Hello, readers welcome to new post**.** In this post, we will learn how to solve** node equations**. Node equation re technique that used to solve different circuits in the electrical power system in a simple way. It makes our work easy and simple related to find the parameters used in the system like volts current and power.

**So **let get started

**How to Solve Node Equation**

- The common point in the circuitry where two elements of circuitry are linked is called a node.
- Normally KCL and KVL are used to solve the different equations existing in the circuitry.

**To**the understanding of node, equation let’s take a circuitry and solve it.

- In this circuitry, nodes are denoted with a number in the circle.
- Current sources are linked at nodes number three and four and other elements are taken as admittance.
- This is the usage of single subscript notation to make the voltage values of every node according to the reference node
- If we apply KCL at node number one current is moving away from the node so the equation will be

(V1-V3)Yc+(V1-V2)Yd+(V1-V4) Vf=0

- At not number three we have

V3Ya-(V3-V2)Yb+(V3-V1)Yc=I3

- After simplifying this expression we have
- For node number one

V1(Yc+Yd+Yf)-V2Yd-V3Yc-V4Yf=0

- For node three

-V1Yc-V2Yb+V3(Ya+Yb+YC)=I3

- Like this equation can be designed for nodes two and four and this equation can be resolved to find the values of volts
- By using the values of volts V1, V2 V3, and V4 current in all branches of circuitry can be determined
- Now we write the above four equations in matrix form and we have.
- this form of the equation helps us to easily solve them and the parameters of every node also remain in the mind.
- the matrix that we form is denoted as Ybus and known as bus admittance matrix.
- there are some rules you must follow to make Ybus admittance.

- All the diagonal components Yii is equal to the addition of admittance linked to the node.
- The components that are not in diagonal equal to the negative of total admittance linked among the nodes i and j
- the diagonal admittance is known as self admittance mutual admittance is known as mutual admittance.
- after the application of Ybus rules, we have a new matrix

- The number in the circle denotes the number of nodes.
- Let us take components for Yc admittance that we have

- this matrix can also be defined as
- now we transform this admittance matrix to an impudence matrix so we have

that is all bout the How to Solve Node Equations i have solved detailed circuitry for you to understand node equation if you have still any queries ask in the comments thanks for reading have a nice day.