upon an electric arc which, thanks to the valve environment, can only be established in one way of the current. For lower voltages, argon gas electron tube and vacuum tube were used. Power electronics reliability and efficiency have been greatly improved thanks to semiconductors technologies. Nowadays, the AC to DC conversion is performed thanks to silicon-based components.
1.1.1.2 Un-commanded rectification
The basic rectification - called half-wave rectification - uses a single diode to prevent the backward displacement of charge carriers. In figure 1.1.1a, the principle is shown in a schematic way. The big advantage is the system simplicity as a single diode is necessary. But in half-wave rectification, the load is only fed during half the time. Thus the average output voltage is at most half of the input one and the output signal contains unwanted harmonics.
(a) Half-wave
(b) Full-wave
(c) Graetz
To improve the power quality, other scheme exists such as the full-wave rectification. To perform such a rectification, at least two diodes are needed: one conducting when the current is positive (from the load point of view) and one when it is negative([5, 6] and figure 1.1.1b). It is also possible to use 4 diodes in a Graetz rectifier as in figure 1.1.1c. It uses 2 additional diodes but still is more interesting from an economical point of view: compared to the full-wave rectifier, only two connections to the secondary side of the transformer is needed.
The output of those rectifiers presents a strong electrical noise that can be reduced with appropriate filtering units combining inductors and capacitors to remove unwanted harmonics in the signal.
It is also possible, using the same principle to convert three-phase power to DC power in a very efficient and clean way. Simply using full-wave rectifiers, one per phase, with their outputs in parallel yields a signal whose oscillating frequency is six times higher than the input one as shown in figure 1.1.2 [5, 6].
Figure 1.1.2 – Graph of the voltage rectification from three-phase system
1.1.1.3 Commanded rectification
Semiconductors provide three different components:
1) Diodeis the simplest one. A current can only flow in one direction through a diode [7]. That is the reason we named the rectifier in section 1.1.1.2 un-commanded. 2) Thyristors is an “improved diode”. The current can only flow in one direction and
thyristors allow to control when they start conducting [5].
3) Transistors are the latest of the components. They are equivalent to fully control-lable switches.
1.1 Conversion technologies 5
• LCC1 uses thyristors to convert power. It is the technology offering the highest
power range with the disadvantage to be more expensive [8].
• VSC2 uses Insulated-Gate Bipolar Transistors (IGBTs) instead of diodes or
thyris-tors. While invented in the late 1970s, the IGBT technology became interesting for power electronics in the 2000s. The VSC are available for smaller power than LCC with a lower efficiency [8]. Still, development is on its way and works to improve the efficiency. The major advantage of transistors is their low cost, easing the recent development of HVDC lines. With appropriate design VSC allow for bi-directional power flow. If they have at least two conversion stages, they can either rectify or invert power [9].
A method for calculation of the conversion losses for IGBT modules is found in [2]. There might be conduction losses or switching losses depending – among others – on the switching frequency fsw, the nominal current Inom and the actual current flowing
through the converter. The other parameters are listed in [2]. Running the calculation for a converter with a rated current Inom = 1200A, for frequencies varying in the range
fsw = 1.5− 20 kHz and loading of 25, 50, 75 and 100% give the values displayed in table
1.1.1. fsw Converter loading kHz 25% 50% 75% 100% 1.5 0.89 1.68 2.61 3.68 5 2.04 3.40 4.91 6.56 10 3.68 5.87 8.20 10.68 15 5.32 8.33 11.49 14.79 20 6.96 10.80 14.78 18.91
Table 1.1.1 – Conversion losses for IGBT modules in kW
1.1.2
From DC to AC
1.1.2.1 Historical review
As for rectification in section 1.1.1.1, an electromechanical conversion was first the only way to invert from DC to AC. The vacuum tube technology was then used to convert DC to AC, especially for the first HVDC links. The transistor is the power electronics component that first replaced the vacuum tube at commercial scale. Nowadays, IGBT are widely used in power electronics.
1.1.2.2 Principles
To recreate an alternating current from a direct current, we need to carry current in one way and then in the other way. We can do that with two switches: one will conduct
the current in one way while the other is opened and vice versa. With the appropriate frequency of switching we control the power waveform and frequency.
It is common to use pulse-width modulation3 which generates square-waves of
differ-ent width to recreate a sine wave signal. The faster the commutation, the higher the harmonics frequency and thus the easier it is to filter them. But the faster the commu-tation, the higher the commutation losses. A low-frequency example is shown in figure 1.1.3, with 6 oscillations per period. Nowadays, grid-tied inverters (used for photovoltaic panels for example) reach 94-96% efficiency [5].
Figure 1.1.3 – Power Wave Modulation example
1.1.3
From DC to DC
1.1.3.1 Historical review
As explained in section 1.3.3 for AC to DC and DC to AC, electromechanical conver-sion was the only way to convert DC power from one voltage to another. With power electronics, DC to DC conversion is available at high efficiencies.
1.1.3.2 Linear converter
A linear converter consists of a variable resistor continuously adjusting a voltage divider network to maintain a constant output voltage. The resistor is in parallel with a diode. Only half the alternating waveform is flowing through the load. The other half flows through the diode during its conducting periods. According to the Ohm law, the higher the voltage drop, the higher the losses [5]. Those highly inefficient devices are currently replaced by switched-mode converters.
1.1.3.3 Switched-mode converters
To convert one DC voltage to another, a solution is to store the input energy in either magnetic field storage components (inductors or transformers) or electric field storage
1.1 Conversion technologies 7
components (capacitors) and to release it at another voltage. The efficiency of such devices, ranging from 75 to 98% [5, 7], is much better than linear regulators.
Many different topologies exist for DC-to-DC converters. Two properties allow for a ranking of the different topologies [5]:
• Galvanic insulation may be performed by a DC-to-DC converter. If the galvanic insulation is requested, the presence of a transformer is necessary in the layout. Thus, the input DC power is to be inverted to AC first. Then, the AC intermediary power goes through a transformer before a final rectification.
• The path of the energy flow can either be simultaneous or in two steps. Simul-taneous means the energy goes directly from the input, through the storage and to the load. In a two-steps process, the energy is first stored and then released to the load. Simultaneous converters cannot step the voltage up.
The topologies may also be characterized depending on the switching mode of the solid-state components:
• Hard-switched means that the transistors switch quickly while under both high current and voltage. This reduces the efficiency and the reliability of the system [10]. • Resonant means that the voltage across the transistor is shaped by an LC cir-cuit. Thanks to that resonance, either the current or the voltage can be zero when switching. Opposed to the hard-switch mode, the resonant mode is also named soft-switching mode. This technology represents a major opportunity for efficiency and reliability improvement.
The way the device is operated is also divided in two categories, referring to the current shape:
• Continuous means the current never equals 0 during operation.
• Discontinuous means the current goes back to zero before the end of the conversion cycle.
1.1.4
From AC to AC
Figure 1.1.4 – Dimmer for AC power modulation
AC power is stepped up or down using transformers [11]. The physical principle can easily be found in the literature. A common approximate for distribu-tion transformer efficiency is 98%. Some experimen-tal transformers using superconducting windings can achieve 99.9% efficiency. But they are far from being profitable.
a sin wave. Using a thyristor it is possible to obtain the desired output power. The figure 1.1.4 shows the output signal of a dimmer with a cycle ratio of 1
2, i.e. the thyristor
becomes conducting during one half of the wave cycle (or commute every 1
4 cycle).
1.1.5
Switched-mode power supply
At last, a “mixed” kind of power converters is of interest. By mixed, it is meant that those Switched-Mode Power Supply (SMPS) use rectification, inversion and voltage levelling during their conversion steps. But they also are the most common type as they are used to power every modern electronic load.
Their topologies is the result of a few different constraints:
• Galvanic insulation is necessary to ensure a good user’s safety. The International Electro-technical Commission (IEC) defines 4 different appliances classes [12]. Each class define a different level of protection, the symbols are shown in figure 1.1.5. Class 0 – meaning no galvanic protection – is omitted.
(a) Class 1 (b) Class 2 (c) Class 3 Figure 1.1.5 – Appliances safety classes
• Controlled voltage is another constraint for sensitive loads such as electronics. The expected output voltage has to remain within safety limits whatever the load. A real time control of the output power is therefore necessary.
• Power quality is essential for sensitive loads. Harmonics are to be avoided as much as possible, both on AC and DC sides.
• Weight and bulk must be as low as possible.
• Energy efficiency should be maximized to save on thermal dissipation elements and input energy.
As described in [5, 13], the following progression of conversion can be observed, as summarized in figure 1.1.6:
1.1 Conversion technologies 9
2. High-frequency inverter: the rectified power is inverted to AC power at high frequency (typically 20-30 kHz). This is the stage which allows control over the power flow – PWM – and output voltage. The regulation mechanism is detailed in item 5.
3. Transformer: the high frequency AC current is levelled to the desired output voltage(s). The transformer also ensure part of the galvanic insulation (the feedback loop, if any, also must be isolated). Thanks to the high frequencies, the transformer is much smaller than a 50/60 Hz equivalent.
4. Output rectifier: once the voltage is at the desired level, the power is rectified to DC [5, 13, 14]. Similarly to the input rectifier, the high-frequency inverter noise is filtered to provide an high quality output.
5. Regulator: located between the DC output and the high-frequency inverter, the output voltage and current can be regulated that way.
1.2
Typical household and office appliances and their
working principles
The conversion technique is closely related to the kind of load to be supplied. Some will not require high-quality power, while other will. The amount of existing appliances is tremendous. Therefore it is necessary to constitute categories by operation principle. The operation principle indicates which kind of power conversion is performed in the appliance. Each principle is defined as follow:
• “Pure AC” appliances: Many appliances use an induction motor to work. Induc-tion motors are used in appliances requesting more mechanical power than possible through universal motors. Whether they command or not the rotational speed of the motor changes the way the input power is transformed:
Variable drive is found when control of the speed is necessary. The induction motor exploits the changing nature of the alternating current to create a mag-netic field. Therefore, the induction motor must be fed with AC. According to equation 1.2.1, the synchronous speed ns is directly proportional to the power
frequency f if the number of poles p of the motor is kept constant. ns =
120× f
p (1.2.1)
The power has to be rectified first and then inverted to control the motor speed closely. A variable drive would work if fed with DC power.
Fixed speed can be used when no speed variation is necessary which means a sin-gle frequency – usually the grid frequency. It was the case in cooling (refriger-ator, freezer) and heating (heat pump) appliances, the control only command if the cycle is running or not. In case of use in DC, an input inverter would be required. That kind of appliances is disappearing and will be neglected in section 3.4.4.
• “Pure DC” appliances: are the appliances whose working principle requires DC power to run properly:
Magnetroncreates microwaves with the ability to warm up food in micro-waves oven for example. As a magnetron runs on High Voltage Direct Current, the first stage in the energy conversion chain is a rectification. The Magnetron mechanism is completely compatible with Direct Current power feeding. Electronic gathers all new kinds of appliances running on DC power. Due to
the need for a controlled voltage, all those appliances rely on Switched-Mode Power Supplies.
1.3 Protection systems 11
Apparatus Equipment rate (%) Operation principle Pure AC
Refrigerator 99.8 Compression cycle
Freezer 86.1
Washing machine 94.2 Induction motor
Dishwasher 48.8
Pure DC
Microwave oven 83.7 Magnetron
TV 97.1
Electronic Video recorder & DVD 83.3
Land-line phone 88.1
Cell phone 78.9
Personal computer 62.8
Internet connection 54.7
Table 1.2.1 – Main appliances with their operation principle, INSEE 2008 [15]
1.3
User’s and apparatus protection in AC and DC
1.3.1
Electrical accident, user’s point of view
From a user’s point of view, the power represents the risk of getting electrified. An electrifying contact can be of two kinds:
• Direct contact happens when touching directly or through a conducting object an active part. An active part is defined as a part used to carry current. In other words, a direct contact happens due to a lack of information or judgement. One may say that with the appropriate knowledge such an accident would have been avoided.
• Indirect contact happens when touching directly or through a conducting object an inactive part. An inactive part is defined as a part usually grounded. In other words, an indirect contact happens when a fault occurs and bring to a certain potential a part which should be at ground potential. One can say that this kind of accident is unfortunate.
1.3.2
Electrical fault, as seen from the grid
Depending on how the electrifying happens, three kind of faults are identified:
Short-circuit occurs when the current find a low-resistive path. This requires the con-nection of two parts at different voltages.
Over-current is the consumption by a given component or group of components of an excess amount of power. Over-current may happen in a large range of cases including a short circuit.
Leakage currents is another kind of electrical fault. Due to a fault, some current does not return to the feeding transformer through the neutral conductor but through the ground.
1.3.3
Protection mechanisms for users and components in AC
systems
The protection is ensured thanks to fuses and circuit breakers. Actual European norms for newly built homes recommend the use of circuit breakers. The reason for that decision is that a fuse can be simply replaced by a conducting material (a copper conductor for example) thus removing the fuse protection. Their role is simply to open the circuit when detecting a fault.
A fuse is simply made of a metal wire that melts when too much current flows. They are perfectly compliant with DC systems at same RMS value.
The circuit breaker are designed to detect the three kinds of faults described in section 1.3.2. A circuit breaker may combine the following detection systems [12, 16] :
• Magnetic tripping consists in a conducting solenoid winded up around an actu-ator made of soft-iron. A basic law of electromagnetism is that any wire driven by a current creates a magnetic field. In a solenoid, it can be demonstrated that it creates a magnetic field parallel with the solenoid axis inside it. The higher the current in the solenoid, the higher the pulling force on the actuator. This is a quick system but with low precision regarding the current. As a result, magnetic circuit breakers protect against short circuits.
• Thermal tripping consists in a conducting bi-metal plate. Due to the different thermal properties of the plate, the two sides of the bi-metal will not thermally expand the same way under an increased current. Thus, the plate will twist until engaging a switch. This is a slow mechanism due to thermal conduction but highly accurate. Therefore, the bi-metal protects against over-currents.
• Residual-current device or differential circuit breaker consists in a magnetic torus – the magnetic circuit – around which are winded up: the phase and neutral conductors for single-phase systems as well as an additional inductor to measure the magnetic field difference in the magnetic circuit. Being driven by alternating current, each conductor creates a varying magnetic field in the torus. Under normal operation, the current going through the phase and coming back from the neutral are the same in opposite directions. The magnetic fields created in the torus are of same value and opposite direction so that the sum evens out. In case of leakage in the circuit, some current will not return along the neutral conductor. The magnetic fields in the torus will not cancel each other out any more. According to Lenz law, e =−dΦ
dt, a voltage e will appear between the measuring inductor terminals if the
1.4 DC and new trends 13
• Arc interruption, is an essential component of circuit breakers. A “breaker”, has to be able to open safely. A circuit breaker can be switched open under voltage. Thus, it must be able to extinguish the arc. In low voltage AC circuit breakers, the arc is divided in several arcs in parallel thanks to metal plates. The metal plates also perform a cooling of the arcs. Those actions will both increase the voltage across the arc and decrease the conductivity of air. The system is designed to reach certain conditions leading to auto-extinction at a zero-crossing point of the AC signal [16].
1.3.4
Ensuring electrical safety for users and components in a
DC layout
From section 1.3.3, the main problems to ensure electrical safety in DC are the differential current detection and the arc interruption. As stated above, the arc interruption is based upon a zero-crossing point with voltage-temperature conditions favourable to the arc extinction. But in DC systems, this zero-crossing point will never happen [16].
A solution is to generate oscillations so to create a zero-crossing point when a breaker opening is necessary [10]. This is the same approach as for resonant converters. Using such a solution makes a radical change in the safety components. The time at which the circuit will have to be opened is decided by a detection device. The detection can therefore consist of short-circuit, overload and leakage current. Once detected, the device send the order to a couple of switches to open. This starts an oscillatory period using capacitors and inductors and the soft-switching is possible.
The components are already commercially available [17]. But as they are not as widespread as AC components, their selling price is high.
1.4
DC and the future of electricity in buildings
New power usage and generation appear nowadays, along with new concerns for environ-ment. Section 1.4 reviews the advantages of DC system to make the existing power grid compliant with new trends.
1.4.1
Environmental concerns, the 20-20-20 target
For a few years, environmental concerns have gained visibility. In Europe, the European Commission defined the 20-20-20 target in March 2007 [18]. The three targets are:
• Emissions: reduce by 20% – compared to 1990 – the greenhouse gases emissions by 2020.
• Renewables: 20% of the primary energy consumption in 2020 should be provided by renewables energy sources.
All those targets have major impacts on the power grid and its future evolution. And they all are linked together. For example, reducing the primary energy use through effi-ciency improvements will make it easier to provide the remainder with energy generated using renewables.
1.4.2
Improving the overall efficiency
As stated in the climate and energy package, the efficiency is a key measure towards the fulfilment of the targets. This means considering each step of the energy cycle, from generation to consumption, and tracking the waste of energy. From that perspective, AC leads to a certain amount of losses due to its fluctuating nature.
1.4.2.1 AC intrinsic losses
AC power leads to various phenomena creating power leakages. The electromagnetic phenomena are the leading reason for intrinsic losses in AC systems [11].
The fluctuating nature of AC power creates varying magnetic fields Φ. As described by Lenz law, a varying field creates a voltage that tends to counterbalance its variation:
e =−dΦ dt
As a result, a various range of undesired currents appear in all the components of an AC scheme (cables, transformers). The resulting effects are skin or proximity effects.
Reactive power is another problem in AC which reduces the power components ability to deliver active power. The equilibrium of the active and reactive power balance requires careful supervision.
1.4.2.2 Electronics
While the typical consumption profile of appliances in power grid has been the same for over a century, this situation is changing with the widespread use of electronics at home and offices.
The concerned appliances are televisions, video recorders, personal computers, phones and others (see table 1.2.1). As of INSEE 2008, 97% french households owns a television and over 90% owns a telephone (land-line or mobile). Those figures only take into account the households but every offices are equipped with computers and photocopiers. The figure 1.4.1 shows the increase in sales of Information and Communications Technology (ICT). There is an obvious trend to get equipped with electronics.
1.4 DC and new trends 15
Figure 1.4.1 – Sales of ICT units from 1990 to 2009, INSEE 2010
1.4.2.3 Renewable sources
Along with the new environmental awareness, new power generation sources are increasing in number as illustrated in figure 1.4.2. Those power units require conversion stages before the grid connection. The steps can be of two types:
DC-to-AC some generation units such as fuel cells and Photo-voltaic (PV) panels gen-erate DC power. To get connected to the grid, either an AC or DC one, they need some conversion steps. But, while the connection to an AC grid would require both a DC-to-DC step-up rectification and a DC-to-AC inversion, the connection to a DC grid would save the inversion.
AC-to-AC some generation units such as windmills generate AC power at another fre-quency than the frefre-quency of the grid. Thus, the generated power needs to be rectified and inverted at the grid frequency. In a DC grid scheme, the rectifier stage would be enough, saving the losses of the inverter stage.
1.4.3
The “Smart grid” trends
“Smart grid” is an expression that become more present in everyday life. The root of the concept is to implement ICT in power grids to improve them. What “improve” means is wide: more reliable, safer, cheaper, cleaner,...
Figure 1.4.2 – Cumulated installed PV capacity, RTE 2011
1.4.3.1 Grid ageing
Power grids in the countries members of the Organisation for Economic Co-operation and Development (OECD) are ageing. In France, most of the 220kV-grid was deployed between 1900 and 1938. It was reinforced in the 70’s with a 400kV-grid to transport the power generated by nuclear power plants. The grid topology and material is 40 years old. The necessary refurbishment and strengthening of national grids is a major opportu-nity to adapt its topologies to new consumption and generation trends. One opportuopportu-nity with direct current is to save on consumption and losses to make available some trans-mission capacity without building new lines. If DC systems saves on losses, they would postpone the expansion of the grid until the consumption increase reaches the new max-imal transmissible power.
1.4.3.2 From a centralised to a distributed grid
Another concept and root of the smart grid is the shift from a centralised toward a distributed grid. In the current grid, there are plants on one side of the power lines opposing to loads on the other side. This is a centralised scheme.
1.5 Conclusion of the chapter 17
1.4.3.3 Micro-grids
A micro-grid is, by definition, formed when an electrical region capable of autonomous operation is islanded from the remainder of the grid [19]. Compared to today’s systems, the major point is the ability to ensure autonomous operation. Nowadays, when the feeding point of a consumption area breaks down, the concerned area is not anymore supplied with power even if some local units generate the sufficient amount of power within the area. The reason is simply that the area is not equipped with the systems necessary to ensure the required safety and quality. Two major challenges with micro-grids can be defined [20]:
• Operation mode can either be connected or islanded. The micro-grid must be able to handle the shift from one to the other mode while keeping the safety level constant. The mode choice depend on economical, safety and reliability parameters. Within each mode, the priority can be changed: ensuring the supply whatever the cost or minimizing the generation costs.
• Voltage and frequency management is another issue to be handled by the micro-grid whatever the mode. The controlling unit must have some generation units under control, called distributed generation units, with appropriate response time and power capacity.
To develop micro-grids, a distribution of intelligence is necessary. This may make a better use of distributed generation, reduce the line losses and increase system reliability. Consumption sites would therefore be like islands able to “live” disconnected. The strong decoupling between the feeding grid and the micro-grid makes it easier to use DC power as the AC to DC conversion might be centralised at the control unit level.
1.5
Conclusion of the chapter
Chapter 1 gives a first explanation about a wide range of aspects of DC systems. Because AC systems are the existing ones, the given explanations always kept them as a reference. In the light of chapter 1, DC systems seem promising in the necessary evolution of the actual grid, although some problems remain to be solved.
Cable ageing under Low Voltage Direct
Current stress
Existing cables available on the market are designed for existing installations. This means that low voltage common type building cables are designed, tested and guaranteed for AC grids. Other cables are also available on the market for DC applications such as PV, telecommunications, ˙.. But they are of specific type. For PV farms, cables are designed to sustain severe outdoor constraints – especially UV ageing. In telecommunications, the extra low voltage in use, 48V, cannot be compared with the 230V of distribution grids.
The scope of the study are the LV cables used in distribution networks and buildings with voltages up to 1kV. Three types of insulations are of interest: Polyvinyl chloride (PVC), Halogen Free Fire Resistant (HFFR) or reticulated polyethylene (XLPE).
2.1
Description of ageing phenomena
Electrical ageing phenomena are the results of physical and chemical processes accelerated or driven by an electric field [21]. The theory for calculating electric field in a cable is detailled in A.1.
The phenomena leading to partial or complete deterioration of an insulation can be ranked either in degradation or breakdown phenomena. The difference is the time to breakdown: up to around 1000 hours for breakdown mechanisms while degradation occurs above 1000 hours. A schematic view of the different phenomena on a Voltage-time referential is given in 2.1.1, they are [21]:
• Breakdown
– Thermal breakdown when the heat produced by resistive heating in the cable is not balanced by heat losses, the temperature of every components increases up to thermal breakdown,
– Electrical breakdown avalanche breakdown when small currents are multi-plied by an increase in the number of charge carriers at very high fields. – Electromechanical breakdown is due to electrostatic attraction compressing
the insulation and thus decreasing its width. The width variation is related to the Young modulus of insulation polymers,
– Partial discharge happens in the gaseous content of micro-voids1, above a
certain voltage. The electrical discharges erode the internal surfaces and help electrical trees to grow,
2.1 Description of ageing phenomena 19
• Degradation
– Electrical tree is the result of partial discharges. This is the resulting degradation phenomenon provoked by the partial discharges breakdown phe-nomenon,
– Water tree occurs when the insulation is in contact with an aqueous elec-trolyte. Some chemicals reactions happen under the electrical field that grad-ually lead to the insulation breakdown.
Figure 2.1.1 is a general overview of the possible phenomena – either in AC or DC.
2.2
Basic calculations of some ageing phenomena
From the theory shown in section 2.1 and appendix A.1, a basic calculation of ageing phenomena is performed. The first step is to assess the electric field magnitude. According to equation A.1.2, the calculation results are shown in table A.2.1 for different voltages and typical building cables.
Those results shows that the insulation thickness is around 1mm. We can define an equivalent thickness seq calculated in 2.2.1, which represents the thickness of a plate of
insulating material reproducing the same electric field constraint. seq =R2 ln
R2
R1
(2.2.1) If s is the real insulation thickness, we have R2 = R1 +s and s ≈ 1 mm. Thus the
radius ratio can be rewritten in equation 2.2.2. R2
R1
= 1 + s R1
(2.2.2) As s ≈ R1 (see table A.2.1) in our case study, we can simplify seq using Taylor series
in equation 2.2.3. seq =R2ln R2 R1 =R2ln 1 + s R1 ≈ s→R1 (R1+s) s R1 ≈ s→R1 s + s 2 R1 ≈ s→R1 s (2.2.3)
We can assume that seq ≈ 1mm, which allows to assume that the electric field in the
insulation is proportional to the voltage – with unit V/mm.
From the point of view of breakdown phenomena, we are in the range 0 to 1 kV/mm – or 0 to 1 × 106V /m. Comparing this value with the inventory of breakdown and
degradation phenomena from figure 2.1.1, there might only be thermal breakdown and water treeing leading to breakdown.
2.3
Conclusion of the chapter
2.3 Conclusion of the chapter 21
The calculations showed that risks of breakdown or degradation are very low. Ther-mal breakdown and water treeing degradation were identified as the two possible causes for breakdown. The first phenomenon – thermal breakdown – can be limited or avoided through a good thermal design of the cable or sufficiently high safety coefficients to ac-count for possible hazardous electrical installations. There is nothing different compared to AC cables. The second phenomenon – water treeing – may occur in presence of an aqueous liquid in contact with the cable insulation. This might be easily avoided with appropriate electrical installations.
Technical comparison of AC and DC
sys-tems
The review of LV networks lead to a mixed conclusion about the potential of LVDC to efficiently replace LVAC. Chapter 3 aims to run a technical comparison between LVAC and LVDC.
The different components of a distribution power grids can be ranked under the 4 following categories:
Cables they were studied in terms of ageing in chapter 2 and they will be studied in terms of efficiency in section 3.2,
Conversion power conversion is present at every stage of the transport and distribu-tion and especially when considering DC in the actual all-AC distribudistribu-tion power grid. The conversion will be estimated from articles to perform a consumption comparison,
Protection this is specific to low-voltage grids with appropriate protection systems. Section 1.3.3 showed that appropriate components exists but are not yet on the shelf. The protection components will not be considered in the technical comparison, Appliances the appliances are the reason of the distribution power grid. The rise of
pure DC technologies is also a reason for the questions around LVDC. The power consumption of appliances will be compared in AC and DC systems.
Chapter 3 starts with a literature review of the advantages of AC versus DC grids in section 3.1. Section 3.2 continues with a comparison of the cable losses, to assess if there is a loss reduction when switching from AC to DC. Section 3.3 considers different distribution layout and assess their efficiency in terms of transmissible power. Finally, a consumption comparison is carried out in section 3.4.4 using a Monte Carlo simulation at a multi-household scale.
3.1
General comparison of AC and DC advantages
From [22, 23] a general overview of AC and DC systems pros and cons can be drawn. Those advantages extracted from the literature will be quantified in the other sections of chapter 3.
3.1.1
AC advantages over DC
3.1 AC versus DC in literature 23
Safety of users and components is ensured by fuses or circuit-breakers – fuses are now forbidden for private installations. Those components were described in section 1.3.3. The safety is a big advantage for AC, mostly thanks to a century of research, developments and installations.
Voltage control of the overall system. While reactive power is an issue as it reduces the power-carrying capacity of a given cable, it presents the huge advantage to allow for a separate control of voltage without modifying the active power as in DC systems. Knowledge and experience are obvious advantages for AC systems. With over a century of operation, an extended knowledge of system sizing, construction and operation has been built.
3.1.2
DC advantages over AC
Distributed generation is often producing DC power or using DC power in its conver-sion steps. Using a direct current grid would reduce the necessary converconver-sion steps – saving an inverter in the case of generation units – but not the entire power con-version. According to [22], we can assume that removing a conversion step represent an 2.5% increase in efficiency.
Storage and Uninterrupted Power Supply are provided thanks to batteries relying on DC power. Using a DC grid would reduce the conversion steps but not completely remove the power conversion unit.
Electronics represent an increasing load both in households and offices as explained in section 1.2.
Variable speed drives are similar to wind turbine with a reversed power conversion process. Using DC grid would save conversion steps but not entirely remove the power conversion unit.
Voltage control is also an issue in DC systems, especially when combined with AC ones. DC systems offers more choice and thus increase the need for further calculations. On the other hand, a combination of AC and DC might if correctly piloted -increase the voltage stability thanks to the capacity of AC-DC converter to either consume or produce reactive power at interfaces [9, 22, 24].
3.2
Power cables efficiency under Low Voltage Direct
Current conditions
Cables are an obvious part of the power distribution system. Inserted in-between each conversion step, cables can consume a significant amount of energy in losses. A frequent assertion is that using DC may save cable losses. For a cable manufacturer as Nexans, reduced losses means that the same copper cross-section area could carry more power in DC than AC and lead to less copper sales which in turns means less benefits.
3.2.1
Methodology
When talking about cable efficiency, we want to compare the amount of losses. For a cable, the losses are closely related to the impedance.
The assessment of the cable efficiency is presented in two steps: 1. Theory for the calculation of energy losses in cables,
2. Analytical calculations for simplified models to have order of magnitudes,
3.2.2
Energy losses in cables
Three types of phenomena can lead to power losses:
• Magnetic losses are related to hysteresis cycles of materials. In short, hystere-sis is the property of a material to follow a different magnetic path whether it is loaded or unloaded. The area resulting of the cycle difference are the magnetic losses. But, a) in AC systems the materials used in cables all can be considered non-magnetic. This means that magnetic fields have a low effect on the mate-rial properties b) in DC systems there is no oscillating phenomena and thus no hysteresis cycle. Therefore, we neglect the magnetic losses in the cable efficiency comparison.
• Resistive losses is the phenomena of heating of a conductor when driven by a current. This is described by the Joule’s first law in equation 3.2.1, where Pjoule is
the dissipated power in W , R the resistivity in Ω and I the current in A.
Pjoule =R× |I|2 (3.2.1)
3.2 Cables under LVDC conditions 25
The electromagnetic influences arise from the changing magnetic field in an AC layout. By definition, when a conductor is in varying magnetic field, electromo-tive forces are generated. Therefore, due to that potential difference applied on a resistive material, a current – named Eddy, Induced or Foucault – appears.
According to Lenz law, An induced current is always in such a direction as to oppose the motion or change causing it. Those induced currents move the charge carriers – electrons in cable conductors – and increases the effective resistivity as the conductor cross area is not uniformly used. Two effects issuing from that phenomena are:
– Skin effect is caused by the time varying magnetic field of the conductor. It is thus an auto-induction phenomena. It is characterized by the skin depth δ defined for good conductors in equation 3.2.2, where ρ is the conductor resistivity, ω the current angular frequency (ω = 2π × f) and µ = µ0µr the
absolute magnetic permeability of the conductor. δ =r 2ρ
ωµ (3.2.2)
– Proximity effect is caused by the time varying magnetic field of external – close – conductors. This effect typically appears in cable bundles. Proximity and skin effect combine itself in cables which gives complex current density profiles.
To assess those two effects standards define the AC effective resistance RAC as the
DC resistance RDC increased of ys by the skin effect and yp by proximity effect.
• Dielectric losses are losses related to the dielectric nature of the cable (insulation and conductor). Standards [25] states that the dielectric losses can be neglected at low voltage.
Due to those different losses, the cable resistivity will be modified. The cable will have to dissipate the heat generated by Joule heating in the conductor. That heat transfer, precisely defined in [25], will lead to an increase of the temperature of each component of the cable. When one of the components reaches its limit temperature, the current carried by the cable is named the ampacity.
3.2.3
Analytical calculations
3.2.3.1 Simple calculation of the skin effect for a single cable
For this simplified calculation, we consider a single cable fed with 50Hz-AC power. The skin depth is given in equation 3.2.2. The geometric layout of a simple cross-section is shown in figure 3.2.1.
d
δ
Figure 3.2.1 – Geometry parameters of the cable section
In order to run a comparison between AC and DC we want to calculate the effective sections in AC (SAC), and DC (SDC). As no varying-field exists in
DC mode, the effective section is not modified and therefore SDC is given by the simple expression in
equation 3.2.3. SDC =
Πd2
4 (3.2.3)
On AC mode, the current density is modified by Eddy currents [11]. And the current density distri-bution is modified according to equation 3.2.4. The skin depth δ is therefore the length from the outer border at which the current density has fallen to 1/e · JS.
J(d) = JSe−
d
δ (3.2.4)
From figure 3.2.1, the three following cases can be distinguished:
• d < 2 δ,the skin effect is out of concern as the penetration depth exceeds the diam-eter,
• d = 2 δ, the skin effect still does not impact the AC effective resistance but this is the key point,
• d > 2 δ, the skin effect increases the effective resistance. The effective conducting section SAC is given in equation 3.2.5.
SAC = ( πδ(d− δ) if d > 2δ πd2 4 if d ≤ 2δ (3.2.5) The skin effect is effective at f = 50Hz if and only if SAC < SDC. This corresponds to
dlim = 18.45mm or SAC =SDC = 267.38mm2. The table B.1.1 and figure B.1.1 shows a
3.2 Cables under LVDC conditions 27
3.2.3.2 Calculation of skin and proximity coefficients according to standards The IEC 60287 standard [26] describes how to estimate the skin and proximity effects. Their influence on the cable resistivity is calculated with help of two factors ys and yp
defined as the increase of DC resistance RDC when the cable configuration is used in AC:
RAC = (1 +ys+yp)RDC (3.2.6)
The skin effect factor is calculated thanks to equation 3.2.7 from [26]: ys= x4 s 192 + 0.8 x4 s (3.2.7) where, xs = 8π f RDC 10−7ks
f is the power frequency and ks a coefficient related to the rigidity of the conductor.
given in [26] as ks = 1 for rigid conductors.
In a similar manner, the proximity effect factor is calculated using equation 3.2.8 from [26] for two single-core cables.
yp = x4 p 192 + 0.8 x4 p dc s 2 × 2.9 (3.2.8) where, x2 p = 8π f RDC · 10 −7 kp
dc is the diameter of the conductor in mm, s the distance between conductor axes and
kp is once more related to the conductor rigidity, the value kp = 1 is taken according to
[26].
For three single-core cables (case of three-phase systems for example), the formula is modified as shown in equation 3.2.9 from [26].
yp = x4 p 192 + 0.8 x4 p dc s 2 0.312 dc s 2 + 1.18 x4 p 192 + 0.8x4 p + 0.27 (3.2.9) Calculations were performed for two arrangements of three three conductors: 1) a configuration with 2 cables, 2) a configuration with 3 cables in a flat arrangement (geom-etry explained in figure 3.2.2a, 3) a configuration with 3 cables in a trefoil arrangement (geometry explained in figure 3.2.2b.
The complete results for 2 cables are in table B.2.1, while the tables B.2.2 and B.2.3 shows the calculation results for 3 cables configurations.
(a) Flat (b) Trefoil
Figure 3.2.2 – Two possible conductor arrangement for 3 cables [26]
2 cables the sum ys+yp does not go over 5 · 10−5. If we introduce the definition of ys
and yp in the resistive losses, we have in equation 3.2.10.
PJ oule,AC =RACI2
= (1 +ys+yp)RDCI2
= (1 +ys+yp)PJ oule,DC (3.2.10)
This means that skin and proximity effects in simple one-phase household configu-ration do not increase the losses by more than 5 · 10−3%.
3 cables no difference appears between the trefoil and flat configuration. The sum ys+yp
is larger than above, as shown in figure 3.2.3b the proximity coefficient yp is the one
making the difference. This is due to the three-conductors of a three-phase system. The sum of the two factors is less than 1 · 10−2 of losses increase up to 120mm2.
But this is already a large cross-section area allowing to transmit up to 120kW under 230V for a three-phase system. For comparison, typical cross-section area of 70mm2 [2] are used in distribution systems. Still, at such a level, 2.46 · 10−2kW are
dissipated as resistive losses at full load. At the price of the french regulated power market – ≈ 0.115e/kWh – this corresponds to around 24e per year assuming the cable is at full load all the year. This is to be compared with the 120 000e that could be retrieved for the selling of the whole cable capacity. With that hypothesis favourable to the DC case, the economical difference is not significant enough at the scale of the distribution grid to finance the shift from AC to DC.
3.2.3.3 Conclusion on the skin and proximity effects
From those calculations it appears that the skin and proximity effects are not signifi-cant for single-phase systems with small cross-section area. But the influence becomes significant when the cross-section area increases as well as the number of conductors. Considering a typical 50Hz-transformer with 98% efficiency, the 2% of losses in the trans-former are in the same order of magnitude as the 1% losses of a 120mm2 three-phases
3.3
Low Voltage DC layouts comparison
3.3.1
Comparison generalities
The comparison of different layouts depends on what is to be compared. In our study, the interest is to determine which configuration is the most interesting on existing power lines:
• Household lines, from the distribution grid feeder to the loads within a house. All over the world single-phase AC systems are used as displayed in figure 3.3.1a. • Distribution lines, from MV/LV transformers to the household feeders. In
Eu-rope, the most common layout is a three-phase system with return conductor. Four cables are used in such grids and would be available for DC layouts. But in a three-phase AC grid, only one return conductor – with same cross-section – is added to carry the unbalanced power. With a similar thinking, only one return conductor is necessary for bipolar DC (see section 3.3.2 for a technical explanation of the similarities). The figure 3.3.2 describes how the cables are distributed and how the lines are connected.
In the perspective to reuse the existing grid and just shifting from AC to DC, an interesting aspect is to know if it will be able to supply the same load or a higher load at the same distance from the MV/LV power feeder. Therefore, the transmissible power has been chosen as the comparison factor.
At each step of the comparison, we will differentiate the household configurations from the distribution configurations. In each case, different LVDC layouts are possible:
1. Household power grid:
• AC single-phase (configuration 1, figure 3.3.1a)
• DC unipolar configuration with return conductor (configuration 2, figure 3.3.1b) 2. Distribution power grid:
• AC three-phase with return conductor (configuration 3, figure 3.3.2a) • DC unipolar with 2 return conductors (configuration 4, figure 3.3.2b) • DC bipolar with 2 return conductors (configuration 5, figure 3.3.2c)
The following sections will first present the theoretical calculations of transmissible power for each configuration and then apply the theory to the case study.
3.3.2
Transmissible power
The voltage fed to every load of the grid must be within ±5% of the nominal voltage. But the transmissible power is also limited by the cable ampacity. The transmissible power is the maximal value satisfying to both ampacity and voltage limitations.
3.3 LVDC layouts 31
N
U
1I
1I
1Z
1 (a) AC single-phase+U
N
R
1I
1I
1 (b) DC unipolar Figure 3.3.1 – Possible grid layouts at household scaleP
1
P
2
P
3
N
Z
1
Z
2
Z
3
I
1
I
3
I
1
+ I
2
+ I
3
I
2
V
2
V
3
V
1
return conductor(a) AC three-phase with return conductor
3.3.2.1 Household power grid
In a household typical power installation, only phase and neutral conductors are used. The chosen model is depicted in figure 3.3.3.
L Zcable Zcable I Feeder Unom U (L)
Figure 3.3.3 – A simple scheme of a load fed by a single-phase system
Our interest is only the voltage drop in the cable. As any appliance in a single-phased system is fed by a phase and neutral conductor, a 2L cable length will be considered for an appliance distant of L of the power feeder. The cable resistance is calculated in equation 3.3.1.
R(L) = ρ2L
S (3.3.1)
where R is the cable resistance in Ω, ρ the specific resistivity at 80◦C in Ω · m, L the cable length
in m and S the cable cross-section area in m. As demonstrated in section 3.2, the cable resistance is not much changed by the AC varying magnetic field. But in AC-fed system, cables have a certain reactance causing voltage drop. The reactance X is calculated according to equation 3.3.2, where L is the cable length, ω the power pulsation and ` the linear inductance. From literature ` = 1 mH/km [2].
X(L) = 2L ω` (3.3.2)
The voltage along the line UAC(L)will vary from the nominal voltage UAC,0 according
to equation 3.3.3. UAC(L) = q [UAC,0(L)− R(L) I] 2 − [X(L) I]2 (3.3.3)
The maximal power Pmax,∆V a load at distance L can consume with respect to the
5% voltage drop limitation is calculated in equation 3.3.4 for an AC single-phase system. P∆V,1(L) = 0.05× U2 AC(L) |Zcable| = 0.05× U 2 AC(L) pR(L)2+X(L)2 (3.3.4)
The second limitation in transmissible power Pmax,1 arise from the cable ampacity
Imax,1. Equation 3.3.5 shows how to calculate Pmax,1.
Pmax,1(L) = UAC(L)· Imax,1· cos φ (3.3.5)
where cos φ is the power factor.
3.3 LVDC layouts 33
In configuration 2, the same calculations steps for household DC system are performed without the reactive impedance of the cable.
The limitation Pmax,2 associated with the cable ampacity Imax,2 is know from equation
3.3.7.
Pmax,2 =UDC· Imax,2 (3.3.7)
The voltage level at distance L from the load is given in equation 3.3.8 with UDC,0
the nominal voltage at feeding point.
UDC(L) = UDC,0(L)− R(L) I (3.3.8)
The maximal current the cable can carry with respect to the voltage drop condition is I∆V,2, calculated in equation 3.3.9.
I∆V,2=
0.05× UDC(L)
R(L) (3.3.9)
From those values, the maximal power a load can consume at a distance L from the power source without exceeding the 5% voltage drop condition is P∆V,2, calculated in
equation 3.3.10.
P∆V,2 =UDC(L)× I∆V,2
= 0.05 S UDC(L)
2
2ρ L (3.3.10)
And the transmissible power Ptrans,2 configuration 2 is:
Ptrans,2 = min (Pmax,2 , P∆V,2) (3.3.11)
3.3.2.2 Distribution power layout
In European distribution power grids, the transmission lines contains 4 conductors: 1 for each of the 3 phases plus a neutral conductor (configuration 3, figure 3.3.2a). The ampacity Imax,3 gives the maximum transmissible power in equation 3.3.12.
Pmax,3(L) =
√
3UAC(L) Imax,3 cosφ
= 3VAC(L) Imax,3 cosφ (3.3.12)
where VAC is the line-to-neutral voltage, UAC the line-to-line voltage and cos φ the power
The line impedance Zcable,3 is defined in equation 3.3.14.
Zcable,3(L) = R3(L) + j X3(L) (3.3.14)
where the real part of Zcable,3, R3(L) is defined in equation 3.3.15 as the resistance of 3
conductors with a cross-section area S – for each conductor – for a length L. We consider an equilibrated three-phase system i.e. no current in the return conductor.
R3(L) = 3× ρ
L
S (3.3.15)
For a short power line – L < 50 km – the reactance can be defined as in equation 3.3.16. ω is the power pulsation, ` the line linear reactance and L the line length.
X3(L) = 3 ω ` L (3.3.16)
From equations 3.3.15 and 3.3.16, the line impedance Zcable,3can be calculated in equation
3.3.17. Z3 = 3L ρ S +j ω` (3.3.17) The maximum current flowing in the line with respect to the voltage drop limitation I∆V,3 is defined in equation 3.3.18.
I∆V,3= 5%
VAC
Z (3.3.18)
The maximum complex power S∆V,3 that can be transmitted is calculated in equation
3.3.19. S∆V,3= 3× VAC(L) I∆V,3 ∗ = 3VAC× 5%VAC(L) ej φ Z = 3× 5% Z VAC(L) 2ej φ (3.3.19)
This gives in equation 3.3.20 the maximum real transmissible power with respect to voltage drop limitation P∆V,3.
3.3 LVDC layouts 35
The transmissible power Ptrans,3 is given in equation 3.3.21.
Ptrans,3 = min{Pmax,3, P∆V,3} (3.3.21)
For DC systems, we consider unipolar and bipolar layouts. A simplified scheme is displayed in figures 3.3.2b and 3.3.2c. First, a unipolar system – configuration 1 – is considered with 4 conductors (using the classical 3 phase and 1 neutral layout in Europe). Out of those 4 conductors, 2 will serve at voltage +U and the 2 remaining as return conductor. This configuration, which is far less efficient than three-phase AC and DC Bipolar, is presented because less costly than DC Bipolar. In DC Unipolar, conductor insulations only have to be designed for a voltage drop of UDC while in a DC Bipolar
system, the insulation must be designed for the full voltage 2 · UDC.
In DC system a voltage UDC(L) is fed to the load. From the cable properties, the
ampacity Imax,4of one cable is known. The maximal power related to ampacity calculation
is calculated in equation 3.3.22.
Pmax,4 =UDC(L) (2Imax,4) (3.3.22)
The voltage drop limitation can be calculated with equation 3.3.23 where ρ is the conductor resistivity in Ω · m, L the load distance in one way in m and S the cable cross-section area in m2.
P∆V,4(L) =
0.05 UDC(L)2
2ρ L S (3.3.23)
Equations 3.3.22 and 3.3.23 give in equation 3.3.24 the transmissible power at length L for a DC unipolar scheme.
Ptrans,4(L) = min (Pmax,4, P∆V,4) (3.3.24)
For configuration 5 the layout is described in figure 3.3.2c. It uses 3 conductors: 1 at +U, 1 at −U and 1 ground conductor. One conductor of the original AC scheme is saved. As for the AC three-phase system, an equilibrated system under operation conditions is considered. Applying that hypothesis yields:
R1 =R2 =⇒ I2 =−I1 ⇐⇒ I1+I2 = 0
With that hypothesis, the return conductor has a similar usage as the neutral conduc-tor of AC three-phase systems as it carries imbalanced power. In a DC Bipolar scheme, the ampacity is not modified and so does Pmax,5 in equation 3.3.25.
But the absence of current in the return path of an ideal bipolar system reduces the voltage drop by half. The maximal transmissible power according to voltage drop conditions can be calculated with equation 3.3.26.
P∆V,5(L) =
0.05 UDC(L)2
ρ L S (3.3.26)
The transmissible power in configuration 5 Ptrans,5is calculated according to equation
3.3.27.
Ptrans,5(L) = min (Pmax,5, P∆V,5) (3.3.27)
3.3.3
Results and analysis
3.3.3.1 Household power grids
The calculation was detailed in section 3.3.2. As the matter is building cables, 1.5 mm2
and 2.5 mm2 conductors were considered. The table B.3.1 shows the complete results of
the calculation and figure 3.3.4 synthesises the results.
In the light of those results, it is obvious that Extremely Low Voltage (ELV) are not suitable for power installation even in houses. Therefore, at least 120V is necessary to use the existing installations with conductors typically of 1.5, 2.5 and exceptionally 6 mm2. In order to exploit the full benefit of DC systems, 326V-systems appear the most
interesting.
3.3.3.2 Distribution power grids
For the distribution layout comparison, the figure 3.3.5 shows the evolution with length of the transmissible power for the three configurations 3, 4 and 5. As this is difficult to represent different Voltage/Cross-section area couples on the same graph, the turning point – defined as the length at which the limiting condition changes – is considered.
From figure 3.3.6 the voltage drop in a DC layout is much lower that in an AC one. This is the illustration of the effect of reactance in AC. On the other hand the figure 3.3.5 shows that AC three-phase systems carries more power over short distances. This is the illustration of the 3 phases available to carry power in a AC three-phase layout while only 2 are available in a DC unipolar or bipolar one.
3.3 L VDC la y outs 37
Figure 3.3.4 – Synthesis of the power limitation capacity (in kW) for a single-phase building installation
A C a nd D C comparison
Figure 3.3.5 – Transmissible power versus load distance for the three distribution configurations with 120mm2conductors under 500V
3.3 L VDC la y outs 39
Figure 3.3.6 – Transmissible power limitation change for the three configurations with single conductors of 400mm2 cross-section area
