Fast Decoupled Load Flow (FDLF)

An important and useful property of the current system is that the change in real power is primarily controlled by the charges in the voltage angles, but not in voltage magnitudes. On the other hand, the charges in the reactive effect are primarily influenced by the charges in voltage magnitudes, but not in the voltage angles. a) During normal steady-state operation, the voltage magnitudes are all nearly equal to 1.0. b). Since the transmission lines are mostly reactive, the conductances are quite small compared to the susceptance (G ij <<.

The above two equations are FDLF equations, by evaluating these equations in each iteration, the unknown conditions, i.e.

Form Y-bus neglecting line resistances

No Line Z=R+jX Z≈jX Y=1/jX

Identify unknowns and related power flow equations

VUnknowns

FDLF Sub-Matrices

FDLF Iterations

Power Mismatches

YCos

Unknown δs

Unknown Vs

CONTENTS 1. Solving linear equations

Solving non-linear equations

Solving Power-flow/ Load-flow problems

MATLAB code to solve the above equations

Remarks)

MATLAB code to solve the load flow problem

Step2: Construct Y bus Y=[-9i 5i 4i

Step 3 (a): Inital values for V2 and V3 V2=1; V3=1;

It can be observed that by using the Gauss-siedel method, the solution for linear, non-linear equations and also for load flow problems can be obtained. In the GS method, convergence is affected by the choice of dim bus and the presence of series capacitors.

CONTENTS 1. NRLF using polar co-ordinates

An example for NRLF using MATLAB 3. An example for NRLF from Textbook
NRLF using polar co-ordinates
Compute ∆Pi (for PV and PQ buses) and ∆Qi (for all PQ buses).If all the values are less than prescribed tolerance, stop the iterations, calculate slack bus powers (P1 and Q1) and print
If the convergence criterion is not satisfied , evaluate elements of the jacobian matrix
Solve for corrections of voltage angles and magnitudes
Update voltage angles and magnitudes by adding the corresponding changes to the previous values and return to step 2

The voltage and angle (|v| and δ) at slack bus are fixed, assume |v| and δ at all PQ buses and δ at PV buses. Calculate ∆Pi (for PV and PQ buses) and ∆Qi (for all PQ buses). If all values are less than the prescribed tolerance, stop the iterations, calculate slack bus effects (P1 and Q1) and print the prescribed tolerance, stop iterations, calculate slack bus effects (P1 and Q1) and print the entire current flow solution including line currents. Update the stress angles and magnitudes by adding the corresponding changes to the previous values and returning to step 2.

Explain the terms correction vector, mismatch vector and Jacobian matrix by taking an example of a 4-bus system with one PV bus, one Slack bus and two PQ buses.

Explanation can be done using NRLF algorithm shown in earlier slide

G G Bus-1

P4, Q4PV Bus

Specified/Known Values at different buses

Unknown Values

The Jacobian matrix in the NRLF method is obtained by partial derivation of the corresponding real and reactive powers with unknown states. Angular states (δ) are related to actual power flows, and voltage states (V) to reactive power flows. The Jacobian matrix formulation is the heart of the NRLF method, it can be formulated as shown in the next slide.

By using both the power mismatch vector and the Jacobian matrix, the correction vector can be found out using the NRLF method as The corrections are added to initial values to obtain the new states or the next iterative values. After the problem is converged, complete load flow solution is printed along with slack bus effects P1 and Q1 and line flows.

An example for NRLF method using MATLAB

G Bus-1

Slack Bus V1=1.0 pu

PQ Bus PL2=0.9 pu

PV Bus

Question. Obtain the power flows using NRLF method for the 3 bus system shown in the figure

The unknown states are[δ2, δ3, V2]

The corresponding power flow equations for unknown states are [P2, P3, Q2]

Obtain the Ybus of the system,

PCos

QSin

The next step is to evaluate the elements of Jacobian matrix J
The next step is to find the corrections vector for next iteration using NRLF method
The updated values of states are obtained by adding the corrections with initial values, i.e
If all the values are less than prescribed tolerance, stop the iterations, calculate slack bus powers (P1 and Q1) and print the entire power flow solution including line flows

The next step is to find the correction vector for the next iteration using the NRLF method. If all values are less than the specified tolerance, stop the iterations, calculate the loose bus powers (P1 and Q1) and print the complete power flow solution, including the line flows. and Q1) and print the complete power flow solution including the line flow.

Output

0.9667 delta2

2.7596 delta3

The real and reactive power loss in the line connecting Bus-i and Bus-k can be calculated using

COMPLETE POWER FLOW SOLUTION

Example problem from Nagrath and Kothari

Matlab program for Numerical example 2 using NR method

Comparison with GS method

It was observed that GS method takes 32 iterations to obtain the same result as shown in the next slide.

Comparison of GS and NR methods

Gauss- Siedel

It takes more number of iterations to solve the same problem

The overall program execution time is slightly more

Time per iteration is less

Initial value can be taken randomly

It requires lesser storage memory

Applicable only to small systems

Newton-Raphson

It takes lesser number of iterations

The overall program execution time is lesser

Initial value is to be taken carefully

It requires more storage memory

Introduction*

Power angle curve 3. Swing Equation

Methods to improve steady state stability 5. Example 12.1

Power System Stability

Rotor Angle Stability

Steady State Stability or Small-Signal Stability

Transient Stability

Classification of Power System Stability

Power-Angle Relation: (P-δ curve)

The Swing Equation

VARDHAMAN COLLEGE OF ENGINEERING

It is the amount of energy received in unit time on a unit surface perpendicular to the sun's direction at the average distance of the earth from the sun. The solar constant actually varies by +/- 3% due to the Earth's slightly elliptical orbit around the Sun. The simplest and cheapest techniques are to let crops dry naturally in the field, or to spread grain and fruit in the sun after harvest. The disadvantage of these methods is that the crops and grain are subject to damage by birds, rodents, wind, and rain, and contamination by windblown dust and dirt.

In warm, dry climates, the collector may not even be necessary. The south side of the enclosure itself can be glazed to allow sunlight to dry the material. The Earth's surface heats and cools unevenly, creating atmospheric pressure zones that cause air to flow from areas of high to low pressure. The wind has played an important role in the history of human civilization. The part of the wind turbine that collects energy from the wind is called the rotor.

As air passes by the blade, a difference in wind speed and pressure is created between the upper and lower surfaces of the blade. The pressure on the bottom surface is greater and thus acts to "lift" the blade. Tip speed is the ratio of blade rotation speed to wind speed. BOD/COD gives an indication of the proportion of pollutants in wastewater that are biodegradable.

It prevents cracks that occur due to the hydrostatic pressure in the lower parts from moving into the upper parts of the gas holder. The life of the drum is short (up to 15 years; in tropical coastal areas about five years). It is considered a renewable energy resource because the heat coming from the Earth's interior is essentially unlimited.

Usually, some waste steam from the turbine (in flash and steam plants) can be condensed for this purpose. Part of the heat obtained from the warm seawater must be led to a cooler thermal sink. This series of steps would be repeated continuously with the same working fluid whose Sow path and representation of the thermodynamic process formed closed loops and hence the name “closed cycle.” The specific process adopted for the OTEC closed cycle is the Rankine, or steam power, cycle.

The name 'open cycle' comes from the fact that the working fluid (steam) is discharged after a single pass and has different initial and final thermodynamic states; Therefore, the path and the Sow process are 'open'. Essential features of an OTEC open cycle. Isothermal reversible expansion of the gas at the "hot" temperature, T1 (isothermal addition or absorption of heat).

CONTENTS 1. Important Formulae

Series Reactors

Problems on Symmetrical Faults

Important Formulae in Symmetrical fault analysis