Basic SI units and formulas associated with Electricity

Term definitions

As mentioned elsewhere, the Watt (W) is the derived SI unit of power, and is defined as one joule per second. When talking about electricity, it is a measure of energy used or generated at a point in time. 1 Kilowatt (kW) = 1000 Watts.
It is often represented by the letter P.

The Ampere (A) is the base SI unit of current. It is normally represented by the letter I.

Voltage (V) is the derived SI unit of electric potential. It is normally represented by the letter V.

Fomulas:

These three units can be tied together in the formula

P = V * I where P is measured in Watts, V is in Volts, & I in Amps. For example. if your current was initially in mA, this must be converted to Amps before using in the formula (eg 300mA = 0.3 Amps)

Example 1

A tape player connected to a 12V car battery draws 800mA of current. How much power is it consuming?

P = V * I = 12 * 0.8 = 9.6 Watts

Example 2

A mains operated electric jug draws 9.5 Amps while operating. How much power is it consuming? Assume the mains is 240V AC.

P = V * I = 240 * 9.5 = 2280 Watts or 2.28 kW

Note: The formula for measuring power when dealing with AC is P = V * I * pf. In the above example, pf would be extremely close to 1, so it can be ignored.

Appliances which plug into standard 240V power outlets are supposed to have a maximum power rating of 2400 Watts. This equates to a maximum current of 10 Amps at 240 Volts.

Measurements of Power

• The Watt (symbol W) is the derived SI unit of power, and is defined as one joule per second. When talking about electricity, it is a measure of energy used or generated at a point in time. 1 Kilowatt (kW) = 1000 Watts.
• The Watt-hour (symbol Wh) is a measure of energy used or generated over a period of time. Our electricity providers normally bill us in units of Kilowatt-hours (kWh), one kWh simply being 1000 Wh. Note that the kilowatt-hour is a measure of the instantaneous power multiplied by time and not divided as we are probably more familiar with. eg km/h, being kilometers travelled in an hour. The time period is always related to an hour.
 Examples: An appliance drawing 1000 Watts (1 kW) for 1 hour is said to have consumed 1 kWh of electricity. An appliances drawing 2 kW for a period of 2 hours has consumed 4 kWh of electricity. A clock radio rated at 2 W will draw 48 Wh or 0.048 kWh over a 24 hour period. A 1000 Watt toaster takes 3 minutes to cook toast. The electricity consumed will be 1000 Watts * (3 minutes / 60 minutes) = 50 Wh or 0.05 kWh.

Hot Water Power Consumption Formula Derivation

The following two formula are used to derive the resultant third formula:

Formula 1

Without going into too much detail here (check with Senior High school Physics Texts for explanations):

 Q = m*c*T where: Q is the amount of heat energy (Joules) m is the mass of the substance (kg) c is the specific heat capacity of the substance (joule/kg/°K) T is the change in Temperature (K or °C)

The mass (m) of water is 1 kg per litre, so the number of litres to be heated can be substituted here.

The specific heat (c) of water is 4200.

Formula 2

 1 KWh = 3.6 MJ (By definition, 1 Joule = 1 Watt per second. Knowing that there are 1000 Watts in a kW and 3600 seconds in an hour, the above formula can be derived).

Resultant formula

By combining these two formulas and substituting the specific heat of water value for the constant, the following formula is arrived at:

 P = (4.2 * L * T ) / 3600 where: P is the power used in KWh L is the number of litres of water heated T is the Temperature difference between the hot water ended up with and the cold water started with in °C.

Voltage & Frequency

 Abbreviation Definition Common Sources AC Alternating Current Household mains DC Direct Current Batteries, Solar Photovoltaic Cells/Panels

AC mains in Australia is usually specified as either 230 or 240V, with a frequency of 50 Hz. (cycles per second).

This specified voltage is what is called an RMS (Root Mean Square) voltage. It's not a constant voltage like DC. Voltage and current are constantly varying around a reference point, following a sinewave pattern. (The waveform on the mains is rarely a pure sinewave. It is often distorted or 'dirty', due in part to some equipment drawing power in spurts rather than at a constant rate). 50 cycles of this sinewave are completed every second. The peak-to-peak voltage of this sinewave is the RMS voltage multiplied by 1.414 (the square root of 2). If we assume the RMS voltage to be 240 Volts, the voltage from one peak of the sine wave to the other is 240 * 1.414 or 340 Volts.

This actual RMS voltage from the mains is not usually very steady. It varies with loads on the circuit, location and the time of day. The voltage at my house varies from around 230V to over 250V.

Electric Lights & Frequency

Normal flourescent and incandescent lights turn on and off 100 times per second (twice the frequency), but because of our persistence of vision, they appear to stay on. With electronic controllers used occasionally on normal flourescent lights and usually on one-piece CFL's, extra circuitry is included which converts the 240V AC into DC, then back into AC but at a frequency of around 20 to 30 kHz (20,000 to 30,000 cycles per second), which usually eliminates any perceivable flicker. It also enables the tube to run more efficiently.

Electricity Charges - Normal & Off Peak tarrifs

Background

Electricity is charged in units of kWh. Different electricity providers charge differing amounts per kWh, and may vary the amount charged at different times of the day.

Electricity suppliers would like us to use a constant amount of electricity over the day. Their turbines which generate the electricity cannot easily be turned on and off to meet transient demands for power. The peak demand periods are normally in the evening and early mornings. To encourage us to use electricity at other times of the day, a lot of providers offer cheaper electricity at those less popular times.

In domestic situations, heating water is the most common use of this 'Off Peak' power. The power comes in on the same power lines, but there is a controller in the meter box that can receive signals sent by the electricity supplier which switches on or off power to the devices connected to this circuit. The water is heated when power is available, and stored for use later on. See more info on the Hot Water page.

Charges

Normal Domestic electricity in Australia is usually around 11 to 14 cents per kWh. Integral Energy, which is my retailer, charges just over 11.5 cents per kWh (incl GST) at present.

Off Peak 2 electricity is provided outside peak demand periods. To try and minimise consumption peaks, each house is allocated a 'channel'. Each channel switches power on and off to the off-peak circuits at slightly different times. The channel that my controller is programmed to respond to on weekdays switches power on between then following times: 10pm and midnight, 1.30am and 7am, 9.30am and 4pm, with extended hours on the weekends. Integral Energy charges around 7.5 cents per kWh.

Off Peak 1 electricity is usually provided overnight on weekdays (approximately 11pm to 6am) and extended hours over the weekend. Integral Energy charges around 4.4 cents per kWh.

Solar Panel Ratings

Solar Panels produce their stated output power under 'Standard Operating Conditions'. These are:

• Irradiance = 1000 W/m² (bright sunshine at midday, perpendicular to the panel)
• Air Mass = 1.5 (Air mass is a measure of the distance through the atmosphere that the sun's rays must travel before they reach the earth. A value of 0 would be measured just above the earth's atmosphere. A value of 1.0 occours when the sun is directly overhead, and represents the shortest path through the earth's atmosphere. At other times the value is greater than this. 1.5 is selected as an average value.
• Cell Temperature of 25° C.

In the real world. some of these conditions aren't normally sustained for long periods if they're reached at all.

The BP mono-crystalline cells in this system along with poly-crystalline cells from some other manufacturers both suffer decreased output power at higher temperatures. In general, each 1°C increment in cell temperature above 25°C decreases output power by 0.4 or 0.5%. To put this in some perspective, on a mild sunny Winter's day in Sydney, the air temperature was around 16°C, and the temperature on the panels hovered around 36°C.
To get a cell temperature of 25°C, you would probably need a sunny day with maximum air temperature of under 10°C. This doesn't happen too often in large parts of Australia.

In the above example, the decrease in maximum peak power would be around 5%, taking the 'rated' 1350 Watts system peak down to around 1280 Watts.

Haze and other airborne material also have a detrimntal effect on possible output power.

Maximum Power Point (MPP) Tracking

 The red line of this graph shows the typical output curve of the 9 12V solar panels connected in series. By deriving output power from multiplying current by voltage, we come up with the blue line. It can be seen that at the knee of this curve, which correspondes to the knee of the Solar panel output curve, the maximum power possible is being produced. The figures at this point are approximately 153 Volts and 8.6 Amps, which produce around 1316 Watts. By varying the load presented to the PV panels, the current into and voltage across the load can be controlled. MPP tracking seeks to keep the inverter operating at as close to the knee of the curve as prevailing light condition permit, therby producing the maximum amount of power possible.

True North

Magnetic North (as read by a compass) varies with time and location. There are maps and tables available that show the corrections for given locations. In Sydney at present, Magnetic North is around 13° East of True North (or True North is 13° West of Magnetic North). As an example of how this variation changes over time, in 1993 the difference between the two in Sydney was 12.62°. In 2003, this had changed to 13.03°. Solar Panels of all descriptions should ideally face True North.