**1.The rules for calculating parallel circuit parameters**The rules for calculating parallel circuit parameters are summarized as follows:

(1) The total current (I

_{T}) is the sum of the currents of each branch.

I

_{T}=I

_{1}＋I

_{2}＋I

_{3}＋…＋I

_{n}

(2) The voltage at both ends of the branch is equal to the voltage of the power supply for the branch.

E

_{s}=V

_{1}=V

_{2}=V

_{3}=…=V

_{n}

(3) The total resistance (R

_{T}) is equal to the reciprocal of the sum of the 1/R term.

R

_{T}=1/(1/R

_{1}＋1/R

_{2}＋1/R

_{3}＋…＋1/R

_{n})

(4) The total power (P

_{T}) is the sum of the power of each branch.

P

_{T}=P

_{1 }+P

_{2}+P

_{3}+…+P

_{n}

**2.Constant current source**The constant current source can provide a constant current rather than a constant voltage to the load. For example, photovoltaic batteries are constant current sources, while batteries and mains generators are constant voltage sources that can provide a constant voltage to the load. For a constant current source, the power supply voltage will vary with the load, and for a constant voltage source, the power supply current will vary with the load. Photovoltaic systems require one or more loads to consume all the current output by the system. (Most wind turbines are constant voltage sources.)

In Figure 1, two current sources are connected in parallel to output current to the load. Note that the output current direction of the two power supplies is the same (the head direction is the same). When the arrow direction is the same, the current through the load will add up.

I

_{R}=0.5＋0.8=1.3A

In some applications, one power supply cannot provide enough current, and multiple power supplies need to be used in parallel at this time.

example 1

In Figure 2, two PV cells output current to the load R_{L}. Calculate I_{RL}, V_{RL} and P_{RL }(PV cell can be considered as a constant current source.)

I_{RL}=I_{1}＋I_{2}=1.5A＋1.5A=3A

V_{RL}=I_{RL}×R_{L}=3×40V=120V

P_{RL}=V_{RL}×I_{RL}=120×3W=360W

Note that if R_{L} = 50 ohms, then V_{RL} = 3×50V = 150V. Here the current is constant and the voltage varies with the load.

Example 2

There are two PV arrays connected in parallel, as shown in Figure 3. The rated output voltage of each array is DC12V and the current is 10A. Calculate E_{L}, I_{L}, P_{L}, and load polarity E_{L1} and E_{L2}.

PV arrays A and B are connected in parallel, so

E_{L}=DC12V

I_{L}=I_{A}＋I_{B}=(10＋10)A=20A

Power（P_{L}）=E_{L}×I_{L}=12×20W=240W

The load polarity E_{L1} is negative (-), and E_{L2 }is positive (+).

**3.Shunt circuit**Each branch of the parallel circuit can shunt current, so it can be used as a shunt. Figure 4 shows the method of calculating the branch current.

I

_{X}=(R

_{T}/R

_{X})×I

_{T}

In the formula, I

_{X}is the branch current that needs to be calculated; I

_{T}is the total current; Rx is the branch resistance that needs to be calculated; and R

_{T}is the total circuit resistance.

Example 3

For the circuit shown in Figure 5, use the shunt calculation formula to calculate the current flowing through each branch.

(1) First calculate the total circuit resistance

R_{T}=(R_{1}×R_{2})/(R_{1}＋R_{2})=(330×220)/(330＋220)Ω=132Ω

(2) Then apply the shunt formula

I_{R1}=(R_{T}/R_{1})×I_{T}=132/330×0.6A =0.24A

I_{R2}=(R_{T}/R_{2})×I_{T}=132/220×0.6A=0.36A

Note that the sum of the currents of each branch is equal to the total current.

Example 4

In Figure 6, R_{1}=50Ω, R_{2}=75Ω. Calculate I_{1} and I_{2}.

(1) First calculate the total circuit resistance.

R_{T}=(R_{1}×R_{2})/(R_{1}＋R_{2})=(50×75)/(50＋75)Ω=30Ω

(2) Then apply the shunt formula.

I_{1}=(R_{T}/R_{1})×I_{T}=30/50×2A =1.2A

I_{2}=(R_{T}/R_{2})×I_{T}=30/75×2A=0.8A