<p>Unforeseen changes in production or consumption in power systems lead to changes in grid frequency. This can cause damages to the system, or to frequency sensitive equipment at the consumers. The system operator (SO) is the responsible for balancing production and consumption in the system. The regulating market is the market place where the SO can sell or purchase electricity in order to balance unforeseen events. Producers acting on the regulating market must be able to change their production levels fast (within minutes) when required. Hydropower is therefore suitable for trading on the regulating market because of its flexibility in power production. This thesis describes models that hydropower owners can use to generate optimal bidding strategies when the regulating market is considered.</p><p>When planning for trading on the market, the prices are not known. Therefore, the prices are considered as stochastic variables. The planning problems in this thesis are based on multi-stage stochastic optimization, where the uncertain power prices are represented by scenario trees. The scenario trees are generated by simulation of price scenarios, which is achieved by using a model based on ARIMA and Markov processes. Two optimization models are presented in this thesis:</p><p>* Model for generation of optimal bidding strategies for the regulating market.</p><p>* Model for generation of optimal bidding strategies for the spot market when trading on the regulating market is considered.</p><p>The described models are applied in a case study with real data from the Nordic power system.</p><p>Conclusions of the thesis are that the proposed approaches of modelling prices and generation of bidding strategies are possible to use, and that the models produces reasonable data when applied to real data.</p> / <p>Oväntade produktions- eller konsumtionsändringar i kraftsystem leder till ändringar i nätfrekvens. Detta kan orsaka skador på systemet eller på frekvenskänslig utrustning hos konsumenterna. Systemoperatören (SO) är den ansvarige för att balansera produktion och konsumtion i kraftsystemet. Till sin hjälp har SO reglermarknaden, som är den handelsplats där SO köper eller säljer el för att balansera oväntade händelser i systemet. Producenter som agerar på reglermarknaden måste snabbt (inom minuter) kunna ändra sina produktionsnivåer om så behövs. Vattenkraft är därför lämplig för handel på reglermarknaden på grund av dess flexibilitet i kraftproduktion. Denna avhandling beskriver modeller som vattenkraftägare kan använda för generering av optimala budstrategier då reglermarknaden beaktas.</p><p>När en producents planering för handel på marknaden utförs är marknadspriserna okända. Dessa är därför betraktade som stokastiska variabler. Planeringmodellerna som presenteras i denna avhandling är baserade på multi-periodisk stokastisk programmering, där de osäkra marknadspriserna är representerade av ett scenarieträd. Scenarierna i trädet genereras genom simulering av marknadspriser. En prismodell, baserad på ARIMA- och Markovprocesser, har därför utvecklats. Två olika optimeringsmodeller presenteras i denna avhandling:</p><p>* Model för generering av optimala budstrategier för reglermarknaden.</p><p>* Model för generering av optimala budstrategier för spotmarknaden då handel på reglermarknaden beaktas.</p><p>Modellerna tillämpas i en studie där data från den nordiska elmarknaden appliceras. Slutsatser i avhandlingen är att de föreslagna ansatserna för modellering av priser och generering av budstrategier är möjliga att anvÄanda, samt att modellerna producerar rimliga resultat när applicerade på verkliga data.</p>

We consider a hydrothermal scheduling problem with a mid-term horizon(HTSPM) modeled as a large-scale multistage stochastic program with stochastic monthly inflows of water to each hydro generator. In the HTSPM we seek an operating policy to minimize the sum of present and expected future costs, which include thermal generation costs and load curtailment costs. In addition to various simple bounds, problem constraints involve water balance, demand satisfaction and power interchanges. Sampling-based decomposition algorithms (SBDAs) have been used in the literature to solve HTSPM. SBDAs can be used to approximately solve problem instances with many time stages and with inflows that exhibit interstage dependence. Such dependence requires care in computing valid cuts for the decomposition algorithm. In order to help maintain tractability, we employ an aggregate reservoir representation (ARR). In an ARR all the hydro generators inside a specific region are grouped to effectively form one hydro plant with reservoir storage and generation capacity proportional to the parameters of the hydro plants used to form that aggregate reservoir. The ARR has been used in the literature with energy balance constraints, rather than water balance constraints, coupled with time series forecasts of energy inflows. Instead, we prefer as a model primitive to have the time series model forecast water inflows. This, in turn, requires that we extend existing methods to compute valid cuts for the decomposition method under the resulting form of interstage dependence. We form a sample average approximation of the original problem and then solve this problem by these special-purpose algorithms. And, we assess the quality of the resulting policy for operating the system. In our analysis, we compute a confidence interval on the optimality gap of a policy generated by solving an approximation on a sampled scenario tree. We present computational results on test problems with 24 monthly stages in which the inter-stage dependency of hydro inflows is modeled using a dynamic linear model. We further develop a parallel implementation of an SBDA. We apply SBDA to solve the HTSPM for the Brazilian power system that has 150 hydro generators, 151 thermal generators and 4 regions that each characterize an aggregate reservoir. We create and solve four different HTSPM instances where we change the input parameters with respect to generation capacity, transmission capacity and load in order to analyze the difference in the total expected cost. / text

This dissertation proposes new methods to improve the efficiency of electricity markets with respect to market monitoring and reserve allocation. We first present new approaches to monitor the level of competition in electricity markets, a critical task for helping the markets function smoothly. The proposed approaches are based on economic principles and a faithful representation of transmission constraints. The effectiveness of the new approaches is demonstrated by examples based on medium- and large-scale electric power systems. We then propose a new system-operation model using stochastic optimization to systematically allocate reserves under uncertainty. This model aims to overcome the difficulties in both system and market operations caused by the integration of wind power, which results in a higher degree of supply uncertainty. The numerical examples suggest that the proposed model significantly lower the operation costs, especially under high levels of wind penetration. / text

We consider the problem of staffing large-scale service centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints. We introduce formulations for a class of staffing problems, minimizing the cost of staffing while requiring that the long-run average QoS achieves a certain pre-specified level. The queueing models we use to define such service center staffing problems have random inter-arrival times and random service times. The models we study differ with respect to whether the arrival rates are deterministic or stochastic. In the deterministic version of the service center staffing problem, we assume that the customer arrival rates are known deterministically. It is computationally challenging to solve our service center staffing problem with deterministic arrival rates. Thus, we provide an approximation and prove that the solution of our approximation is asymptotically optimal in the sense that the gap between the optimal value of the exact model and the objective function value of the approximate solution shrinks to zero as the size of the system grows large. In our work, we also focus on doubly stochastic service center systems; that is, we focus on solving large-scale service center staffing problems when the arrival rates are uncertain in addition to the inherent randomness of the system's inter-arrival times and service times. This brings the modeling closer to reality. In solving the service center staffing problems with deterministic arrival rates, we provide a solution procedure for solving staffing problems for doubly stochastic service center systems. We consider a decision making scheme in which we must select staffing levels before observing the arrival rates. We assume that the decision maker has distributional information about the arrival rates at the time of decision making. In the presence of arrival-rate uncertainty, the decision maker's goal is to minimize the staffing cost, while ensuring the QoS achieves a given level. We show that as the system scales large in size, there is at most one key scenario under which the probability of waiting converges to a non-trivial value, i.e., a value strictly between 0 and 1. That is, the system is either over- or under-loaded in any other scenario as the size of the system grows to infinity. Exploiting this result, we propose a two-step solution procedure for the staffing problem with random arrival rates. In the first step, we use the desired QoS level to identify the key scenario corresponding to the optimal staffing level. After finding the key scenario, the random arrival-rate model reduces to a deterministic arrival-rate model. In the second step, we solve the resulting model, with deterministic arrival rate, by using the approximation model we point to above. The approximate optimal staffing level obtained in this procedure asymptotically converges to the true optimal staffing level for the random arrival-rate problem. The decision making scheme we sketch above, assumes that the distribution of the random arrival rates is known at the time of decision making. In reality this distribution must be estimated based on historical data and experience, and needs to be updated as new observations arrive. Another important issue that arises in service center management is that in the daily operation in service centers, the daily operational period is split into small decision time periods, for example, hourly periods, and then the staffing decisions need to be made for all such time periods. Thus, to achieve an overall optimal daily staffing policy, one must deal with the interaction among staffing decisions over adjacent time periods. In our work, we also build a model that handles the above two issues. We build a two-stage stochastic model with recourse that provides the staffing decisions over two adjacent decision time periods, i.e., two adjacent decision stages. The model minimizes the first stage staffing cost and the expected second stage staffing cost while satisfying a service quality constraint on the second stage operation. A Bayesian update is used to obtain the second-stage arrival-rate distribution based on the first-stage arrival-rate distribution and the arrival observations in the first stage. The second-stage distribution is used in the constraint on the second stage service quality. After reformulation, we show that our two-stage model can be expressed as a newsvendor model, albeit with a demand that is derived from the first stage decision. We provide an algorithm that can solve the two-stage staffing problem under the most commonly used QoS constraints. This work uses stochastic programming methods to solve problems arising in queueing networks. We hope that the ideas that we put forward in this dissertation lead to other attempts to deal with decision making under uncertainty for queueing systems that combine techniques from stochastic programming and analysis tools from queueing theory. / text

The main topic of this research is the efficient operation of a modernized distribution grid from both the customer side and utility side. For the customer side, this dissertation discusses the planning and operation of a customer with multiple demand response programs, energy storage systems and distributed generators; for the utility side, this dissertation addresses the implementation and assessment of voltage/VAR control and conservation voltage reduction in a distribution grid with distributed generators. The objectives of this research are as follows: (1) to develop methods to assist customers to select appropriate demand response programs considering the integration of energy storage systems and DGs, and perform corresponding energy management including dispatches of loads, energy storage systems, and DGs; (2) to develop stochastic voltage/VAR control techniques for distribution grids with renewable DGs; (3) to develop optimization and validation methods for the planning of integration of renewable DGs to assist the implementation of voltage/VAR control; and (4) to develop techniques to assess load-reduction effects of voltage/VAR control and conservation voltage reduction. In this dissertation, a two-stage co-optimization method for the planning and energy management of a customer with demand response programs is proposed. The first level is to optimally select suitable demand response programs to join and integrate batteries, and the second level is to schedule the dispatches of loads, batteries and fossil-fired backup generators. The proposed method considers various demand response programs, demand scenarios and customer types. It can provide guidance to a customer to make the most beneficial decisions in an electricity market with multiple demand response programs. For the implementation of voltage/VAR control, this dissertation proposes a stochastic rolling horizon optimization-based method to conduct optimal dispatches of voltage/VAR control devices such as on-load tap changers and capacitor banks. The uncertainties of renewable DG output are taken into account by the stochastic formulation and the generated scenarios. The exponential load models are applied to capture the load behaviors of various types of customers. A new method to simultaneously consider the integration of DGs and the implementation of voltage/VAR control is also developed. The proposed method includes both solution and validation stages. The planning problem is formulated as a bi-level stochastic program. The solution stage is based on sample average approximation (SAA), and the validation stage is based on multiple replication procedure (MRP) to test the robustness of the sample average approximation solutions of the stochastic program. This research applies big data-driven analytics and load modeling techniques to propose two novel methodologies to assess the load-reduction effects of conservation voltage reduction. The proposed methods can be used to assist utilities to select preferable feeders to implement conservation voltage reduction.

This thesis investigates how estimates of reservoir compartmentalization impact facility sizing decisions and the degree to which inaccurate estimates destroy project value. An uncertainty analysis workflow is proposed and an asset development optimization model is specified to simulate the decision making process during concept selection. The model endogenizes drilling decisions and includes a real option to expand facility capacity after the uncertain variables are realized. The value of information analysis suggests that cost of erroneous estimates of reservoir compartmentalization is significant and can reduce asset value by more than 30%. We also find that the negative impacts are larger when the degree of compartmentalization is underestimated (too optimistic) than when it is overestimated (too pessimistic). / text

Reservoir systems are subject to several uncertainties that are the result of imperfect knowledge about system behavior and inputs. A major source of uncertainty arises from the inability to predict future inflows. Fortunately, it is often possible to generate probabilistic forecasts of inflow volumes in the form of probability density functions or ensembles. These inflow forecasts can be coupled with stochastic management models to determine reservoir release policies and provide stakeholders with meaningful information of upcoming system responses such as reservoir levels, releases, flood damage risks, hydropower production, water supply withdrawals, water quality conditions, navigation opportunities, and environmental flows, among others. This information on anticipated system responses is also expressed in the form of forecasts that must reliably represent the actual system behavior when it eventually occurs. The first part of this study presents an assessment methodology that can be used to determine the consistency of ensemble forecasts through the use of relative frequency histograms and minimum spanning trees (MST). This methodology is then used to assess a management model's ability to produce reliable ensemble forecasts. It was found that neglecting to account for hydrologic state variables and improperly modeling the finite management horizon decrease ensemble consistency. Several extensions to the existing management model are also developed and evaluated. The second portion of this study involves the management of the uncertainties in reservoir systems. Traditional management models only find management policies that optimize the expected values of system benefits or costs, thereby not allowing operators and stakeholders to explicitly explore issues related to uncertainty and risk management. A technique that can be used to derive management policies that produce desired probabilistic distributions of reservoir system outputs reflecting stakeholder preferences is developed. This technique can be embedded in a user-interactive framework that can be employed to evaluate the trade-offs and build consensus in multi-objective and multi-stakeholder systems. The methods developed in this dissertation are illustrated in case studies of real reservoir systems, including a seven-reservoir, multi-objective system in California's Central Valley.

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In this thesis, we provide computationally efficient algorithms with provable statistical guarantees, for the problem of active learning, by using ideas from sequential analysis. We provide a generic algorithmic framework for active learning in the pool setting, and instantiate this framework by using ideas from learning with experts, stochastic optimization, and multi-armed bandits. For the problem of learning convex combination of a given set of hypothesis, we provide a stochastic mirror descent based active learning algorithm in the stream setting.

The subject of this thesis is to study approximation algorithms for some network design problems in face of uncertainty. We consider two widely studied models of handling uncertainties - Robust Optimization and Stochastic Optimization. We study a robust version of the well studied Uncapacitated Facility Location Problem (UFLP). In this version, once the set of facilities to be opened is decided, an adversary may close at most β facilities. The clients must then be assigned to the remaining open facilities. The performance of a solution is measured by the worst possible set of facilities that the adversary may close. We introduce a novel LP for the problem, and provide an LP rounding algorithm when all facilities have same opening costs. We also study the 2-stage Stochastic version of the Steiner Tree Problem. In this version, the set of terminals to be covered is not known in advance. Instead, a probability distribution over the possible sets of terminals is known. One is allowed to build a partial solution in the first stage a low cost, and when the exact scenario to be covered becomes known in the second stage, one is allowed to extend the solution by building a recourse network, albeit at higher cost. The aim is to construct a solution of low cost in expectation. We provide an LP rounding algorithm for this problem that beats the current best known LP rounding based approximation algorithm.