A Data Set for State and Parameter Estimation in Power Systems

This data set consists of data from three power system models of different scales (IEEE 14, IEEE 118 and PanTaGruEl). For each of these systems, 5 different cases are provided, they are sorted from the least to the most "advanced" system operations.

Data are stored in HDF5 format (as H5T_NATIVE_FLOAT) which can be read by (mostly) any language (e.g. Python, Matlab or Julia).

Description of the different cases:

Case 1# consists of 2000 samples. Each sample is obtained by: firstly, defining total active and reactive loads in the system which are then distributing to the buses and, secondly, dispatching generation (this is performed by running an OPF (Optimal Power Flow) with Matpower). The same distribution factors were used for every samples.

Case 2# is similar to case 1# with the addition of independent white noises to each bus load.

Case 3# differs from case 1# in that independent active and reactive bus loads are randomly drawn.

Case 4# is similar to case 3#, but some generators are randomly drawn to be in maintenance. This set of generators is independently generated for each sample.

Case 5# is similar to case 4#, plus the generation cost of each generator is randomly drawn from a predefined range. Costs are independently generated for each sample.

General Description:

Each data set case file contains the following elements:

V (\(N_{\rm bus} \times N_{\rm sample}\) matrix): Voltage magnitudes,

theta (\(N_{\rm bus} \times N_{\rm sample}\) matrix): Voltage phases,

P (\(N_{\rm bus} \times N_{\rm sample}\) matrix): Active power injections (i.e. = generation - load),

Q (\(N_{\rm bus} \times N_{\rm sample}\) matrix): Reactive power injections,

idgen (\(N_{\rm gen}\) vector): index of generator buses,

id_slack: index of the bus used as slack bus,

epsilon (\(N_{\rm line} \times 2\) matrix): list of the lines in the system (Each row corresponds to a line. Entries are buses’ indices.),

b (\(N_{\rm line}\) vector): line susceptances,

g (\(N_{\rm line}\) vector): line conductances,

bsh (\(N_{\rm bus}\) vector): shunt susceptances,

gsh (\(N_{\rm bus}\) vector): shunt conductances.

Visualization:

The data set also includes bus coordinates.

Some theory:

The incidence matrix B is defined as

\(B_{ij} = \left\{\begin{array}{l}-1,\; \text{if line $j$ starts at bus $i$,}\\1,\; \text{if line $j$ ends at bus $i$,}\\ 0,\; \text{otherwise.} \end{array}\right.\)

(“Ends” and “starts” are purely conventional, but they have to be assigned to account for the direction power flows in the system. We use the first column of epsilon as "starts" and the second one as "ends".)

The admittance matrix Y is obtained by

\(y = g + ib,\\ y_{\rm sh} = g_{\rm sh} + ib_{\rm sh},\\ Y = B\,{\rm diag}(y)\,B^\top + {\rm diag}(y_{\rm sh}) .\)

Defining the complex power injections and voltages, respectively, as

\(S = P + iQ,\\ \underline{V} = V \cdot e^{i \theta}, \)

where \(\cdot\) denotes the element-wise product. One has the following relation

\(S = \underline{V} \cdot {\rm conj}(Y\, \underline{V}).\)

This relation is equivalent to the power flow equations.