No. It is the total cost (based on offers) of generation, minus the total value
(based on bids) of the dispatchable loads.
If you have a case where all of the loads are dispatchable (not true for
t_auction_case) and have bids that accurately reflect their value, and
generators offer their true costs, then the objective function would be equal
to the negative of the social welfare.
That said, the runmarket() does maximize the welfare or system net benefits as
defined by the bids and offers.
Ray
On Oct 27, 2023, at 2:29 AM, Dr. D. Karthikaikannan
<karthikaikan...@eee.sastra.edu> wrote:
thank you sir.
is that the objective function value 2985.78 $/hr represents the social
welfare (supplier profit for the given offers +consumer net surplus for the
given bid).
________________________________
From:
bounce-127850109-88225...@list.cornell.edu<mailto:bounce-127850109-88225...@list.cornell.edu>
<bounce-127850109-88225...@list.cornell.edu<mailto:bounce-127850109-88225...@list.cornell.edu>>
on behalf of Ray Daniel Zimmerman <r...@cornell.edu<mailto:r...@cornell.edu>>
Sent: Thursday, October 26, 2023 11:31 PM
To: MATPOWER-L <matpowe...@list.cornell.edu<mailto:matpowe...@list.cornell.edu>>
Subject: Re: What the objective function denotes in the smart market
I see what’s going on. Turns out the explanation is simple. There are 2 sets of
“costs” that are in play here.
1. The original generator costs in mpc.gencost. These represent the actual
costs of the units.
2, The “costs” derived from the bids and offers. These are used for the actual
optimization. You can find them in mpc_out.genoffer.
The cost displayed in the Market Summary output is based on 1. The objective
function is based on 2.
>> sum(totcost(mpc_out.genoffer,mpc_out.gen(:,PG)))
ans =
2.9858e+03
>> mpc_out.f
ans =
2.9858e+03
Hope this clears things up.
Ray
On Oct 26, 2023, at 3:05 AM, Dr. D. Karthikaikannan .
<karthikaikan...@eee.sastra.edu<mailto:karthikaikan...@eee.sastra.edu>> wrote:
Dear sir,
this is the coding and results
clc
clear
mkt.OPF='AC';
mkt.auction_type=1;
mpc=loadcase('t_auction_case');
define_constants
offers.P.qty=[...
12 24 24
12 24 24
12 24 24
12 24 24
12 24 24
12 24 24];
offers.P.prc=[...
20 50 60;
20 40 70;
20 42 80;
20 44 90;
20 46 75
20 48 60];
bids.P.qty=[...
10 10 10
10 10 10
10 10 10];
bids.P.prc=[...
100 70 60;
100 50 20;
100 60 50];
[mpc_out,co,cb,f,dispatch,success,et]=runmarket(mpc,offers,bids,mkt);
sum(totcost(mpc_out.gencost,mpc_out.gen(:,PG)))
================================================================================
| Market Summary |
================================================================================
Dispatch period duration: 1.00 hours
Gen Bus Pg Price Revenue Fix+Var Strt/Stp Total Earnings
# # (MW) ($/MWh) ($) Cost ($) Cost ($) Cost ($) ($)
--- --- -------- -------- -------- -------- -------- -------- --------
1 1 35.32 50.000 1765.78 1172.63 0.00 1172.63 593.16
2 2 36.00 50.241 1808.66 1200.00 0.00 1200.00 608.66
3 220 36.00 50.337 1812.13 1200.00 0.00 1200.00 612.13
4 27 36.00 51.024 1836.87 1200.00 0.00 1200.00 636.87
5 23 36.00 52.170 1878.11 1200.00 0.00 1200.00 678.11
6 13 36.00 52.983 1907.40 1200.00 0.00 1200.00 707.40
7 7 -30.00 51.821 -1554.62 -3000.00 0.00 -3000.00 1445.38
8 15 -10.00 54.031 -540.31 -1000.00 0.00 -1000.00 459.69
9 30 -20.00 55.621 -1112.42 -2000.00 0.00 -2000.00 887.58
-------- -------- -------- -------- -------- --------
Total: 155.32 7801.60 1172.63 0.00 1172.63 6628.97
Converged in 0.14 seconds
Objective Function Value = 2985.78 $/hr
================================================================================
| System Summary |
================================================================================
How many? How much? P (MW) Q (MVAr)
--------------------- ------------------- ------------- -----------------
Buses 30 Total Gen Capacity 360.0 -90.0 to 360.0
Generators 6 On-line Capacity 360.0 -90.0 to 360.0
Committed Gens 6 Generation (actual) 215.3 101.1
Loads 20 Load 211.6 106.3
Fixed 17 Fixed 151.6 82.3
Dispatchable 3 Dispatchable 60.0 of 90.0 24.0
Shunts 2 Shunt (inj) -0.0 0.2
Branches 41 Losses (I^2 * Z) 3.67 12.27
Transformers 0 Branch Charging (inj) - 17.3
Inter-ties 7 Total Inter-tie Flow 33.1 21.8
Areas 3
Minimum Maximum
------------------------- --------------------------------
Voltage Magnitude 0.974 p.u. @ bus 20 1.083 p.u. @ bus 13
Voltage Angle -6.50 deg @ bus 20 0.12 deg @ bus 220
P Losses (I^2*R) - 0.54 MW @ line 27-30
Q Losses (I^2*X) - 2.96 MVAr @ line 12-13
Lambda P 50.00 $/MWh @ bus 1 57.18 $/MWh @ bus 20
Lambda Q -0.00 $/MWh @ bus 1 1.79 $/MWh @ bus 20
================================================================================
| Bus Data |
================================================================================
Bus Voltage Generation Load Lambda($/MVA-hr)
# Mag(pu) Ang(deg) P (MW) Q (MVAr) P (MW) Q (MVAr) P Q
----- ------- -------- -------- -------- -------- -------- ------- -------
1 1.050 0.000* 35.32 0.75 - - 50.000 -
2 1.049 -0.486 36.00 13.64 5.04 2.95 50.241 -
3 1.030 -1.912 - - 22.32 11.16 51.115 0.317
4 1.032 -1.896 - - 8.83 1.86 51.126 0.274
5 1.034 -1.747 - - - - 50.896 0.232
6 1.032 -1.820 - - - - 51.061 0.265
7 1.021 -2.430 - - 30.00* 15.00* 51.560 0.522
8 1.028 -2.005 - - 13.95 13.95 51.170 0.357
9 1.039 -0.872 - - - - 50.938 0.212
10 1.043 -0.381 - - 6.74 2.32 50.875 0.182
11 1.039 -0.872 - - - - 50.938 0.212
12 1.039 -3.223 - - 13.02 8.72 52.983 -
13 1.083 -0.657 36.00 34.42 - - 52.983 -
14 1.024 -3.944 - - 7.21 1.86 53.896 0.334
15 1.023 -3.733 - - 10.00* 4.00* 53.831 0.500
16 1.008 -4.377 - - 4.07 2.09 54.400 0.944
17 0.986 -5.212 - - 10.46 6.74 55.387 1.601
18 0.990 -5.526 - - 3.72 1.05 56.052 1.385
19 0.975 -6.406 - - 11.04 3.95 57.077 1.762
20 0.974 -6.499 - - 2.56 0.81 57.176 1.794
21 1.050 -0.009 - - 3.39 2.17 50.476 0.027
220 1.053 0.116 36.00 10.73 - - 50.337 -
23 1.047 -2.011 36.00 20.13 22.32 11.16 52.170 -
24 1.038 -1.042 - - 10.11 7.79 51.769 0.403
25 1.050 -0.923 - - - - 51.532 0.260
26 1.030 -1.388 - - 4.07 2.67 52.541 0.935
27 1.067 -0.547 36.00 21.38 - - 51.024 -
28 1.036 -1.789 - - - - 51.000 0.135
29 1.032 -2.447 - - 2.79 1.05 53.305 0.821
30 1.006 -4.043 - - 20.00* 5.00* 55.280 1.361
-------- -------- -------- --------
Total: 215.32 101.05 211.64 106.31
================================================================================
| Branch Data |
================================================================================
Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)
# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr)
----- ----- ----- -------- -------- -------- -------- -------- --------
1 1 2 14.77 -4.03 -14.73 0.85 0.041 0.12
2 1 3 20.54 4.78 -20.33 -6.15 0.207 0.79
3 2 4 17.15 3.09 -16.98 -4.77 0.170 0.48
4 3 4 -1.98 -5.01 1.99 5.02 0.003 0.01
5 2 5 13.06 3.41 -12.98 -5.24 0.087 0.35
6 2 6 15.48 3.34 -15.34 -5.08 0.141 0.42
7 4 6 -3.40 0.60 3.40 -0.60 0.001 0.00
8 5 7 12.98 5.44 -12.88 -6.27 0.095 0.23
9 6 7 17.22 7.96 -17.12 -8.73 0.104 0.28
10 6 8 10.91 9.43 -10.89 -9.35 0.020 0.08
11 6 9 -8.45 -3.37 8.45 3.53 0.000 0.16
12 6 10 -4.83 -1.92 4.83 2.07 0.000 0.14
13 9 11 0.00 0.00 0.00 0.00 0.000 0.00
14 9 10 -8.45 -3.53 8.45 3.62 0.000 0.09
15 4 12 9.56 -2.70 -9.56 2.94 -0.000 0.24
16 12 13 -36.00 -31.46 36.00 34.42 0.000 2.96
17 12 14 6.59 3.12 -6.53 -2.99 0.059 0.13
18 12 15 11.03 6.95 -10.92 -6.75 0.110 0.20
19 12 16 14.92 9.72 -14.66 -9.14 0.264 0.59
20 14 15 -0.68 1.13 0.68 -1.13 0.004 0.00
21 16 17 10.59 7.04 -10.46 -6.74 0.127 0.30
22 15 18 17.84 6.87 -17.45 -6.10 0.384 0.77
23 18 19 13.73 5.06 -13.60 -4.77 0.131 0.28
24 19 20 2.56 0.82 -2.56 -0.81 0.002 0.01
25 10 20 0.00 0.00 0.00 0.00 0.000 0.00
26 10 17 0.00 0.00 0.00 0.00 0.000 0.00
27 10 21 -12.24 -4.92 12.29 5.03 0.048 0.11
28 10 220 -7.78 -3.09 7.83 3.19 0.045 0.10
29 21 220 -15.68 -7.20 15.71 7.25 0.027 0.05
30 15 23 -17.60 -2.99 17.91 3.60 0.304 0.61
31 220 24 12.46 0.29 -12.30 -0.04 0.168 0.25
32 23 24 -4.22 5.37 4.28 -5.25 0.055 0.11
33 24 25 -2.10 -2.45 2.11 2.48 0.018 0.03
34 25 26 4.12 2.76 -4.07 -2.67 0.056 0.08
35 25 27 -6.24 -5.24 6.31 5.37 0.066 0.13
36 28 27 -5.99 -7.88 5.99 8.25 0.000 0.37
37 27 29 10.55 3.56 -10.31 -3.10 0.240 0.46
38 27 30 13.15 4.21 -12.62 -3.20 0.536 1.00
39 29 30 7.52 2.05 -7.38 -1.80 0.137 0.26
40 8 28 -3.06 -4.60 3.07 2.51 0.012 0.04
41 6 28 -2.91 -6.42 2.92 5.37 0.008 0.02
-------- --------
Total: 3.672 12.27
================================================================================
| Voltage Constraints |
================================================================================
Bus # Vmin mu Vmin |V| Vmax Vmax mu
----- -------- ----- ----- ----- --------
1 - 0.950 1.050 1.050 118.677
21 - 0.950 1.050 1.050 227.579
25 - 0.950 1.050 1.050 51.254
================================================================================
| Dispatchable Load Constraints |
================================================================================
Gen Bus Active Power Limits
# # Pmin mu Pmin Pg Pmax Pmax mu
---- ----- ------- -------- -------- -------- -------
7 7 4.092 -30.00 -30.00 0.00 -
Gen Bus Reactive Power Limits
# # Qmin mu Qmin Qg Qmax Qmax mu
---- ----- ------- -------- -------- -------- -------
7 7 8.175 -15.00 -15.00 0.00 -
================================================================================
| Branch Flow Constraints (S in MVA) |
================================================================================
Brnch From "From" End Limit "To" End To
# Bus |Sf| mu |Sf| |Smax| |St| |St| mu Bus
----- ----- ------- -------- -------- -------- ------- -----
15 4 0.000 9.93 10.00 10.00 1.710 12
ans =
1.1726e+03
what the objective function value represents?
________________________________
From:
bounce-127836391-88225...@list.cornell.edu<mailto:bounce-127836391-88225...@list.cornell.edu>
<bounce-127836391-88225...@list.cornell.edu<mailto:bounce-127836391-88225...@list.cornell.edu>>
on behalf of Ray Daniel Zimmerman <r...@cornell.edu<mailto:r...@cornell.edu>>
Sent: Friday, October 20, 2023 2:53 AM
To: MATPOWER-L <matpowe...@list.cornell.edu<mailto:matpowe...@list.cornell.edu>>
Subject: Re: What the objective function denotes in the smart market
Can you send me the details I need to reproduce your result? The simple OPF on
that case does show consistency between the objective function value and the
sum of the generator costs.
>> r = runopf('t_auction_case');
>> sum(totcost(r.gencost, r.gen(:, PG)))
ans =
-245.2078
>> r.f
ans =
-245.2076
—Ray
On Oct 17, 2023, at 12:25 AM, Dr. D. Karthikaikannan
<karthikaikan...@eee.sastra.edu<mailto:karthikaikan...@eee.sastra.edu>> wrote:
this is the result i got it when i run for t_auction_case
================================================================================
| Market Summary |
================================================================================
Dispatch period duration: 1.00 hours
Gen Bus Pg Price Revenue Fix+Var Strt/Stp Total Earnings
# # (MW) ($/MWh) ($) Cost ($) Cost ($) Cost ($) ($)
--- --- -------- -------- -------- -------- -------- -------- --------
1 1 35.32 50.000 1765.78 1172.63 0.00 1172.63 593.16
2 2 36.00 50.241 1808.66 1200.00 0.00 1200.00 608.66
3 220 36.00 50.337 1812.13 1200.00 0.00 1200.00 612.13
4 27 36.00 51.024 1836.87 1200.00 0.00 1200.00 636.87
5 23 36.00 52.170 1878.11 1200.00 0.00 1200.00 678.11
6 13 36.00 52.983 1907.40 1200.00 0.00 1200.00 707.40
7 7 -30.00 51.821 -1554.62 -3000.00 0.00 -3000.00 1445.38
8 15 -10.00 54.031 -540.31 -1000.00 0.00 -1000.00 459.69
9 30 -20.00 55.621 -1112.42 -2000.00 0.00 -2000.00 887.58
-------- -------- -------- -------- -------- --------
Total: 155.32 7801.60 1172.63 0.00 1172.63 6628.97
Converged in 1.14 seconds
Objective Function Value = 2985.78 $/hr
I crossed the objective function value by using
sum(totcost(mpc_out.gencost,mpc_out.gen(:,PG))). the answer is 1172.63.
what the value 2985.78 represents.
|
________________________________
From:
bounce-127828667-88225...@list.cornell.edu<mailto:bounce-127828667-88225...@list.cornell.edu>
<bounce-127828667-88225...@list.cornell.edu<mailto:bounce-127828667-88225...@list.cornell.edu>>
on behalf of Ray Daniel Zimmerman <r...@cornell.edu<mailto:r...@cornell.edu>>
Sent: Tuesday, October 17, 2023 1:45 AM
To: MATPOWER-L <matpowe...@list.cornell.edu<mailto:matpowe...@list.cornell.edu>>
Subject: Re: What the objective function denotes in the smart market
The smartmarket code simply sets up the cost functions and generator limits for
the OPF problem. The OPF minimizes total generation cost. In the case that
includes dispatchable loads, modeled as negative generation, this cost is
essential the cost of the normal generators plus the negative cost of the
dispatchable loads. This is the same as the net benefit (value of dispatchable
load minus cost of generation), with a change of sign.
If that still doesn’t seem to match for you, please give me minimal example I
can use to reproduce what you’re seeing.
Ray
On Oct 14, 2023, at 12:17 AM, Dr. D. Karthikaikannan
<karthikaikan...@eee.sastra.edu<mailto:karthikaikan...@eee.sastra.edu>> wrote:
Dear sir,
In optimal power flow the objective function is sum of the cost function and
benefit function of generator and load respectively. I run smart market and
cross checked the objective function displayed with the corresponding cost
function and generation using total cost function and it is not equal. what
actually the objective function value denotes in smart market.
D.Karthikaikannan
