Changes between Initial Version and Version 1 of Ticket #6240, comment 2


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Timestamp:
2021-05-11T23:14:28Z (4 years ago)
Author:
Francesco Casella

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  • Ticket #6240, comment 2

    initial v1  
    77When this happens, the two (or more) ensuing islands can settle into new steady states with different frequencies. Hence, if a single, whole-system-wide reference is still used, the phase angle of currents and voltages of the now disconnected island(s) will continue to rotate permanently with a frequency that is the difference between the local island frequency and the frequency of the island where the original root node was picked. This is very inconvenient, because it prevents variable step-size solvers to increase the step size, once the system settles to the new steady state.
    88
    9 This problem could be avoided by allowing to dynamically add or remove the unbreakable branches corresponding to {{{Connections.branch()}}} statements in the connection graph of [https://specification.modelica.org/v3.5/Ch9.html#equation-operators-for-overconstrained-connection-based-equation-systems1 Section 9.4], based on the status of the breaker component. It would then be possible to break up the original synchronous connections established by transmission lines when their admittance is brought to zero, thus modelling effects of circuit breakers on the synchronous sub-system topology.
     9This problem could be avoided by allowing to dynamically add or remove the unbreakable branches corresponding to {{{Connections.branch()}}} statements in the connection graph of [https://specification.modelica.org/v3.5/Ch9.html#equation-operators-for-overconstrained-connection-based-equation-systems1 Section 9.4], based on the status of the breaker components, and to add or remove the equations that show up in the same if-equation branches where the {{{Connections.branch()}}} statements are declared. It would then be possible to break up the original synchronous connections established by transmission lines when their admittance is brought to zero, thus modelling effects of circuit breakers on the synchronous sub-system topology.
    1010
    1111As a consequence, two or more disjoint connection graphs would be formed at the time of the breaker openings, each corresponding to a new synchronous island. The new graph topology should be analyzed at this point, picking a new root node for each newly formed island in the grid. Then, instead of having a single phase reference for the entire system, which would no longer be adequate, one would now have two or more independent phase references, one for each island, which would ensure that the variables of each island reach a steady state, thus avoiding the persistent sinusoidal oscillations found in the case of a statically determined connection topology.
    … …  
    2020In general, handling overconstrained connector variables dynamically at runtime could be quite a big deal, because Modelica tools normally cannot handle structural dynamics at runtime. However, the special case of scalar overconstrained connector variables with zero-dimensional {{{equalityConstraint()}}} function output turns out to be very easy to implement, and is enough to address the issue with the synchronous AC grids. This is demonstrated by the attached examplary case.
    2121
    22 The attached package contains components to build conceptual models of phasor-based AC power grid models. The components are overly simplified and only retain the minimal features that are needed to analyze this language semantics extension.
     22The attached package contains components to build conceptual models of phasor-based AC power grid models, and will be used to demonstrate the proposed approach. The components are overly simplified and only retain the minimal features that are needed to analyze this language semantics extension.
    2323
    2424In this case, the overconstrained variable is actually not the phase angle but rather the angular velocity of the phasor reference frame, which is sufficient to ensure that all state variables are constant when the synchronous islands are all operating in steady state.
    … …  
    8686The generated code should then perform the following operations during initialization and each time any condition triggering a conditional equation containing {{{Connections.branch}}} statements changes:
    8787- re-build the connection graphs of all the structurally unconnected sub-graphs to which the branches that changed their activation status belong, according to the rules set forth in [https://specification.modelica.org/master/connectors-and-connections.html#equation-operators-for-overconstrained-connection-based-equation-systems1 Section 9.4], only accounting for branches that are actually active
    88 - in case a previously de-activated branch is re-established, check that the corresponding connection equation involving the overconstrained connector variables is actually verified within some tolerance, otherwise aborting the simulation; this would correspond to the requirement that two islands can only be reconnected if the are operating exactly at the same frequency or phase. This check can be defined by adding one more function {{{reconnectable()}}} to the overconstrained type definition, which returns a boolean indicating if the reconnection is feasible (see below).
    89 - identify disjoint sub-graphs that are each structurally connected, re-build the sub-graphs, and select one root node for each of them, according the standard rules set forth in [https://specification.modelica.org/v3.4/Ch9.html#converting-the-connection-graph-into-trees-and-generating-connection-equations Section 9.4.2]
     88- in case a previously de-activated branch is re-established, check that the corresponding connection equation involving the overconstrained connector variables is actually verified within some tolerance, otherwise abort the simulation; this would correspond to the requirement that two islands can only be reconnected if the are operating exactly at the same frequency or phase. This check can be defined by adding one more function {{{reconnectable()}}} to the overconstrained type definition, which returns a boolean indicating if the reconnection is feasible (see below).
     89- identify disjoint sub-graphs that are each structurally connected, and select one root node for each of them, according the standard rules set forth in [https://specification.modelica.org/v3.4/Ch9.html#converting-the-connection-graph-into-trees-and-generating-connection-equations Section 9.4.2]
    9090- break all loops in those sub-graphs
    9191- set each overconstrained connector variable of each sub-graph to be equal to the value of the corresponding root node variable (this can be done trivially via pointers!)
    … …  
    123123I suppose this feature could be implemented rather easily in OpenModelica, as a first prototype implementation of this language extension. It could be tested in an extended version of the attached package, including some more examples with a bit more nodes and edges in the connection graphs, and finally tested on an extended version of the [https://github.com/powergrids PowerGrids library], that already envisioned such a feature.
    124124
     125Another application of this extension could be incompressible fluid systems. These systems require a component setting the pressure for each connecte subsystem. When closing some strategic valves, it is possible to split the circuit in two or more unconnecte parts. At that point, new pressure-setting components (i.e. root nodes) should be identified, one for each newly formed subsystem.
     126
    125127If the experiments with the prototype are successful, this could form the basis of an MCP to introduce this feature into the next version of the Modelica Specification.