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Copy file name to clipboardExpand all lines: docs/user_manual/calculations.md
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@@ -57,10 +57,13 @@ Output:
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- Power flow through branches
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- Deviation between measurement values and estimated state
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In order to perform a state estimation, the system should be observable. If the system is not observable, the calculation will raise either a `NotObservableError` or
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a `SparseMatrixError`.
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In short, meeting the requirement of observability indicates that the system is either an overdetermined system (when the number of measurements is larger than the number of unknowns.
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For each node, there are two unknowns, `u` and `u_angle`. Due to the relative nature of `u_angle` (relevant only in systems with at least two nodes), in total the following conditions should be met:
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In order to perform a state estimation, the system should be observable. If the system is not observable,
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the calculation will raise either a `NotObservableError` or a `SparseMatrixError`.
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In short, meeting the requirement of observability indicates that the system is either an overdetermined
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system (when the number of independent measurements is larger than the number of unknowns) or an exactly
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determined system (the number of independent measurements equals the number of unknowns).
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For each node, there are two unknowns, `u` and `u_angle`. Due to the relative nature of `u_angle`
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(relevant only in systems with at least two nodes), in total the following conditions should be met:
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$$
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\begin{eqnarray}
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- two times the number of nodes with a voltage sensor with magnitude and angle
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- two times the number of nodes without appliances connected
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- two times the number of nodes where all connected appliances are measured by a power sensor
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- two times the number of branches with a power sensor
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- two times the number of branches with a power sensor and/or a current sensor
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```{note}
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Having enough measurements does not necessarily mean that the system is observable. The location of the measurements is
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also of importance. Additionally, there should be at least one voltage measurement.
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also of importance, i.e., the measurements should be topologically independent. Additionally, there should be at least one voltage measurement.
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```
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```{note}
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Global angle current measurements require at least one voltage angle measurement to make sense.
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```
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```{warning}
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Based on the requirements of observability mentioned above, users need to satisfy at least the following conditions for state estimation calculation in `power-grid-model`.
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-`n_voltage_sensor >= 1`
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- If no voltage phasor sensors are available, then the following conditions should be satisfied: `n_unique_power_sensor >= n_bus - 1`. Otherwise: `n_unique_power_sensor + n_voltage_sensor_with_phasor >= n_bus`
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- If no voltage phasor sensors are available, then the following conditions should be satisfied: `n_unique_power_or_current_sensor >= n_bus - 1`. Otherwise: `n_unique_power_or_current_sensor + n_voltage_sensor_with_phasor >= n_bus`
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`n_unique_power_sensor` can be calculated as sum of following:
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`n_unique_power_or_current_sensor` can be calculated as sum of following:
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- Zero injection or zero power flow constraint if present for all nodes.
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- Complete injections for all nodes: All appliances in a node are measured or a node injection sensor is present. Either of them counts as one.
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- Exploit the neighbourhood of all transformers (see {hoverxreftooltip}`user_manual/calculations:Initialization and exploitation of regulated transformers`)
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- Re-run the iteration in the above if any of the tap positions changed by the exploitation.
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In the case where the control side of the regulator and the tap side of the transformer are at the same side, the control logic of taps will be reverted (see `user_manual/calculations:Initialization and exploitation of regulated transformers`).
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In the case where the control side of the regulator and the tap side of the transformer are at the same side, the control logic of taps will be reverted (see `user_manual/calculations:Initialization and exploitation of regulated transformers`).
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The exploitation of the neighbourhood ensures that the actual optimum is not accidentally missed due to feedback mechanisms in the grid.
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```{note}
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| regulator control side != transformer tap side |`tap_max`|`tap_min`| step up | step down |
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| regulator control side == transformer tap side |`tap_min`|`tap_max`| step down | step up |
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##### Search methods used for tap changing optimization
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Given the discrete nature of the finite tap ranges, we use the following search methods to find the next tap position along the exploitation direction.
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