Add 6 points diagram to compute Qmin/Qmax of generators in ACOPF

docs/optimizer/acOptimalPowerflow.md

@@ -16,6 +16,7 @@ Please note that:
   even if the user designates these generators as fixed in the parameter file `param_generators_reactive.txt` (see [Configuration of the run](inputs.md#configuration-of-the-run)).
   Therefore, when the optimization results are exported, **these generators are exported with a reactive power target of $0$**.
 - **Neither current limits nor power limits** on branches are considered in the optimization.
+- Branches with one side open are considered in optimization. 
 
 ## Constraints
 

docs/optimizer/inputs.md

@@ -42,12 +42,12 @@ Please note that for these parameters, the AMPL code defines default values whic
 In addition to the previous parameters, the user can specify which parameters will be variable or fixed in the ACOPF solving (see [AC optimal powerflow](acOptimalPowerflow.md)).
 This is done using the following files:
 
-| File                                  | Description                                                                                                                                             | Default behavior of modified values                                               |
-|---------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------|
-| `param_transformers.txt`              | Ratio tap changers with a variable transformation ratio (real variable)                                                                                 | Transformation ratios are fixed                                                   |
-| `param_shunt.txt`                     | Shunts with a continuous variable susceptance and which can be modified and/or connected (only if possible bus is defined in `ampl_network_shunts.txt`) | Shunt susceptances are fixed                                                      |
-| `param_generators_reactive.txt`       | Generators with a constant reactive power production. If this value is not consistent (> PQmax), the reactive power production stays variable           | Coherent reactive power productions (see [P/Q unit domain](preprocessing.md#pq-unit-domain)) are variable |
-| `param_buses_with_reactive_slack.txt` | Buses with attached reactive slacks if configurable parameter buses_with_reactive_slacks = "CONFIGURED"                                                 | Only buses with no reactive power production have reactive slacks attached        |    
+| File                                  | Description                                                                                                                                             | Default behavior of modified values                                                                         |
+|---------------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------------------------------------------------------------------|
+| `param_transformers.txt`              | Ratio tap changers with a variable transformation ratio (real variable). Note that ratio tap changers on branches with one side open are not optimized. | Transformation ratios are fixed                                                                             |
+| `param_shunt.txt`                     | Shunts with a continuous variable susceptance and which can be modified and/or connected (only if possible bus is defined in `ampl_network_shunts.txt`) | Shunt susceptances are fixed                                                                                |
+| `param_generators_reactive.txt`       | Generators with a constant reactive power production. If this value is not consistent (> PQmax), the reactive power production stays variable           | Coherent reactive power productions (see [P/Q unit domain](preprocessing.md#pq-unit-domain)) are variable   |
+| `param_buses_with_reactive_slack.txt` | Buses with attached reactive slacks if configurable parameter buses_with_reactive_slacks = "CONFIGURED"                                                 | Only buses with no reactive power production have reactive slacks attached                                  |    
 
 All of these files share the same format: 2 columns #"num" "id".
 

docs/optimizer/preprocessing.md

@@ -14,10 +14,11 @@ Let $V_{s}^{min}$ (resp. $V_{s}^{max}$) be the low (resp. high) voltage limit of
 
 Branches with an impedance magnitude, **calculated in per unit**, lower than the configurable threshold `Znull` (see section [Configuration of the run](inputs.md#configuration-of-the-run)) are considered as non-impedant. 
 These branches will have their reactance replaced by the threshold `Znull` (in p.u.), **even if the reactance specified in `ampl_network_branches.txt` is negative**.
+Note that for lines considered as non-impedant and connecting two different nominal voltage levels, the conductances and susceptances are cancelled in order to avoid numerical instabilities.
 
 ## Impedance of transformers
 
-In the calculations of the ACOPF (see [AC optimal powerflow](acOptimalPowerflow.md)), the transformers with an impedance (specified in `ampl_network_branches.txt`) considered as null (see [Zero-impedance threshold](#zero-impedance-threshold))  **are treated as lines**. Then, the transformation ratios/phase shifts are ignored, as well as the impedance specified in the tap changer table `ampl_network_tct.txt`.
+In the calculations of the ACOPF (see [AC optimal powerflow](acOptimalPowerflow.md)), the impedance specified in tap changer table `ampl_network_tct.txt` is ignored for transformers with an impedance (specified in `ampl_network_branches.txt`) considered as null (see [Zero-impedance threshold](#zero-impedance-threshold)). Note that the transformer ratios and phase shiftings are considered anyway.
 
 For phase shifters transformers considered as impedant, the reactance values from the tap changer table (in `ampl_network_tct.txt`) replace the reactance specified in `ampl_network_branches.txt`. The resistance is then calculated proportionally. 
 For the ratio tap changers, the impedance stays as specified in `ampl_network_branches.txt`. **Please notice there is no specified handling for cases where resistance and/or reactance is negative or if there is both a ratio tap changer and a  phase shift transformer on the same branch.**
@@ -28,29 +29,58 @@ The following corrections apply successively to determine consistent domains for
 
 To determine the consistent domain of produced active power, the bounds of the domains $P_g^{min}$ and $P_g^{max}$, as well as the target $P_g^{t}$ of generator $g$ (all specified in `ampl_network_generators.txt`) are used.
 
-Let $P_{g}^{min,c}$ and $P_{g}^{max,c}$ be the corrected active bounds:
+Let $P_{g}^{min,c}$ and $P_{g}^{max,c}$ be the corrected active bounds. Note that these bounds are used to determine the generator's reactive bounds, and they can be used in the optimization if the user specifies a value for
+`coeff_alpha` different from 1 (see [Configuration of the run](inputs.md#configuration-of-the-run)).
+
+$P_{g}^{min,c}$ and $P_{g}^{max,c}$ are computed using the following:
 
 - By default, $P_{g}^{min,c} = \text{defaultPmin}$ and $P_{g}^{max,c} = \text{defaultPmax}$ (see [Configuration of the run](inputs.md#configuration-of-the-run))
 - If $|P_g^{max}| \geq \text{PQmax}$, then $P_{g}^{max,c} = \max(\text{defaultPmax}, P_g^t)$
 - If $|P_g^{min}| \geq \text{PQmax}$, then $P_{g}^{min,c} = \min(\text{defaultPmin}, P_g^t)$
 - If $|P_{g}^{max,c} - P_{g}^{min,c}| \leq \text{minimalQPrange}$, then $P_{g}^{max,c} = P_{g}^{min,c} = P_{g}^t$ (active power is fixed).
 
-To determine the consistent domain of produced reactive power, the reactive power diagram (specified in `ampl_network_generators.txt`) of generator $g$ is used: $qp_g$ (resp. $qP_g$) and $Qp_g$ ($QP_g$) when $P_{g}^{min,c}$ (resp. $P_{g}^{max,c}$) is reached.
-Let $qp_g^c$ (resp. $qP_g^c$) and $Qp_g^c$ (resp. $QP_g^c$) be the bounds of the corrected reactive diagram, and $Q_{g}^{min,c}$ and $Q_{g}^{max,c}$ be the corrected reactive bounds:
+To determine the consistent domain of produced reactive power, the reactive power diagram (specified in `ampl_network_generators.txt`) of generator $g$ is used: $qp_g$ (resp. $qp0_g$, $qP_g$) and $Qp_g$ (resp. $Qp0_g$, $QP_g$) when $P_{g}^{min,c}$ (resp. $0$, $P_{g}^{max,c}$) is reached.
+Let $qp_g^c$ (resp. $qp0_g^c$, $qP_g^c$) and $Qp_g^c$ (resp. $Qp0_g^c$, $QP_g^c$) be the bounds of the corrected reactive diagram, 
+and $Q_{g}^{min,c}$ and $Q_{g}^{max,c}$ be the corrected reactive bounds, used in the optimization:
 
 - By default, $qp_g^{c} = qP_{g}^{c} = - \text{defaultPmin} \times \text{defaultQmaxPmaxRatio}$ and $Qp_{g}^{c} = QP_{g}^{c} = \text{defaultPmax} \times \text{defaultQmaxPmaxRatio}$ (see [Configuration of the run](inputs.md#configuration-of-the-run))
 - If $|qp_{g}| \geq \text{PQmax}$, then $qp_{g}^{c} = -\text{defaultQmaxPmaxRatio} \times P_{max}^{g,c}$.  
-  Same with $qP_{g}^{c}$.  
+  Same with $qP_{g}^{c}$, $qp0_{g}^{c}$.  
 - If $|Qp_{g}| \geq \text{PQmax}$, then $Qp_{g}^{c} = \text{defaultQmaxPmaxRatio} \times P_{max}^{g,c}$.  
-  Same with $QP_{g}^{c}$.  
+  Same with $QP_{g}^{c}$, $Qp0_{g}^{c}$.  
 - If $qp_{g}^{c} > Qp_{g}^{c}$, the values are swapped.  
-  Same with $qP_{g}^{c}$ and $QP_{g}^{c}$.  
-- If the corrected reactive diagram is too small (the distances between the vertices of the reactive diagram are lower than $\text{minimalQPrange}$), then $qp_{g}^{c} = Qp_{g}^{c} = qP_{g}^{c} = QP_{g}^{c} = \frac{qp_{g}^{c} + Qp_{g}^{c} + qP_{g}^{c} + QP_{g}^{c}}{4}$ (reactive power is fixed).  
-- $Q_{g}^{min,c} = \min(qp_{g}^{c}, qP_{g}^{c})$ and $Q_{g}^{max,c} = \min(Qp_{g}^{c}, QP_{g}^{c})$
-
-Please note that in the end, **the corrected bounds are rectangular**, not trapezoidal, and they are used only in the reactive OPF (see [AC optimal powerflow](acOptimalPowerflow.md). The trapezoidal diagram should be added shortly. 
-In addition, bounds $qP_{g}^0$ and $Qp_{g}^0$ are not used, as generators with zero active power will be excluded from the optimisation (see [AC optimal powerflow](acOptimalPowerflow.md#generalities)).
-
-The general correction of the generator's reactive power diagram $g$ is illustrated in the following figure:
-![Reactive diagram correction](_static/img/reactive-diagram.png){width="50%" align=center}
-
+  Same with $qP_{g}^{c}$ and $QP_{g}^{c}$, $qp0_{g}^{c}$ and $Qp0_{g}^{c}$.  
+- If the corrected reactive diagram is too small between $P_{g}^{min,c}$ and $P_{g}^{max,c}$ (the distances between the vertices of the reactive diagram are lower than $\text{minimalQPrange}$), 
+then $qp_{g}^{c} = Qp_{g}^{c} = qP_{g}^{c} = QP_{g}^{c} = \frac{qp_{g}^{c} + Qp_{g}^{c} + qP_{g}^{c} + QP_{g}^{c}}{4}$ (reactive power is fixed). The same applies if the diagram
+is too small between $P_{g}^{min,c}$ and 0, or 0 and $P_{g}^{max,c}$.
+
+Then, the corrected reactive bounds ($Q_{g}^{min,c}$ and $Q_{g}^{max,c}$) are interpolated between the points forming the hexagonal diagram.
+The general case corresponds to the active target being between the active bounds ($P_{g}^{min,c}$ and $P_{g}^{max,c}$). The interpolating formula is as follows:
+- $Q_{g}^{min,c} = qp_{g}^{c} + \frac{P_{g}^{t}-P_{g}^{min,c}}{P_{g}^{max,c}-P_{g}^{min,c}}(qP_{g}^{c}-qp_{g}^{c})$
+- $Q_{g}^{max,c} = Qp_{g}^{c} + \frac{P_{g}^{t}-P_{g}^{min,c}}{P_{g}^{max,c}-P_{g}^{min,c}}(QP_{g}^{c}-Qp_{g}^{c})$
+
+The formula also applies when the active target is between $0$ and $P_{g}^{min,c}$, or $0$ and $P_{g}^{max,c}$. For the last case, the interpolating formula becomes:
+- $Q_{g}^{min,c} = qp0_{g}^{c} + \frac{P_{g}^{t}}{P_{g}^{max,c}}(qP_{g}^{c}-qp0_{g}^{c})$
+- $Q_{g}^{max,c} = Qp0_{g}^{c} + \frac{P_{g}^{t}}{P_{g}^{max,c}}(QP_{g}^{c}-Qp0_{g}^{c})$
+
+This is illustrated in the following figure:
+![Reactive diagram between 0 and Pmax](_static/img/reactive-bounds-ptarget-between-0-pmax.PNG){width="50%" align=center}
+
+The following corner cases are important to clarify:
+- If the generator has an active power target located between $0$ and $P_{g}^{min,c}$ (e.g., during ramp up), the 
+interpolation is performed between the points $0$ and $P_{g}^{min,c}$, as follows:
+![Reactive diagram between 0 and Pmin](_static/img/reactive-bounds-ptarget-between-0-pmin.PNG){width="50%" align=center}
+
+- If the generator has a target greater (resp. smaller) than its upper (resp. lower) active power bound, and 
+this bound is greater (resp. smaller) than $0$, then the corrected reactive bounds are taken at $P_{g}^{max,c}$ (resp. $P_{g}^{min,c}$), as follows:
+![Reactive diagram taken at Pmax](_static/img/reactive-bounds-ptarget-higher-than-pmax.PNG){width="50%" align=center}
+
+- If corrected active bounds $P_{g}^{min,c}$ and $P_{g}^{max,c}$ are too close, and the target
+  of the generator is located between these points, then the corrected reactive bounds are taken as the midpoint of the extreme points of the diagram. The same applies
+  if $0$ and $P_{g}^{min,c}$ or $0$ and $P_{g}^{max,c}$ are too close, and that the target is located between.
+  This is illustrated below:
+![Reactive diagram when active bounds are too close](_static/img/reactive-bounds-ptarget-in-active-bounds-too-close.PNG){width="50%" align=center}
+
+Please note that in the end, the corrected bounds are used in the reactive OPF (see [AC optimal powerflow](acOptimalPowerflow.md). 
+In addition, note that bounds $qP_{g}^0$ and $Qp_{g}^0$ are only used to interpolate the corrected bounds $Q_{g}^{min,c}$ and $Q_{g}^{max,c}$, 
+as generators with zero active power are excluded from the optimisation (see [AC optimal powerflow](acOptimalPowerflow.md#generalities)).