Analysis and Application of Optimization Techniques to Power System Security and Electricity Markets

Determining the maximum power system loadability, as well as preventing the system from being operated close to the stability limits is very important in power systems planning and operation. The application of optimization techniques to power systems security and electricity markets is a rather relevant research area in power engineering. The study of optimization models to determine critical operating conditions of a power system to obtain secure power dispatches in an electricity market has gained particular attention. This thesis studies and develops optimization models and techniques to detect or avoid voltage instability points in a power system in the context of a competitive electricity market. A thorough analysis of an optimization model to determine the maximum power loadability points is first presented, demonstrating that a solution of this model corresponds to either Saddle-node Bifurcation (SNB) or Limit-induced Bifurcation (LIB) points of a power flow model. The analysis consists of showing that the transversality conditions that characterize these bifurcations can be derived from the optimality conditions at the solution of the optimization model. The study also includes a numerical comparison between the optimization and a continuation power flow method to show that these techniques converge to the same maximum loading point. It is shown that the optimization method is a very versatile technique to determine the maximum loading point, since it can be readily implemented and solved. Furthermore, this model is very flexible, as it can be reformulated to optimize different system parameters so that the loading margin is maximized. The Optimal Power Flow (OPF) problem with voltage stability (VS) constraints is a highly nonlinear optimization problem which demands robust and efficient solution techniques. Furthermore, the proper formulation of the VS constraints plays a significant role not only from the practical point of view, but also from the market/system perspective. Thus, a novel and practical OPF-based auction model is proposed that includes a VS constraint based on the singular value decomposition (SVD) of the power flow Jacobian. The newly developed model is tested using realistic systems of up to 1211 buses to demonstrate its practical application. The results show that the proposed model better represents power system security in the OPF and yields better market signals. Furthermore, the corresponding solution technique outperforms previous approaches for the same problem. Other solution techniques for this OPF problem are also investigated. One makes use of a cutting planes (CP) technique to handle the VS constraint using a primal-dual Interior-point Method (IPM) scheme. Another tries to reformulate the OPF and VS constraint as a semidefinite programming (SDP) problem, since SDP has proven to work well for certain power system optimization problems; however, it is demonstrated that this technique cannot be used to solve this particular optimization problem

Toward the Integration of DC Microgrids into a Hybrid AC/DC Paradigm

The recent penetration of distributed generation (DG) into existing electricity grids and the consequent development of active distribution networks (ADNs) have prompted an exploration of power distribution in a dc microgrid paradigm. Although dc power distribution has been implemented in aircraft, ships, and communication centres, the technology is still at an early stage and must be investigated with respect to technical feasibility when applied to distribution systems. In particular, the operation of a dc microgrid in both grid-connected and islanded modes and its integration into an existing ac infrastructure are subject to significant challenges that impede the practical realization of dc microgrids. On one hand, because the dc voltage profile is coupled with the injected active power at the system buses, it is seriously influenced by the intermittent nature of renewable resources such as solar and wind energy. In islanded operating mode, the presence of system resistance leads to a further trade-off between an appropriate system voltage profile and a precise power management scheme. On the other hand, the development of hybrid ac/dc microgrids introduces a fresh operational philosophy that enhances power sharing among ac and dc subgrids through the coupling of ac and dc steady-state variables. With these challenges as motivation, the primary goal of this thesis was to develop effective power management schemes and a steady-state analysis tool that can enable the reliable integration of dc microgrids into a smart hybrid ac/dc paradigm. Achieving this objective entailed the completion of three core studies: 1) the introduction of a robust control scheme for mitigating voltage regulation challenges associated with dc distribution systems (DCDSs) that are characterized by a high penetration of distributed and renewable generation, 2) the proposal of a supervisory control strategy for precise DG output power allocation that is based on DG rating and operational costs yet guarantees an appropriate voltage profile for islanded dc microgrids, 3) the development of an accurate and comprehensive power flow algorithm for analyzing the steady-state behaviour of islanded hybrid ac/dc microgrids, and 4) the optimization of hybrid ac/dc microgrids configuration. As the first research component, a novel multi-agent control scheme has been developed for regulating the voltage profile of DCDSs that incorporate a large number of intermittent energy sources. The proposed control scheme consists of two sequential stages. In the first stage, a distributed state estimation algorithm is implemented to estimate the voltage profile in DCDSs, thus enhancing the interlinking converter (IC) operation in regulating the system voltages within specified limits. If the IC alone fails to regulate the system voltages, a second control stage is activated and executed through either equal or optimum curtailment strategy of the DG output power. A variety of case studies have been conducted in order to demonstrate the effectiveness, robustness, and convergence characteristics of the control schemes that have been developed. The second element of this research is a multi-agent supervisory control that has been created in order to provide precise power management in isolated DC microgrids. Two aspects of power management have been considered: 1) equal power sharing, which has been realized via a proposed distributed equal power sharing (DEPS) algorithm, and 2) optimal power dispatch, which has been achieved through a proposed distributed equal incremental cost (DEIC) algorithm. Both algorithms offer the additional advantage of affording the ability to restore the average system voltage to its nominal value. Real-time OPAL-RT simulations have demonstrated the effectiveness of the developed algorithms in a hardware-in-the-loop (HIL) application. The third part of the research has introduced a sequential power flow algorithm for hybrid ac/dc microgrids operating in islanded mode. In contrast to the conditions in grid-connected systems, variable rather than fixed ac frequencies and dc voltages are utilized for coordinating power between the ac and dc microgrids. The primary challenge is to solve the power flow problem in hybrid microgrids in a manner that includes consideration of both the absence of a slack bus and the coupling between the frequency and dc voltage though ICs. In the proposed algorithm, the ac power flow is solved using the Newton-Raphson (NR) method, thereby updating the ac variables and utilizing them accordingly in a proposed IC model for solving the dc problem. This sequential algorithm is iterated until convergence. The accuracy of the algorithm has been verified through detailed time-domain simulations using PSCAD/EMTDC, and its robustness and computational cost compare favourable with those of conventional algorithms. The final part highlights the implementation of the developed steady-state models in obtaining an optimum hybrid microgrid configuration. The system configuration could be manipulated by changing the DG droop settings as well as the network topological structure. The contribution of both approaches has been investigated, through an optimum power flow (OPF) formulation, in improving the system loadability as the primary measure of the hybrid microgrid performance

Optimizing Control of a Power System during an Emergency

Population growth, infrastructure and economy puts pressure and demand on the existing power supplies. It puts strains on the current power systems which causes instabilities in the systems. This is an ongoing challenge which needs an immediate solution. The objective of this thesis is voltage stability. This is examined with the help of constructing a small power system using a programming language called Matlab. Optimization tools provided by Matlab are used to find the maximum possible pre-contingency load, while still maintaining a stable system. To find feasible solutions in Matlab, system models, such as load models and power line models are simplified. The results show that a system which has experienced a fault can successfully recover by using a linear load recovery model and an exponential load recovery model. Certain constraints, such as generator ramping and limitations on the field voltages in the generators are implemented. Feasible olutions are found although constraints might have made it more difficult under the course of this study. These findings are rough approximations of how a small power system can operate. Though, this can give valuable information on how a more complex system might act before and after a contingency as well as suitable recovery paths. Although the thesis is more suited for those who have some knowledge in control or power systems, a reader without a technical background can enjoy the paper too

Stochastic Modeling and Analysis of Power Systems with Intermittent Energy Sources

Electric power systems continue to increase in complexity because of the deployment of market mechanisms, the integration of renewable generation and distributed energy resources (DER) (e.g., wind and solar), the penetration of electric vehicles and other price sensitive loads. These revolutionary changes and the consequent increase in uncertainty and dynamicity call for significant modifications to power system operation models including unit commitment (UC), economic load dispatch (ELD) and optimal power flow (OPF). Planning and operation of these “smart” electric grids are expected to be impacted significantly, because of the intermittent nature of various supply and demand resources that have penetrated into the system with the recent advances. The main focus of this thesis is on the application of the Affine Arithmetic (AA) method to power system operational problems. The AA method is a very efficient and accurate tool to incorporate uncertainties, as it takes into account all the information amongst dependent variables, by considering their correlations, and hence provides less conservative bounds compared to the Interval Arithmetic (IA) method. Moreover, the AA method does not require assumptions to approximate the probability distribution function (pdf) of random variables. In order to take advantage of the AA method in power flow analysis problems, first a novel formulation of the power flow problem within an optimization framework that includes complementarity constraints is proposed. The power flow problem is formulated as a mixed complementarity problem (MCP), which can take advantage of robust and efficient state-of-the-art nonlinear programming (NLP) and complementarity problems solvers. Based on the proposed MCP formulation, it is formally demonstrated that the Newton-Raphson (NR) solution of the power flow problem is essentially a step of the traditional General Reduced Gradient (GRG) algorithm. The solution of the proposed MCP model is compared with the commonly used NR method using a variety of small-, medium-, and large-sized systems in order to examine the flexibility and robustness of this approach. The MCP-based approach is then used in a power flow problem under uncertainties, in order to obtain the operational ranges for the variables based on the AA method considering active and reactive power demand uncertainties. The proposed approach does not rely on the pdf of the uncertain variables and is therefore shown to be more efficient than the traditional solution methodologies, such as Monte Carlo Simulation (MCS). Also, because of the characteristics of the MCP-based method, the resulting bounds take into consideration the limits of real and reactive power generation. The thesis furthermore proposes a novel AA-based method to solve the OPF problem with uncertain generation sources and hence determine the operating margins of the thermal generators in systems under these conditions. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a pdf. The AA-based approach is benchmarked against the MCS-based intervals, and is shown to obtain bounds close to the ones obtained using the MCS method, although they are slightly more conservative. Furthermore, the proposed algorithm to solve the AA-based OPF problem is shown to be efficient as it does not need the pdf approximations of the random variables and does not rely on iterations to converge to a solution. The applicability of the suggested approach is tested on a large real European power system

A Control-variable Regression Monte Carlo Technique for Short-term Electricity Generation Planning

In the day-to-day operation of a power system, the system operator repeatedly solves short-term generation planning problems. When formulating these problems the operators have to weigh the risk of costly failures against increased production costs. The resulting problems are often high-dimensional and various approximations have been suggested in the literature. In this article we formulate the short-term planning problem as an optimal switching problem with delayed reaction. Furthermore, we proposed a control variable technique that can be used in Monte Carlo regression to obtain a computationally efficient numerical algorithm.Comment: 50 pages, 6 figure

Optimization Methods Applied to Power Systems Ⅱ

Electrical power systems are complex networks that include a set of electrical components that allow distributing the electricity generated in the conventional and renewable power plants to distribution systems so it can be received by final consumers (businesses and homes). In practice, power system management requires solving different design, operation, and control problems. Bearing in mind that computers are used to solve these complex optimization problems, this book includes some recent contributions to this field that cover a large variety of problems. More specifically, the book includes contributions about topics such as controllers for the frequency response of microgrids, post-contingency overflow analysis, line overloads after line and generation contingences, power quality disturbances, earthing system touch voltages, security-constrained optimal power flow, voltage regulation planning, intermittent generation in power systems, location of partial discharge source in gas-insulated switchgear, electric vehicle charging stations, optimal power flow with photovoltaic generation, hydroelectric plant location selection, cold-thermal-electric integrated energy systems, high-efficiency resonant devices for microwave power generation, security-constrained unit commitment, and economic dispatch problems

Distributionally Robust and Structure Exploiting Algorithms for Power System Optimization Problems

The modern power systems are undergoing profound changes as the large-scale integration of renewable energy and increasingly close interconnection of regional power grids. The intermittent renewable sources are bringing significant uncertainties to system operation so that all the analysis and optimization tools for the power system steady-state operation must be able to consider and manage the uncertainties. The large-scale interconnection of power systems increases the difficulty in maintaining the synchronization of all generators and further raises the challenging problem of systematically design multiple local and wide-area controllers. In both steady-state and dynamical problems, the large-scale interconnection is increasing the problem scale and challenging the scalability of analysis, optimization and design algorithms. This thesis addresses the problems of power system operation optimization under uncertainties and control parameter optimization considering time delays. The contributions are as follows. This thesis proposes data-driven distributionally robust models and algorithms for unit commitment, energy-reserve-storage co-dispatch and optimal power flow problems based on novel ambiguity sets. The problem formulations minimize the expected operation costs corresponding to the worst-case distribution in the proposed ambiguity set while explicitly considers spinning reserve, wind curtailment, and load shedding. Distributionally robust chance constraints are employed to guarantee reserve adequacy and system steady-state security. The construction of ambiguity set is data-driven avoiding presumptions on the probability distributions of the uncertainties. The specific structures of the problem formulation are fully exploited to develop a scalable and efficient solution method. To improve the efficiency of the algorithms to solve the operation and control optimization problems, this thesis investigates computational techniques to exploit special problem structures, including sparsity, chordal sparsity, group symmetry and parallelizability. By doing so, this thesis proposes a sparsity-constrained OPF framework to solve the FACTS devices allocation problems, introduces a sparsity-exploiting moment-SOS approach to interval power flow (IPF) and multi-period optimal power flow (MOPF) problems, and develops a structure-exploiting delay-dependent stability analysis (DDSA) method for load frequency control (LFC). The power system stabilizers (PSS) and FACTS controllers can be employed improve system damping. However, when time delays are considered, it becomes more difficult to analyzing the stability and designing the controllers. This thesis further develops time-domain methods for analysis and synthesis of damping control systems involving time delays. We propose a model reduction procedure together with a condition to ensure the $\epsilon$-exponential stability of the full-order system only using the reduced close-loop system model, which provides a theoretical guarantee for using model reduction approaches. Then we formulate the damping control design as a nonlinear SDP minimizing a carefully defined $H_2$ performance metric. A path-following method is proposed to coordinately design multiple damping controllers

Pharmacokinetics and biotransformation of biopharmaceuticals:by liquid chromatography with unit-mass and high-resolution mass spectrometric detection

Unlike the current situation for small-molecule drugs, the biotransformation of biopharmaceuticals is a largely unexplored field. Although much attention is paid to (the prevention of) degradation and structural alteration of protein-based drugs in pharmaceutical formulations, almost nothing is known about what happens to such a drug once it is dosed to a patient. An important reason for this is the fact that it is virtually impossible to investigate biotransformation using LBAs, because they typically cannot distinguish unchanged and biotransformed versions of the drug. With the increasing use of LC-MS/MS for protein quantification, it is now becoming more and more evident that in vivo chemical and enzymatic reactions of biopharmaceuticals are very common. Pharmacologically, biotransformation may affect the activity of a protein drug and, from an analytical perspective, it can also have a large influence on the concentration result that is reported.If we look at biopharmaceutical analysis from a more technical and instrumental point of view. So far, most protein LC-MS methods are being performed using triple-quadrupole mass spectrometry after sample digestion and further sample processing. This type of mass spectrometry has unit-mass resolution and its use for protein quantification essentially is an extension of the typical approach for small-molecule analysis. Very little is known about the quantitative possibilities of other high-resolution mass spectrometry (HRMS) approaches for biopharmaceuticals. HRMS is extensively used for qualitative purposes, such as the structural elucidation or confirmation of both small and large molecules, because of its high mass accuracy, but it also offers the option for quantitative analysis and extensive data re-processing. It can thus be used as an alternative detection technique for digested protein analysis with improved selectivity compared to unit-mass MS and it also is capable of quantifying intact proteins, which is virtually impossible on triple-quadrupole instrumentation