I’m sorry, I do not have time to look into the details of your problem right
now, but if you want to be sure your solution satisfies voltage limits and line
flow limits, it may be possible to use MATPOWER’s OPF for the optimization,
rather than using the power flow just for constraint evaluation. Have you
considered whether you can cast your problem in the form of the extended OPF
described in section 6.3 of the User’s Manual
<http://www.pserc.cornell.edu/matpower/manual.pdf>, by adding some user-defined
variables, constraints and costs?
Ray
> On Apr 6, 2015, at 11:48 AM, Electric <[email protected]> wrote:
>
> Dear Professor Zimmerman
>
> Many thanks for your time and feedback.
> Sorry for the following long message. I've tried to shorten it as much as
> possible.
>
> Regarding to your earlier reply i.e., Of course, there is no way for me
> to know if the updates to X produced by your algorithm make sense or lead to
> a convergent solution., I agree with you. However, I can point out some hints
> that may clarify my question. I am running a multi objective congestion
> management framework to mitigate congestion in power system. In this
> framework, congestion is released by rescheduling of generations and loads.
> Rescheduling is modeled by considering up and down generation shift and up
> and down load decrements and also load shedding. There are10 generation units
> and 19 loads in New England test case. Therefore we have (2*10+2*19+19=77)
> design variables(Please note that the number 2 is added to consider both up
> and down values, the last 19 variables are for load shedding). For the sake
> of simplicity and conciseness, I explain the pseudo code of e-constraint MMP
> method for solving this problem and show where this updating of generation
> and load (described in first email) is applied. Let's assume we have 2
> objective function in this framework i.e., F1(.)=Cost of congestion,
> F2(.)=Stability index. F1 and F2 are both explicit functions of
> [X1,X2,...X77]. where [X1,...,X10] and [X11,...X20] are up and down
> generation shifts i.e., for Unit j we have DP{j,up}, DP{j,down}. [X21,..X39]
> and [X40,..X58] represent the up and down demand rescheduling, for load K
> we have DP{k,up} and DP{k,down} . Other elements of vector X (58 to 77) are
> assigned for load shedding. (D indicates DELTA or difference)
> So the cost function is expressed as follows:
> F1(.)= B{j,up}*DP{j,up} + B{j,down}*DP{j,down}+B{k,up}*DP{k,up}
> * B{k,down}*DP{k,down}+B{k,shed}*DP{Dk,shed}.
> Where B is a vector that contains the corresponding bids of each action. For
> example the ISO must pay B{1,up} $ for asking unit 1 to increase the
> generation per MW.
> F2(.) is also defined explicitly with the design variables. Some constant
> which are derived from sensitivity analysis are used to calculate this
> security index.
> F2(.)=Sum ( M(j) [DP{j,up} +DP{j,down}] )
> some constraints of this MMP problem i.e., bounds of design variables , are
> easily applied to solver (fmincon) of this MMP problem. But there are some
> other constraints that cannot be easily calculated such as nodal balance or
> min-max of buses voltage and line loadings. To consider these implicit
> constraints I use MATPOWER power flow. and update generation and load values
> for next iteration of fmincon solver.
> Here is the pseudo code:
> % e-constraint scheme
> Minimize F1(X)
> Subject to: all constraints
> F2(X)> e{i} % i=1:5
> This scheme is run for N times . Therefore, N solutions are obtianed.
> So we can expand this pseudo code as follows:
>
> for i=1:5
> [X_temp,F_temp]=fmincon( 'F1',
> Xstart,[];[];[];[];VLB,VUB,@(X)constraints(X,i))
> end
>
> function f=F(X)
> F1(.)= B{j,up}*DP{j,up} + B{j,down}*DP{j,down}+B{k,up}*DP{k,up}
> * B{k,down}*DP{k,down}+B{k,shed}*DP{Dk,shed}.
> end
>
> function [C Ceq]=constraints(X,i)
> % first the explicit constraints are defined. like this:
> C(1)= X(1)-X(11)-750;
> % then implicit constraints are considered. for line loading we have:
> define_constants;
> mpopt = mpoption('OUT_ALL', 0);
> load_set=[1,3:4,7:9,12,15:16,18,20:21,23:29]; % Buses that have loads.
> mpc.gen(1:10,PG)=mpc.gen(1:10,PG)+X(1:10)'-X(11:20)'; % This is where I need
> to update the generation values (PG). In each iteration, DP{j,up} and
> DP{j,down} i.e., Up and Dpwn generation shift, are added to initial value of
> generator active power.
> mpc.bus(load_set,PD)=mpc.bus(load_set,PD)+X(21:40)'-X( 41:59) % I ignored
> load shedding for the sake of simplicity.
> RES=runpf(mpc,mpopt);
> flow_from = sqrt(RES.branch(:, PF).^2 + RES.branch(:, QF).^2);
> flow_to = sqrt(RES.branch(:, PT).^2 + RES.branch(:, QT).^2);
> flow = (flow_from + flow_to)/2;
> loading = flow ./ RES.branch(:, RATE_A);
> max_loading=max(loading);
> C(2) = max_loading-1; % Inequality
> % At last e-constraint method constraint is considered.
> C(3)=F2(X)- e{i} % the values of e1,e2,...,e5 are defined before.
> end
> ----------------------------------------------------------------
> Also, I wanted to know, is there any more efficient way to consider lines
> loading and other implicit constraints?
> In other word, how can I consider nodal balance constraint, Vmin<V<Vmax and
> lines loading without running power flow?
> For example the constraint of constraint of active power nodal balance for
> all system buses is calculated this way in many related paper. (I couldnt
> implement it )
> PGn -PDn=abs(V{j}) sum(abs[Y{h,n} .V{h}]*cos(d{n}-d{h}-tetha{n,h}))
> where n is bus number. h is a set of all system buses. h is the bus that
> connects Y to n.
>
> to calculate each point (considering e1,..e5, we have 5 points here), fmincon
> should call 'constraint' sub-function many times(500). Hence, the power flow
> is run in each calling and this impose a lot of computational burden to this
> problem (it takes hours to find all 5 points).
> This computation time doesn't make sense in mathematical programming (how
> ever in heuristic methods it is the normal way of considering nodal balance
> and ... ).
>
> Also, I think I should not be worry about nodal balance constraint provided
> that I use power flow already to check lines loading. is that right?
>
>
> Thanks in advance.
>
>
>
>
>
>
> On Mon, Apr 6, 2015 at 5:30 PM, Ray Zimmerman <[email protected]
> <mailto:[email protected]>> wrote:
> I don’t see any issues with the way you are calculating the line loading
> constraint, except that any branch(:, RATE_A) entries equal to zero,
> indicating and unconstrained branch, would cause problems. Of course, there
> is no way for me to know if the updates to X produced by your algorithm make
> sense or lead to a convergent solution.
>
> Ray
>
>
>> On Apr 3, 2015, at 11:17 PM, Electric <[email protected]
>> <mailto:[email protected]>> wrote:
>>
>> Dear Manish Thapa
>> No. This is not about modeling a battery. I am trying to solve a multi
>> objective optimization problem which have 3 objective functions. first
>> objective function is Cost of congestion management and the other objective
>> functions are security indexes.
>> All of these 3 objective functions are functions of a design vector
>> [X1,X2,...X77]. where [X1,...,X10] is up generation shifts of unit j i.e.,
>> DP{Gj,up}. [X11,..X20] is down generation shifts of unit j i.e.,
>> DP{Gj,down}.[X21,..X40] represent the DP{Dk,up}. Other elements of vector X
>> are assigned to DP{Dk,down} and load shedding analogous parameters of V
>> demand side bidding. (D represent Delta : Pold-Pnew
>> Cost1= B{Gj,up}*DP{Gj,up} * B{Gj,down}*DP{Gj,down} + B{Dk,up}*DP{Dk,up} *
>> B{Dk,down}*DP{Dk,down} +B{Dk,shed}*DP{Dk,shed} .
>> B sets are the cost of each actions. for example B{Gj,up} is cost of up
>> generation shift for unit j.
>> Other objective functions (security indexes) are also functions of these
>> sets ,[X1,X2,...X80] or [ DP{Gj,up}, DP{Gj,down}, DP{Dk,up},
>> DP{Dk,down},DP{Dk,up}, DP{Dk,shed} .
>> So, I have a set of mathematical equations to calculate objective functions.
>> The constraints are also explicitly, functions of this design vector. But
>> one of these constraint (Lines loading) is implicit function of the design
>> vector. So I have to calculate the load flow based on the obtanied design
>> vector ( calculated by a MMP method , epsilon constraint or weighted sum,
>> with fmincon solver of matlab) to check the lines loading inequality
>> constraint. So I have to update the design vector in each iteration.
>>
>> On Sat, Apr 4, 2015 at 4:04 AM, Manish Thapa <[email protected]
>> <mailto:[email protected]>> wrote:
>> Are you trying to model sort of a battery with this?
>>
>> On Sat, Apr 4, 2015 at 2:34 AM, Electric <[email protected]
>> <mailto:[email protected]>> wrote:
>> I am running a Multi Objective Mathematical Programming (MMP) method to
>> remove congestion (overloading of lines) in a power system.
>> The objective function, and all constraints apart from one of them i.e,
>> loading of lines, are scripted in Matlab, But I am using Matpower to
>> consider loading of lines as an inequality constraint (Loading Lji<1). I am
>> pretty sure that there is some problem in my code for considering the
>> inequality constraint of lines loading.
>>
>> I am using the script bellow to to consider the inequality constraint of
>> lines loading.
>>
>> function [C Ceq] = constraints(X,Dat,mpc)
>> mpc = loadcase('case39_congestion');
>> Ceq=[ ];
>> %----- First we have some constraints that are not calculated by Matpower.
>> % Then I have to consider lines loading.
>> define_constants;
>> mpopt = mpoption('OUT_ALL', 0);
>> load_set=[1,3:4,7:9,12,15:16,18,20:21,23:29];
>> mpc.gen(1:10,PG)=mpc.gen(1:10,PG)+X(1:Dat.SG)'-X(Dat.SG+1:2*Dat.SG)';
>> mpc.bus(load_set,PD)=mpc.bus(load_set,PD)+...
>> X(2*Dat.SG+1: 2*Dat.SG+Dat.SD)'-X( 2*Dat.SG+Dat.SD+1 :
>> 2*Dat.SG+2*Dat.SD)';
>> RES=runpf(mpc,mpopt);
>> flow_from = sqrt(RES.branch(:, PF).^2 + RES.branch(:, QF).^2);
>> flow_to = sqrt(RES.branch(:, PT).^2 + RES.branch(:, QT).^2);
>> flow = (flow_from + flow_to)/2;
>> loading = flow ./ RES.branch(:, RATE_A);
>> max_loading=max(loading);
>> C = max_loading-1; % Inequality constraint
>> end
>>
>> Where X is deign vector of the congestion management problem. X is changes
>> by fmincon solver.
>>
>> max_loading after few iteration of fmincon appears to be in order of 100
>> (134,150) which doesn't make sense (The loading of base case is 0.75).
>>
>> I am thinking the problem is about updating generator active power and
>> demands Active power.
>>
>>
>
>
