A Generalized Linear Optimal Power Flow Method




AC power on the grid contains two related components that are determined by grid design and operation. The ‘real’ component is generated by a power source and load on the system, transferring energy to a load on the grid. The ‘reactive’ component is generated by capacitance and consumed by inductance.  This particular component is responsible for generating heat and dissipating power. The magnitude of the apparent power – the power detected in the power lines – is the combined magnitude of the real and reactive components. When dispatching power from generators to loads on the grid, the independent system operators (ISOs) or regional transmission organizations (RTOs) must determine how much power is being sent through each individual line to avoid overloading the lines and causing grid failure. Additionally, ISOs can optimize their power flow on the grid for to accommodate a variety of fluctuations including transmission losses, line congestion, pollution, production costs, market profit or reliability. This optimization is typically completed by a DC power flow model and a few other non-linear models that are available. These methods each harbor a set of associated problems including: approximation errors, calculation time, high development costs, dependence upon an existing operating point, and lack of convergence upon a solution.


Description of Technology


This technology is a linear power flow model that optimizes power flow while retaining the cross-linkage between the real and reactive components of power. Approximations are made to linearize the model reducing run-time and giving reliable convergence of the solution. In addition, a linearized transmission line constraint model was created so that the linearized optimal power flow method can better optimize. This model is more robust than existing models built for DC power flow models because it considers both the real and reactive power constraints of transmission lines.


Key Benefits

  • Improved Accuracy: More accurate than current DC power flow models
  • Speed: This device has a faster run time than non-linear models and converges more reliably
  • Easy Implementation: Can easily be integrated into existing control models
  • No modifications are required for the system hardware
  • Applicability: can be integrated with all grid conditions without requiring a set operating point



  • Optimization of power flow for ISO and RTOs
  • Parameter optimization (i.e. cost, pollution and line losses)


Patent Status


Provisional Application Filed: 61/867,447




Joydeep Mitra


Tech ID




Patent Information:


For Information, Contact:

Raymond Devito
Technology Manager
Michigan State University
Joydeep Mitra