When more than two generators with different characteristics sharing a load a droop control is used

I dont mean that.........i mean as load increase the generated power increase, I want to know at what bevavior generated power changed to achieve max system loadability for IEEE 30 bus system

Dear Alaa Eldin,

In my opinion, an optimal power flow (OPF) could help you in this task. There are a lot of formulations for OPF solution. In this case, the OPF would provide the maximum loadability and the power generated by each machine (optimal sharing).

The optimization toolbox of MATLAB is very effective for initial studies (see fmincon function) . In this case, the formulation would be:

maximize f(x) = lambda

subject to

Pg - (1 + lambda)*Pd - Pinjection = 0

Qg - (1 + lambda)*Qd - Qinjection = 0

xmin < x xmax

where :

lambda is a factor associated to the load (maximizing lambda, you will maximize the load)

The equations are associated with power balance at each busbar.

Pg, Qg: real and reactive power generated

Pd, Qd: nominal load (initial value of load / base case)

Pinjection, Qinjection: mathematical expressions that stands for the power injected at each busbar. This expression is a function of the system variables and network parameters (such as those of SSSC).

xmin, xmax: variable bounds (angles, voltages, etc).

The solution of this problem (I recommend the solver fmincon of MATLAB), will provide the results (optimal solution) required.

Hope That Helps

Regards,

Wesley

Dear Wesley Peres

I agree with you,but my question is how generator active power increased as load increased .as you know PV bus has constant power generation or you mean that all PV buses give its max output power and slak bus give the remaining power

Before the introduction of non-dispatchable technologies such as wind and solar, generation (MW) was entirely dispatchable. Each generator could technically operate at any desired MW output between a minimum load (depending on the prime mover technology) and full power output.

Obviously, each prime mover would have a different cost and a different efficiency as power is changed. Most utility scale machines are designed for maximum efficiency at (or near) full power output.

Thus, the actual generation dispatch in a system is decided via an optimization at the system dispatch center (unit commitment or generation dispatch).

Long story short: without cost functions for the generators, you have no way to determine what is a "realistic" dispatch. On the other hand, on a simplified and simplistic system such as IEEE 30 buses, you can use any dispatch you want.

The easiest way is to use load flow analysis and get the values of P,Q,V and DELTA at all the buses of a power system and than decide about the contribution of each generator to the supply of load in the system

Dear Alaa Eldin,

your problem is to find the share of generation between various generators when load is increased to the maximum limit. To do this you have to understand few things about various bus definitions. Generators are connected to two types of buses. They  are:

1. PV bus- here the power out put is always constant and the voltage is also maintained constant. But the reactive power and delta(theta) varies. In your case what ever the load is the output of this generator is always same, hence no need to calculate load sharing or generation sharing.

2. V delta bus(slack bus)- Here  voltage and delta is constant and the power generated varies. So for your case just consider 2 slack bus model. One will be the mother slack and should not be controlled during the simulation. Now let us assume that delta for mother slack be 0.2 degree and 2nd be 0.1. Now this means for a 100 MW load increase the mother slack will supply 66.6MW and 2nd generator will supply 33.3MW.(pardon me if my calculations are wrong). That is the load sharing mainly depends on the angle delta.

Note:- This will work only if all other constraints are satisfied. That is generation limit, line limit, voltage limit etc.

Regards

Chittesh VC