See Also
The power flow problem entails solving a system of nonlinear equations. Solving a nonlinear system requires the use of an iterative algorithm to hone in on the correct solution. Many nonlinear system solvers have been developed, and PowerWorld provides access to the full Newton-Raphson method with an optimal multiplier and the fast decoupled method.
Usually, the power flow computation converges quickly. However, it is certainly possible to model conditions for which no Power Flow Solution exists, or for which the algorithm cannot converge to the solution within the maximum number of iterations specified. For such situations, the message log will provide a message indicating that the computation failed to converge. Furthermore, unless blackouts are disabled, the screen is grayed, and a message indicating a blackout has occurred is shown.
In order to calculate the power flow solution, simply press the Solve Power Flow button on the main Program Toolbar. Clicking Solve Power Flow actually performs several pre-processing activities and then runs three nested loops which solve the power flow: MW Control (Outer) Loop, Controller (Middle) Loop, and Power Flow (Inner) Loop.
Pre-Processing Activities
The Power Flow Loop is where the traditional power flow matrix equations are solved.
When a transmission branch status is changed from OPEN to CLOSED across a branch that has a large voltage angle difference, this can introduce a very large initial power flow mismatch and cause the inner power flow loop to diverge. Angle Smoothing will alleviate this large angle difference by smoothing the angles in the system around the newly closed in branch resulting in much better power flow convergence. Angle smoothing will also work if a series of branches are all closed in together. A message will be written to the message log to indicate this is occurring. Angle smoothing should be enabled by default, but an option exists with the Advanced Power Flow Solution Options to disable this. Angle smoothing works best for individual branches or a series of branches that have been closed that are not electrically near other branches that have been closed. If modifying a case and adding in new transmission lines that are electrically near each other, it might be better for solution convergence to disable angle smoothing.
Generators are allowed to remotely regulate any bus in the system. However, if there is no transmission path between the generator terminal bus and the remotely regulated bus which does not pass over any other PV buses, then the generator will not be able to regulate this bus remotely. Additionally this will introduce a numerical condition that makes the inner power flow loop not converge. This pre-processing activity ensures catches this condition and prevents these generators from performing voltage regulation. A message will be written to the message log to indicate this is occurring.
Estimate MW Change Needed
When large changes in generation or load are made to the system, then ultimately this entire mismatch will show up at the island slack buses during the first inner power flow loop. This can cause the inner power flow loop to not converge. When automatic generation control is enabled for this system, then this pre-processing activity will automatically try to initialize generator outputs throughout the system to prevent the entire mismatch from appearing at the slack bus. Eventually the MW Control (Outer) Loop will be executed to bring generators to their proper outputs as specified by the Area or Island AGC choices.
Low Impedances Lines Voltage Profile
When pre-processing the voltage profile, Simulator will look at groupings of buses connected by very low impedances lines. If a bus in a grouping of energized buses has a zero voltage while other buses in the group do not, the zero voltage will be changed to the first non-zero voltage found in the grouping. This provides a much more reliable solution.
Estimate Voltages at Buses that Have Just Been Connected
As part of the pre-processing of voltages, voltages and angles at buses that have just had their status changed from Disconnected to Connected will be estimated assuming that the voltages and angles at buses that have not just changed status remain fixed. This will better facilitate power flow convergence. A message will be written to the message log to indicate this is occurring.
Three Nested Loops
Power Flow (Inner) Loop : Red Loop
The Power Flow Loop is where the traditional power flow matrix equations are solved. There are several Common and Advanced Solution options which affect this loop. In the message log, a RED outline will be drawn around the inner power flow loop. Additionally, a PURPLE outline will be drawn around any generator Mvar limit checking which occurs inside this loop. For details on the equations used to solve the power flow loop see the topic on Equation Basics.
Controller (Middle) Loop : Green Loop
Once the Power Flow Loop is solved, control devices check if their control requirements are being met. Control devices are checked in the following order or precedence.
If any control devices requiring changes, then these changes are made and the power flow loop is re-solved. This continues until no more control loop changes are made. There are several Common and Advanced Solution options which affect this loop. In the message log, a GREEN outline will be drawn around this loop.
MW Control (Outer) Loop : Blue Loop
After the Control Loop has completed, the MW Control loop is entered and generation (and possibly load) is moved to meet the MW control options set in the case. Normally, MW control is done by area control with each area varying generation to meet its own load, losses and interchange. However, you may also use island-based control to dispatch MWs by island. If any MW control is needed, then the Control Loop and Power Flow Loop interaction must be repeated and so on. In the message log, a BLUE outline will be drawn around this loop.
A depiction of these loops and how you will see them represented in the message log is shown in the following figure.
