Microsoft Word 2012, Källén, M.,-Energy Efficiency Opportunities within the Heat Treatment Industry

2.4 

Three Phase Electricity System 

A three phase system consists of three sinus-shaped alternating currents which are 120° out of 

phase with each other. The three phases are connected to a neutral conductor. The voltage 

between two phases is called principal voltage and the voltage between one phase and the 

neutral conductor is called phase voltage, see figure 3. [10] 

 

Figure 3. The relationship between the phases and the voltages where U

h

 is the principal 

voltage and U

f

 is the phase voltage. 

 

The following equation can be derived from figure 3: 

 

 

 

 

°

√

 

 

 

 

 

 

(1) 

where U

h

 is the principal voltage and U

f

 is the phase voltage. 

The power load for a three phase system is called apparent power load and consists of a 

constant part, called active power load, and a varying part, called reactive power load. The 

reactive power load is zero over time. The angle between the active power load and the 

apparent power load is called the phase difference and is denoted φ, see figure 4. 

 

---

 

 

10 

 

 

Figure 4. The relationship between the power loads where S is the apparent power load, P is 

the active power load and Q is the reactive power load.  

 

The apparent power load can be calculated according to: 

 

 

 

 

3

 

 

 

 

 

 

 

(2) 

where U

f

 is the phase voltage and I

f

 is the phase current. Using equation (1) and (2) and the 

relationship shown in figure 4, the active power load can be calculated according to: 

 

 

 

 

√3

cos  

 

 

 

 

 

(3) 

The principal voltage and the phase difference are obtained from the instantaneous 

measurements and the phase current is the mean value for the logging period. The electricity 

consumption is then calculated by: 

 

 

 

 

   

 

 

 

 

 

(4) 

where is 

 the logging time.