Power Flow Analysis Solution Techniques in PSS/E

In PSS?E there are many power flow solution methods available to solve the steady-state power flow analysis. Each method uses iterative techniques to solve the power system nonlinear algebraic equations by adjusting voltages at all systems buses to satisfy Kirchhoff’s current laws and system demand as well.

Moreover, the real and reactive power mismatch practically should be zero (with small tolerance) at each bus and the total system generation should be balanced with system demand.

In PSS/E the regular Gauss-Seidel methods and modified Gauss-Seidel are available. Both these methods are fast per iteration basis, but the convergence time is slower than the Newton-Raphson methods. Similarly, the PSS/E include the Newton Raphson methods comprises

• Full Newton-Raphson
•  Decoupled Newton-Raphson
• Fixed-slope Decoupled Newton-Raphson

Above mentioned methods use the first-order Taylor series expansion of the load flow equations and with the use of Jacobian Matrix and the iterations are continued until system convergence reached.  However, the time to reach the solution in these methods is fast as compare to the Gauss-Seidel method.

So, in this regard power system engineer is required to perform training exercises to find the optimum combination of these iterative methods for every network model.

As per experience shared by PSS/E user support the following sequence is the most useful approach to solve the power system network:

1.  Initialize all voltages to either unity amplitude, or to scheduled amplitude if given, and initialize all phase angles to zero. (This step is referred to as a flat start.)
2. Execute Gauss-Seidel iterations until the adjustments to the voltage estimates decrease to, say, 0.01 or 0.005 per unit in both real and imaginary parts.
3. Switch to Newton-Raphson iterations until either the problem is converged, or the reactive power output estimates for generators show signs of failure to converge.
4. Switch back to Gauss-Seidel iterations if the Newton-Raphson method does not settle down to a smooth convergence within 8 to 10 iterations.

 A.  Causes of Solution Failures in PSS/E

1. Sometimes when we solve the power system network and failure in convergence occurs due to the solution crosses the feasible region and unable to return its vector. So, in order to find a situation that provides the solution, but the voltage vector cannot be found one of the solution methods. It means that system has many problems which lead to divergence of the solution, at this time system should be solved by the successive application of more than one method.
2. In the second scenario, the solution may not converge due to an infeasible operating point and system face voltage collapse at that time due to poor/insufficient reactive power support to the load and system as well. Then the system required proper reactive power compensation to the distribution network to solve the case.
3. Third but not least, the divergence of power flow can be caused by many control adjustments model in different components of the power system network, such as:

•  Tap-Changing or Phase-Shifting Transformers
• Switchable Shunt Capacitors or Reactors
• Area Interchange Control
• HVDC lines and FACTS device controls.

Because controls of each component have two different operating modes with its local control objectives and power flow solution methods automatically adjust the control settings to meet the set voltage and flows of the respective equipment. As a result of poor coordinated control, adjustment leads to non-convergence of the solution.

B.  Some Important Steps to address Solution Failures in PSS/E

1. The first step is in the power flow solution, the power system network should be implemented in PSS/E correctly in terms of network topology and parameters of all components as well. Simply in the PSS?E Check Data tab is toolbar is available in the Power Flow Section where you can get different Violation reports of branches and transformer of the network model However it is difficult to find the data errors in such a large network.
2. In the second step most specifically with the Newton-Raphson solution methods that are mostly used by PSS/E user so in order to address the convergence issues with this method, the first trick is to change the power flow solution parameters.

• To keep the solution within the feasible region i.e. to slow down solution reduce the Newton-Raphson solution acceleration factor so that divergence may not occurs.
• increase the iteration limit in cases where convergence is slow
• increase the mismatch tolerance in cases with slow convergence or near voltage collapse.
• increase the automatic adjustment threshold tolerance to activate switched shunt adjustments sooner in the iteration process to allow better voltage control before voltage collapse starts to occur.

3. Change the power flow control options.

• disable local controls to avoid the effects of small adjustments to the Jacobian that may lead to divergence
• ignore the reactive power limits of the generators to increase the feasible solution space
• prevent the automatic adjustments of switchable shunts and transformer taps after a certain number of iterations to avoid oscillation.

 4.    Change the network model.

The system swing is meant to absorb the difference between total system generation and the sum of system loads and losses. From a mathematical standpoint, any generator bus could be assigned as the system swing.

• Sometimes, changing the swing bus may help convergence
• change the remote voltage control to local voltage control for more effective control
• change the control mode of some switchable shunts from discrete to continuous temporarily, in order to better understand the reactive power needs of the system.

5.    Apply the non-divergent power flow solution method.

• The non-divergent Newton-Raphson power flow solution is designed to terminate the iterative process before the bus voltage vector is driven to a state where large mismatches and unrealistic voltages are present.
•  The resulting voltage vector obtained using the non-divergent solution method, although not sufficiently accurate to represent a converged power flow solution, can often provide a relatively good indication of the state of the network, in terms of severe voltage depression and reactive power deficiency in some parts of the power system.

6)   Use a voltage-dependent load model.

• A load model may consist of several components in the power flow solution: constant power, constant current (load changing in direct proportion to voltage), as well as constant impedance or admittance (load changing according to the square of voltage).
• By using a voltage-dependent load model, a drop-in voltage in the power system would result in a reduction in load, thus reducing the real and reactive power needs of the system. This may allow the system voltages to stabilize, instead of collapsing.
• PSS?E has a user-adjustable constant power load characteristic threshold (PQBRK), which will automatically change the constant power load representation to a voltage-dependent representation in the power flow equations if the voltage at a load bus falls below the threshold.

7.   Use the optimal power flow.

A power flow case that fails to converge or is near or in voltage collapse can be represented as an optimal power flow problem.

• The PSS?E OPF solution automatically changes control variables to achieve the best solution with respect to a stated quantitative performance measure, i.e., an objective function and a set of variable constraints to satisfy. If the voltage collapse is due to a deficiency in reactive power support, PSS?E OPF can be used to identify the location and size of reactive compensation devices.

8.    In addition, the power flow solution convergence monitor

• It can provide useful information for identifying the cause of non-convergence (e.g., whether the solution is oscillating because of conflicting controls, solution convergence is too slow, or the initial bus voltage estimates are poor), so that appropriate measures can be taken to assist solution convergence. One or more of the above techniques may be applied, as needed.