# Sensitivity analysis

## Introduction

The sensitivity analysis module is dedicated to computing the linearized impact of small network variations on the state variables of some components.

A sensitivity value is the numerical estimation of the partial derivative of the observed function with respect to the variable of impact. The sensitivity analysis can also be seen as the computation of partial derivatives on the network model. For example, it may be used to know, among a group of selected lines, which are the most impacted by a change in a generator production or a change of tap on a phase tap changer. The user story about RSC capacity calculation provides an example of application of the sensitivity analysis.

## Sensitivity analysis inputs

### Network

The first input for the sensitivity analysis module is an IIDM network.

### Sensitivity factors

Aside from providing an input network, it is necessary to specify which equipments are going to be studied:

• what impacted equipments are selected to be monitored (lines for example)
• according to a change on which component (a generator’s production or a group of generator’s production, or the tap position of a phase tap changer, etc.)

It is also necessary to specify which quantity is being observed: the active power or the intensity on the monitored equipments.

This set of information constitutes the sensitivity factors. These factors correspond to the definition of the expected partial derivatives to be extracted from the input network. A standard sensitivity analysis input thus comprises of a list of sensitivity factors, each one constituted of:

• a sensitivity variable (the variable of impact)
• a sensitivity function (the observed function).

The currently available sensitivity factors are:

• BranchFlowPerInjectionIncrease : calculates the linear impact of a specific injection increase on a specific branch’s active flow (in MW/MW)
• BranchFlowPerLinearGlsk : calculates the linear impact of a linear combination of injections (GLSK) increase on a specific branch’s active flow (in MW/MW)
• BranchFlowPerPSTAngle : calculates the linear impact of a PST angle increase on a specific branch’s active flow (in MW/°)
• BranchIntensityPerPSTAngle : calculates the linear impact of a PST angle increase on a specific branch’s current (in A/°)

#### How to provide the sensitivity factors input

The sensitivity factors may be created directly through Java code, or be provided to PowSyBl via a JSON file. This file should contain a list of JSON objects, each one representing a sensitivity factor. The example below shows how to write a JSON file to perform a sensitivity analysis on the active power through a line, with respect to an injection on the network.

[ {
"@c" : ".factors.BranchFlowPerInjectionIncrease",
"function" : {
"@c" : ".BranchFlow",
"id" : "BRANCH_FLOW_ID",
"name" : "My monitored branch",
"branchId" : "BRANCH_ID_IN_NETWORK"
}
} ]


### Contingencies

The sensitivity analysis may also take, optionnally, a list of contingencies as an input. When contingencies are provided, the sensitivity values shall be calculated on the network at state N, but also after the application of each contingency. The contingencies are provided in the same way than for the security analysis. This then constitutes a systematic sensitivity analysis.

At the moment the only available sensitivity simulator officially compatible with PowSyBl is the one available through Hades2, an RTE freeware tool. In this case, the network is provided only once in state N, and then all the calculations are done successively by modifying the Jacobian matrix directly in the solver based on the contingencies input. The network is thus loaded only once, which improves performance.

## Sensitivity analysis outputs

### Sensitivity values

The outputs of the sensitivity analysis are called sensitivity values. These values are a list of objects associated to each sensitivity factor, for each state of the network:

• The actual value of the partial derivative
• The reference value of the variable at linearization point
• The reference value of the function at linearization point These results may be serialized in JSON or CSV format.

### Example of interpretation

Let’s imagine that one wants to compute the impact of an increase of active power generation of the generator G on the branch B. The sensitivity analysis input will contain one sensitivity factor, of type BranchFlowPerInjectionIncrease, and we do not provide any input contingencies.

After the computation, let us consider that the values of the three elements of the sensitivity result are:

• a value of -0.05 for the partial derivative
• a variable reference value of 150
• a function reference value of 265

This can be interpreted in the following way:

• an increase of 100 MW on generator G may be approximated on branch B as a 5MW decrease of the active flow from side 1 to side 2
• the initial generation on generator G is 150MW
• the initial active flow on branch B is 265MW from side 1 to side 2

## Implementations

At the moment, the only sensitivity analysis implementation compatible with PowSyBl is the one provided with the Hades2 freeware, developped by RTE. Read this documentation page to learn how to install and configure PowSyBl to use the load flow of Hades2.

## Configuration

To use Hades2 and perform sensitivity analyses, you first need to add these lines to your YML configuration file:

load-flow:


(it is actually the same configuration as for the load flow). Then, provide the path to your Hades2 installation:

hades2:


Then, you need to configure the load flow calculation itself, because the sensitivity analysis of Hades2 relies on an initial load flow calculation. For example:

load-flow-default-parameters:
voltageInitMode: DC_VALUES
transformerVoltageControlOn: false
specificCompatibility: true

dcMode: false


Finally, you need to choose which parameters specific to sensitivity analyses to use.

hades2-default-sensitivity-parameters:
computeSensitivityToPsts: true
computeSensitivityToInjections: false
resultsThreshold: 0


The complete list of parameters specific to sensitvity analyses is provided below:

Supported parameters

• computeSensitivityToPsts is a boolean: when set to false, Hades2 will not output any sensitivity results for factors involving phase tap changers
• computeSensitivityToInjections is also a boolean: when activated, Hades2 will output the sensitivity values with respect to all injections on the network, regardless of which factors were specified by the user. This may result in a very high number of sensitivity values, and degrade performance.
• to filter the results, it is possible to use the parameter resultsThreshold: all sensitivity values lower, in absolute value, to that threshold value, will not be present in the Hades2 output. For example, if that threshold is set to 0.1, the only sensitivity values Hades2 will output will be the ones lower than -0.1 and the ones greater than 0.1. Using this parameter may be very useful to improve performances, since the time spent to exchange output data between Hades2 and PowSyBl may be significant when large numbers of sensitivity values are present in the output.

Unsupported parameters:

• equationTypePst may be set to ANGLE_SHIFT_EQ or FLOW_EQ, depending on whether the user wants to compute the sensitivity to angle shift modification, or flow modification, respectively. However, at the moment the flow modification sensitivity cannot be computed since the corresponding factor does not exist.
• computeInitialLoadflow should have the effect to enable or disable the initial loadflow computation before sensitivity values are calculated, but it doesn’t seem to have any effect.
• hubPtdf is not supported at the moment: if we integrate the PTDF calculation ype of Hades2 we should make it work but at the moment sensiDC calculations seem to fit our needs.

## Going further

To go further about the sensitivity analysis, check the following content: