# Probabilistic stability analysis and optimisation for smart power systems using stochastic distribution shaping

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Dr Qichun Zhang Applications accepted all year round Self-Funded PhD Students Only

Future power systems will be significantly different from their present states. The main factor we have to consider is the uncertainties. The power system consists of the electricity generation, power transmission and distribution network with customers. With the development of smart grid, the stability analysis becomes more and more complex due to the increasing uncertainties within the system. For example, the network-based uncertainties, control-based uncertainties, etc.

Traditionally, the performance of the power system needs to be analysed based on the model however the accurate model is impossible to obtain with the uncertainties. As a result, the novel framework has to be established considering the uncertainties of the system. In other words, we need to find an approach to describe the uncertainties within the system.

Motivated by Monte Carlo method and probability theory, the probabilistic analysis should be developed combining the dynamics of the power system, where the stochastic distribution modelling can be adopted to characterise the future power system. Following this idea, the uncertainties can be included into the modelling procedure even if the uncertainties have not been identified in advance. Based on the probabilistic description, the control, optimisation and fault diagnosis can be achieved to enhance the performance of the complex smart power system.

To summarise the challenges mentioned above, the following tasks should be completed in this PhD programme:

1) The power system modelling: The accurate model cannot be obtained while the probability density function based modelling should be considered to reflect the complete properties of the uncertainties. Note that the dynamics of the power system might be very fast which results in the difficult for real-time probabilistic modelling.

2) The probability density function shaping or shifting: It is difficult to change the probability density function shape even if the model has been established where the non-linearity and non-Gaussian distribution strongly affect the performance of the control design and optimisation.

3) Since the experiments for smart power system are expensive, the simulation pilot system should be designed and developed based on the practical data, and the presented model can be trained as a benchmark while the novel control and optimisation algorithms can be validated before the practical implementation.

To solve the fore-mentioned problems, stochastic distribution control theory will be used firstly. In particular, the model structure should be confirmed for the smart power system and the parameters should be obtained by the data-based learning. Once the probabilistic model
has been established, the novel control, optimisation and fault diagnosis methods should be developed in terms of shaping the probability density function. However, which type of the system model can be properly achieve the probability density function based design requirement is still an open question.

The following 3-year schedule has been made for completing the project as a PhD research programme. In year one, the literature reviews for the existing power system analysis tools will be done while the stochastic distribution analysis should be overviewed. The novel probability density function based model should be established to describe the uncertainties of the system and the novel control/optimisation methods should be developed based on the probabilistic model in the second year. In the third year, the model and presented methods will be validated via simulation platform development and the final results will be tested in real experiment.

This project is based on the collaboration with University of Liverpool, where the experimental data should be supplied by University of Liverpool and National Grid, UK.

## References

Mifeng Ren, Qichun Zhang & Jianhua Zhang (2019) An introductory survey of probability density function control, Systems Science & Control Engineering, 7:1, 158-170

Milanović JV. 2017 Probabilistic stability analysis: the way forward for stability analysis of sustainable power systems. Phil. Trans. R. Soc. A 375: 20160296.

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