Читать книгу Mathematical Programming for Power Systems Operation - Alejandro Garcés Ruiz - Страница 20

The problem of state estimation is classic in power systems. It is also a key component in Supervisory Control And Data Acquisition (SCADA) systems. The problem consists in determining the most probable state of the system from redundant measurements and knowledge of the topology and electrical relations of the grid. When the variables to be measured are active and reactive powers, a non-convex problem is obtained with the same degree of complexity as the load flow. Modern technologies such as the phasor measurement units (PMUs) allow to include direct measures of voltages and angles.

The problem can be also formulated in power distribution networks and microgrids, both AC and DC. Figure 1.5 shows, for example, a microgrid with a centralized control. Each active element of the network can have both voltage and current measurement. We can use these measurements in order to find the most likely state of the system based on the least squares model as shown below:

(1.6)

Figure 1.5 Example of a microgrid with a centralized control/measurement in the aggregator.

where J, U are measurements of current and voltage, respectively; I, V are the corresponding estimations and M, N are diagonal matrices that represent the weight of each measurement. The state estimation problem is closely related to the optimal power flow. In fact, some authors call this problem as the inverse power flow problem. The problem is studied in more detail in the second part of the book (Chapter 12).

Another operation problem, closely linked to the state estimation, is the identification of the network. In this case, we have measurements of both voltages and currents at different operating points. Our goal is to estimate the value of the nodal admittance matrix from these measurements. In this case, the optimization model is the following:

(1.7)

The decision variable is the nodal admittance matrix Y, and the objective function is the norm of error between measurements and estimations².

The model can include information about the structure of the matrix Y. For example, we already know that the matrix is symmetric and, some of its entries are zero. In that case, the optimization model is the following:

(1.8)

Both AC and DC grids may handle this type of estimation. In this case, we only presented the DC case because it is easier to develop. The entire model must be implemented in an aggregator structure, as depicted in Figure 1.5.