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Load Flow Calculations


Load Flow Calculations


Describing the Network for a Five-bus Power System

  • Calculates the load flow given a five-bus power system 
  • Applicable in electrical engineering, specifically involving electricity and energy 
  • Performs using series, matrices, arrays, transmission lines and transformer data, pi equivalents, pi shunt, shunt data, Jacobian matrix, Newton-Raphson algorithm, iteration, line losses, etc.

     This worksheet using PTC Mathcad shows you how to describe the network for a five-bus power system, using a matrix containing the transmitting and receiving bus numbers, the series impedance, and shunt admittance.  You can also capture shunt data and bus data in matrices. To begin, you are shown how to enter data in an array series and the data of the shunt equipment in another array. Shunt elements may represent reactive power compensation at certain system buses.  In this case, the reactance of the corresponding compensation device (capacitor or inductor) is calculated and its admittance can be entered in an array. You are also shown how to enter the bus data. 

     After that you are shown how to define auxiliary arrays, calculate the net power injections at each bus, initialize the voltage and angle vectors, and initialize the bus matrix. This worksheet shows you how to form the bus matrix and the Jacobian matrix. You are then shown how to iteratively solve for voltage and phased until convergence is reached along with line losses.

     Solving for the load flow entails:

  • initializing the system arrays, functions and indices 
  • constructing the system bus matrix 
  • constructing the system Jacobian matrix and inverting it 
  • iteratively solving for voltage and phase until convergence is reached

     All data, notation, calculations, formulas, solutions, and images are provided to aid you in your own calculations.

     Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.


Re: Load Flow Calculations

Hi ,

how to change the power flow program if only one transformer feeds the line and there are several loads+

I tried but didin'succeeded, The Jacobianmatrice inverse shows nothing

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