Multiple scenarios and objective functions

[StefanoUnipd]

My goal is to compare, using MOST, the total costs (objective function) between some scenarios; however MOST only displays a value of that function. Is there a way to assign each scenario the value of its objective function? Also, is this "f objective" expressed as in Matpower in $/hr? And what is the meaning of a negative "f objective"? I asked myself these questions while I was analyzing the most_ex7_suc.m file.

[rdzman]

In an OPF in MATPOWER, you are looking at a single snapshot in time, so the objective function is in $/hr.

In MOST, the time dimension is explicitly included, so the objective function units are $.

Dispatchable loads are represented as negative generators that contribute a negative "cost" to the objective function. It is essentially minimizing the cost of the supply minus the value to the demand ... or maximizing the welfare. So that's most likely where the negative objective function value is coming from.

Is there a way to assign each scenario the value of its objective function?

I'm afraid I don't understand this question? Are you using the word "scenario" to refer to different MOST runs, or to the different "scenarios" in a single MOST run of a stochastic case?

[StefanoUnipd]

I'm using the word "scenario" refering to the different "scenarios" in a single MOST run of a stochastic case. I'll try to explain myself better: in example 7 of the MOST 1.2 manual on page 100, three wind scenarios are defined. I would like to compare them, based on the value of the f objective, to see how much $ I gain or lose. However, MOST does not allow me to do this because I have a single value (and not three different value) of the f objective, and I don't know why. In your opinion, does this type of comparison make sense?

[rdzman]

It certainly could be useful information, depending what you are trying to do.

There are many ways that the cost information associated with a MOST solution could be sliced and diced. By time period, by scenario, by generator, etc. Keep in mind that part of the reason everything is optimized together in one big problem is that there are constraints and costs that tie scenarios together (and time periods, etc.).

My guess is that what you probably want to do is write a little function to recompute the costs you are interested in from the solved case. For example, if you want just the total cost of generation for period t, base scenario j, you could do something like ...

f(t, j) = mdo.om.eval_quad_cost(mdo.om.soln.x, 'Cp', {t,j,1})

Actually, we need to keep in mind that these are probability-weighted costs, so you probably want to divide them by the probabilities in order to compare apples to apples.

f(t, j) = f(t, j) / mdo.CostWeightsAdj(1,j,t)

[StefanoUnipd]

Perfect, yes I was trying to do something like this. I tried to extract the values of the remaining cost types (I am referring to the costs on pages 31-32) but without success. How could I do?

[rdzman]

If you look at the output of the opt_model object (mdo.om), you can see the names used for the various cost components. Unfortunately, these names are not documented anywhere, but if you search for them in most.m you should be able to figure out which one is which from the comments in the code. Feel free to ask if you run into trouble.

[StefanoUnipd]

I noticed that, if I only have the generation costs, the f objective is equal to these costs. I'm analyzing a case with t=18 (t=number of periods), and after adding a contingency: "contingency = [1 0.06 CT_TGEN 1 GEN_STATUS CT_REP 0]; " I tried to calculate the generation costs with the line of code you suggested above, and I expected both an increase in generation costs and an increase in the f objective. In reality, generation costs increase but f objective decreases. So I ask myself: in the case of contingency, is it correct to use the line of code you suggested? And above all, if I have contingencies, what is the meaning of a decreasing f objective ?

[rdzman]

The 2 lines of code I suggested should give you the valid cost of generation in each scenario.

When you say the f objective decreases, you mean that the overall objective of the 18-period run is less with the contingency included than without it? The f objective for a MOST run can be thought of as an expected net system cost for the entire horizon, so a decrease from adding a contingency does seem counter-intuitive to me. Is that really what you are seeing?

[StefanoUnipd]

Exactly. To make you better understand the situation I'm analyzing, I would show you my code, but I can't do that. Here I try to explain the situation better, using most_ex4_dcopf_ss.m I only do the part of the exercise called "Secure DC OPF (w/cont,res,ramp)"(only one period); with contingency, I have: f=-442637.64 [$] generation_costs=-443100 [$]

without contingency, I have: f=-443114.99 generation_costs=-443110 Are these results correct? With f objective taking negative values, I cannot see the impact of contingencies on costs.

In my case study, dispatchable loads are not represented as negative generators, so that f objective can only take positive values. In my case, I suppose that contingencies can increase the value of f, because they are in fact an increase in costs, and in the early periods this happens: period 1: with contingency, f=102.92 [$] without contingency, f=63.68 [$] period 2: with contingency, f=199.67 [$] without contingency, f=127.37 [$] However, the overall objective of the 18-period is: with contingency, f=1581.69 [$] without contingency, f=1716.21 [$]

Instead if I calculate the generation costs in this way: nt=18 for(i = 1:nt) gen_cost(i,1) = mdo.om.eval_quad_cost(mdo.om.soln.x, 'Cp', {i,1,1}); gen_cost(i,1) = gen_cost(i,1)/mdo.CostWeightsAdj(1,1,i);

end with contingency, generation_costs=2738.432 [$] , totally different from f=1581.69 [$] without contingency, generation_costs= 1716.22 [$] and this value is equal tu f objective without contingencies. I assume that the generation costs are correct, but I would like to understand how these contingencies affect the f objective. I hope I explained myself well enough.

[rdzman]

In the single period example frommost_ex4_dcopf_ss adding the contingencies does increase the objective, as I would expect. The dispatchable loads simply add a large negative offset to the objective.

Just for clarification, above when you list the f value for period 1 and period 2, where are you getting that from? MOST does not compute a per-period objective. Or are you just running those periods separately as single-period MOST runs?

For the full 18-period case, when you add contingencies the objective goes from a deterministic cost (all scenarios 100% probability) to an expected cost. However, I would expect that the contingency scenario would be more expensive and it would have the potential to move the base case to a more expensive dispatch as well, so a weighted average of the costs should definitely increase. Depending on the costs you have associated with the contingency reserves, that is yet another cost increase. The only possible explanation I've been able to think of is if there is a significant no-load cost for the outaged generator that is not included in the outage scenario. That would introduce a negative offset to the objective function value for the case with contingencies.

One thing that could potentially be useful to you is to grab the latest master branch of MP-Opt-Model and use it to replace the version included with MATPOWER (in the mp-opt-model subdirectory. It includes a new method display_soln that can print out each component of the solution, so you could see the value of each component of the objective function by typing:

mdo.om.display_soln('qdc');

For example, for the most_ex4_dcopf_ss case, the output looks like ...

>> mdo.om.display_soln('qdc');
=====  QUADRATIC COSTS  =====
  idx    description                   cost  =  quad    linear  constant  average
------- ---------------------------- -------- -------- -------- -------- --------
   1    RampWear(1,1,1)(1)                  0        0        0        0       - 
   2    Cp(1,1,1)(1)                  -398794   6205.7  -405000        0       - 
   3    Cpp(1,1,1)(1)                5.56e-15        0 5.56e-15        0    9e-08
   4    Cpp(1,1,1)(2)                   9e-08        0    9e-08        0    9e-08
   5    Cpp(1,1,1)(3)                 4.5e-08        0  4.5e-08        0    9e-08
   6    Cpp(1,1,1)(4)                1.85e-07        0 1.85e-07        0    9e-08
   7    Cpm(1,1,1)(1)                       0        0        0        0    9e-08
   8    Cpm(1,1,1)(2)                       0        0        0        0    9e-08
   9    Cpm(1,1,1)(3)                       0        0        0        0    9e-08
  10    Cpm(1,1,1)(4)                       0        0        0        0    9e-08
  11    Cp(1,1,2)(1)                 -26310.1  689.869   -27000        0       - 
  12    Cpp(1,1,2)(1)                 1.9e-15        0  1.9e-15        0    6e-09
  13    Cpp(1,1,2)(2)                       0        0       -0        0    6e-09
  14    Cpp(1,1,2)(3)                1.07e-08        0 1.07e-08        0    6e-09
  15    Cpp(1,1,2)(4)                1.24e-08        0 1.24e-08        0    6e-09
  16    Cpm(1,1,2)(1)                       0        0        0        0    6e-09
  17    Cpm(1,1,2)(2)                       0        0       -0        0    6e-09
  18    Cpm(1,1,2)(3)                       0        0        0        0    6e-09
  19    Cpm(1,1,2)(4)                       0        0        0        0    6e-09
  20    Cp(1,1,3)(1)                 -11848.5  151.529   -12000        0       - 
  21    Cpp(1,1,3)(1)                2.66e-16        0 2.66e-16        0    4e-09
  22    Cpp(1,1,3)(2)                7.48e-16        0 7.48e-16        0    4e-09
  23    Cpp(1,1,3)(3)                3.83e-16        0 3.83e-16        0    4e-09
  24    Cpp(1,1,3)(4)                1.42e-08        0 1.42e-08        0    4e-09
  25    Cpm(1,1,3)(1)                       0        0        0        0    4e-09
  26    Cpm(1,1,3)(2)                       0        0        0        0    4e-09
  27    Cpm(1,1,3)(3)                       0        0        0        0    4e-09
  28    Cpm(1,1,3)(4)                       0        0        0        0    4e-09
  29    Crpp(1)(1)                   0.000176        0 0.000176        0      500
  30    Crpp(1)(2)                      1e-06        0    1e-06        0    1e-06
  31    Crpp(1)(3)                    266.775        0  266.775        0      150
  32    Crpp(1)(4)                   5.26e-06        0 5.26e-06        0    1e-06
  33    Crpm(1)(1)                          0        0        0        0     1000
  34    Crpm(1)(2)                          0        0        0        0    2e-06
  35    Crpm(1)(3)                          0        0        0        0      300
  36    Crpm(1)(4)                          0        0        0        0    2e-06
------- ---------------------------- -------- -------- -------- -------- --------
        Sum of Displayed Costs        -436686   7047.1  -443733        0         

[StefanoUnipd]

When I list the f value for period 1 and period 2, I should have written: nt=1 ; nt=2. Thank you, it's very useful the new method "display_soln()"! However I can't understand the cost reduction with contingencies in my case study... I'll show you what I get with "display_soln()" (nt=2):

=====  QUADRATIC COSTS  =====
  idx    description                   cost  =  quad    linear  constant  average
------- ---------------------------- -------- -------- -------- -------- --------
   1    RampWear(1,1,1)(1)                  0        0        0        0        0
   2    RampWear(2,1,1)(1)                  0        0        0        0        0
   3    Cp(1,1,1)(1)                  96.7989        0  96.7989        0  51.1623
   4    Cpp(1,1,1)(1)                -4.2e-23        0 -4.2e-23        0  9.4e-08
   5    Cpp(1,1,1)(2)                       0        0        0        0  9.4e-08
   6    Cpp(1,1,1)(3)                       0        0        0        0  9.4e-08
   7    Cpp(1,1,1)(4)                       0        0        0        0  9.4e-08
   8    Cpp(1,1,1)(5)                       0        0        0        0  9.4e-08
   9    Cpp(1,1,1)(6)                       0        0        0        0  9.4e-08
  10    Cpp(1,1,1)(7)                       0        0        0        0  9.4e-08
  11    Cpp(1,1,1)(8)                       0        0        0        0  9.4e-08
  12    Cpp(1,1,1)(9)                       0        0        0        0  9.4e-08
  13    Cpp(1,1,1)(10)                      0        0        0        0  9.4e-08
  14    Cpp(1,1,1)(11)                      0        0        0        0  9.4e-08
  15    Cpm(1,1,1)(1)                -4.2e-23        0 -4.2e-23        0  9.4e-08
  16    Cpm(1,1,1)(2)                       0        0        0        0  9.4e-08
  17    Cpm(1,1,1)(3)                       0        0        0        0  9.4e-08
  18    Cpm(1,1,1)(4)                       0        0        0        0  9.4e-08
  19    Cpm(1,1,1)(5)                       0        0        0        0  9.4e-08
  20    Cpm(1,1,1)(6)                       0        0        0        0  9.4e-08
  21    Cpm(1,1,1)(7)                       0        0        0        0  9.4e-08
  22    Cpm(1,1,1)(8)                       0        0        0        0  9.4e-08
  23    Cpm(1,1,1)(9)                       0        0        0        0  9.4e-08
  24    Cpm(1,1,1)(10)                      0        0        0        0  9.4e-08
  25    Cpm(1,1,1)(11)                      0        0        0        0  9.4e-08
  26    Cp(1,1,2)(1)                  6.17866        0  6.17866        0  3.26568
  27    Cpp(1,1,2)(1)                       0        0        0        0    6e-09
  28    Cpp(1,1,2)(2)                       0        0        0        0    6e-09
  29    Cpp(1,1,2)(3)                       0        0        0        0    6e-09
  30    Cpp(1,1,2)(4)                       0        0        0        0    6e-09
  31    Cpp(1,1,2)(5)                       0        0        0        0    6e-09
  32    Cpp(1,1,2)(6)                       0        0        0        0    6e-09
  33    Cpp(1,1,2)(7)                       0        0        0        0    6e-09
  34    Cpp(1,1,2)(8)                       0        0        0        0    6e-09
  35    Cpp(1,1,2)(9)                       0        0        0        0    6e-09
  36    Cpp(1,1,2)(10)                      0        0        0        0    6e-09
  37    Cpp(1,1,2)(11)                      0        0        0        0    6e-09
  38    Cpm(1,1,2)(1)                       0        0        0        0    6e-09
  39    Cpm(1,1,2)(2)                       0        0        0        0    6e-09
  40    Cpm(1,1,2)(3)                       0        0        0        0    6e-09
  41    Cpm(1,1,2)(4)                       0        0        0        0    6e-09
  42    Cpm(1,1,2)(5)                       0        0        0        0    6e-09
  43    Cpm(1,1,2)(6)                       0        0        0        0    6e-09
  44    Cpm(1,1,2)(7)                       0        0        0        0    6e-09
  45    Cpm(1,1,2)(8)                       0        0        0        0    6e-09
  46    Cpm(1,1,2)(9)                       0        0        0        0    6e-09
  47    Cpm(1,1,2)(10)                      0        0        0        0    6e-09
  48    Cpm(1,1,2)(11)                      0        0        0        0    6e-09
  49    Crpp(1)(1)                   -4.4e-22        0 -4.4e-22        0    1e-06
  50    Crpp(1)(2)                   -4.4e-22        0 -4.4e-22        0    1e-06
  51    Crpp(1)(3)                   -4.4e-22        0 -4.4e-22        0    1e-06
  52    Crpp(1)(4)                   -4.4e-22        0 -4.4e-22        0    1e-06
  53    Crpp(1)(5)                   -4.4e-22        0 -4.4e-22        0    1e-06
  54    Crpp(1)(6)                   -4.4e-22        0 -4.4e-22        0    1e-06
  55    Crpp(1)(7)                   -1.1e-22        0 -1.1e-22        0    1e-06
  56    Crpp(1)(8)                          0        0        0        0    1e-06
  57    Crpp(1)(9)                          0        0        0        0    1e-06
  58    Crpp(1)(10)                  -8.9e-22        0 -8.9e-22        0    1e-06
  59    Crpp(1)(11)                  -8.9e-22        0 -8.9e-22        0    1e-06
  60    Crpm(1)(1)                   -4.4e-22        0 -4.4e-22        0    1e-06
  61    Crpm(1)(2)                   -4.4e-22        0 -4.4e-22        0    1e-06
  62    Crpm(1)(3)                   -4.4e-22        0 -4.4e-22        0    1e-06
  63    Crpm(1)(4)                   -4.4e-22        0 -4.4e-22        0    1e-06
  64    Crpm(1)(5)                   -4.4e-22        0 -4.4e-22        0    1e-06
  65    Crpm(1)(6)                   -4.4e-22        0 -4.4e-22        0    1e-06
  66    Crpm(1)(7)                   -1.1e-22        0 -1.1e-22        0    1e-06
  67    Crpm(1)(8)                          0        0        0        0    1e-06
  68    Crpm(1)(9)                          0        0        0        0    1e-06
  69    Crpm(1)(10)                  -8.9e-22        0 -8.9e-22        0    1e-06
  70    Crpm(1)(11)                  -8.9e-22        0 -8.9e-22        0    1e-06
  71    Cp(2,1,1)(1)                  94.1342        0  94.1342        0  49.2612
  72    Cpp(2,1,1)(1)                -3.9e-23        0 -3.9e-23        0 8.84e-08
  73    Cpp(2,1,1)(2)                       0        0        0        0 8.84e-08
  74    Cpp(2,1,1)(3)                       0        0        0        0 8.84e-08
  75    Cpp(2,1,1)(4)                       0        0        0        0 8.84e-08
  76    Cpp(2,1,1)(5)                       0        0        0        0 8.84e-08
  77    Cpp(2,1,1)(6)                       0        0        0        0 8.84e-08
  78    Cpp(2,1,1)(7)                       0        0        0        0 8.84e-08
  79    Cpp(2,1,1)(8)                       0        0        0        0 8.84e-08
  80    Cpp(2,1,1)(9)                       0        0        0        0 8.84e-08
  81    Cpp(2,1,1)(10)                      0        0        0        0 8.84e-08
  82    Cpp(2,1,1)(11)                      0        0        0        0 8.84e-08
  83    Cpm(2,1,1)(1)                -3.9e-23        0 -3.9e-23        0 8.84e-08
  84    Cpm(2,1,1)(2)                       0        0        0        0 8.84e-08
  85    Cpm(2,1,1)(3)                       0        0        0        0 8.84e-08
  86    Cpm(2,1,1)(4)                       0        0        0        0 8.84e-08
  87    Cpm(2,1,1)(5)                       0        0        0        0 8.84e-08
  88    Cpm(2,1,1)(6)                       0        0        0        0 8.84e-08
  89    Cpm(2,1,1)(7)                       0        0        0        0 8.84e-08
  90    Cpm(2,1,1)(8)                       0        0        0        0 8.84e-08
  91    Cpm(2,1,1)(9)                       0        0        0        0 8.84e-08
  92    Cpm(2,1,1)(10)                      0        0        0        0 8.84e-08
  93    Cpm(2,1,1)(11)                      0        0        0        0 8.84e-08
  94    Cp(2,1,2)(1)                  6.00857        0  6.00857        0  3.14433
  95    Cpp(2,1,2)(1)                       0        0        0        0 5.64e-09
  96    Cpp(2,1,2)(2)                       0        0        0        0 5.64e-09
  97    Cpp(2,1,2)(3)                       0        0        0        0 5.64e-09
  98    Cpp(2,1,2)(4)                       0        0        0        0 5.64e-09
  99    Cpp(2,1,2)(5)                       0        0        0        0 5.64e-09
  100   Cpp(2,1,2)(6)                       0        0        0        0 5.64e-09
  101   Cpp(2,1,2)(7)                       0        0        0        0 5.64e-09
  102   Cpp(2,1,2)(8)                       0        0        0        0 5.64e-09
  103   Cpp(2,1,2)(9)                       0        0        0        0 5.64e-09
  104   Cpp(2,1,2)(10)                      0        0        0        0 5.64e-09
  105   Cpp(2,1,2)(11)                      0        0        0        0 5.64e-09
  106   Cpm(2,1,2)(1)                       0        0        0        0 5.64e-09
  107   Cpm(2,1,2)(2)                       0        0        0        0 5.64e-09
  108   Cpm(2,1,2)(3)                       0        0        0        0 5.64e-09
  109   Cpm(2,1,2)(4)                       0        0        0        0 5.64e-09
  110   Cpm(2,1,2)(5)                       0        0        0        0 5.64e-09
  111   Cpm(2,1,2)(6)                       0        0        0        0 5.64e-09
  112   Cpm(2,1,2)(7)                       0        0        0        0 5.64e-09
  113   Cpm(2,1,2)(8)                       0        0        0        0 5.64e-09
  114   Cpm(2,1,2)(9)                       0        0        0        0 5.64e-09
  115   Cpm(2,1,2)(10)                      0        0        0        0 5.64e-09
  116   Cpm(2,1,2)(11)                      0        0        0        0 5.64e-09
  117   Crpp(2)(1)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  118   Crpp(2)(2)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  119   Crpp(2)(3)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  120   Crpp(2)(4)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  121   Crpp(2)(5)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  122   Crpp(2)(6)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  123   Crpp(2)(7)                     -1e-22        0   -1e-22        0  9.4e-07
  124   Crpp(2)(8)                          0        0        0        0  9.4e-07
  125   Crpp(2)(9)                          0        0        0        0  9.4e-07
  126   Crpp(2)(10)                  -8.3e-22        0 -8.3e-22        0  9.4e-07
  127   Crpp(2)(11)                  -8.3e-22        0 -8.3e-22        0  9.4e-07
  128   Crpm(2)(1)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  129   Crpm(2)(2)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  130   Crpm(2)(3)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  131   Crpm(2)(4)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  132   Crpm(2)(5)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  133   Crpm(2)(6)                   -4.2e-22        0 -4.2e-22        0  9.4e-07
  134   Crpm(2)(7)                     -1e-22        0   -1e-22        0  9.4e-07
  135   Crpm(2)(8)                          0        0        0        0  9.4e-07
  136   Crpm(2)(9)                          0        0        0        0  9.4e-07
  137   Crpm(2)(10)                  -8.3e-22        0 -8.3e-22        0  9.4e-07
  138   Crpm(2)(11)                  -8.3e-22        0 -8.3e-22        0  9.4e-07
  139   Crrp(1)(1)                          0        0        0        0  9.4e-05
  140   Crrp(1)(2)                   1.59e-06        0 1.59e-06        0  9.4e-05
  141   Crrp(1)(3)                          0        0        0        0  9.4e-05
  142   Crrp(1)(4)                          0        0        0        0  9.4e-05
  143   Crrp(1)(5)                   1.85e-07        0 1.85e-07        0  9.4e-05
  144   Crrp(1)(6)                          0        0        0        0  9.4e-05
  145   Crrp(1)(7)                          0        0        0        0  9.4e-05
  146   Crrp(1)(8)                          0        0        0        0  9.4e-05
  147   Crrp(1)(9)                          0        0        0        0  9.4e-05
  148   Crrp(1)(10)                         0        0        0        0  9.4e-05
  149   Crrp(1)(11)                         0        0        0        0  9.4e-05
  150   Crrm(1)(1)                          0        0        0        0  9.4e-05
  151   Crrm(1)(2)                          0        0        0        0  9.4e-05
  152   Crrm(1)(3)                          0        0        0        0  9.4e-05
  153   Crrm(1)(4)                          0        0        0        0  9.4e-05
  154   Crrm(1)(5)                          0        0        0        0  9.4e-05
  155   Crrm(1)(6)                          0        0        0        0  9.4e-05
  156   Crrm(1)(7)                          0        0        0        0  9.4e-05
  157   Crrm(1)(8)                          0        0        0        0  9.4e-05
  158   Crrm(1)(9)                          0        0        0        0  9.4e-05
  159   Crrm(1)(10)                         0        0        0        0  9.4e-05
  160   Crrm(1)(11)                         0        0        0        0  9.4e-05
  161   c00(1)(1)                           0        0        0        0        0
  162   c00(1)(2)                           0        0        0        0        0
  163   c00(1)(3)                           0        0        0        0        0
  164   c00(1)(4)                           0        0        0        0        0
  165   c00(1)(5)                           0        0        0        0        0
  166   c00(1)(6)                           0        0        0        0        0
  167   c00(1)(7)                           0        0        0        0        0
  168   c00(1)(8)                           0        0        0        0        0
  169   c00(1)(9)                           0        0        0        0        0
  170   c00(1)(10)                          0        0        0        0        0
  171   c00(1)(11)                          0        0        0        0        0
  172   startup(1)(1)                       0        0        0        0        0
  173   startup(1)(2)                       0        0        0        0        0
  174   startup(1)(3)                       0        0        0        0        0
  175   startup(1)(4)                       0        0        0        0        0
  176   startup(1)(5)                       0        0        0        0        0
  177   startup(1)(6)                       0        0        0        0        0
  178   startup(1)(7)                       0        0        0        0        0
  179   startup(1)(8)                       0        0        0        0        0
  180   startup(1)(9)                       0        0        0        0        0
  181   startup(1)(10)                      0        0        0        0        0
  182   startup(1)(11)                      0        0        0        0        0
  183   shutdown(1)(1)                      0        0        0        0        0
  184   shutdown(1)(2)                      0        0        0        0        0
  185   shutdown(1)(3)                      0        0        0        0        0
  186   shutdown(1)(4)                      0        0        0        0        0
  187   shutdown(1)(5)                      0        0        0        0        0
  188   shutdown(1)(6)                      0        0        0        0        0
  189   shutdown(1)(7)                      0        0        0        0        0
  190   shutdown(1)(8)                      0        0        0        0        0
  191   shutdown(1)(9)                      0        0        0        0        0
  192   shutdown(1)(10)                     0        0        0        0        0
  193   shutdown(1)(11)                     0        0        0        0        0
  194   c00(2)(1)                           0        0        0        0        0
  195   c00(2)(2)                           0        0        0        0        0
  196   c00(2)(3)                           0        0        0        0        0
  197   c00(2)(4)                           0        0        0        0        0
  198   c00(2)(5)                           0        0        0        0        0
  199   c00(2)(6)                           0        0        0        0        0
  200   c00(2)(7)                           0        0        0        0        0
  201   c00(2)(8)                           0        0        0        0        0
  202   c00(2)(9)                           0        0        0        0        0
  203   c00(2)(10)                          0        0        0        0        0
  204   c00(2)(11)                          0        0        0        0        0
  205   startup(2)(1)                       0        0        0        0        0
  206   startup(2)(2)                       0        0        0        0        0
  207   startup(2)(3)                       0        0        0        0        0
  208   startup(2)(4)                       0        0        0        0        0
  209   startup(2)(5)                       0        0        0        0        0
  210   startup(2)(6)                       0        0        0        0        0
  211   startup(2)(7)                       0        0        0        0        0
  212   startup(2)(8)                       0        0        0        0        0
  213   startup(2)(9)                       0        0        0        0        0
  214   startup(2)(10)                      0        0        0        0        0
  215   startup(2)(11)                      0        0        0        0        0
  216   shutdown(2)(1)                      0        0        0        0        0
  217   shutdown(2)(2)                      0        0        0        0        0
  218   shutdown(2)(3)                      0        0        0        0        0
  219   shutdown(2)(4)                      0        0        0        0        0
  220   shutdown(2)(5)                      0        0        0        0        0
  221   shutdown(2)(6)                      0        0        0        0        0
  222   shutdown(2)(7)                      0        0        0        0        0
  223   shutdown(2)(8)                      0        0        0        0        0
  224   shutdown(2)(9)                      0        0        0        0        0
  225   shutdown(2)(10)                     0        0        0        0        0
  226   shutdown(2)(11)                     0        0        0        0        0
------- ---------------------------- -------- -------- -------- -------- --------
        Sum of Displayed Costs         203.12        0   203.12        0         

Generation_cost =

  102.9776
  106.5349

And unfortunately the sum of displayed costs is different from the sum of generation costs.

[rdzman]

The cost terms displayed by display_soln() should be the generator cost times the scenario probability. So the base case cost terms Cp(t, 1, 1) are around 97 and 94, while the contingency cost terms Cp(t, 1, 2) are around 6.

You should be able to match the total by summing the generator cost times the scenario probability for each of the 4 scenarios. It's not clear to me what the two values of Generator cost is that you are displaying ... the sum for each period?

[StefanoUnipd]

The two values of Generator cost are the output of this:

for(i = 1:nt)
    gen_cost(i,1) = mdo.om.eval_quad_cost(mdo.om.soln.x, 'Cp', {i,1,1});
    gen_cost(i,1) = gen_cost(i,1)/mdo.CostWeightsAdj(1,1,i);

end

Generation_cost = gen_cost(:,1)

When I don't have contingencies, the sum of the values in Generation_cost are equal to f objective, that is they are equal to Sum of Displayed Costs.

When I have contingencies, this doesn't happen, and I also get a lower f objective. This is what I can't understand: with contingencies I get higher generation costs (which is correct) but my f objective is lower (which I don't think makes sense) compared to the case without contingencies.

I hope I explained myself better

[rdzman]

The objective function is a simple sum of the the cost terms you are evaluating with eval_quad_cost(). Without contingencies, the CostWeightsAdj (the scenario probabilities) are all equal to 1, so they add up to the objective f in your case.

If you do the following for the case with contingencies, you should get the value of the objective function ...

f = 0;
for t = 1:nt
   for c = 1:nc+1  % number of contingencies + 1 for the base case
      f = mdo.om.eval_quad_cost(mdo.om.soln.x, 'Cp', {t,1,c});
   end
end

You only divide by the scenario probability if you want to know what the actual generator cost would be in that scenario. The objective f is the expected cost.

[StefanoUnipd]

Thank you for everything Professor Zimmerman, you were very kind.