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Renewable Energy 31 (2006) 2370–2384 Technical Note Distributed generation from renewable sources in an isolated DC network V. Azbe , R. Mihalic Faculty of electrical engineering, University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia Received 17 January 2005; accepted 5 January 2006 Available online 10 March 2006 Abstract This article describes a direct current (DC) isolated network that is infed with distributed generation from renewable sources and cogeneration units. The sources are connected to the network via DC/DC converters to keep the voltage within a defined range and to ensure the required power flow. The consumption is directly connected to the DC network, without any DC/DC converter. The storage is located at a single point in the network. A simulation analysis based on a DC-network model shows that it is possible to operate a DC network with standard elements used for the generation side as well as for the consumption side. The key elements are the DC/DC converters, which control the voltage of the network and optimize the operation of the sources. r 2006 Elsevier Ltd. All rights reserved. Keywords: Distributed generation; Renewable sources; Power system control; DC network 1. Introduction The electrical output of generators for the exploitation of renewable sources is either direct current (DC), or alternating current (AC) of variable frequency. However, electrical storage elements are of the DC type, which means that in AC networks infed with renewable sources DC/AC converters are required. If, on the other hand, the network operates as a DC system, then many of these converters are not needed or can be replaced with simple, cheap DC/DC converters. In our study we looked at the possibilities of constructing an isolated DC electrical power system using more-or-less standard elements. ARTICLE IN PRESS www.elsevier.com/locate/renene 0960-1481/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2006.01.001 Corresponding author. Tel.: +386 1 4768 415; fax: +386 1 4768 289. E-mail address: [email protected] (V. Azbe).

Distributed Generation Isolated DC Network

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Renewable Energy 31 (2006) 2370–2384

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www.elsevier.com/locate/renene

Technical Note

Distributed generation from renewable sources inan isolated DC network

V. Azbe�, R. Mihalic

Faculty of electrical engineering, University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia

Received 17 January 2005; accepted 5 January 2006

Available online 10 March 2006

Abstract

This article describes a direct current (DC) isolated network that is infed with distributed

generation from renewable sources and cogeneration units. The sources are connected to the network

via DC/DC converters to keep the voltage within a defined range and to ensure the required power

flow. The consumption is directly connected to the DC network, without any DC/DC converter. The

storage is located at a single point in the network. A simulation analysis based on a DC-network

model shows that it is possible to operate a DC network with standard elements used for the

generation side as well as for the consumption side. The key elements are the DC/DC converters,

which control the voltage of the network and optimize the operation of the sources.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Distributed generation; Renewable sources; Power system control; DC network

1. Introduction

The electrical output of generators for the exploitation of renewable sources is eitherdirect current (DC), or alternating current (AC) of variable frequency. However, electricalstorage elements are of the DC type, which means that in AC networks infed withrenewable sources DC/AC converters are required. If, on the other hand, the networkoperates as a DC system, then many of these converters are not needed or can be replacedwith simple, cheap DC/DC converters. In our study we looked at the possibilities ofconstructing an isolated DC electrical power system using more-or-less standard elements.

see front matter r 2006 Elsevier Ltd. All rights reserved.

.renene.2006.01.001

nding author. Tel.: +386 1 4768 415; fax: +386 1 4768 289.

dress: [email protected] (V. Azbe).

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Two models for the digital simulation are presented. The first is a simplified model, whilethe second is a detailed model that includes DC/DC converters with a proper controlcircuit. The results of the digital simulation show that it is possible to realize a DC networkwith distributed generation.

2. The concept of a DC network

2.1. Selection of operating voltage level

One of the major decisions when planning a DC network is the voltage level. This has aneffect on many parameters of the network, like the cross-section of the conductors,insulation, protection, compatibility with existing electrical devices, selection of switchingand protection devices, and many others.

2.1.1. Cross-section of Conductor

The cross-section of the conductor that connects two points of the network must belarge enough to transmit the desired power from one point to another without exceedingthe allowed voltage drop. The minimum cross-section, S, of the conductor is calculated by

S ¼rð2lÞP

DuU2; (1)

where r (Omm2/m) is the specific resistance of the conductor, (2 l) (m) is twice the distancebetween the source and the consumption, P (W) is the transmitted power, Du is themaximum allowed relative voltage drop, and U (V) is the voltage of the source. As can beseen from (1), the cross-section is a quadratic inverse function of voltage.

With the present prices of cables and DC/DC converters, a simple calculation shows thatin the case of a nominal voltage level of 48V, it is more economical to convert it to at least230V for transmissions that are longer than 200m. Similarly, if the nominal voltage level is230V, it is economic to convert it to 400V for transmissions that are longer than 5400m,irrespective of the transferred power.

2.1.2. Insulation and protection against electric shock

When considering operational safety, lower voltages are more appropriate than higherones. Voltages under 50V are, to a large extent, harmless to the human body.

Regulations define voltage bands, which are the basis for other requirements that dealwith protection against electric shock [1–3]. Regulations define two voltage bands at thelow-voltage level, which are different for DC and AC installations. The voltage bands arepresented in Table 1. The higher voltages allowed for DC might be an advantage of DCnetworks over AC networks.

Table 1

Voltage bands for DC and AC voltages

Band I Band II

Alternating Current 0–50V 50–1000V

Direct Current 0–120V 120–1500V

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In addition, lower voltages require less insulation for electric devices, and non-isolatedDC/DC converters can be applied, which means a significant cost reduction.

2.1.3. Compatibility with existing electrical devices

When selecting a nominal voltage based on the voltage level of existing electrical devices,we see that those devices are mainly manufactured for 230/110V AC or 12/24V DC; thelatter is a relatively low voltage for building a network to cover at least a few residentialhouses.Initially, it might appear problematic to connect an AC device to a DC voltage without a

DC/AC converter. However, many electrical devices, like incandescent lamps, heaters anduniversal motors, can also be infed with DC at the same voltage level. Some other devices,like modern electronic devices, need minimal changes to operate with DC voltage. The wayto connect AC devices to the network is described in more detail later in the text, in Section2.4 and if the AC device cannot be adapted to run with DC voltage, a DC/AC convertercan be used. However, the problem with this solution is that the price of the DC/ACconverter might be considerably higher than the price of the device itself.Another consideration is that a new standard voltage of 42V DC for automotive

vehicles will soon be applied. This means that a lot of electrical devices will bemanufactured for this voltage level, and so this voltage might be high enough for buildingan economic network for a small, isolated village.

2.2. The main principle of voltage and power-flow control

In contrast to AC, where the power flow is controlled mainly by the phase angle betweentwo points, the power flow in a DC network is controlled by the voltage difference betweenthose two points. As the power flows from the point with the higher voltage to the pointwith the lower voltage, different voltages are present at different points in the network.Regulations for AC low-voltage networks allow operational voltages to be 10% lower or10% higher than the nominal voltage. The same demands should be valid for a DCnetwork if the consumption is directly connected to the network. This demand can besatisfied by a sufficiently low resistance of the conductors between different points of thenetwork.Because the level of production does not always correspond to the level of consumption,

an excess or deficit of produced power is stored or retrieved from a battery as required.The basis of voltage and power-flow control is that a battery with a DC/DC converter

can maintain a stable voltage, while other DC/DC converters ensure the produced powerflowing from the sources to the network and the optimum operation of the sources. Thisconcept is presented in Fig. 1, and based on this concept we have developed a model for adigital simulation. As presented in Fig. 1, a DC/DC converter, with a battery, maintains aconstant voltage for the network at the point of connection by taking energy in and out ofthe battery as required. This DC/DC converter is bi-directional, and the controlledparameter is the voltage on the network side of the converter. When the battery becomesfully charged, i.e., the voltage of the battery reaches the maximum-allowed value,additional control of the battery voltage stops the charging.At the opposite end of the network, DC/DC converters close to the sources ensure the

produced power flows to the network. These converters take care of the optimizedoperation of the sources, so the controlled parameter of these DC/DC converters is the

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Fig. 1. Concept of voltage and power-flow control.

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input voltage, i.e., the voltage of the sources. The output voltage of those convertersautomatically reaches the level that causes power to flow to the consumers or to thebattery. When the charging of a battery stops and the production of the sources is higherthan the consumption, the voltage of the network rises until the maximum-allowed voltageis reached. At this point additional control of the network voltage lowers the power flow tothe network. The power flow to the network can be lowered either by reducing theproduction of a source by setting the operational voltage away from the optimum voltageor by taking the produced power away to a discharging resistance in the form of an air orwater heater. The presented voltage and power-flow control strategy should be valid evenif the network is extended and includes many sources and consumers. The parameters thatneed to change with a scaled-up network are the storage capacity and the cross-section ofthe conductors.

2.3. Electrical parameters of distributed generators

Solar cells, wind turbines, micro-hydro turbines, fuel cells and diesel engines are typicalsources of small-scale generation. The use of renewable sources like the sun, wind andhydro depends on the natural environment, whereas fuel cells and diesel generators can runon demand.

The cogeneration of heat and electrical energy is one of the interesting fields ofdistributed generation. Cogeneration units for residential use that are powered by a dieselengine have been commercially available for many years, whereas cogeneration systemswith fuel cells are in the test phase and should be available soon [4].

The connections of sources to the network are described in the following sections.

2.3.1. Solar cells

Although solar cells produce DC voltage, they should be connected to the network via aDC/DC converter. The reasons for using a converter are as follows:

(a)

Solar cells produce a DC voltage that is not constant. It depends a lot on the current ofthe cell and on ambient conditions like the solar radiation level and the temperature.The open-circuit voltage of a solar cell is about 40% higher than its best—maximum-power—operating voltage, which is not allowed if the voltage of the network has toremain within the limits of 10%.
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(b)

If the load is heavier than the produced power, the voltage of the solar cell collapses. ADC/DC converter would prevent this.

(c)

The maximum-power operating voltage depends to a small extent on the cells’temperature and on the solar radiation level. A DC/DC converter can maintain thisoperating voltage to extract the maximum power from the solar cell. This maximum-power-point tracking function is not necessary, but it slightly increases the energyproduction of solar cells. The maximum-power point can be set by measuring the celltemperature and the solar radiation or by measuring the open-circuit voltage or thegradient of the power [5,6].

A DC/DC converter ensures all these tasks with a proper control of the input voltage atthe solar cells’ side. The generated output voltage ensures that the produced power flows tothe network. When the network cannot receive all the power from the solar cells, the DC/DC converter increases the input voltages to keep the output voltage within the definedrange. Because the input voltage increases, the power of the solar cells decreases.

2.3.2. Wind turbines

Almost all wind turbines under 20 kW use permanent-magnet generators that are veryefficient and easy to maintain [7]. The output voltage of a wind turbine alternates at avariable frequency. The voltage and frequency depend on the rotation speed, which in turndepends on the wind speed. Wind-turbine sets are usually already equipped with an AC/DC converter, typically a simple diode bridge rectifier. To connect it to the network, anadditional DC/DC converter should be capable of regulating the proper power flow to thenetwork. Because small wind turbines usually have blades with a fixed pitch angle, aconstant ratio between the wind speed and the rotor speed should be maintained in orderto achieve the most efficient wind-turbine operation. This can be achieved by propercontrol of the DC/DC converter; it controls the current of the wind-turbine generatoraccording to the power and the frequency of the generator [8].When the network cannot receive all the energy from the wind turbine, the excess energy

needs to be transmitted to the discharging resistance, or the production of the wind turbineshould be lowered by setting the rotational speed away from the optimum point.

2.3.3. Fuel cells

Fuel cells are a fast-developing technology, but they remain relatively expensive forwidespread use. As a fuel they use hydrogen, which can be extracted from natural gas, oilderivatives or from other hydrogen-rich material.Fuel cells produce a DC voltage, which varies depending on the output power. The

operating voltage at maximum output power is about 50% lower than the open-circuitvoltage [9]. This means that a direct connection to a constant-voltage DC network is notpossible. A DC/DC converter should be used to provide proper power transmission to thenetwork.

2.4. Consumption

The consumption of one residential house in the presented model of a DC network isbased on the following devices: lights, refrigerator, deep freeze, washing machine,dishwasher, electric iron, hair drier, microwave oven, TV set, hi-fi and video equipment,

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Fig. 2. Cumulative diagram of daily consumption.

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computer, oil burner, and other household appliances. The devices that are not includedare kitchen range, oven, water heater and other heaters that consume a lot of energy andare not economically well suited for use in island networks that are powered fromrenewable sources. Taking into account the possible coincidence of loads, the maximumpower consumption of one house in the presented model of a network is 2.3 kW,and this lasts for about 10min. The cumulative diagram of the daily consumption is shownin Fig. 2.

The total daily energy consumption is about 7 kWh per house. Large loads like thewashing machine, which contains a water heater of about 2 kW, should be in operation at atime when other devices are turned off and the production of the sources is high.

The way to connect electrical devices to a DC network is described in the followingsections.

2.4.1. Lighting

Incandescent light bulbs can be directly infed with DC at the same voltage level. As theenergy consumption of energy-saving light bulbs is much lower, the use of these bulbs ispreferable when using renewable sources. Existing energy-saving light bulbs have anintegrated AC/AC converter to convert a 230V, 50Hz voltage to higher voltages andfrequencies over 20 kHz.Some energy-saving lights are available for 12V DC.

2.4.2. Deep freezer and refrigerator

Deep freezers and refrigerators have AC motors to run a compressor. To change themotor to run at DC voltage would be a complicated task for the non-expert, but not sodifficult for manufacturers. At the moment the simplest way is to use a DC/AC converterthat is capable of dealing with a starting power of about five times the nominal power ofthe compressor.

A few models for 12 or 24V exist, but they are expensive units. With current prices, abetter solution is an AC refrigerator with a DC/AC converter.

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2.4.3. Washing machine

The energy consumption of a washing machine is about 1 kWh over the operating cycle.The electrical devices in a washing machine are a water heater, a motor, a pump andelectronics. The main part of the energy consumption is the water heating. A water heaterof about 2 kW is installed, and this heater could be connected to 230V DC directly. Themotor in a modern washing machine is a universal motor, regulated with an AC/DCconverter. An AC/DC converter is also used for the electronics, and it is not difficult tochange an AC/DC converter to a DC/DC converter. So only the pump, which consists ofan AC permanent-magnet motor with a nominal power of about 30W, should be infedwith a DC/AC converter or replaced with a universal motor.

2.4.4. Dishwasher

A dishwasher contains a water heater, similar to that in a washing machine, and can bedirectly connected to a DC voltage. The pump, rated at about 250W, contains anasynchronous motor, which needs a DC/AC converter, or it should be replaced with auniversal motor

2.4.5. Household appliances

Household appliances, like a blender or a vacuum cleaner, mainly contain universalmotors, which can run on either AC or DC voltage. Other parts of the devices, likeswitches or speed controls, must be considered before the devices are connected to a DCvoltage. Some appliances, like electric irons and hair driers, can, with minimal changes, beconnected to a DC voltage.

2.4.6. Electronic devices

Electronic devices, like a TV set, a video recorder, hi-fi equipment, a computer or amicrowave oven run on DC voltage that is derived from an AC/DC converter inside thedevice. This converter should be rearranged to work as a DC/DC converter in order toconnect the device to a DC voltage.

2.4.7. Switches

Special attention should be focused on switches that disconnect inductive loads. In ACnetworks the arc that can occur is interrupted as the voltage crosses a zero value. In DCnetworks the voltage does not cross a zero value, so the interruption of the arc is moredifficult, especially if voltages over 48V are applied.For electrical installations in buildings, DC switches, circuit breakers, fuses and residual

current devices are available. Switches in existing AC electrical devices must be taken intoconsideration prior to connecting to a DC voltage.

2.5. Energy storage

Energy storage is the key consideration for island networks with distributed generationfrom renewable sources; this is because the production and consumption of electricity arenot easily synchronized. However, various kinds of energy storage are possible for small-scale distributed generation. There are different types of batteries, like lead–acid,nickel–cadmium, nickel–metal–hydride, alkaline, lithium–polymer, available in themarket, and new types of batteries, like sodium–sulfur and sodium–salt batteries, as well

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Fig. 3. Relationship between battery voltage and capacity.

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as super-carbon capacitors, are the subjects of intense research. Another type of energystorage is low-speed or high-speed flywheels, which can store the kinetic energy of arotating mass. Superconducting magnetic energy storage is also being developed, but so faronly for larger capacities of over 500 kWh. Reversible fuel cells can also be used for energystorage.

In the presented model of the network, a lead–acid battery is used for the energy storage.This kind of storage is still the best choice in terms of price.

The voltage of a lead–acid battery depends on the level of discharge. As seen from Fig. 3,the voltage difference between a fully charged battery and a maximum-allowed dischargedbattery is about 40%. This voltage difference can be lowered if we charge a battery at aconstant voltage of 2.3V per cell when the charge level goes over 85%. This is one reasonwhy a battery cannot be directly connected to a DC network. Another reason is a specialfunction of the DC/DC converter, which should provide regular charging and dischargingof the battery.

When the storage is fully charged and the production of the sources is higher thanconsumption, voltage of a battery rises until the maximum-allowed voltage is reached. Atthis point the production of sources should be lowered, or produced energy should beconsumed by a discharging resistance.

The capacity of a battery depends a lot on the rate of discharging. To achieve highefficiency, discharging power (in kW) should, in principle, not be greater than one tenth ofthe capacity (in kWh). But in the presented model of a DC network, where the peak powerlasts for only about 10min a day, the maximum discharging power can be greater, aboutone-third of capacity, and loss of capacity in this case is less than 4% of total capacity.

3. Digital simulation

The behavior of a DC network was simulated in two stages. The first stage of simulationof DC network involved simplified elements. Results of this simulation confirmed our basicidea about voltage and power-flow control. The second stage was a simulation of the DC

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network with detailed elements. The main feature of this second stage was the modeling ofthe DC/DC converters with proper control circuits.Digital simulation was carried out with the program PSCAD/EMTDC, which includes

basic components of power electronics necessary for construction of DC/DC converters.

3.1. The model of a DC network

Examined network model connects three residential houses. Distance between eachhouse is up to 500m, and each house produces electrical energy from renewable sourcesthat matches the size of its own average consumption. A battery, which is located in one ofthe houses, represents the energy-storage system for all three houses. This could be themodel for a small mountain village.In the worst case, the network should be able to transmit the peak power of sources to

the energy storage and peak power of consumption from energy storage to the place ofconsumption. Nominal voltage of the network is 230V DC, because of compatibility withexisting electrical devices and small cross-section of conductors.The model of the network is presented in Fig. 4, where source 1 represents solar cells,

source 2, a wind turbine and source 3, fuel cells. All sources and the storage are connectedto the network via a DC/DC converter, whereas consumption is directly connected to thenetwork without any DC/DC or DC/AC converter.

3.2. Simplified model for long-term digital simulation

In the first stage we created a model of a DC network that consists of simplified modelsof sources. Each source, together with a DC/DC converter, is presented as a controlledcurrent source, the current of which depends on previously defined power. A battery with a

Fig. 4. Model of a DC network.

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DC/DC converter is presented as a constant voltage source. This model can be used foranalyzing the behavior of a DC network over a longer period, e.g., a 24-h period, becausesimulation is fast.

Results of digital simulation of the simplified model are presented in Fig. 5. This figurepresents voltage, production, and consumption at one of the points of the networkbetween 2 and 7 pm. The first graph presents the voltage U2 according to the model inFig. 4. A wind turbine is connected to the network at this point. The second graph presentsthe produced power of the wind turbine, and the third graph presents the consumption atthis point. As can be seen from the graphs, voltage is proportional to the differencebetween production and consumption.

At the point where solar cells and consumption 1 are connected to the network, similarconditions are established. The voltage U3 at the point where the battery is connected tothe network stays constant, as was predefined.

The main finding of this digital simulation is that voltage at each point of network canbe within defined limits, provided the conductors are appropriately sized according to (1).

Fig. 5. Results of a long-term digital simulation of a simplified DC network.

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3.3. Detailed model for a short-term digital simulation

In the next stage we created a detailed model of a DC network. The main work was tocreate the models of DC/DC converters with their controlling circuits and models ofsources according to their U– I characteristics.As DC/DC converters consist of high-frequency switches that operate at 25 kHz, time

step of a digital simulation must be short, i.e., under 10 ms. This results in simulation beingslow, and so it is only useful for a short-term simulation of transients.Compatibility of the simplified and the detailed models was checked with test

simulations. Results show that steady-state conditions and the slow transients are equalin both models.

3.3.1. Model of a DC/DC converter for the connection of sources to grid

Because the voltage level of the network is higher than voltage of sources, we used astep-up DC/DC converter, which is presented in [10]. Fig. 6 presents the basic structure ofthe converter. It consists of an inductor, a capacitor, a diode and an IGBT, which iscontrolled with on/off signal.The on/off signal is generated by a PWM control circuit. Fig. 7 presents the basic

structure of the PWM control circuit constructed in our model.The difference between actual voltage of the source, Uin, and optimum voltage of source,

Uref, is compared with the constant-frequency saw-tooth oscillator signal. When saw-toothsignal becomes higher than voltage difference, IGBT turns on, and when saw-tooth signalbecomes lower than voltage difference, IGBT turns off.

3.3.2. The model of a DC/DC converter for the connection of a battery to the grid

A battery is connected to the grid with a bi-directional DC/DC converter. Structure ofthe converter used in our model is a combination of a step-up converter and a step-downconverter with a common inductor. The converter is presented in Fig. 8. The step-upconverter transmits power from the battery to the network when the IGBTout and thediode Dout are active, whereas the step-down converter transmits power from the networkto the battery when the IGBTin and the diode Din are active.Each IGBT has a control circuit like that shown in Fig. 7, only that the reference voltage

Uref is compared with Uout and not with Uin. The reference voltage Uref is the constantnominal voltage of the network.

Fig. 6. Model of a DC/DC converter for the connection of sources.

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Fig. 7. PWM controlling circuit.

Fig. 8. Model of a DC/DC converter for the connection of a battery.

V. Azbe, R. Mihalic / Renewable Energy 31 (2006) 2370–2384 2381

3.3.3. Model of the sources

Solar cells were modeled as a controlled voltage source, the voltage of which depends onthe current, the solar radiation and the temperature of the solar cells. The voltagedependency was defined in tabular form by applying linear interpolation between thepoints.

The fuel cells were modeled in the same way, but in this case the voltage depends only onthe current.

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The wind turbine was modeled as a permanent-magnet generator, i.e., a three-phasesynchronous generator with constant excitation. The output voltage, the amplitude andfrequency of which varies according to the rotational speed, is first rectified with a three-phase bridge rectifier and then connected to a DC/DC converter.

3.3.4. Results of digital simulation

Various scenarios in a DC network were simulated. In this article a short circuit on thecable between source 1 and a battery, according to Fig. 4, is presented.During the short circuit the produced power of the sources remains constant and the

consumption is presented as a constant resistance.Fig. 9 shows the voltages U2 and U3 according to Fig. 4, and the current of the wind

turbine and the battery during the short circuit. The power of the DC/DC converter with

Fig. 9. Digital simulation of the short circuit.

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the battery that controls the constant voltage is limited, and consequently the voltage ofthe network decreases. The DC/DC converters with the sources transfer the producedpower to the network. Because the voltage of the network is lower, the currents increase inorder to transfer the desired power.

The current peaks at the beginning of the short circuit are the consequence ofdischarging the capacitors at the output of the DC/DC converters.

After the short circuit is removed, the network is restored. The conditions are presentedin Fig. 10, which shows the same voltages and currents as in Fig. 9. The voltage increasesand the capacitors in the DC/DC converters are charged until the nominal voltage isreached. Because the faulty line was disconnected, larger currents flow from the battery tothe consumption over the other two lines. Larger currents cause the voltage U2 to be lowerthan it was before the short circuit.

Fig. 10. Digital simulation after the short circuit is removed.

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4. Conclusion

This article proposes a low-voltage DC network as an alternative to an AC network.First, we made the main concept one of voltage and power-flow control, and then, on thebasis of electrical energy generation, transmission, storage and consumption, weconstructed a model of a DC network for a digital simulation. The battery and sourcesare connected to the grid via DC/DC converters, which play the main role in ensuringproper power flow and voltage stability for the network.The article shows that a DC network with distributed generation is very realizable when

applying simple DC/DC converters, while standard elements on the generation side as wellas on the consumption side are applied. This kind of DC network needs no central controland no communication between the different elements of the network.Dc voltage has several technical and economic advantages over AC voltage: the control

of a DC network is much easier and DC/DC converters are, in general, simpler andcheaper than DC/AC converters.Finally, we believe that isolated DC networks with distributed generation from

renewable sources could be one of the most promising alternatives for the electrification ofdeveloping countries, where villages are often far away from the utility grid.

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