Amp-Hours and Appliances
People living in off grid tiny homes and vans often use propane or butane as a cooking fuel and sometimes to heat enclosed spaces, even if they have a solar power arrangement. The impression is that electric cooking appliances put an excessive strain on off grid solar power systems and drain batteries excessively. The same could be said of electrical off grid air conditioning systems. So let's do some calculations to determine if it is theoretically possible to power cooking, heating and cooling appliances with solar and/or batteries.
My background is in electrical engineering and physics. Physicists often start analyzing a system from the point of view of energy. Most natural physical systems are in a state of minimum stable energy configuration or are in the process of reaching a minimum stable energy configuration. So let's analyze the off grid system from the point of view of energy. Since every system interacts with it's surroundings, energy is often changing, whether in very small amounts or large. We can take this into account by looking at the concept of Power where Power = Energy / Time. Different physical quantities are used to analyze the energy and power of different physical systems.
In typical electrical circuit systems current (I) and voltage (V) are used to analyze the power, where Power = I*V. This relationship holds even if I and V vary in time, like in an AC circuit, though it is more complex since the power changes in time. This can simplified by looking at average power and rms currents and voltages:
Pavg = Irms*Vrms
Since most off grid systems power a small number of appliances this is a good approximation.
So let's say we are looking at an electric hot plate:
Electric Hot Plate
The description says it can deliver 1000W of power, we may assume they mean 1000W AVERAGE power. Now, we may also assume that the heating element alone uses 1000W, this means that other elements in the hot plate may also consume power. So, the total average power consumed by this hot plate could well be over 1000W, say 1100W.
Since the off grid deep cycle batteries are the source of power, these batteries must provide at least 1100W. There are other losses in the system, the power inverter that converts DC to AC is NOT 100% efficient, some of the DC power is wasted in form of heat. The DC wires have a non-zero resistance, etc. So, let's say the battery must provide 1200W of power.
Since the batteries provide electricity in DC form, we have
1200 = I*V
We have different options for V. It is possible to configure batteries that output 12V, 24V, 36V, or 48V. Here are the different options:
1200/12 = 110.4A
1200/24 = 55.2A
1200/36 = 36.8A
1200/48 = 27.6A
Often the lower the current, the lower the losses. The following website has a nice calculator:
BatteryStuff Calculator
If we look at some of the material regarding batteries we will quickly find that the electrical properties of batteries are rarely analyzed from the viewpoint of power or energy, what is more useful is to look at the concept of Amp-Hour:
Ampere Hour
"An ampere hour is not a unit of energy. In a battery system, for example, accurate calculation of the energy delivered requires integration of the power delivered (product of instantaneous voltage and instantaneous current) over the discharge interval.[3] Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power."
Batteries are more complex due to their electrochemical nature:
Amp Hour Rate
It becomes apparent that the number of electrons that flow between the terminals of a battery is a more useful quantity to analyze the electrical discharge properties of a battery than is power or energy.
Since the current and voltage provided by batteries changes as the battery discharges it is best to use a calculator to compute the size of battery or batteries needed:
Battery Sizing
For our purposes we would need a 258 Ah battery operating at 12v to run our hotplate for 45 minutes at 1000W.
If we buy the typical deep cycle battery for solar applications we would need to get 2 of the following:
Flooded Battery
It is quite large and heavy at 110lbs each for a total of 220lbs!
If we instead operate the DC system at 48V, then we would need approximately 56 Ah. We could take 4 12 volt, 56 Ah flooded, agm, or gel batteries and connect them in series to obtain the 48 volts. We would end up with a battery system nearly as large and heavy as before. But there is another way, one word lithium.
There are lithium deep cycle batteries that operate at 12 volts with the necessary Ah:
Lithium 12v
Each battery weighs only 25 lbs, compared to the 50+ pounds for comparable non-lithium battery. So if we get 4 of these lithium batteries and wire them in series to obtain 48v then we would have the necessary voltage and current to power our hot plate with only 100 lbs of batteries.
There are other ways to reduce the number and size of batteries, and that is to use more efficient cooking and heating techniques. For example using a 1000 watt microwave oven to heat or cook food is much more efficient. It often only takes 2-3 minutes to bring a bowl of water to boiling temperature and about 1 minute to heat up small frozen foods, veggie dog or veggie hamburger patty.
Lets say we use a 1000W microwave oven for 3 minutes to heat up or cook foods. With all losses taken into account we may need 1200W from the batteries. 3 minutes is equivalent to 0.05 hours, if we run our numbers through the same calculator as above we get 26 Ah for gel and 20 Ah for AGM at 12volts!
This is much less than what was needed for the hot plate, if we get a 50 Ah battery (just in case we want to cook or heat up other foods) the battery sizes and weights drop to 33lbs. If we get a lithium battery then we only need 15 lbs.
Probably the best way to cook off-grid or in a van is to use a parabolic solar cooker:
Parabolic Solar Cooker
or solar oven
Solar Oven
It is much, much more efficient than converting the sunlight to electricity and storing it in large batteries. So the best approach would be to use the parabolic solar cooker and oven to cook during the day and simply use a microwave to heat up at night. This is a much better use of solar power.
This could even be used to heat enclosed spaces. A solar water heater
Solar Water Heater
could be used to heat water during the day. At night, if needed, the water could be run through a series of pipes in the tiny home or van and the heat expelled in the enclosed area, in a manner very similar to a radiator system.
The most efficient use of Solar Power bypasses the conversion to electricity and storage in batteries. Parabolic solar grill instead of hot plate, solar oven instead of electric oven, solar water heater instead of electric space heater. Most important is to reduce the amount of energy lost into the environment, whether keeping cool or keeping hot.
My background is in electrical engineering and physics. Physicists often start analyzing a system from the point of view of energy. Most natural physical systems are in a state of minimum stable energy configuration or are in the process of reaching a minimum stable energy configuration. So let's analyze the off grid system from the point of view of energy. Since every system interacts with it's surroundings, energy is often changing, whether in very small amounts or large. We can take this into account by looking at the concept of Power where Power = Energy / Time. Different physical quantities are used to analyze the energy and power of different physical systems.
In typical electrical circuit systems current (I) and voltage (V) are used to analyze the power, where Power = I*V. This relationship holds even if I and V vary in time, like in an AC circuit, though it is more complex since the power changes in time. This can simplified by looking at average power and rms currents and voltages:
Pavg = Irms*Vrms
Since most off grid systems power a small number of appliances this is a good approximation.
So let's say we are looking at an electric hot plate:
Electric Hot Plate
The description says it can deliver 1000W of power, we may assume they mean 1000W AVERAGE power. Now, we may also assume that the heating element alone uses 1000W, this means that other elements in the hot plate may also consume power. So, the total average power consumed by this hot plate could well be over 1000W, say 1100W.
Since the off grid deep cycle batteries are the source of power, these batteries must provide at least 1100W. There are other losses in the system, the power inverter that converts DC to AC is NOT 100% efficient, some of the DC power is wasted in form of heat. The DC wires have a non-zero resistance, etc. So, let's say the battery must provide 1200W of power.
Since the batteries provide electricity in DC form, we have
1200 = I*V
We have different options for V. It is possible to configure batteries that output 12V, 24V, 36V, or 48V. Here are the different options:
1200/12 = 110.4A
1200/24 = 55.2A
1200/36 = 36.8A
1200/48 = 27.6A
Often the lower the current, the lower the losses. The following website has a nice calculator:
BatteryStuff Calculator
If we look at some of the material regarding batteries we will quickly find that the electrical properties of batteries are rarely analyzed from the viewpoint of power or energy, what is more useful is to look at the concept of Amp-Hour:
Ampere Hour
"An ampere hour is not a unit of energy. In a battery system, for example, accurate calculation of the energy delivered requires integration of the power delivered (product of instantaneous voltage and instantaneous current) over the discharge interval.[3] Generally, the battery voltage varies during discharge; an average value or nominal value may be used to approximate the integration of power."
Batteries are more complex due to their electrochemical nature:
Amp Hour Rate
It becomes apparent that the number of electrons that flow between the terminals of a battery is a more useful quantity to analyze the electrical discharge properties of a battery than is power or energy.
Since the current and voltage provided by batteries changes as the battery discharges it is best to use a calculator to compute the size of battery or batteries needed:
Battery Sizing
For our purposes we would need a 258 Ah battery operating at 12v to run our hotplate for 45 minutes at 1000W.
If we buy the typical deep cycle battery for solar applications we would need to get 2 of the following:
Flooded Battery
It is quite large and heavy at 110lbs each for a total of 220lbs!
If we instead operate the DC system at 48V, then we would need approximately 56 Ah. We could take 4 12 volt, 56 Ah flooded, agm, or gel batteries and connect them in series to obtain the 48 volts. We would end up with a battery system nearly as large and heavy as before. But there is another way, one word lithium.
There are lithium deep cycle batteries that operate at 12 volts with the necessary Ah:
Lithium 12v
Each battery weighs only 25 lbs, compared to the 50+ pounds for comparable non-lithium battery. So if we get 4 of these lithium batteries and wire them in series to obtain 48v then we would have the necessary voltage and current to power our hot plate with only 100 lbs of batteries.
There are other ways to reduce the number and size of batteries, and that is to use more efficient cooking and heating techniques. For example using a 1000 watt microwave oven to heat or cook food is much more efficient. It often only takes 2-3 minutes to bring a bowl of water to boiling temperature and about 1 minute to heat up small frozen foods, veggie dog or veggie hamburger patty.
Lets say we use a 1000W microwave oven for 3 minutes to heat up or cook foods. With all losses taken into account we may need 1200W from the batteries. 3 minutes is equivalent to 0.05 hours, if we run our numbers through the same calculator as above we get 26 Ah for gel and 20 Ah for AGM at 12volts!
This is much less than what was needed for the hot plate, if we get a 50 Ah battery (just in case we want to cook or heat up other foods) the battery sizes and weights drop to 33lbs. If we get a lithium battery then we only need 15 lbs.
Probably the best way to cook off-grid or in a van is to use a parabolic solar cooker:
Parabolic Solar Cooker
or solar oven
Solar Oven
It is much, much more efficient than converting the sunlight to electricity and storing it in large batteries. So the best approach would be to use the parabolic solar cooker and oven to cook during the day and simply use a microwave to heat up at night. This is a much better use of solar power.
This could even be used to heat enclosed spaces. A solar water heater
Solar Water Heater
could be used to heat water during the day. At night, if needed, the water could be run through a series of pipes in the tiny home or van and the heat expelled in the enclosed area, in a manner very similar to a radiator system.
The most efficient use of Solar Power bypasses the conversion to electricity and storage in batteries. Parabolic solar grill instead of hot plate, solar oven instead of electric oven, solar water heater instead of electric space heater. Most important is to reduce the amount of energy lost into the environment, whether keeping cool or keeping hot.
Comments
Post a Comment