The Beauty or the Beast ? This is the Question. A Pyomo-SVM model for power system security assessment

One of the main responsibilities of a Transmission System Operator (TSO) is to keep the system safe and reliable. It means that not only the dispatch solutions should be economically justifiable but also the security of the power system as well as the physical constraints should be satisfied. Several factors determine the optimal dispatch of generating units such as

• Wind-Demand pattern (peak demand, ramp rates, simultaneous changes of wind and demand)
• Economic data
• Network data
• Security constraints

Usually, the first one is the key one in determining the optimal dispatch problem.

The question is :

Is it possible to predict if a demand-wind pattern can cause a risky situation for a power system?

Is this pattern the Beauty or the Beast?

Security constrained Optimal Power Flow is one of the tools frequently used to find the optimal dispatch of generating units while maintaining the security of a power system within the desired limits.

The OPF works as a function: it receives a set of inputs and will provide a vector of output.

A system operator usually has a forecast for the demand and RES generation values. It will then need to run the Market engine or an OPF to see how the network flows will be determined.

The difficulty of running an OPF is that it is usually a computationally expensive tool specially for large scale practical power systems. The system operator might need a faster tool to quickly analyse the Wind-Demand pattern for the upcoming day and check if it might cause any overloading in the system or not.Data preparation:

The system under study is the modified IEEE118 bus network. (see this post)

In this phase, it is required to have the demand and wind pattern for a number or days (let's call it the training set). For each demand-wind pattern the OPF is executed. For simplicity no N-1 constraint is considered. All line limits are relaxed. Once the OPF is solved, all line flows are found and it can be checked if any line limit is violated (y=1) or not (y=-1). Y is called the label of each demand-wind pattern.

The OPF results:

On some specific days, the demand-wind pattern causes the overloading of some lines (the line limits were relaxed in the original OPF). The label of these patterns are (Y=1). The risky lines are specified with the red lines as follows:

The rest of the daily patterns are (evaluated and) found to be safe (Y=-1) as follows:

As you can imagine, distinguishing the risky and safe patterns (by just looking at them) is almost impossible. Is there any quick way to check the security impacts of a pattern?

SVM phase :

The Support Vector Machine (SVM) is a supervised machine learning technique which can be used to distinguish if a demand-wind pattern is a safe or a risky one. It is called supervised since it requires a label for each observation. The SVM is usually used for binary classification (to be or not to be).

Once the database is created, it can be used to train the SVM. The trained SVM will then be used to check the upcomming patterns. The performance of the SVM is tested and it is found to be accurate in %90.1 of the cases.

Pyomo

The SVM used in this post is formulated as a quadratic optimisation problem in Pyomo and solved using Gurobi solver. Pyomo is an open source package for modeling the optimisation problems. It can be linked with several commercial and open-source solvers. Here is the SVM code in Python.

The kernel used in this code is a linear one. Changing the kernel into a nonlinear one might improve the accuracy of the pattern detection.

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