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The transition towards low carbon energy system requires increasing the volumes of renewable generation and low carbon technologies connected to distribution networks as well as encouraging the uptake of energy-efficient appliances. These new network participants and the corresponding expansion in distribution network assets required to meet the expected levels of demand/generation will change the traditional active and reactive power flows at the Transmission-Distribution grid interface. The changes in reactive power exchanges will place significant challenges on Transmission System Operator (TSO) to maintain voltages at the transmission networks within limits particularly during system minimum demand periods due to the injection of reactive power. For instance, National Grid, the Great Britain (GB) TSO has been facing the challenge of managing the reactive power injections through Grid Supply Points (GSPs).The frequency of voltage issues is expected to grow gradually due to the anticipated volumes of low carbon technologies and expansions in distribution networks. In this respect, adequate solutions should be in place to maintain voltages at the transmission networks within limits. However, the traditional methods adopted by TSO to manage reactive power by using VAr compensators such as shunt reactors may not be a cost-effective solution due to the volume and the frequency of network issues. The pace advancements of communications and the rolling of smart meters provide opportunity for TSO to manage reactive power injections by using the existing flexibility in demand to shift portion of their power consumption to the system minimum demand periods. Furthermore, controlling power factor of Distributed Generation (DG) can mitigate the reactive power issues. However, adequate planning framework is needed to assess the capability of demand response and power factor control to manage reactive power flows at the Transmission-Distribution grid interface. To do so, this thesis presents a multi-period AC Optimal Power flow (OPF) able to manage reactive power flows throughout the planning horizon by both the optimal scheduling of demand and the optimal control of DG power factor. To cater for uncertainty related to the potential flexibility in demand, multiple scenarios are created and incorporated in the OPF so that more robust conclusions can be drawn. To understand the effectiveness of demand response and DG power factor control solutions considering the design of distribution networks, the proposed optimisation-based planning approach have been investigated on both real rural Irish distribution network and urban distribution networks from the UK Generic Distribution System (GDS). The reactive power exchanges are assessed based on the European Demand Connection Code (ESTNO-E). The results show a significant reduction in the reactive power injections to the transmission system during the periods of minimum demand and the proposed schemes could be adopted as potential solutions for the management of reactive power injections at the transmission / distribution interface which could otherwise be very crucial from the investment perspective for the deployment of reactive power compensation devices at various interfaces between distribution and transmission networks to fulfil the future grid code requirements.

Transition towards low-carbon energy systems requires an increase in the volume of renewable Distributed Generation (DG), particularly wind and photovoltaic, connected to distribution networks. To facilitate the connection of renewable DG without the need for expensive and time-consuming network reinforcements, distribution networks should move from passive to active methods of operation, whereby technical network constraints are actively managed in real time. This requires the deployment of control solutions that manage network constraints and, crucially, ensure adequate levels of energy curtailment from DG plants by using other controllable elements to solve network issues rather than resorting to generation curtailment only. This thesis proposes a deterministic distribution Network Management System (NMS) to facilitate the connections of renewable DG plants (specifically wind) by actively managing network voltages and congestion in real time through the optimal control of on-load tap changers (OLTCs), DG power factor and, then, generation curtailment as a last resort. The set points for the controllable elements are found using an AC Optimal Power Flow (OPF). The proposed NMS considers the realistic modelling of control by adopting one-minute resolution time-series data. To decrease the volumes of control actions from DG plants and OLTCs, the proposed approach departs from multi-second control cycles to multi-minute control cycles. To achieve this, the decision-making algorithm is further improved into a risk-based one to handle the uncertainties in wind power throughout the multi-minute control cycles. The performance of the deterministic and the risk-based NMS are compared using a 33 kV UK distribution network for different control cycles. The results show that the risk-based approach can effectively manage network constraints better than the deterministic approach, particularly for multi-minute control cycles, reducing also the number of control actions but at the expense of higher levels of curtailment. This thesis also proposes energy storage sizing framework to find the minimum power rating and energy capacity of multiple storage facilities to reduce curtailment from DG plants. A two-stage iterative process is adopted in this framework. The first stage uses a multi-period AC OPF across the studied horizon to obtain initial storage sizes considering hourly wind and load profiles. The second stage adopts a high granularity minute-by-minute control driven by a mono-period bi-level AC OPF to tune the first-stage storage sizes according to the actual curtailment. The application of the proposed planning framework to a 33 kV UK distribution network demonstrates the importance of embedding real-time control aspects into the planning framework so as to accurately size storage facilities. By using reactive power capabilities of storage facilities it is possible to reduce storage sizes. The combined active management of OLTCs and power factor of DG plants resulted in the most significant benefits in terms of the required storage sizes.

Optimization plays a central role in the control and operation of electricity power networks. In this thesis we focus on two very important optimization problems in power systems. The first is the optimal power flow problem (OPF). This is an old and well-known nonconvex optimization problem in power system. The existence of local solutions of OPF has been a question of interest for decades. Both local and global solution techniques have been put forward to solve OPF problem but without any documented cases of local solutions. We have produced test cases of power networks with local solutions and have collected these test cases in a publicly available online archive (http://www.maths.ed.ac.uk/optenergy/LocalOpt/), which can be used now by researchers and practitioners to test the robustness of their solution techniques. Also a new nonlinear relaxation of OPF is presented and it is shown that this relaxation in practice gives tight lower bounds of the global solution of OPF. The second problem considered is how to split a network into islands so as to prevent cascading blackouts over wide areas. A mixed integer linear programming (MILP) model for islanding of power system is presented. In recent years, islanding of power networks is attracting attention, because of the increasing occurrence and risk of blackouts. Our proposed approach is quite flexible and incorporates line switching and load shedding. We also give the motivation behind the islanding operation and test our model on variety of test cases. The islanding model uses DC model of power flow equations. We give some of the shortcomings of this model and later improve this model by using piecewise linear approximation of nonlinear terms. The improved model yields good feasible results very quickly and numerical results on large networks show the promising performance of this model.

As Electric Vehicles (EVs) continue to grow in the market, they invite mixed reactions from different stakeholders. A major concern is whether the present electrical infrastructure can support the additional load generated by the electrification of the transportation sector. Thus, an intricate analysis of the load changes induced by EVs, both now and in the future, is needed to vouch for the grid’s reliability. For this study, a synthetic grid with a current installed capacity of 3813.6 MW, serving 307,236 customers, is selected. It is based on Austin Energy’s transmission network over the city of Austin, Texas. A DC-Optimal Power Flow approach is then used to test the grid’s supply and demand balance in different EV growth scenarios through 2030 and 2050. Predictions from the federal, state, and local administrative levels are used to model the future number of EVs. For the load shape, a simulated average EV charging curve is superimposed with projected hourly loads in Austin based on historical demand growth. The daily peak load is varied from 2116.69 MW with 28,964 EVs on an average day in 2023 to 4352.91 MW with 1.26 million EVs in 2050. Our analysis shows that the grid’s capacity can sustain till 2030, but falls short by 539 MW in 2050. The results from this study replicate Austin’s current EV growth and can form a basis for utilities like Austin Energy to plan their expansion in the coming years

In light of current energy policies responding to rapid climate change, much attention has been directed to developing feasible approaches for transitioning energy production from fossil-based resources to renewable energy (RE). Although existing studies analyze RE's regional dispatch and capacity planning, they do not fully explore the impacts of the energy storage system (ESS) technology's technical and economic characteristics on RE integration and energy transition. To fill this gap, we propose an integrated optimal power flow and multiple criteria decision-making model (OPF-MCDM) to minimize system cost under operational constraints and evaluate the operational performance of ESS technologies with multiple criteria. Through analysis of hundreds of scenarios, the proposed method can identify the most critical features of ESS technologies to enhance RE integration and achieve New York State's climate goals from 2025 to 2040. For example, we discover that hydrogen energy storage (HES), with the highest energy loss values, requires greater installed capacities (7,419 MW of RE and 398 MW of ESS) than the lithium-ion battery (LIB) in 2040 and generates 4.2% more carbon dioxide emissions than LIB on average. Based on the cross-sensitivity analysis in the multidimensional evaluation, underground compressed air energy storage (CAES) performs the best, and HES performs the worst when reaching zero carbon dioxide emissions target in 2040. The proposed OPF-MCDM’s results can also be conveniently generalized to select ESS technology based on the criteria preferences from RE integration and energy transition studies and serve as a reference for ESS configurations in future energy and power system planning.

Renewable energy sources are indispensable components of sustainable electrical systems that reduce human dependence on fossil fuels. However, due to their intermittent nature, there are issues that need to be addressed to ensure the security and resiliency of these power systems. This dissertation formulates several practical problems, from an optimization perspective, stemming from the increasing penetration of intermittent renewable energy to power systems. A number of Optimal Power Flow (OPF) formulations are investigated and new formulations are proposed to control both operations and planning risks by utilizing the Conditional Value–at–Risk (CVaR) measure. Our formulations provide system operators and investors analysis tools to minimize their expected cost while hedging against risk from various sources of uncertainty. A security–constrained OPF formulation with a CVaR constraint to limit the risk of system line overloading in the case of contingencies is proposed. A novel inverse problem formulation of OPF for uncertainty quantification where we approximate the distribution of wind power forecast errors with a probability mass function (PMF) given the generator outputs is also proposed. This PMF facilitates the application of CVaR constraints in controlling the operations risks of line overloading and load shedding due to the uncertainty of wind power forecast error. A stochastic multi–period investment and planning model with economic risk constraints facing an uncertain environment around distributed energy resources technology costs and regulatory policies is also investigated. The efficacy of the proposed formulations is demonstrated using a wide range of case studies representing practical scenarios.

Massive infrastructure networks such as electric power, natural gas, or water systems play a pivotal role in everyday human lives. Development and operation of these networks is extremely capital-intensive. Moreover, security and reliability of these networks is critical. This work identifies and addresses a diverse class of computationally challenging and time-critical problems pertaining to these networks. This dissertation extends the state of the art on three fronts. First, general proofs of uniqueness for network flow problems are presented, thus addressing open problems. Efficient network flow solvers based on energy function minimizations, convex relaxations, and mixed-integer programming are proposed with performance guarantees. Second, a novel approach is developed for sample-efficient training of deep neural networks (DNN) aimed at solving optimal network dispatch problems. The novel feature here is that the DNNs are trained to match not only the minimizers, but also their sensitivities with respect to the optimization problem parameters. Third, control mechanisms are designed that ensure resilient and stable network operation. These novel solutions are bolstered by mathematical guarantees and extensive simulations on benchmark power, water, and natural gas networks.

Growing rate of electricity demand and environmental concerns promote the development of renewable energy sources (RESs), offering opportunities to operate electricity networks in a more active, efficient and economical pattern. Microgrids have been recognised as one of the most promising applications to integrate RESs and maximise their potentials, which typically consist of distributed generators (DGs), energy storage systems (ESSs), demand-side management (DSM) and are designed to work within both grid-connected and stand-alone modes as autonomous sections of a medium-voltage distribution network (MVDN). However, a large-scale of RESs integration brings technical challenges to the MVDN operation due to their intermittent nature and limited predictability. Moreover, decision-making regarding multiple microgrids would give rise to computational inaccuracy or complexity, e.g. modelling via mixed-integer non-convex programming (MINCP), unless the system scheduling and dispatch problems are appropriately interpreted. Plenty of researchers have been concentrating on optimal energy management for microgrids with considering RESs penetration, while some of them has certain limitations in terms of mathematical modelling and optimisation. In this thesis, after an investigation in the field of research, the general aim is to design a multi-purpose high-level energy management framework for microgrids with adequate consideration of operational and technical constraints that can also be solved with an appropriate trade-off between modelling accuracy and computational efficiency. Mixed-integer second-order cone programming (MISOCP) is proposed to model network components and relative optimisation routines, addressing optimal power flow (OPF) and decision-making problems within or in between microgrids, which enables applying well-developed commercial solvers, e.g. CPLEX. The framework design is subjected to a comprehensive procedure with detailed mathematical models for each individual section. Numerical simulations are sufficiently conducted and discussed, validating the effectiveness and solution quality of the proposed framework. Finally, key findings and major contributions are concluded.

The energy industry is undergoing through a reconstruction from a monopolistic electricity market to a more open and transactive one. The next ­generation grid is a level playing field in terms of electricity transactions, where all customers have an equal opportunity. The emerging concepts of electricity prosumers are expected to have a significant impact on the retail electricity market. As a result, there is an urgent need to control the interactions among numerous consumers and pro­sumers. The existing control approaches can be divided into three categories, namely, centralized control, decentralized control, and distributed control. The majority of existing literature focuses on the centralized control. In most cases, the dedicated communication links are required to ex­change data between the central controller and the local agents. The centralized control approaches are suitable for relatively small­-scale systems without reconstructing the existing communication and control networks. However, as the number of consumers and prosumers are increasing to hun­dreds of thousands, there are some technical barriers on the centralized control-­based economic operations such as heavy computation burden and single point of failure. The decentralized control is an intermediate solution to address the above mentioned challenges. The overall objective is to maximize the benefits of local agents and there is no guarantee that the decisions made by each local agents can contribute to the global optimal decision of the entire system. The distributed control has the potential to solve the economic operation problems of multiple consumers and prosumers. Lo­cal agents can share information through two-­way communication links in order to find the global optimal decision. Application of distributed control methods in power system increase system’s scalability, alleviate monopoly and monopsony, improve the privacy and distribute computational load among various entities.

Distribution system state estimation (DSSE) is a core task for monitoring and control of distribution networks. Widely used Gauss-Newton approaches are not suitable for real-time estimation, often require many iterations to obtain reasonable results, and sometimes fail to converge. Learning-based approaches hold the promise for accurate real-time estimation. This dissertation presents the first data-driven approach to `learn to initialize' -- that is, map the available measurements to a point in the neighborhood of the true latent states (network voltages), which is used to initialize Gauss-Newton. In addition, a novel learning model is also presented that utilizes the electrical network structure. The proposed neural network architecture reduces the number of coefficients needed to parameterize the mapping from the measurements to the network state by exploiting the separability of the estimation problem. The proposed approach is the first that leverages electrical laws and grid topology to design the neural network for DSSE. It is shown that the proposed approaches yield superior performance in terms of stability, accuracy, and runtime, compared to conventional optimization-based solvers. The second part of the dissertation focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with large-scale integration of renewables, where adjustments of real and reactive output power from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this dissertation leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm – a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using several multi-phase distribution networks with renewables.

The rapid load growth coupled with large-scale renewable generation sources remote from population centers demands future transmission grids to carry larger amounts of bulk power. For long distance transmission, high voltage direct current (HVdc) technology is superior to the conventional 50/60-Hz high-voltage alternating current (HVac) approach. Unfortunately, the lack of dc circuit breakers limits the application of HVdc technology to point-to point transmission links only. Thanks to advances in semiconductor materials and control methods, modern power converters make low-frequency HVac (LF-HVac) transmission systems possible. This new method of bulk power transmission overcomes the challenges in forming practical HVdc grids. Similarly, future distribution systems are expected to accommodate growing load demand in addition to increasing number of local inverter-based photovoltaic (PV) generations. Based on the aforementioned motivation, the objective of this dissertation is to develop power flow (PF) and optimal power flow (OPF) analysis methods for planning and operation of multi-frequency transmission systems that inherently employ a large number of converters. Similar steady-state analysis for a future distribution grid with high PV penetration, either as a standalone system or in coupling to a transmission grid, defines the second subject of the presented work. LF-HVac transmission scheme is recently proposed for long-distance bulk-power transmission by reducing the operating ac frequency to a low and variable value as determined by operational objectives and constraints. A multi-frequency HVac - HVdc system is formed by interconnecting conventional 50/60-Hz HVac grids to LF-HVac grids and HVdc lines. With respect to the first and major focus of this dissertation, a novel concept of an LFHVac grid employing converters with a centralized control is proposed. In addition, PF and OPF in a multi-frequency HVac - HVdc system are formulated by completely representing the steady-state models of HVac, HVdc, and LF-HVac grids as well as power converters, subject to all planning and operational constraints. The PF and OPF problems are solved by efficient algorithms based on the Newton-Raphson and predictor-corrector primal-dual interior-point methods (PCPDIPM), respectively. The proposed approach is applicable for a multi-frequency power system having arbitrary numbers of buses and topologies. Based on the PF results, the dependence of system MW losses on converter dispatch as well as the operating voltage and frequency in an LF-HVac is discussed and compared to that in HVdc transmission. On the other hand, the OPF analysis is applied to determine a suitable rated voltage in planning phase as well as optimal real-time operating frequency and dispatch of generators, shunt capacitors, and converters in operation phase. At the distribution side, high PV penetration might introduce voltage violations and reverse power flow. Besides the primary function of providing local generation, inverter-based PVs operating in grid-supporting mode can mitigate these consequences and minimize total losses with suitable dispatch. Therefore, the second focus of this work is to propose an exact OPF formulation and PCPDIPM-based solution algorithm to determine real-time dispatch of all inverters, switched capacitors, and voltage regulators with tap changers. The objective is to minimize total system losses, PV curtailment, and operations of capacitors and voltage regulators, in addition to elimination of voltage violations and reverse power flow. Effective computational strategies are proposed to allow real-time applications of the solution approach with a large number of constraints and variables. The accuracy and quality of the numerical solution in improving system performance are validated using practical distribution circuits with 15-minute load and PV data. High PV penetration also makes distribution systems more active and increases their impacts on the upstream transmission grids. As an extension of the work in distribution systems, a PF formulation as well as unified and sequential solution algorithms for joint transmission and distribution (T&D) systems are proposed, considering their physical coupling at substations. The potential effects of distributed PVs on transmission performance are also investigated. In addition, an OPF formulation and unified solution approach are proposed to determine the optimal operation for a joint T&D system. The objective is to minimize the total system losses while satisfying all operational constraints from both transmission and distribution sides.

The primary focus of the dissertation is to develop distributionally robust optimization (DRO) models and related solution approaches for decision making in energy and healthcare service systems with uncertainties, which often involves nonlinear constraints and discrete decision variables. Without assuming specific distributions, DRO techniques solve for solutions against the worst-case distribution of system uncertainties. In the DRO framework, we consider both risk-neutral (e.g., expectation) and risk-averse (e.g., chance constraint and Conditional Value-at-Risk (CVaR)) measures. The aim is twofold: i) developing efficient solution algorithms for DRO models with integer and/or binary variables, sometimes nonlinear structures and ii) revealing managerial insights of DRO models for specific applications. We mainly focus on DRO models of power system operations, appointment scheduling, and resource allocation in healthcare. Specifically, we first study stochastic optimal power flow (OPF), where (uncertain) renewable integration and load control are implemented to balance supply and (uncertain) demand in power grids. We propose a chance-constrained OPF (CC-OPF) model and investigate its DRO variant which is reformulated as a semidefinite programming (SDP) problem. We compare the DRO model with two benchmark models, in the IEEE 9-bus, 39-bus, and 118-bus systems with different flow congestion levels. The DRO approach yields a higher probability of satisfying the chance constraints and shorter solution time. It also better utilizes reserves at both generators and loads when the system has congested flows. Then we consider appointment scheduling under random service durations with given (fixed) appointment arrival order. We propose a DRO formulation and derive a conservative SDP reformulation. Furthermore, we study a scheduling variant under random no-shows of appointments and derive tractable reformulations for certain beliefs of no-show patterns. One preceding problem of appointment scheduling in the healthcare service operations is the surgery block allocation problem that assigns surgeries to operating rooms. We derive an equivalent 0-1 SDP reformulation and a less conservative 0-1 second-order cone programming (SOCP) reformulation for its DRO model. Finally, we study distributionally robust chance-constrained binary programs (DCBP) for limiting the probability of undesirable events, under mean-covariance information. We reformulate DCBPs as equivalent 0-1 SOCP formulations under two moment-based ambiguity sets. We further exploit the submodularity of the 0-1 SOCP reformulations under diagonal and non-diagonal matrices. We derive extended polymatroid inequalities via submodularity and lifting, which are incorporated into a branch-and-cut algorithm incorporated for efficiently solving DCBPs. We demonstrate the computational efficacy and solution performance with diverse instances of a chance-constrained bin packing problem.

Uncertainties that result from renewable generation and load consumption can complicate the optimal power flow problem. These uncertainties normally influence the physical constraints stochastically and require special methodologies to solve. Hence, a variety of stochastic optimal power flow formulations using chance constraints have been proposed to reduce the risk of physical constraint violations and ensure a reliable dispatch solution under uncertainty. The true uncertainty distribution is required to exactly reformulate the problem, but it is generally difficult to obtain. Conventional approaches include randomized techniques (such as scenario-based methods) that provide a priori guarantees of the probability of constraint violations but generally require many scenarios and produce high-cost solutions. Another approach is to use an analytical reformulation, which assumes that the uncertainties follow specific distributions such as Gaussian distributions. However, if the actual uncertainty distributions do not follow the assumed distributions, the results often suffer from case-dependent reliability. Recently, researchers have also explored distributionally robust optimization, which requires probabilistic constraints to be satisfied at chosen probability levels for any uncertainty distributions within a pre-defined ambiguity set. The set is constructed based on the statistical information that is extracted from historical data. Existing literature applying distributionally robust optimization to the optimal power flow problem indicates that the approach has promising performance with low objective costs as well as high reliability compared with the randomized techniques and analytical reformulation. In this dissertation, we aim to analyze the conventional approaches and further improve the current distributionally robust methods. In Chapter II, we derive the analytical reformulation of a multi-period optimal power flow problem with uncertain renewable generation and load-based reserve. It is assumed that the capacities of the load-based reserves are affected by outdoor temperatures through non-linear relationships. Case studies compare the analytical reformulation with the scenario-based method and demonstrate that the scenario-based method generates overly-conservative results and the analytical reformulation results in lower cost solutions but it suffers from reliability issues. In Chapters III, IV, and V, we develop new methodologies in distributionally robust optimization by strengthening the moment-based ambiguity set by including a combination of the moment, support, and structural property information. Specifically, we consider unimodality and log-concavity as most practical uncertainties exhibit these properties. The strengthened ambiguity sets are used to develop tractable reformulations, approximations, and efficient algorithms for the optimal power flow problem. Case studies indicate that these strengthened ambiguity sets reduce the conservativeness of the solutions and result in sufficiently reliable solutions. In Chapter VI, we compare the performance of the conventional approaches and distributionally robust approaches including moment and unimodality information on large-scale systems with high uncertainty dimensions. Through case studies, we evaluate each approach's performance by exploring its objective cost, computational scalability, and reliability. Simulation results suggest that distributionally robust optimal power flow including unimodality information produces solutions with better trade-offs between objective cost and reliability as compared to the conventional approaches or the distributionally robust approaches that do not include unimodality assumptions. However, considering unimodality also leads to longer computational times.

As the electric power supply systems are undergoing major changes with the integration of renewables, the issues related to voltage regulation and system protection are arising. In this scenario, advanced voltage regulation technologies that provide voltage control at the grid-edge, that is at the low-voltage secondary side of the distribution circuit, have emerged as a potential solution to address the shortcomings of traditional voltage control practices in distribution systems. In this work, these technologies are modeled and algorithms are developed to strategically deploy them, tune their control parameters, and evaluate their voltage regulation performance. A two-stage optimization framework is proposed for optimal placement and real-time control of the low-voltage static var compensators to minimize the energy losses while maintaining the voltage regulation. Integration of high levels of distributed generation such as photovoltaic (PV) systems impacts the voltage regulation by causing steady-state voltage variations and transient voltage fluctuations. This work further develops a procedure to tune the control parameters of PV smart inverters to mitigate these voltage issues. Furthermore, the PV penetration levels in a distribution network can be increased without creating voltage problems by dynamic controlled reactive power absorption at several strategic buses. This concept is modeled and demonstrated in this work. Furthermore, the high levels of PV generation can interfere with the overcurrent protection schemes prevalent in distribution networks. An analytical approach is proposed in this work to estimate the distribution feeder PV accommodation limits with respect to overcurrent protection issues as the impact criteria, without needing to simulate numerous PV screening scenarios to assess the impact

Humanity is currently facing a global energy crisis. This is due to the shortage in the conventional energy resources while the demand for energy is rising. In response to this crisis, research in designing more energy efficient systems has gained significant importance. The Microgrids (MGs) are one of the main key elements in giving significant momentum to efficient decentralized energy generation. From the perspective of MGs power management, economical scheduling for generators, energy storage, and demand loads are critical. Performance optimization processes are needed to minimize the operating costs while considering operational constraints. In this thesis, the optimal power flow problem for managing energy sources with storage devices is presented for dc microgrids. The power management model has been examined in various scenarios. One of them is based on a network of a six-bus power system, including an energy storage device coupling at a certain bus. The other scenario is based on the same model but including more energy storage devices. After analyzing the results of these scenarios, several conclusions have been made such as when the energy storage should charge/discharge to minimize costs. The study shows the feasibility of optimal power flow operation in DC microgrids.

Substations are joints in the power system that represent nodes that are vital to stable and reliable operation of the power system. They contrast the rest of the power system in that they are a dense combination of critical components causing all of them to be simultaneously vulnerable to one isolated incident: weather, attack, or other common failure modes. Undoubtedly, the loss of these vital links will have a severe impact to the to the power grid to varying degrees. This work creates a cascading model based on protection system misoperations to estimate system risk from loss-of-substation events in order to assess each substation's criticality. A continuation power flow method is utilized for estimating voltage collapse during cascades. Transient stability is included through the use of a supervised machine learning algorithm called random forests. These forests allow for fast, robust and accurate prediction of transient stability during loss-of-substation initiated cascades. Substation risk indices are incorporated into a preventative optimal power flow (OPF) to reduce the risk of critical substations. This risk-based dispatch represents an easily scalable, robust algorithm for reducing risk associated with substation losses. This new dispatch allows operators to operate at a higher cost operating point for short periods in which substations may likely be lost, such as large weather events, likely attacks, etc. and significantly reduce system risk associated with those losses. System risk is then studied considering the interaction of a power grid utility trying to protect their critical substations under a constrained budget and a potential attacker with insider information on critical substations. This is studied under a zero-sum game theoretic framework in which the utility is trying to confuse the attacker. A model is then developed to analyze how a utility may create a robust strategy of protection that cannot be heavily exploited while taking advantage of any mistakes potential attackers may make.

The future distribution system is envisioned to be a network of distributed energy resources (DER), being able to operate in both the grid connected and islanded modes. In essence, the future electrical distribution systems will operate as medium-voltage (MV) microgrids. This dissertation presents a study of the optimal power flow (OPF) based on generalized benders decomposition (GBD) for optimally scheduling DERs and managing voltage regulation device operations to enable the economic and secure operations of the future MV distribution systems. Key model considerations include multi-phase unbalanced distribution system network, conservation voltage reduction (CVR), and multi-interval energy scheduling. Further, the optimal operating decisions are studied when the MV microgrid is in different operational modes, such as the 1) grid-connected mode, 2) islanded mode, and 3) grid-connected to islanded mode transition. Excellent algorithm performance has been achieved on the IEEE test feeder models. The use of an external engine for solving the unbalanced power flow and obtaining the sensitivities for the decomposed sub-problems allows the OPF to handle scaled-up models with the increased number of decision variables, constraints, and network buses. To support solution of large-scale problems, parallel computational strategies are recommended in order to achieve solution performance required by operations.Among the output of the GBD-based OPF, the primal solution provides optimal operation set point decisions while the dual solution provides system marginal-cost based energy prices such as the locational marginal prices (LMP) for single-phase nodes. These important OPF outcomes can facilitate the economic electricity market design in the distribution system involving both DERs and end-use demands. In this dissertation, a new method based on the GBD-based OPF has also been proposed using the unbalanced power system model linearized around the near-optimal operational state to calculate LMPs for single-phase buses and support the economic market design of the distribution system.Also in this dissertation, the approximation of nodal voltage sensitivities is studied based on observations made about the radial distribution system. As a result, voltage sensitivities can be efficiently computed for all network nodes simply based on the power flow solution and topology searches. The results are validated on the IEEE test feeder models using the perturbation analysis. The proposed method can be applied to large unbalanced radial distribution systems for supporting distribution system planning and operation.

The commodification of computing, sensors, actuators, data storage and algorithms has unleashed a new wave of automation throughout society. Motivated by the promise of new capabilities, quality improvements, or efficiency gains, data-driven technologies have captured the attention and imagination of the public and many domain experts. Though opportunities are ample, the rapid introduction of data-driven functionality also triggers well-founded concerns about safeguarding critical values, such as safety, privacy and justice.In the context of operating electric distribution networks, the need for data-driven monitoring and control is explained by the irreversible transition from fossil to renewable generation and the accompanied electrification of our economy in areas like transportation and heating.The traditional fit-and-forget paradigm of designing networks conservatively for the projected peak loads assumed unidirectional power flow, predictable future demand and monotonic voltage drops, and allowed for operating at near-100\% reliability with minimal requirement for sensing and actuation. The intermittent nature of Distributed Generation (DG), its ability to feed power back to the grid and cause bidirectional power flow, and the diversifying and nonlinear behavior of electric loads are all eating away at the robustness of this approach, causing Distribution System Operators (DSOs) to put caps on the allowable DG and revisit their design and operating practice. Rather than making traditional expensive network reinforcements in often aging physical infrastructures, DSOs are trying to increase the observability and controllability of their networks by leveraging new sensing and actuation technologies and exploring the ability to use data-driven algorithms to help with the integration of more DG in a more distributed (in space and time) and cost-effective way. This dissertation works towards this vision by formulating a systematic control-theoretic approach for integrating data-driven monitoring and control in the operation of electric distribution networks. Firstly, a Bayesian approach to state estimation overcomes the constraint of limited available real-time sensors by integrating voltage forecasting. A second class of tools discussed is the use of machine learning to decentralize Optimal Power Flow (OPF) methods, by utilizing inverter-interfaced Distributed Energy Resources (DERs). The Decentralized OPF method lets each DER learn a policy that contributes to network objectives from its local historical data and measurements alone. This approach is formulated as a compression and reconstruction problem through an information-theoretic lens, providing fundamental limits of reconstruction and a strategy for optimal communication to improve learning-based reconstruction of optimal policies throughout a network.Lastly, the ambition to control networks in a distributed fashion triggers concerns about privacy-sensitive information that may be inferred from an agent's shared data. For a general class of algorithms, a new notion of local differential privacy is integrated that allows each agent to customize the protection of local information captured in constraints and objective functions.The ultimate goal of the work presented in this dissertation is to contribute to a framework for the integral and value-sensitive design and implementation of data-driven methodologies in critical infrastructure. To address the inherent cross-disciplinary nature of this larger goal, the final chapter explains how each automated decision-making tool reflects and affects values important to its stakeholders. The chapter argues that in order to enable beneficial integration of such tools, practitioners need to reflect on their epistemology and situate the design of automated decision-making in its inherently dynamic and human context.

With Power System being restructured in the vision of Smart Grid, it is important now more than ever to find suitable locations to place Distributed Generators (DG). Distributed generators, which may be renewable, are not limited to specific locations as in the case of conventional generators. Several papers have been published that make suggestions on where the optimal location of DG should be in a system. Objectives ranging from loss minimization to total cost minimization have been the factor for such studies. In this study, a new method is introduced that hopes to improve a current system in three ways by maximizing load, minimizing the locational marginal price and improving line contingency scenarios. The proposed methodology is simulated using MATPOWER’s Optimal Power Flow on the IEEE 14 bus test system.

Power networks are undergoing a transition from the traditional model of centralised generation towards a smart decentralised network of renewable sources and energy storage systems, organised into autonomous microgrids. Energy storage systems can provide a range of power network services, particularly when distributed throughout the network. The introduction of distributed energy storage represents a fundamental change for power networks, increasing the network control problem dimensionality and adding long time-scale dynamics associated with the storage systems' state of charge levels. The lack of appropriate control and management strategies has been identified as a limiting factor for integrating distributed energy storage systems into microgrids. Managing microgrids with many small distributed energy storage systems requires new scalable control strategies, that are robust to power network and communication network disturbances. The traditional microgrid control model consists of a primary control level for decentralised load sharing, a centralised secondary control level to correct frequency/voltage offsets and a slower centralised tertiary control level for power flow optimisation. This thesis proposes and develops the use of multi-agent control for both the secondary and tertiary control levels of microgrids with distributed energy storage systems. Multi-agent control removes the need for a central controller, providing increased robustness, scalability and flexibility, while achieving a range of control objectives that are not possible with a decentralised strategy. On the secondary microgrid control level, multi-agent state of charge balancing is proposed as a scalable means of coordinating distributed energy storage systems. Under the proposed multi-agent state of charge balancing strategies, distributed storage systems cooperate based on limited neighbour-to-neighbour communication, so that they use their combined power and energy capacities to maintain stability and power quality in the microgrid. Multi-agent control strategies are developed for both AC and DC microgrids, and DC microgrids with heterogeneous energy storage technologies. Building on the linear multi-agent control results, a multi-agent sliding mode control strategy is proposed for DC microgrids with distributed battery energy storage systems. This control strategy enforces charge/discharge limits and prevents circulating currents between the batteries, increasing efficiency and battery lifetime. State of charge synchronisation under the multi-agent sliding mode control strategy is proved for very general assumptions on the nonlinear battery dynamics. For the tertiary control level, a new convex approximation of the AC microgrid dynamic optimal power flow problem is presented, i.e. the problem of optimally coordinating the energy flows between distributed energy storage systems over a time horizon, considering renewable generation and load predictions. The availability of fast and robust solvers for convex optimisation problems makes it suitable for a receding horizon model predictive control implementation. Unlike existing convex optimal power flow methods based on decoupled real and reactive power flow models, line losses, voltage constraints and converter current constraints are addressed in the optimisation. Using similar power flow approximations, a new convex formulation of the DC microgrid dynamic optimal power flow problem is also presented. Based on the new convex formulation, the AC microgrid dynamic optimal power flow problem is divided between autonomous agents, which cooperatively reach an optimal solution using only local power network information and neighbour-to-neighbour communication. Under the proposed multi-agent dynamic optimal power flow strategy, the information required by each agent is independent of the communication network topology, providing increased flexibility and robustness compared with existing distributed optimal power flow methods.

This dissertation is concerned with the design of branch-and-cut algorithms for a variety of nonconvex nonlinear problems pertaining to power systems operations and planning. By understanding the structure of specific problems, we can leverage powerful commercial optimization solvers designed for convex optimization and mixed-integer programs. The bulk of the work concerns the Alternating Current Optimal Power Flow (ACOPF) problem. The ACOPF problem is to find a minimum cost generation dispatch that will yield flows that can satisfy demand as well as various engineering constraints. A standard formulation can be posed as a nonconvex Quadratically Constrained Quadratic Program with complex variables. We develop a novel spatial branch-and-bound algorithm for generic nonconvex QCQP with bounded complex variables that relies on a semidefinite programming (SDP) relaxation strengthened with linear valid inequalities. ACOPF-specific domain reduction or bound tightening techniques are also introduced to improve the algorithm's convergence rate. We also introduce second-order conic valid inequalities so that any SDP can be outer-approximated with conic quadratic cuts and test the technique on ACOPF. Another application is the incorporation of convex quadratic costs in unit commitment, which is a multi-period electric generation scheduling problem. We show that conic reformulation can both theoretically and practically improve performance on this mixed-integer nonlinear problem. We conclude with methods for approximating a mixed-integer convex exponential constraint. Applications include capital budgeting, the system reliability redundancy problem, and feature subset selection for logistic regression.

Distributed Energy Resources (DER) have the potential to both improve the manner in which the electric power distribution system is operated and provide services to the bulk electric grid. A key question that has emerged in academic circles is the manner in which DER is governed to provide such utility. While many of the suggested approaches are mathematically elegant and demonstrate positive performance in simulations, they face enormous barriers to implementation due to their reliance on knowledge of network models and burdensome communications requirements. This dissertation focuses on the application of an Extremum Seeking (ES) control approach to manage individual DER, that does not require utility network models and or communication between agents. Results achieved from the application of this technique are shown to be equivalent to those derived from centrally-based optimization strategies that utilize convex relaxation techniques. Initially, I explore the use of Extremum Seeking to manage reactive power resources to perform voltage constrained optimization in balanced radial distribution systems. Next, also for balanced and radial distribution systems, I extend this work to consider the management of four-quadrant-capable DER to enable voltage-constrained distribution substation real power and voltage reference tracking. My approach essentially allows the distribution feeder to act as a controllable (P,V) bus when viewed from the perspective of the Transmission System Operator. Finally, in an attempt to extend my results to 3-phase distribution systems, I derive a linear approximation to unbalanced power flow and explore a new objective of using reactive power resources to regulate and balance system voltages. While the latter-most piece does not specifically consider ES, it lays the necessary foundation for the application of the approach in unbalanced systems.

The restructuring of the electric energy market and the proliferation of intermittent renewable-energy based power generation have introduced serious challenges to power system operation emanating from the uncertainties introduced to the system variables (electricity prices, congestion levels etc.). In order to economically operate the system and efficiently run the energy market, a statistical analysis of the system variables under uncertainty is needed. Such statistical analysis can be performed through an estimation of the statistical moments of these variables. In this thesis, the Point Estimate Methods (PEMs) are applied to the optimal power flow (OPF) problem to estimate the statistical moments of the locational marginal prices (LMPs) and total generation cost under system uncertainty. An extensive mathematical examination and risk analysis of existing PEMs are performed and a new PEM scheme is introduced. The applied PEMs consist of two schemes introduced by H.P. Hong, namely, the 2n and 2n+1 schemes, and a proposed combination between Hong's and M. E Harr's schemes. The accuracy of the applied PEMs in estimating the statistical moments of system LMPs is illustrated and the performance of the suggested combination of Harr's and Hong's PEMs is shown. Moreover, the risks of the application of Hong's 2n scheme to the OPF problem are discussed by showing that it can potentially yield inaccurate LMP estimates or run into unfeasibility of the OPF problem. In addition, a new PEM configuration is also introduced. This configuration is derived from a PEM introduced by E. Rosenblueth. It can accommodate asymmetry and correlation of input random variables in a more computationally efficient manner than its Rosenblueth's counterpart.

The electric power system is undergoing dramatic transformations due to the emergence of renewable resources. However, integrating these resources into the electric grid has proven to be difficult for two main reasons: these resources are uncertain and distributed. This thesis discusses how uncertainty and distributedness of the new resources are manifested as challenges in time and spatial scales, and how we can optimally control the power grid to overcome these challenges. The theme of this thesis is that in order to control the new resources, we need a better understanding of the physical power flow in the system. To illustrate the spatial-scale challenge, we consider the voltage regulation problem for distribution networks. With a deep penetration of distributed energy resources the voltage magnitudes in a distribution system can fluctuate significantly. To control these resources such that voltage profiles remain flat, we need to coordinate the tens of thousands of households in the distribution network. By studying the geometry of power flows in the network, we show that even though the voltage regulation problem is non-convex, it can be convexified exactly through a semidefinite relaxation . Based on this insight, we an optimal and decentralized algorithm for this problem. Only communication between electrical neighbors are required in the algorithm, thus allowing it to scale to problem of large sizes. The second problem we consider is dispatching generators in the transmission network under deep penetration of wind power. Because of on/off and ramp-rate constraints, traditional generators need to be dispatched before the actual time of delivery of energy. On the other hand, wind power cannot be dispatched and is difficult to predict in advance. This creates a mismatch in time-scale between the controls (traditional generators) and the randomness in the system (wind). We capture this challenge as a two-stage stochastic dispatch problem. In contrast to the standard Monte Carlo solutions, we show that the dimensional of the problem can be reduced dramatically by using forecast informations. This dimensional reduction is based on a better understanding of congested DC optimal power flow problems. Using this reduction, we show how to calculate the optimal reserve margin for the system in the presence of renewables, and quantify the intrinsic impact of uncertainties on the system cost.

Transient stability is a major concern in power system security and reliability because it is the most common type of instability and its impacts can cause greatest economic losses. For enhancing the energy security, it requires the power system operation to be evaluated during both the planning and the operation stage. Many online/offline transient stability assessment techniques have already been developed for this purpose. However, due to the increase in energy demand, the modern power system has grown to a very sophisticated and large system for which extent transient stability assessment methods may not be able to handle. In addition, the new published regulation rules and new concepts such as the smart grid have also pushed the requirement for transient stability assessment to a higher level. Thus, this dissertation is intended to study large scale power system transient stability. It starts from establishing an analytical approach for power system transient stability assessment. Based on the results, the disadvantages of traditional concepts used in transient stability assessment have been discussed. In order to overcome the difficulties encountered by classical approaches, a new technique for estimating the generator rotor angle difference in multi-machine power system is developed. It is more practical and has been applied to study the impact of wind power generation on power system transient stability afterwards. Since recently there is a significant increase in the importance of renewable energy and its related optimizations in power systems, the final goal of this dissertation focuses on the power system optimal power flow technique with wind power penetration and transient stability constrains. For making results more convincible, the South Carolina offshore wind speed data is used as the availability of wind power. An approach for maintaining the power system economic operation within the security range has been given at the end of this dissertation.

This work concerns the formulation and solution of a multi-period security-constrained optimal power flow problem for real-time electricity market operations. The solution of the proposed problem is intended to be part of the core pricing procedure for electricity trading in open markets where real energy, reactive energy, voltages support, and other system resources and services can all be traded in discrete bids and offers. Traditionally, real-time dispatching operations only involve solving single-period security-constrained optimal power flow problems. This work demonstrates the need for solving multi-period security-constrained optimal power flows. The nonsmoothness of the offer/bid-driven optimal power flow problem is studied. Three techniques, namely, a trust-region based augmented Lagrangian method, a step-controlled primal-dual interior point method, and a modified constrained cost variables method, are developed for reliable and efficient computation of large-scale nonsmooth optimal power flows. Numerical studies show that these techniques are reliable and better than some existing ones. To reduce the computational complexity, two decomposition techniques are proposed and studied. In the first one, the auxiliary problem principle method is extended to handle inequality constraints created from generator ramping limits. In the second one, binding time-coupling and contingency-coupling constraints are estimated, ranked, and filtered before the computation is decomposed and parallelized using standard block matrix computation techniques. According to experimental results, the most promising way of solving large-scale multi-period security-constrained optimal power flow problems in real time is to combine the second decomposition method with the modified constrained cost variables method. The optimal power flow formulation and relevant computation techniques proposed in this work balance the needs for: (1) deterministic convergence, (2) accurate computation of nodal prices, (3) support of both smooth and nonsmooth costings of a variety of resources and services, such as real energy, reactive energy, voltage support, etc., (4) full active and reactive power flow modeling of large-scale systems, and (5) satisfactory worst-case performance that meets the real-time dispatching requirement.

The NERC August 14th Blackout report brought out by the task force cited 'failure to ensure operation within secure limits' as one of the main reasons. Many of the numerous recommendations focused on the need for better real-time tools for operators and reliability coordinators. In the absence of such tools the operators are limited to operating in conservative secure operating regions established using offline studies. At the same time, with the fast inception of deregulation, the need to ensure a reliable and secure power system has become all the more vital. The success of a competitive market is dependent upon a reliable and secure transmission system at all times. This dissertation investigates ideas for analytical and intelligent techniques to obtain generation dispatches that would be first-swing stable for a certain set of credible contingencies (three-phase faults) with their respective fault clearing times. In a deregulated environment, fair operation is dependent upon maximum utilization of available resources. Conventionally the maximum utilization has been made possible by use of the optimal power flow where certain objective(s) are maximized/minimized subject to certain constraints through various mathematical programming techniques. Due to the extremely large computation times required to carry out dynamic security assessment of large disturbances, constraints to ensure dynamic stability, more specifically transient stability have been ignored from state of the art optimal power flow routines today. Rather, such limits are established using offline studies. Since, these limits are established from forecasted data, they are kept on the conservative side to ensure that the power system would be transiently stable for a certain set of credible contingencies. One of the major obstacles of including dynamic security assessment subroutines within the optimal power flow method for real-time operations is the heavy computational burden since it requires solution of differential equations. Another is the extremely high analytical and programming complexity involved with inclusion of constraints to ensure that the 'solution of the differential equations is within certain bounds'. This would enhance the already existing state of the art dispatch routines within energy managements systems by allowing operation closer to stability limits.

This dissertation presents a new algorithm for optimal power flow in distribution systems. The new algorithm, Discrete Ascent Optimal Programming (DAOP), will converge to the same solution as the Lagrange multiplier approach as demonstrated by example. An intuitive discussion illustrating the path of convergence is presented along with a theorem concerning convergence. Because no partial derivatives, solutions of simultaneous equations, or matrix operations are required, the DAOP algorithm is simple to apply and program. DAOP is especially suited for programming with pointers. Advantages of the new algorithm include its simplicity, ease of incorporating inequality constraints, and the ability to predict the number of steps required to reach a solution. In addition to optimal power flow, the algorithm, heuristic in nature, can be applied to switch placement design, reconfiguration, and economic dispatch. The basic principles of the algorithm have been used to devise a phase balancing routine which has been implemented in the Distribution Engineering Workstation (DEWorkstation) software package sponsored by the Electric Power Research Institute (EPRI). The new algorithm presented in this dissertation works toward a solution by performing a series of calculations within a finite number of steps. At the start of the algorithm, the assumption is made that no power is flowing in the system. Each step adds a discrete unit of load to the system in such a fashion as to minimize loss. As progress toward the solution is made, more and more load is satisfied and the losses in the system continue to increase. The algorithm is terminated when all system load is satisfied. When the algorithm is finished, the sources which should supply each load have been identified along with the amount of power delivered by each source. Discussion will show that the method will converge to a solution that is within the discrete step size of the optimum. The algorithm can be thought of as an ascent method because the cost (losses) continually increases as more and more load is satisfied. Hence, the name Discrete Ascent Optimal Programming (DAOP) has been given to the algorithm. The new algorithm uses the topology of the power system such that the entire system is not considered at each step. Therefore, DAOP is not an exhaustive state enumeration scheme. Only those portions of the system containing loads most closely connected (via least loss paths) to the sources are first considered. As loads become supplied during the course of the solution, other loads are considered and supplied until the system is fully loaded.