A Robust directly Solvable Inverter-based Energy Management Model to Investigate the effects of Electric Vehicle Employment on Distribution System

Author: Mehrdad Aghamohamadi

Aghamohamadi, Mehrdad, 2022 A Robust directly Solvable Inverter-based Energy Management Model to Investigate the effects of Electric Vehicle Employment on Distribution System, Flinders University, College of Science and Engineering

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Restructuring of power systems, along with the integration of renewable energy resources in electricity networks, have transformed traditional power electricity distribution systems (EDSs) into new active distribution systems (ADSs). In addition, the rapid advancement of technology has enabled the bulk utilization of renewable generation units and battery energy storage (BES) systems in EDSs. The next step in this trend is the employment of electric vehicles (EV) and the coordinated integration of these vehicles into EDS which is investigated in this thesis.

Following contributions are presented in this thesis to achieve the objectives in section 1.2:

Contribution 1: A novel directly solvable set of power flow equations

A new directly solvable power flow problem has been proposed for EDS, introducing a connectivity matrix in line with a new indexing of load flow equations. The new power flow model is developed generally and is capable to be added to any EDS study as the constraints of the model. This means, the power flow calculation does not need to be conducted separately. Therefore, the need of load flow calculation methodologies, such as Newton–Raphson method (NR) and forward backward sweep-based method (FBS), as well as optimization approaches, such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), is eliminated as the proposed model characterizes both load flow and energy management constraints in a single and unified model. This provides users the opportunity of solving the problem with commercial optimization packages, i.e., CPLEX, GAMS, etc., in a single shot with no need to develop further optimization approaches involving iterative procedures and load flow calculations. Note that, the employed modified load flow equations in line with the connectivity matrix can be used in any other EDS study, concerning load flow calculation, as the constraints of the model.

Contribution 2: A general multi-objective energy management model for inverter-based integration of RES, and BES system

The proposed directly solvable power flow problem is used to build up a multi-objective energy management model for RES-BES-equipped distribution systems. The first objective of the model minimizes total EDS power losses, and the second objective minimizes the voltage deviations of each bus over time. These objective functions are optimized being subject to load flow constraints, RES/BES optimal operation, and voltage/current tolerance of EDS. The proposed energy management model enables both active and reactive power controllability of RES and BES systems. New continuous variables are defined for RES and BES representing active and reactive power share of these systems during the operation. Accordingly, BES can absorb active or reactive power in each time slot and inject it back to the network as active or reactive power in another time slot.

Contribution 3: Integration of EV loading into the energy management model and investigating the effects of EV charging on EDS voltage and power loss

Electric vehicle activity is modelled by probability distribution functions. The EV’s dynamic energy balance is modelled based on EV connections and the model is merged into the energy management model.

Contribution 4: The new robust optimization model to characterize uncertainties of RESs employing block coordinate decent method

An adaptive robust optimization (ARO) approach is implemented to deal with the uncertainties of load in operating EDS through the proposed energy management model. Uncertain parameters are characterized by bounded intervals in polyhedral uncertainty sets. The ARO model is a tri-level min-max-min problem which is not directly solvable. Therefore, a decomposition methodology is employed to recast the min-max-min ARO problem into two problems including a master problem and a sub-problem. A column-and-constraints (C&C) generation methodology is used to iteratively solve the decomposed problem through primal cutting planes. Two main decisions are made in ARO, namely "here-and-now" decisions, which are obtained before any uncertainty realizations, and "wait-and-see" decisions, which are obtained after the realization of uncertain parameters. Several binary variables such as BES charging/discharging status must be obtained after uncertainty realizations in the sub-problem to be able to compensate the effects of uncertain load/price as recourse decisions. However, this is not possible by conventional dual-based robust models as considering these binary variables results in a mixed-integer sub-problem and the dual of a mixed-integer model is generally weak, non-tractable and complicated. Therefore, instead of using duality theory in solving the sub-problem, Block Coordinate Descent (BCD) method is used in the proposed model.

In terms of solution methodology, BCD method is used in the robust approach to iteratively solve the inner bi-level max-min sub-problem by means of Taylor series instead of transforming it into a single-level max problem by duality theory in conventional ARO models. BCD technique was originally devised to deal with single-level problems. By extending the application of the BCD technique to solve the two-level max-min sub-problem (resulted from the C&C generation technique), it is possible to avoid duality theory in solving the sub-problem.

Therefore, the associated limitation in considering binary variables in the sub-problem is eliminated. In fact, mixed-integer models (even non-linear models) can be solved in the sub-problem through the proposed BCD robust model. As a result, uncertainty-dependent binary variables such as BES charging/discharging statuses can be obtained after uncertainty realization in the sub-problem as recourse decisions, resulting in more system flexibility in compensating the uncertainty effects of load. Moreover, the linearization of the dualized inner problem is avoided as the Lagrange multipliers are eliminated in this methodology. Thus, the case-sensitivity of the proposed model reduces as it does not reflect dual variables.

The structure of the thesis is given below:

After presenting an introduction to the objectives and scope of the research in the first chapter, the second chapter aims to present a review of recent advancements in both operation and planning of electric vehicle charging stations (EVCSs) in EDSs. In this respect, the conducted review provides supportive insights on the state-of-the-art operation and planning of electric vehicle charging stations in EDSs by introducing the recent trends, methodologies, and novelties in this field of study. The literature has been presented considering both qualitative and quantitative aspects. Since, the focus of this thesis is on the operation of EVCSs, after presenting the literature on operation and planning aspects of these systems, a more detailed operation-based review is conducted on the employment of CSs in electricity distribution system to highlight their associated effects on EDSs.

In the third chapter, a new directly solvable and non-iterative load flow model is proposed to assist with EDS operation at the presence of EV loading, renewable energy sources (RESs) and BES. In particular, a connectivity matrix is introduced to characterize the configuration of EDS and provide a feasible general representation of load flow equations. This enables the proposed modified load flow equations to be mergeable in any type of EDS study as constraints. This way, the power flow model in Chapter 3 is employed and accordingly merged into the proposed energy management model which is presented and discussed in Chapter 4. In chapter 3, first he IEEE 33-bus electricity distribution system is employed to evaluate the effectiveness of the proposed general power flow model. Results are also compared to other power flow solutions such as forward backward Swipe-based method.

The energy management model in Chapter 4 first integrates the employment of inverter-based RES and BES in the operation of power electricity distribution system. the energy management model is evaluated through the same system incorporating BES and RES to illustrate the eff

Keywords: Adaptive robust, block coordinate decent method, Connectivity matrix, directly solvable load flow, electricity distribution system, non-linear programing, plug-in electric vehicles, Power loss minimization, robust optimization, storage system, uncertainty, voltage stability, voltage deviation.

Subject: Engineering thesis

Thesis type: Doctor of Philosophy
Completed: 2022
School: College of Science and Engineering
Supervisor: Amin Mahmoudi