KoCoS Blog

Filtered by estachorra Reset filter

Gas has been getting more and more expensive for a year now, and the price of electricity in Europe is also rising significantly. Are these prices related and what role does which power plant play in this?

Gas shortage. Why is the price of electricity rising at all?
Since in Germany, as in the rest of the world, electricity is mainly generated by fossil fuels, the price of a kilowatt-hour naturally depends on the basic price of gas, coal, oil and, to a certain extent, uranium. If the prices of fossil energy sources rise, the price of electricity also rises.

How have energy prices developed so far?
Concerns about a shortage of gas supplies from Russia have driven gas prices ever higher, and not only in Germany. Power plants paid almost 227.0 percent more for natural gas in June 2022 than in the previous year. The gas bills of many end consumers have tripled. Alongside these rapid increases in prices in the gas market, electricity prices have also risen at the same time. Within one year, for example, the price of electricity on the Leipzig European Power Exchange (EEX) has increased 10-fold (as of August 2022) - from 50 to 565 euros per MWh. Of course, this also has a knock-on effect on consumers: the electricity price for new contracts in mid-November 2022, for a consumption of 4,000 kWh incl. basic fee, was 0.427 euros per kWh - and the trend is uncertain.

And what about electricity from renewable energies?
Electricity from renewable energies is by far the cheapest way to generate electricity. Once wind or solar power plants are built, they consume almost no resources for direct electricity production. However, they do not supply electricity continuously. This means that although energy from these sources is cheap, it is not constantly available everywhere without large storage facilities and well-developed electricity grids. Does the price of electricity fall when more electricity is fed into the grid from renewable sources? No, unfortunately it is not that simple. This is because the electricity market works according to the "merit order" principle.

Definition: Merit order
The merit order is the order in which power plants are deployed, which is determined by the variable electricity production costs. The cheapest power plants are switched on first to meet demand, and the last power plant with the highest marginal costs needed to meet demand determines the price. The merit order thus determines the electricity price on the energy markets.

In a simplified way, this means: All power plants offer their production capacities until enough electricity is produced in Europe to cover demand. However, no distinction is made in the type of generation: All suppliers receive the same price, determined by the most expensive power plant on the grid. In the merit order principle, for example, it does not matter at all how cheaply the renewable electricity was generated. Subsidies for the expansion of renewable energies do not count either.
Thus, at present, a single gas-fired power plant on the grid is enough to greatly increase the price of a kilowatt hour of electricity, regardless of the low costs of other energy sources or "power plants" at that time.

So why is there a "merit order"?
In a conventional market, supply and demand would determine the price - until the time when a product is no longer available. As a result, however, gas-fired power plants would then almost never be in operation, as cost-covering operation is not guaranteed. The "merit order" balances this out so that there is always enough electricity available to meet demand and the grids remain stable.
Each producer offers its electricity in such a way that its costs (marginal costs) are covered. All offers are then successively made until demand is covered - the most expensive power plant used then determines the price for everyone. This power plant only covers its marginal costs, all others make profits. The resulting price is called the marginal price.
Marginal costs are the costs incurred to produce the next commodity or, in this case, the next megawatt hour. Investment or capital costs are not included, but fuel costs, for example, are.
On the energy market, it generally applies that the "product" electricity must not be "sold out", as otherwise the energy supply can be disrupted and, in the worst case, a local or area-wide blackout could occur.

Who invented the merit order principle?
"The marginal price (found through the merit order) is not an artificial rule that someone made up," Lion Hirth elaborates in the Stuttgarter Zeitung. Lion Hirth is junior professor for energy policy at the private Hertie School in Berlin and managing director of the energy consulting company Neon. "It is not an arbitrary choice between alternative market designs, but the natural way prices form in free markets," he continues. Other commodity markets also function according to this principle - "no matter whether it is oil, gas, copper, milk or solar plants", says the energy expert.

What is happening at the moment?
Currently, several developments are coming together: Firstly, about half of the 56 nuclear power plants in France are currently out of operation due to maintenance work or technical defects. Secondly, the low water level of the rivers is hampering the supply of coal to the coal-fired power plants. And thirdly, the gas price is at a high level and, as described above, influences the electricity production costs.

Will coal, nuclear power and renewable energies not suffice?
Unfortunately not. On the one hand, this is because the current capacities of hydropower, wind power and photovoltaics are not sufficient to cover the entire electricity demand, neither in Germany nor in Europe as a whole. In addition, as described above, many conventional power plants are currently shut down or can only be operated to a limited extent.
Furthermore, there is a lack of transmission grid capacities across Europe. Often, for example, the electricity generated on the windy North Sea coast in Germany cannot be transported to the energy-hungry south of Germany. The Federal Network Agency reacts to such a bottleneck with a "Redispatch": the output of wind turbines is reduced in the north and the output demand of the power plants is increased in the south so that an overload of the electricity grid is avoided. Gas-fired power plants, which can adapt their electricity production particularly flexibly and quickly, are often used here. Of course, this also has additional effects on the electricity price.

Opportunities for action and risks
The increased gas price, mainly caused by the war in Ukraine, is also driving up electricity prices. Since electricity is included in the prices of many other products, including breakfast rolls, this is fuelling inflation. For weeks, there have been many discussions on how the price increase could be stopped.
"A discussion about redistributing profits and relieving the burden on consumers, but maintaining savings incentives, i.e. not a simple price cap, is in my opinion the way to go in the short term," says Christoph Maurer, Managing Director of the Aachen-based energy consulting firm Consentec. However, a fundamental change in the market design should definitely not be decided in the short term, he warns. "The risk of then arriving at solutions that have not been thought through and possibly even intensifying the crisis is very high" Maurer, an energy expert, told the Stuttgarter Zeitung.

References: The magazines: "Zeit, Standard and Stuttgarter Zeitung", the technical magazine "Chip", Wikipedia and own research.

Yesterday - Today - Tomorrow

Background
Germany wants to do more for the climate. Following the ruling of the Federal Constitutional Court in March 2021, the German government announced that CO2 emissions are to be reduced by 65% by 2030 compared to 1990 levels and not - as previously planned - by 55%. This basically requires more electrical energy from renewable sources than previously planned.
Depending on how high the demand for electrical energy is estimated to be in 2030, there will be completely different orders of magnitude in which wind and solar power plants will have to be expanded in order to achieve this 65% target.

How will the future energy demand in Germany develop?
So far, the Federal Ministry of Economics and Technology (BMWi) has assumed that electricity consumption will not change significantly over the next nine years until 2030 and will remain at around 580 billion kWh. Looking at the past, this does not seem wrong. "In the last ten, 20 years, electricity consumption has been relatively constant," Johannes Wagner of the Energy Economics Institute at the University of Cologne (EWI) told Deutsche Welle. "We had a gross electricity consumption of about 600 billion kWh over a long period of time. That only went down relatively sharply in 2020 due to special effects from Corona."
But that need not hold true for the future. Various experts believe that the federal government's planning to date is too cautious. Even SPD chancellor candidate Olaf Scholz recently indirectly criticised his ministerial colleague Peter Altmaier (CDU): "Anyone who claims that electricity consumption will remain the same until 2030 is lying to himself and the country."
So what if electricity consumption does not stay the same at all, but perhaps even rises sharply? That is in fact the scenario that various energy experts are assuming. "The expert commission for monitoring the energy transition, of which I am a member, has estimated a value for electricity consumption that is significantly higher than that of the German government," says Veronika Grimm, a member of the government's Council of Experts (the “Wirtschaftsweisen"). "We are moving around a value of 650 billion kWh and are thus still at the lower end of the spectrum," Grimm said in an interview with Deutsche Welle in July 2021.

Energy demand in the first half of 2021
According to Zeit Online, more energy was needed and more CO2 was emitted in the first half of 2021 than in the same period of the previous year with approx. 600 billion kWh. The share of fossil fuels increased compared to the previous year.
A rather cool winter (2020/2021) and the restart of the economy after the Corona slowdown caused energy demand in Germany to rise in the first half of 2021. According to calculations by the Working Group on Energy Balances (AGEB), consumption increased by 4.3% compared to the same period last year, to approx. 625 billion kWh.

Because more electricity was produced with brown and hard coal than in the same period last year, carbon dioxide emissions increased by 6.2%. The consumption of lignite rose by about one third in the first six months of this current year, that of anthracite by almost 23%. The increase in fossil fuels in electricity generation is mainly due to the fact that less wind power was generated.

Estimates of Germany's future electrical energy demand
On 13 July 2021, Federal Minister of Economics and Technology Peter Altmaier presented a first new estimate of Germany's electrical energy demand in 2030.
In the BMWi press release of 13 July 2021, Federal Minister of Economics Peter Altmaier states here, among other things: "The new version of the Climate Protection Act and our new ambitious climate targets, which the Bundestag and Bundesrat passed at the end of June 2021, require an adjustment of our analyses of electricity consumption in 2030."
Today it is already clear that Germany's future energy supply will essentially be based on two energy sources. On the one hand, on electricity from renewable energies and, on the other, on hydrogen produced with the help of renewable energies.
An initial estimate of electricity consumption in 2030, prepared by Prognos AG on behalf of the Federal Ministry of Economics, comes to an electricity consumption of between 645 and 665 billion kWh. The following assumptions were made: 14 million electric cars, 6 million heat pumps and 30 billion kWh of electricity for green hydrogen.
According to the German Wave, the think tank Agora Energiewende also estimates the electrical energy demand in 2030 at 650 billion kWh. The EWI calculates that 685 billion kWh will be needed in nine years. The German Renewable Energy Federation (BEE) assumes 745 billion kWh in 2030 and the Fraunhofer Institute for Solar Energy Systems (ISE) even expects an energy demand of 780 billion kWh in 2030, i.e. 70 to 200 billion kWh more than the Ministry of Economics currently forecasts.

Higher energy demand due to e-cars, heat pumps and electrolysers.
The demand for energy is growing due to the shift to e-mobility and the changing heating of buildings (e.g. with electrically powered heat pumps). It is also becoming apparent that industry will have to switch to synthetic energy sources, such as hydrogen. For the production of green hydrogen through electrolysis, there is in turn an increased demand for electrical energy.
"The German government's goal of creating electrolysis capacities of five gigawatts by 2030 alone will require a considerable amount of additional electricity. To achieve this, we need to estimate an additional 20 billion kWh of electricity," says Veronika Grimm. This energy demand corresponds to more than one sixth of the total energy provided by wind power in 2020.
So more electricity will be consumed. On the other hand, there are of course efficiency gains that reduce electricity consumption. In this area, the German government has set itself the goal of reducing electricity consumption by 25% by 2050 compared to 2008 through greater energy efficiency. However, these efficiency gains cannot compensate for the increased demand for electrical energy.


In addition, Agora Energiewende criticises that economically highly profitable efficiency potentials have not yet been systematically exploited, even though market-ready technologies are already available today.

How large must the growth of renewable energies be?
Based on the electricity estimates of Agora Energiewende, Germany would have to expand about ten gigawatts of photovoltaics, 1.7 gigawatts of onshore wind and four to five gigawatts of offshore wind annually by 2030. In recent years, these outputs were only achieved in the record expansion years.
It will probably not work without its European neighbours. "Currently, Germany exports electricity abroad," says Johannes Wagner (EWI), "in the medium term, we must expect Germany to become a net importer for the time being."
It will be quite challenging and many mechanisms will have to be set in motion to push the expansion of renewable energies, says expert Veronika Grimm.

Sources:
Deutsche Welle, ZEIT ONLINE, dpa, BDEW, Statista, BMWi, AGEB, ZSW, ISE, Agora Energiewende, EWI

Background

Many people use a smartphone with internet access for up to several hours a day. In 2020, the number of smartphones in circulation worldwide was over 8.15 billion [source: statista]. Large amounts of data are in circulation worldwide; on Youtube alone, 400 hours of video material are published every second [source: brandwatch]. The so-called Big Data are exponentially growing amounts of data that can be accessed online and are stored in large server centres. The prerequisite for this is the infrastructure in these server centres, the operation of which is associated with an annually increasing energy consumption.
Google alone receives 3.8 million search queries per minute, according to a study commissioned by Wirtschaftswoche. Facebook members upload about 250,000 pictures every minute and the music service Spotify streams an average of 1.5 million songs every minute.

Energy consumption through internet operation and CO2 emissions

Anyone who makes a search query on Google consumes 0.003 kWh per search query - enough energy to light a 60-watt light bulb for 17 seconds. Each Google user could power a 60-watt light bulb for three hours with their monthly search queries. For the total energy demand, however, the user's internet-capable terminal and internet access would have to be included.
The power consumption of a single search query arises at three different points:

  1. The power consumption of the internet-enabled terminal.
  2. The power consumption of the networks such as the mobile radio station and the internet router.
  3. The electricity consumption of the data centres and data centres with their servers and cooling systems, which in turn consist of air conditioners, fans and recooling.

In 2020, according to the Borderstep Institute, the energy consumption of all server and data centres in Germany was approximately 16 billion kWh. This energy could be used to supply 4.8 million three-person households, with an energy demand of 3,300 kWh/a.
If the internet were a country, it would be the third largest in the world in terms of electricity consumption. Just ahead of India with 1,137 (2020) and after the USA with 3,902 billion kWh (2020). According to current estimates, the operation of the internet currently requires between 1,100 and 1,300 billion kWh/a worldwide.
Currently, the annual energy demand for the use of digital services is less than one percent of the global energy demand (approx. 160,000 billion kWh). According to its own information, the Google Group currently requires 5.7 billion kWh per year, which corresponds to the energy demand of a large American city. According to WDR, 13 per cent of the entire world energy demand will be necessary for internet operation in 2030. Thus, the web, apps and especially the streaming of films and series will soon cause as much CO2 pollution as the entire global air traffic (before Corona), estimates the Borderstep Institute.
The French research project "The Shift-Project" found that the use of online videos alone has CO2 emissions equivalent to the energy needs of Spain in 2018. The climate researchers from France calculated that 23 trees would have to be planted per second to offset the CO2 emissions caused worldwide by Google queries. That would be almost two million trees per day.

Impact of the technology leap to the 5G mobile phone standard

With the technological leap to the mobile phone standard 5G, the energy demand of data centres will increase drastically. This is the conclusion of a study commissioned by E.ON from the University of RWTH Aachen. According to the study, 5G can increase the power demand in data centres by up to 3.8 billion kWh by 2025. That is enough energy to supply the 2.5 million inhabitants of the cities of Cologne, Düsseldorf and Dortmund for a year.
According to the French Shift Project, faster mobile internet access is causing a major shift in usage behaviour. Thanks to 5G, mobile surfing is becoming faster and possibly cheaper at the same time. For example, the average monthly data volume in Germany has already increased a hundredfold from 0.027 to 2.5 gigabytes in the last ten years.
As a general rule, access to the World Wide Web via the mobile network requires significantly more power than via the home cable. Experts even estimate that up to 23 times more energy is needed. The higher the available speed on the road, the lower the need to use the WLAN at home. A vicious energy circle.

Further highlights as a short collection of facts

  1. If you use a streaming service on your TV for one or two hours a day every year, you use enough electricity to run your fridge for half a year.
  2. According to the Shift Project, two hours of Netflix in HD quality consume the same amount of energy as an oven.
  3. According to Stern, a typical email causes an average of one gram of CO2. Since users send an average of 30 emails a day, they could use this energy to light up a 4-watt LED for 15 hours.
  4. According to Canadian network analytics firm Sandvine, almost half of mobile internet traffic on smartphones worldwide is video streaming (49 per cent). Again, YouTube claims just under half of this category (48 per cent). This makes Google's video subsidiary by far the biggest bandwidth hog, claiming nearly a quarter of all mobile internet traffic (23.5 per cent)."[Michael Kroker]
  5. The Shift Project has calculated that half an hour of streaming causes about 1.6 kg of CO2. This corresponds to a car journey of 6.28 km. According to this, streaming was responsible for greenhouse gas emissions last year that were as high as those of Spain. It is assumed that this amount will double in the next 6 years.
  6. 20 Google searches burn an energy-saving light bulb for 1 hour!
  7. 10 hours of high-definition videos consume more energy than all English Wikipedia articles in text format.
  8. The cryptocurrency Bitcoin leaves a significant carbon footprint: the electricity used in the creation of Bitcoin is about 46 billion kWh of electricity per year.
  9. If ten million people watch a film on TV, that triggers only one broadcast. But if ten million people stream a film, that also triggers ten million transmissions, with the corresponding energy demand.

Where to put the heat?

The growth of the streaming industry is increasing the number of data centres. Today, Frankfurt is already the largest internet hub in the world. And each of these data centres has an electricity consumption of a small town. Together they account for 25 percent of the electricity consumption of the city of Frankfurt. The operation of these data centres generates large amounts of heat, which must be compensated for with the help of cooling systems.
According to E.ON, up to 8 billion kWh of waste heat will be available nationwide by 2025. There is great potential here for the sustainable use of this energy. In Germany alone there are more than 53,000 data centres with over 2 million servers. Today, the waste heat from data centres is not yet used consistently. Only 19 percent of the world's data centres reuse parts of their waste heat.
This waste heat is valuable energy. Almost half of the electrical energy used is converted into heat. In the future, data centres can be used to supply heat to housing estates and entire city districts.
According to WDR, another idea comes from Dresden. The servers of a data centre do not have to be located in one place, but can also be operated in a distributed manner. In apartment buildings, for example, servers could be located in the basement and their waste heat used for heating and hot water.

Small cause, big effect

When it comes to environmental and climate protection, even many small things can have a big effect. Many things start with a change in behaviour. Can we perhaps unsubscribe from newsletters that we no longer read? Do you really need to stream the series online "in between" or would you rather relax at home on the sofa in the WLAN? Do all files really have to be stored in a cloud or is the local hard drive sufficient? Should old mails be deleted from the mailbox memory?
In an experiment in 2019, the TV knowledge magazine Galileo asked users of an email service to delete as many emails as possible within one hour. The more than 27,000 participants in the action deleted a total of more than 300,000 mails - an average of eleven - emptied the wastebaskets and thus freed up 50 gigabytes of hard disk capacity on the servers: According to estimates by the data centre, a saving of an estimated 1.7 kilogrammes of CO2. If every user in Germany deleted 11 mails a day, 91,000 t CO2/annum would be saved. That would be the energy consumption of about 125,000 people.

Background: What is a standby mode?

Standby mode is a state of a technical device. It is characterized by temporarily deactivated functions that can be reactivated at any time without waiting - for example, with the help of a remote control. Standby mode is also sometimes referred to as waiting mode or apparent off mode.
Since the electrical device must at least be able to process the control signals, there is a need for the corresponding control signal processing circuit to be active at all times. Thus, the device consumes power even in standby mode. For operation in standby mode, energy worth around four billion euros is required every year in Germany alone.

Less consumption in standby mode due to eco-design directive?

In order to reduce the power consumption for which standby mode is responsible, the European Union passed the so-called “Ecodesign Directive” in 2008. This sets limits for the power requirements of household appliances and consumer electronics in standby mode. In 2013, the regulations, which came into force in 2010, were tightened once again. The German government, under the leadership of the Federal Ministry for Economic Affairs and Energy, transposed the (Ecodesign) Directive 2009/125/EC into German law with the Energy-Related Products Act (EVPG).

By 2020, this should result in EU-wide electricity savings of 72 TWh, which roughly corresponds to the energy supply of 4.5 power plant units (with 800 MW capacity and a realistic full load of about 40% [average full load in Germany from 2015 to 2020: 38.7%]) in this period.

How high is the power consumption in standby mode?

Devices without an information or status display may consume a maximum of 0.5 watts in standby mode. By contrast, electrical devices with an information display - for the time, for example - are subject to a maximum of one watt. For devices with high network availability (HiNA devices) or corresponding functions, a limit of eight watts applies. Other networked devices must remain below a value of two watts since 2019.

This means for the maximum annual power consumption of different device classes with a daily standby duration of 22 hours:

  1. Device without information display (0.5 W): approx. 4 kWh
  2. Device with information display (1 W): approx. 8 kWh
  3. Device with high network availability (8 W): approx. 64 kWh

 

Energy costs in standby mode

For the three device classes described above, the following energy costs result in standby mode (22h), at an average electricity price of 29 cents per kWh (as of 08/21, including fixed price component and the consumption of an average three-person household of 3,300 kWh/a):

  1. Device without information display (0.5 W): approx. 1.16 euros
  2. Device with information display (1 W): approx. 2.32 Euro
  3. Device with high network availability (8 W): approx. 18.56 Euro

In general, the consumption of one watt in standby mode (24h) costs between 2.57 euros and 3.15 euros per year, depending on the electricity tariff.

Example: Digital voice assistant

Owners of a 1st generation voice assistant can expect the following consumption and electricity costs:

  1. In standby mode, i.e. without a question to the assistant or music playback: 2.8 watts.
  2. In assistant mode, when a question is to be answered: 3.2 watts.
  3. In audio playback with medium volume (level 5 of 10): 3 watts.
  4. During audio playback with full volume - level 10 out of 10: 7 watts.


At an average electricity price of 29 cents per kWh, this results in annual electricity costs of 7.09 euros (24.46 kWh) in standby mode (again for a standby duration of 22h). Two hours of music a day (otherwise standby) results in 9.20 euros.

It gets significantly more expensive for 1st generation assistants with an integrated display. These devices cost between approx. 12 and approx. 19 euros per year. However, a positive trend is that newer voice assistants require less energy, especially in standby mode.

How much money can be saved if all devices are switched off completely?

The amount by which the electricity bill can be reduced if the consumer switches off all appliances and does not merely put them into standby mode depends essentially on two factors: First, it depends on how many household and electrical appliances the respective household owns. Secondly, it depends on how old the appliances are. According to information from the consumer advice centre, an average around 10 to 20 percent of electricity consumption is attributable to devices in standby mode. This percentage range has also been observed in power and energy measurements carried out by KoCoS Engineering GmbH, with up to 20 simultaneous measurements using KoCoS EPPE measuring devices, in large properties belonging to the federal states, the federal government or the real estate industry.

The insurance industry assumes an annual savings potential of 330 to 660 KWh for a three-person household. Assuming an electricity price of 29 cents per kWh (see above), this corresponds to a savings potential of approx. 95 euros to approx. 190 euros per year.

 

After charging the smartphone, the charger remains in the socket?

You probably know this: after charging the smartphone, the charger remains in the socket. It is convenient to be able to simply plug in the smartphone cell phone when needed and not have to search for the charging cable. What does this convenience cost us?

Modern chargers must not consume more than 0.3 W according to the Ecodesign Directive. If we again assume a duration of 22h in standby mode, a consumption of 2.4 kWh, again at an electricity price of 0.29 euros/kWh, results in a cost of 0.70 euros per year.

For each one a small amount. But if you extrapolate the additional costs to the total population, the sum is surprisingly high: because in Germany, around 60.7 million people will be using a smartphone in 2020 (source: statista).

Assuming all location devices of these smartphones remained connected to the grid in standby mode, this would result in an annual consumption of more than 145 GWh or 145 million kWh at a cost of approximately 42 million euros/a. When converted to electricity (2020 energy mix), this results in more than 58 tons of C02 emissions per year (source: UBA).

As mentioned above, a German household with three persons consumes on average about 3,300 kWh per year (as of September 2020). The energy required for standby mode could supply around 44,000 three-person households in Germany with electricity for a year. But even the chargers of laptops, tablets or e-readers consume energy when left in the socket.

In practice, the value of the maximum short-circuit current "Isc_max" of a transformer is often needed. On the one hand, to be able to estimate the current carrying capacity of input circuits, such as in the KoCoS fault recorder system SHERLOG. It must also be taken into account that typical protection current transformers used in medium voltage can transmit currents up to 40 times higher than the rated current of the transformer in the event of a short circuit. On the other hand, a typical application is the plausibility check of the parameters of the high current stage of a transformer protection relay during the commissioning or repeat protection test, for example with our relay test system ARTES.

The following formulas are used to estimate the maximum short-circuit current "Ik_max" for three-phase medium-voltage transformers. The determined current value "Ik_max" is in practice somewhat higher than the real short-circuit current "Ik_max_real" which actually occurs. The estimation is therefore made to the "safe side".

The following equations 1 and 2 show that the estimation can be done for the primary as well as for the secondary side. When using equation 1 and equation 2, it should be noted that "usc" must be entered as a percentage in the equations for the relative short-circuit voltage.

If the rated current of the transformer is not explicitly known (for example, only “Srated_transformer” and “uk” are often specified in network calculations for transformers), the tailored quantity equation 3 can be used. Note: This estimation of the maximum short-circuit current applies only to three-phase medium-voltage transformers with a secondary voltage of Unom_sec = 400V. Also, when using equation 3, note that the relative short-circuit voltage "usc" in percent must be inserted into the equation.

When transformers are used, they are often referred to as "voltage-stiff" or "voltage-soft" transformers with regard to the behaviour of the secondary voltage during load changes. Equations 1 and 2 show that the maximum short-circuit current increases with decreasing "uk" (voltage-stiff) and the maximum short-circuit current decreases with increasing "usc" (voltage-soft). The short-circuit voltage “Vsc” and thus also the relative short-circuit voltage “usc” are a measure of the internal resistance of the transformer.

Voltage soft: When loaded, the output voltage of the transformer decreases. The output current hardly changes. The transformer is short-circuit proof (example: welding transformer).

Voltage stiff: Under load, the output voltage of the transformer hardly decreases. The output current increases. The transformer is not short-circuit proof.

As an aid to remembering the behaviour of the transformer's output voltage, a very hard and a soft cushion can be used. If the same amount of pressure is applied to a very hard and a soft pad, the hard pad is depressed significantly less than the soft pad. The depth of the indentation on the cushion is synonymous with the behaviour of the output voltage of the transformer.