Electronic – Phasor simulation versus power flow

phasorpowersimulation

I have a basic question about the utility of a power-flow study versus a phasor simulation of a network.

Here is a description of phasor simulation from the Matlab Simpowersystems manual

"If, in a linear circuit, you are interested only in the changes in magnitude and phase of all voltages and currents when switches are closed or opened, you do not need to solve all differential equations (state-space model) resulting from the interaction of R, L, and C elements. You can instead solve a much simpler set of algebraic equations relating the voltage and current phasors. This is what the phasor solution method does. As its name implies, this method computes voltages and currents as phasors. Phasors are complex numbers representing sinusoidal voltages and currents at a particular frequency. They can be expressed either in Cartesian coordinates (real and imaginary) or in polar coordinates (amplitude and phase). As the electrical states are ignored, the phasor solution method does not require a particular solver to solve the electrical part of your system. The simulation is therefore much faster to execute. You must keep in mind, however, that this faster solution technique gives the solution only at one particular frequency.
"

and the wikipedia definition of a power-flow study

"In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.
"

To do a phasor simulation, I imagine that any load injections can be modeled as current injections at constant voltage or voltage sources at constant current. (?)

My confusion is the following. Why would one do a power-flow study if all the information of the voltages, currents and phase angles can be obtained from a phasor simulation (considering that we don't need to assume steady-state)? Wouldn't one get a more realistic description of the dynamics of the system (and all the corresponding information that power-flow study will provide) with a phasor simulation?

I am obviously confused about what each method is supposed to accomplish or may have made incorrect assumptions. I would be grateful if someone pointed out what that may be.

Best Answer

On the difference between 'load-flow' and 'phasor' studies

A loadflow (power-flow) simulation is a phasor simulation. It is a phasor simulation of a power system at nominal frequency (50Hz or 60Hz.) It assumes that the system is at sinusoidal steady state and that nothing is changing.

The distinction between a 'load flow' study and a 'phasor study' is that a phasor study can be performed at any arbitrary frequency, say 50Hz, 100Hz, 150Hz, whereas a load-flow study is nearly always performed at the power system nominal frequency (50 or 60Hz.)

The generalised 'phasor study' is useful in the study of power system harmonics, which requires simulation of the power system at 50Hz and its harmonic frequencies 100Hz, 150Hz, 200Hz, 250Hz, ... and so on. This is done by running one separate 'phasor study' for each harmonic frequency of interest.

On the difference between load-flow/phasor and dynamic/transient studies

A load-flow study evaluates steady state operation of a power system. We do load-flow studies to check that elements like transformers, overhead lines, and cables won't be overloaded, and that system voltage regulation is within acceptable limits (-6%, +10% for Australian domestic power supply.)

The time scale of interest is hours to days.

The loadflow study is just an exercise in solving a lot of simultaneous linear equations. There is no time dependent element, no differential equations, or anything exciting. You multiply some big matrices together and that's it.

A dynamic/transient study evaluates the behaviour of the power system when a change occurs. The change could be an increase or decrease in load, a line fault, a change in generator output, or a big motor starting.

The objective is to determine if there will be any detrimental effects on the scale of milliseconds to minutes. Detrimental effects might include - voltage spikes/dips, generator frequency slip, protection relay operation.

A dynamic/transient study must take account of the time-dependent response of the electrical and mechanical parts of the power system.

Generators and motors have a mechanical inertia
Capacitors and inductors have energy storage
Iron-cored transformers have remanence/hysteresis
Protection relays are digital signal processors which decide whether the power system is healthy or not, based on the history of the signals they see.
Generators have control systems with sophisticated transfer functions for calculating output voltage set point and governor (throttle) set point

Therefore a transient study involves simulating a system of differential equations evolving over time, with a typical time step of 1 millisecond.

The electrical quantities are still voltages and currents, but there are also a lot of variables in things like 'generator inertial energy' and 'motor rotational speed'.

PS: I do power system studies for a living.

Related Solutions

Electronic – How to model this linear power system in MATLAB

To solve this problem you should look at the ODE solvers in MATLAB.

Note that your function does not describe what the response of the system is to a variation in input power Pm.

Below I have written up an implementation, based on the example in http://www.its.caltech.edu/~ae121/ae121/ode45_Ref2.pdf . In my example I have added a term Pm to the differential equations, so you can see how a disturbance might affect the dynamics.

Unfortunately I don't have MATLAB installed so I can't check whether there are any errors in this, but the idea should be clear.

function main 
% a simple example to solve ODE's
% Uses ODE45 to solve 
%    dx_dt(1) = 1*x(1)+2*x(2)+3*x(3)+4*x(4)
%    dx_dt(2) = 5*x(1)+6*x(2)+7*x(3)+8*x(4)+Pm
%    dx_dt(3) = 9*x(1)+1*x(2)+2*x(3)+3*x(4)
%    dx_dt(4) = 4*x(1)+5*x(2)+6*x(3)+7*x(4)
%set an error
options=odeset('RelTol',1e-6);

%initial conditions
X0 = [0;0;0;0]; 
Pm0=1;

%before disturbance
tspan1 = [-1,0]; 
[t1,X1] = ode45('system',tspan1,X0,options,Pm0);

%during disturbance
tspan2 = [0,1];
[t2,X2] = ode45('system',tspan2,X1(end),options,1.3*Pm0);

%after disturbance
tspan3 = [1,3];
[t3,X3] = ode45('system',tspan3,X2(end),options,Pm0);

time=[t1,t2,t3];
X=[X1,X2,X3];

%plot the results
figure 
hold on
plot(time,X)
legend('x1','x2','x3','x4');ylabel('x');xlabel('t') 
return

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [dx_dt]= system(t,x,Pm) 
%a function which returns a rate of change vector
A = [1,2,3,4;
     5,6,7,8;... 
     9,1,2,3;
     4,5,6,7]
P=[0;Pm;0;0]
dx_dt = A*x+P; 
return

Electronic – Modelling of Electric Power Grid

The way to model the system and solve the system is the following:

Create a one-line power flow diagram
Define your reference bus
Convert everything to per-unit representation
Enumerate all buses
Write down a bus admittance matrix
Now write down your state variables, each load bus has a V and δ, generator buses have only V, and reference buses don't have state variables
To solve the system you can use many methods like Newton-Raphson or Gauss-Siedel

My best suggestion is that you try to get this book: Schaum's Outline of Electrical Power Systems. It has everything you need in an easy to understand format.