It seems to me that you simply want to run an OPF (seems like you are using a 
DC power flow model, so that would be rundcopf 
<http://www.pserc.cornell.edu//matpower/docs/ref/matpower5.1/rundcopf.html>)  
with your loads defined as dispatchable (curtailable) loads. See section 6.4.2 
in the MATPOWER User’s Manual 
<http://www.pserc.cornell.edu/matpower/docs/MATPOWER-manual-5.1.pdf>. You can 
use the load2disp 
<http://www.pserc.cornell.edu//matpower/docs/ref/matpower5.1/load2disp.html> 
function to convert the loads. If the value of the loads is higher than the 
cost of generation, then all load will be served unless load-shedding is 
required to maintain feasibility. The OPF automatically enforces the line flow 
limits.

    Ray


> On Jan 11, 2016, at 5:56 PM, Bijay Hughes <[email protected]> wrote:
> 
> Hi Ray,
> 
> I have a scenario where a line fails, and this initially failed line triggers 
> more failures. This continues until the system experiences a blackout. My 
> plan is to prevent blackout by performing a load-shedding. I have 
> load-shedding protocol as an optimization problem.  
> 
> Objective Function:
> 
> Maximize loads in the bus
> 
> Constraint:
> 
> Power flowing in the branches should be always less than the capacity of 
> lines. 
> 
> My question is how to control the power flow in the lines. I have the 
> capacity of lines. I guess I need to modify the powerflow code runpf.m or 
> makeBdc.m? But the question is which part? Given the capacity of lines, I 
> have to solve for the optimum voltage angles such that the load at the buses 
> is maximized. This will tell me how much load was needed to curtail to 
> minimize the cascading failure. The relation for voltage angles and power 
> flow is given by: Pf = BF * Va + PFINJ in makeBdc.m file. 
> 
>  Any help would be greatly appreciated, Ray. I look forward to your replies. 
> 
> Best,
> 
> Bijay

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