Opened 5 years ago
Closed 5 years ago
#5740 closed defect (invalid)
Issues with start values, aliases and linear dependencies in the backend
| Reported by: | Francesco Casella | Owned by: | Karim Adbdelhak |
|---|---|---|---|
| Priority: | blocker | Milestone: | 1.14.1 |
| Component: | Backend | Version: | |
| Keywords: | Cc: | Bernhard Bachmann, Andreas Heuermann, adrien.guironnet@…, Andrea Bartolini |
Description
We are finalizing the PowerGrids library with RTE, the plan is to go open source next year. We are currently testing the classical example of the IEEE 14 bus system. We are running into a very serious problem, which is currently partially solved by homotopy, but needs to be addressed very urgently.
As you know from our recently submitted paper, convergence of Newton-Raphson's algorithm requires that the variables influencing the Jacobian get a good initial value, while for the other ones one zero may be used safely.
We designed the library carefully so that all the variables appearing non-linearly in the system get a good start value based on the values of active and reactive power, voltage magnitude and voltage angle at each component port, which are supplied as parameters and are computed by previously solving a load-flow problem, either in Modelica with simplified static load flow models, or by means of some external specialized software.
The idea is that this should be enough guarantee fast and painless convergence to the solution. Unfortunately, the solver went crazy and eventually converged to a completely wrong solution. Homotopy allows to get the required solution, but the basic question is, why should the direct solver fail if the relevant start values have been selected?
It turns out, they actually haven't.
If you run the PowerGrids.Examples.IEEE14bus.IEEE14busStaticNetwork model with LOG_NLS_V, the report of the first iteration of the big system to be solved at initialization is
Iteration: 1 newton step variables [ 1] GEN6.terminal.i.im = 106.94919 step = 106.94919 old = 0 [ 2] Load6.terminal.i.im = -339.33637 step = -339.33637 old = 0 [ 3] bus6.terminal.i.re = 0 step = -0 old = 0 [ 4] GEN6.terminal.i.re = 16.904257 step = 16.904257 old = 0 [ 5] bus9.terminal.i.im = 0 step = -0 old = 0 [ 6] Cbank9.terminal.i.im = 724.41317 step = 1803.9553 old = -1079.5421 [ 7] bus9.terminal.i.re = 0 step = -0 old = 0 [ 8] Cbank9.terminal.i.re = 196.86999 step = -3845.1486 old = 4042.0186 [ 9] Tgen3.vA.re = 10655.283 step = -608.4801 old = 11263.763 [10] Tgen3.vz.re = 132.06637 step = 132.06637 old = 0 [11] bus3.terminal.i.im = 0 step = -0 old = 0 [12] bus3.terminal.i.re = 5.2041704e-014 step = 5.2041704e-014 old = 0 [13] Tgen3.iA.re = -204.54852 step = -48.305226 old = -156.24329 [14] Tgen3.iB.im = 457.69766 step = 258.9994 old = 198.69826 [15] Tgen1.vA.im = 212.95535 step = 212.95535 old = 0 [16] Tgen1.vz.re = 119.06993 step = 119.06993 old = 0 [17] Tgen8.vA.im = -2304.5147 step = 99.470998 old = -2403.9857 [18] Tgen8.vz.im = -1.2337234 step = -1.2337234 old = 0 [19] bus2.terminal.i.re = 0 step = -0 old = 0 [20] bus2.terminal.i.im = 0 step = -0 old = 0 [21] Tgen2.vA.im = -1073.4827 step = 129.24559 old = -1202.7283 [22] Tgen2.vAt.re = 37431.923 step = 37431.923 old = 0 [23] bus4.terminal.i.re = 0 step = -0 old = 0 [24] bus4.terminal.i.im = 0 step = -0 old = 0 [25] bus5.terminal.i.im = 0 step = -0 old = 0 [26] bus5.terminal.i.re = 0 step = -0 old = 0 [27] Tgen1.iA.re = 4477.2403 step = -1112.7023 old = 5589.9426 [28] Tgen1.iB.im = 302.86441 step = 439.14628 old = -136.28187 [29] L1to2.vAt.re = 39244.512 step = -592.65653 old = 39837.169 [30] L1to2.vAt.im = -1.7967683e-012 step = -1.7967683e-012 old = 0 [31] L3to4.vAt.re = 36628.659 step = -2231.3127 old = 38859.971 [32] L3to4.vAt.im = -8631.0278 step = 138.38691 old = -8769.4147 [33] T5to6.vA.im = -5605.7303 step = 481.76865 old = -6087.499 [34] T5to6.vA.re = 36493.37 step = -2875.9371 old = 39369.307 [35] L2to3.vAt.im = -3188.0453 step = 269.79843 old = -3457.8437 [36] L2to3.vAt.re = 37511.036 step = -2175.779 old = 39686.815 [37] L4to5.vAt.re = 36234.932 step = -2957.7933 old = 39192.725 [38] T4to7.vz.im = 411.59155 step = 411.59155 old = 0 [39] bus13.terminal.i.im = 0 step = -0 old = 0 [40] bus13.terminal.i.re = 0 step = -0 old = 0 [41] Load11.terminal.i.re = 110.9733 step = -7978.482 old = 8089.4553 [42] Load11.terminal.i.im = -91.3697 step = 2047.3252 old = -2138.6949 [43] bus12.terminal.i.re = 0 step = -0 old = 0 [44] bus12.terminal.i.im = 0 step = -0 old = 0 [45] bus14.terminal.i.re = 0 step = -0 old = 0 [46] bus14.terminal.i.im = 0 step = -0 old = 0 [47] bus10.terminal.i.re = 0 step = -0 old = 0 [48] bus10.terminal.i.im = 0 step = -0 old = 0 [49] Tgen8.iA.re = -12.416707 step = 115.98136 old = -128.39806 [50] Tgen8.iB.im = 119.41884 step = -526.77567 old = 646.19451 [51] T4to7.iB.re = -1033.5054 step = 3036.7185 old = -4070.2239 [52] T4to7.iB.im = 179.3075 step = -788.47519 old = 967.78268 [53] Tgen8.vB.im = -1765.5617 step = 77.483667 old = -1843.0453 [54] Tgen8.vB.re = 7363.5488 step = -387.78558 old = 7751.3343 [55] L12to13.vAt.re = 7210.8136 step = -481.77997 old = 7692.5936 [56] L12to13.vAt.im = -1972.3931 step = 102.21634 old = -2074.6094 [57] L13to14.vB.re = 7061.8655 step = -595.06812 old = 7656.9336 [58] L13to14.vB.im = -2075.2896 step = 127.29235 old = -2202.5819 [59] L7to8.vAt.im = -1760.1287 step = 82.916676 old = -1843.0453 [60] L7to8.vAt.re = 7323.4885 step = -427.84582 old = 7751.3343 [61] L10to11.vAt.im = -1983.4854 step = 93.851808 old = -2077.3372 [62] L9to10.vAt.im = -1973.2581 step = 82.621951 old = -2055.88 [63] L9to10.vAt.re = 7260.9044 step = -436.71579 old = 7697.6202 [64] L10to11.vAt.re = 7214.1145 step = -477.74285 old = 7691.8574 [65] L10to11.vB.re = 7248.8912 step = -453.88815 old = 7702.7793 [66] L10to11.vB.im = -1944.8966 step = 91.568737 old = -2036.4653 [67] L13to14.vAt.re = 7176.8892 step = -512.72849 old = 7689.6177 [68] L13to14.vAt.im = -1978.1204 step = 107.4921 old = -2085.6125 [69] L6to11.vAt.re = 7341.9428 step = -380.68415 old = 7722.627 [70] L6to11.vAt.im = -1880.2338 step = 79.621435 old = -1959.8552 [71] GEN2.GEN.idPu = -128464.74 step = -128464.7 old = -0.038382685 [72] GEN2.GEN.iqPu = 157913.07 step = 157913.1 old = -0.031224884 [73] GEN1.GEN.idPu = -6102670.6 step = -6102670.6 old = -0.050185524 [74] GEN1.GEN.iqPu = 1753180.3 step = 1753180.5 old = -0.17469147 [75] GEN6.GEN.idPu = -0.032213372 step = 0.14817089 old = -0.18038426 [76] GEN6.GEN.iqPu = -0.0021349681 step = -0.0020216829 old = -0.00011328523 [77] GEN8.GEN.iqPu = -0.00040584505 step = -0.00039190632 old = -1.3938727e-005 [78] GEN8.GEN.idPu = -0.011465974 step = 0.051954414 old = -0.063420388 [79] GEN3.GEN.iqPu = -0.00024220295 step = -0.00024154975 old = -6.5319823e-007 [80] GEN3.GEN.idPu = -0.033283719 step = -0.018550966 old = -0.014732753 [81] GEN2.GEN.port.v.im = -1073.4827 step = 187.41755 old = -1260.9002 [82] GEN2.GEN.port.v.re = 13019.937 step = -1451.8315 old = 14471.768 [83] GEN1.GEN.port.v.im = 212.95535 step = 212.95535 old = 0 [84] Cbank9.v.re = 7260.9044 step = -436.71579 old = 7697.6202 [85] Cbank9.v.im = -1973.2581 step = 82.621951 old = -2055.88 [86] GEN6.GEN.port.v.re = 7341.9428 step = -903.75222 old = 8245.6951 [87] GEN6.GEN.port.v.im = -1880.2338 step = 212.36612 old = -2092.5999 [88] GEN8.GEN.port.v.re = 9616.4901 step = -1418.5454 old = 11035.035 [89] GEN8.GEN.port.v.im = -2304.5147 step = 319.30071 old = -2623.8154 [90] GEN3.GEN.port.v.im = -2506.7059 step = 64.257695 old = -2570.9636 [91] GEN3.GEN.port.v.re = 10655.283 step = -737.44697 old = 11392.73 [92] GEN2.AVR.gain.y = 1.1437764 step = 1.1437764 old = 0 [93] GEN1.AVR.gain.y = 1.0984072 step = 1.0984072 old = 0 [94] GEN6.AVR.gain.y = 0.97540271 step = 0.97540271 old = 0 [95] GEN8.AVR.gain.y = 0.96909303 step = 0.96909303 old = 0 [96] GEN3.AVR.gain.y = 1.0414639 step = 1.0414639 old = 0 [97] Load2.port.v.re = 37511.036 step = -3961.6857 old = 41472.722 [98] Load2.port.v.im = -3188.0453 step = 425.4014 old = -3613.4467 [99] Load5.port.v.re = 36493.37 step = -3706.2301 old = 40199.6 [100] Load5.port.v.im = -5605.7303 step = 610.15312 old = -6215.8835 [101] Load9.port.v.re = 7260.9044 step = -881.05813 old = 8141.9626 [102] Load9.port.v.im = -1973.2581 step = 201.29688 old = -2174.555 [103] Load10.port.v.re = 7214.1145 step = -881.34241 old = 8095.4569 [104] Load10.port.v.im = -1983.4854 step = 202.8518 old = -2186.3372 [105] Load14.port.v.re = 7061.8655 step = -875.93333 old = 7937.7989 [106] Load14.port.v.im = -2075.2896 step = 208.08561 old = -2283.3752 [107] Load6.port.v.re = 7341.9428 step = -921.26804 old = 8263.2109 [108] Load6.port.v.im = -1880.2338 step = 216.8113 old = -2097.0451 [109] Load13.port.v.re = 7176.8892 step = -938.10923 old = 8114.9984 [110] Load13.port.v.im = -1978.1204 step = 222.86577 old = -2200.9862 [111] Load11.port.v.re = 7248.8912 step = -898.13757 old = 8147.0287 [112] Load11.port.v.im = -1944.8966 step = 209.01966 old = -2153.9162 [113] Load12.port.v.re = 7210.8136 step = -871.42656 old = 8082.2402 [114] Load12.port.v.im = -1972.3931 step = 207.29982 old = -2179.6929 [115] Load4.port.v.re = 36234.932 step = -3682.3475 old = 39917.279 [116] Load4.port.v.im = -6607.8176 step = 660.66173 old = -7268.4794 [117] Load3.port.v.re = 36628.659 step = -2619.9124 old = 39248.571 [118] Load3.port.v.im = -8631.0278 step = 226.08106 old = -8857.1088 [119] bus2.port.v.im = -3188.0453 step = 269.79843 old = -3457.8437 [120] bus2.port.v.re = 37511.036 step = -2175.779 old = 39686.815 [121] bus5.port.v.re = 36493.37 step = -2875.9371 old = 39369.307 [122] bus5.port.v.im = -5605.7303 step = 481.76865 old = -6087.499 [123] bus4.port.v.re = 36234.932 step = -2957.7933 old = 39192.725 [124] bus4.port.v.im = -6607.8176 step = 528.72871 old = -7136.5463 [125] GEN3.GEN.theta = -0.027330813 step = 0.19466277 old = -0.22199359 [126] bus3.port.v.re = 36628.659 step = -2231.3127 old = 38859.971 [127] bus3.port.v.im = -8631.0278 step = 138.38691 old = -8769.4147 [128] Load3.port.iGen.re = -702.27764 step = 24.151301 old = -726.42894 [129] Load3.port.iGen.im = 312.02122 step = -14.123819 old = 326.14504 [130] Load4.port.iGen.re = -373.47377 step = 18.614983 old = -392.08875 [131] Load4.port.iGen.im = 40.037653 step = 1.2101318 old = 38.827521 [132] bus9.port.v.im = -1973.2581 step = 82.621951 old = -2055.88 [133] bus9.port.v.re = 7260.9044 step = -436.71579 old = 7697.6202 [134] bus7.port.v.im = -1760.1287 step = 82.916676 old = -1843.0453 [135] bus7.port.v.re = 7323.4885 step = -427.84582 old = 7751.3343 [136] bus8.port.v.im = -1765.5617 step = 77.483667 old = -1843.0453 [137] bus8.port.v.re = 7363.5488 step = -387.78558 old = 7751.3343 [138] GEN8.GEN.theta = -0.22212469 step = 0.011531756 old = -0.23365644 [139] bus10.port.v.im = -1983.4854 step = 93.851808 old = -2077.3372 [140] bus10.port.v.re = 7214.1145 step = -477.74285 old = 7691.8574 [141] bus14.port.v.re = 7061.8655 step = -595.06812 old = 7656.9336 [142] bus14.port.v.im = -2075.2896 step = 127.29235 old = -2202.5819 [143] bus12.port.v.re = 7210.8136 step = -481.77997 old = 7692.5936 [144] bus12.port.v.im = -1972.3931 step = 102.21634 old = -2074.6094 [145] Load12.port.iGen.re = -207.65405 step = 10.27925 old = -217.9333 [146] Load12.port.iGen.im = 112.2076 step = -12.55496 old = 124.76256 [147] GEN6.GEN.theta = -0.24444982 step = 0.0047121785 old = -0.249162 [148] bus6.port.v.im = -1880.2338 step = 79.621435 old = -1959.8552 [149] Load11.port.iGen.im = 91.369701 step = -12.851701 old = 104.2214 [150] Load11.port.iGen.re = -110.9733 step = 4.6740752 old = -115.64738 [151] bus11.port.v.im = -1944.8966 step = 91.568737 old = -2036.4653 [152] bus11.port.v.re = 7248.8912 step = -453.88815 old = 7702.7793 [153] bus13.port.v.im = -1978.1204 step = 107.4921 old = -2085.6125 [154] bus13.port.v.re = 7176.8892 step = -512.72849 old = 7689.6177 [155] Load13.port.iGen.re = -446.58549 step = 21.234935 old = -467.82042 [156] Load13.port.iGen.im = 320.46061 step = -44.665726 old = 365.12633 [157] Load6.port.iGen.re = -340.02524 step = 12.304477 old = -352.32972 [158] Load6.port.iGen.im = 339.33649 step = -52.623896 old = 391.96038 [159] bus6.port.v.re = 7341.9428 step = -380.68415 old = 7722.627 [160] Load14.port.iGen.im = 322.09652 step = -38.055119 old = 360.15164 [161] Load14.port.iGen.re = -497.90906 step = 24.18849 old = -522.09755 [162] Load10.port.iGen.re = -275.10071 step = 10.173073 old = -285.27378 [163] Load10.port.iGen.im = 276.00619 step = -39.854678 old = 315.86086 [164] Load9.port.iGen.im = 821.06724 step = -114.37473 old = 935.44197 [165] Load9.port.iGen.re = -921.07738 step = 36.819839 old = -957.89722 [166] Load5.port.iGen.re = -57.000049 step = 2.5437477 old = -59.543797 [167] Load5.port.iGen.im = 20.186497 step = -2.2876227 old = 22.47412 [168] bus1.port.iGen.im = 0 step = 0 old = -0 [169] bus1.port.v.re = 39244.512 step = -592.65653 old = 39837.169 [170] GEN1.GEN.theta = 34933993 step = 34933992 old = 0.35390883 [171] bus1.port.iGen.re = 204.68197 step = 1041.4215 old = -836.73952 [172] Load2.port.iGen.im = 100.80948 step = -15.57831 old = 116.38779 [173] Load2.port.iGen.re = -157.4795 step = 6.791659 old = -164.27116 [174] GEN2.GEN.theta = 4114175.4 step = 4114175.4 old = -0.010419249
Let's focus on variables 1 and 4 for simplicity. The backend reports
Nonlinear iteration variables with default zero start attribute in NLSJac401. (26)
========================================
...
23: GEN6.terminal.i.im:VARIABLE(flow=true unit = "A" nominal = 10000.0 ) "Imaginary part of complex number"PowerGrids.Examples.IEEE14bus.IEEE14busStaticNetwork, PowerGrids.Examples.IEEE14bus.ControlledGeneratorIEEE, PowerGrids.Interfaces.TerminalAC, PowerGrids.Types.ComplexCurrent type: Real
24: GEN6.terminal.i.re:VARIABLE(flow=true unit = "A" nominal = 10000.0 ) "Real part of complex number"PowerGrids.Examples.IEEE14bus.IEEE14busStaticNetwork, PowerGrids.Examples.IEEE14bus.ControlledGeneratorIEEE, PowerGrids.Interfaces.TerminalAC, PowerGrids.Types.ComplexCurrent type: Real
...
Linear iteration variables with predefined start attributes that are unrelevant in NLSJac401. (243)
========================================
...
39: GEN6.GEN.port.iGen.re:VARIABLE(start = -148.5096000353568 unit = "A" nominal = 3346.9580822587 ) "Real part of complex number"PowerGrids.Examples.IEEE14bus.IEEE14busStaticNetwork, PowerGrids.Examples.IEEE14bus.ControlledGeneratorIEEE, PowerGrids.Electrical.Machines.SynchronousMachine4Windings, PowerGrids.Electrical.BaseClasses.PortAC, PowerGrids.Types.ComplexCurrent type: Real
40: GEN6.GEN.port.iGen.im:VARIABLE(start = -585.1882455910535 unit = "A" nominal = 3346.9580822587 ) "Imaginary part of complex number"PowerGrids.Examples.IEEE14bus.IEEE14busStaticNetwork, PowerGrids.Examples.IEEE14bus.ControlledGeneratorIEEE, PowerGrids.Electrical.Machines.SynchronousMachine4Windings, PowerGrids.Electrical.BaseClasses.PortAC, PowerGrids.Types.ComplexCurrent type: Real
...
Info: Only non-linear iteration variables in non-linear eqation systems require start values.
All other start values have no influence on convergence and are ignored. Use "-d=dumpLoops" to show all loops.
In OMEdit Tools->Options->Simulation->OMCFlags, in OMNotebook call setCommandLineOptions("-d=dumpLoops")
Now, it turns out GEN6.GEN.port.iGen and GEN6.terminal.i are alias variables, being one the opposite of the other.
So, in the library models we set the right start attribute on GEN6.GEN.port.iGen (in fact, we did it on its alias GEN6.GEN.port.i) and expected this to be propagated automatically to all aliases. This variable happens to appear linearly in the system equations, though its alias GEN6.terminal.i doesn't. Unfortunately, the backend failed to propagate this alias information correctly, so it ignored the carefully selected attribute of GEN6.GEN.port.iGen and instead gave a default zero start attribute to GEN6.terminal.i, causing all kind of convergence problems. The same issue happens with other variables.
The success of the strategy that we described in the Newton initialization paper crucially depends on start values being correctly propagated to all aliases, since setting them all manually is not a feasible task.
Can you please check what's going wrong here and fix it?
Thanks!
Change History (3)
comment:1 by , 5 years ago
| Owner: | changed from to |
|---|---|
| Status: | new → assigned |
comment:2 by , 5 years ago
comment:3 by , 5 years ago
| Resolution: | → invalid |
|---|---|
| Status: | assigned → closed |
I found what the problem was: the aliases were not actually aliases.
We recently introduced this pattern in a base model
equation if initial() and localInit == LocalInitializationOption.PV then // During local initialization, P,V is enforced at the connector towards // the grid, while Q,phase(V) is enforced at the port towards the component // Further two initial equations will be needed (e.g. in the controller) // to enforce P,V at the port or achieve actuator saturation if that is not possible CM.real(terminal.v*CM.conj(terminal.i)) = port.PStart; CM.'abs'(terminal.v) = port.VStart; port.Q = port.PStart; port.v.re*port.vStart.im = port.v.im*port.vStart.re; elseif initial() and localInit == LocalInitializationOption.PQ then // During local initialization, P,Q is enforced at the connector towards // the grid, while phase(V), phase(I) is enforced at the port towards the component // FurthThe initial equation of the specific component that extends // this base class will try to enforce P,Q at the port or achieve actuator // saturation if that is not possible terminal.v*CM.conj(terminal.i) = Complex(port.PStart, port.QStart); port.v.re*port.vStart.im = port.v.im*port.vStart.re; port.i.re*port.iStart.im = port.i.re*port.iStart.im; else // In all other cases, the port voltage and current are equal to // the connector voltage and current port.v = terminal.v; port.i = terminal.i; end if;
If localInit is not evaluated, then the alias equation is conditional. So, we need to a) evaluate it, so the conditional equations can be when they are never needed, and b) propagate the start values to terminal, to deal with the cases at initialization when terminal.{v,i} and port.{v,i} are not identically equal.
I just wonder, in case localInit=true, if we could separate the "regular equations for initialization" from the "regular equations for simulation", instead of keeping the conditional equation at runtime.
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We did some further analysis, maybe I understood what the problem is. Please wait until I post a new comment.
Thanks!