The aim of this project is to develop new tools using new advancements in mathematical and computational techniques to enable us to assess more scenarios and backgrounds and check whether they comply with SQSS and other industry codes. We will develop and test convex optimisation models and machine learning algorithms that adequately represent voltage and reactive power in the system.

##### Objectives

The project aims to:

- Create a standard pipeline of data flow between NG ESO data format and the prototype OPF
- Where necessary, enhance the prototype OPF to include a reasonable representation of relevant steady-state components models in PowerFactory.
- Create a prototype tool to quantify future reactive power requirements against a very large range of scenarios in planning time-scale that capture uncertainties going forwards.
- To develop an appropriate convex optimization method for inclusion in an AC-OPF model of the GB electricity system that permits assessment of the transmission system’s ability to meet voltage and reactive power requirements.
- Test the model on a representative network in size of GB high-voltage electricity system and validate results using current tools and techniques.
- Provide advice on updates for the NOA process.

### Learnings

##### Outcomes

The main aim of the project is to develop a framework that can enable the NOA team to access the reactive power requirements of a given system. The framework developed in this project will help NGESO to perform the following tasks:

- Year-around assessment of reactive power requirements in the GB system to comply with planning (or operational) voltage standards for a given future year
- Quantification of utilization costs: cost of managing voltage constraints for a given future year
- Quantification of constraint costs: cost of re-dispatch due to network constraints
- Quantification of the value of dynamic commitment and switching of reactive compensation equipment (capacitors, reactors, and high-gain cables)

These capabilities are enabled by the implementation of a series of assessment models, presented in the following below. These models vary in complexity and accuracy and a novel aspect of these models is the ability to decide on the commitment of reactive compensation and line switching.

- AC Optimal Power Flow (ACOPF): A nonlinear assessment model that considers voltage, active and reactive power. No Capacitor/Reactor Commitment or Line switching
- Convex relaxation of ACOPF: A convex approximation of ACOPF and considers voltage, active and reactive power. No Capacitor/Reactor Commitment or Line switching
- Linearised ACOPF: A linear approximation of ACOPF and considers voltage, active and reactive power. With Capacitor/Reactor Commitment and Line switching
- PWL ACOPF: A piece-wise linear approximation of ACOPF and considers voltage, active and reactive power. With Capacitor/Reactor Commitment and Line switching
- DC OPF: A linear approximation of ACOPF and only considers active power. Line switching only, no Capacitor/Reactor Commitment.

As NOA is primarily a planning exercise and consider GB electricity transmission system requirements of a future year, the assessment framework needs to be robust, which means that it should be able to provide accurate results in a reasonable amount of time for a large set of scenarios. Convex and linear relaxations of the assessment models provide a guarantee that the model will return a solution if the underlying problem is feasible. This is a strong result for power system assessment problems, especially involving reactive power and voltage elements.

The models implemented during the timeline of the project are demonstrated on a representative model of the Great British HV electricity network. While the focus of this project is on building modelling capabilities, the studies on a full-scale GB network demonstrates the capability of the model in handling a large problem.

During the demonstration on the full GB network, an effort is made to approximate the HV GB electricity transmission network as close to reality as possible, however, there were several gaps noticed in the data and approximations were made for demonstration. Therefore, the results presented in the final report are only for demonstration of the developed methods and do not provide any investment advice. The input data should be checked for consistency before passing on to the optimisation models, as any data gaps and flawed assumptions around costs would lead to erroneous results.

##### Lessons Learnt

In the following, the main findings from the project are presented.

*Speed-Accuracy Tradeoff of the optimal power flow approximations *

Various approximations of the optimal power flow (OPF) problem were implemented during the first half of this project.

These approximations include:

- Quadratic convex programming (QCP) OPF
- Piecewise linear approximation
- Taylor series based Linear approximation of OPF
- DC OPF

All the above approximations of the nonlinear AC OPF take the form of a convex programming problem: a special class of optimization problems that can be efficiently solved.

Furthermore, QCP approximation provides a theoretical guarantee that if a nonlinear ACOPF is feasible, meaning that a solution to the problem exists then the QCP approximation is guaranteed to converge to a solution. This is a useful property of an approximation as the nonlinear OPF tends to report divergence (possibly due to solver issues) when the problem is feasible. Our tests on a reduced GB network have shown good accuracy of the QCP model in terms of the system voltage profile and the overall losses, compared to the nonlinear ACOPF results.

The piecewise linear approximation of OPF builds a linear model of the nonlinearities. Our experiments demonstrated that the accuracy of the piecewise approximation depends on the number of linear sections used to construct the approximation. However, the increase in accuracy came at a cost of reduction in computational speed.

Taylor series and DCOPF approximations have similar complexities (i.e. time to reach a solution). However, Taylor series approximation was found to be very accurate if a good starting point is provided. Our test shows that the Taylor series approximation results provide better results than the QCP problem if initialized close to the solution of the problem.

*Demonstration of the business capabilities of the models *

The assessment models developed in this project provides the capability to assess reactive power requirements (both the location and magnitude) in the Great British High-Voltage electricity system. This capability is demonstrated in the project on a full-scale representative GB network with more than 900 nodes. It is demonstrated that the assessment model successful identifies the location and magnitude of reactive requirements for a given operational scenario. Furthermore, it was demonstrated that savings can be made if existing reactive compensation is optimally used, something which the developed models are capable.

The developed codes enable the user to quantify both constraint and utilization costs of reactive power requirements. This will allow the user to do a more comprehensive CBA assessment for any investment decision.

*Need for data accuracy *

The main aim of the project was to develop a modelling capability. While a full GB representative models is used for demonstrating the modelling capability in this project, the input data has not been thoroughly checked. Therefore, the outputs presented in the project report are for demonstration purposes. Analysis that recommends investment options should ensure the accuracy of the input data.