Ziad K Shawwash

Game theory has been gaining popularity as an innovative tool in the coordination of multi-reservoir systems for the optimal release and market policies through finding equilibrium. An equilibrium-based decision-making model (EDM) was developed to coordinate release and market decisions to meet demand and trade electricity from the Peace and Columbia systems in the US and Alberta Markets. The Williston and Kinbasket Reservoirs were taken as the main two agents to represent the Peace and Columbia rivers, respectively. Data on demand, inflows, prices, and release limits were provided by BC Hydro; and the Water Value Function for each reservoir was obtained from the Energy Studies Peace and Columbia Optimizers for the December 2019 study. The policies resulting from the game-theoretic model were compared to these of an existing iterative simulation and coordination model, the Energy Studies Models. The model showed reasonable results for the Peace system with low absolute error and mean absolute deviation for the drawdowns from Williston Reservoir, while the drawdowns from Kinbasket Reservoir showed larger error as compared to energy studies. Three different solution algorithms were investigated: social optimum, Nash Support Enumeration, and Mixed Integer Linear Programming. In this case study, the Mixed Integer Linear Programming algorithm to find Nash Equilibrium gave the best strategies and rewards. However, the Nash Support Enumeration algorithm is more adaptable to situations with more than two agents. The results suggest that Game Theory is a promising technique that should be further investigated and enhanced to aide Energy Studies in the coordination of reservoir release policies. To further develop the model results, inverse reinforcement learning algorithms in Stochastic Games were investigated and presented. An effective way to validate and compare this model and the different tools developed by the BC Hydro’s system optimization group is by following a model benchmarking framework detailed in this research.

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Unplanned outages of generating units, also known as forced outages, act as a source of operational uncertainty for hydropower companies like BC Hydro. Forced outages reduce plant availability and causes loss of system flexibility and revenues. A combination of both likelihood of occurrence (frequency) and severity of outage event (duration) truly represents the risks posed by forced outages. Energy studies, using simulation and optimization models, are carried out by utility companies to incorporate different sources of uncertainties and maximize benefits in multi-purpose, multi-reservoir systems. The Department of System Optimization at BC Hydro is developing new quantitative approaches to model uncertainty of forced outages in their operations planning models and system energy studies. In this thesis, statistical properties of forced outage datasets are quantified, and different algorithms to generate scenarios of forced outages are developed. The statistical analysis methods and scenario generation algorithms are applied for a major hydroelectric facility in the BC Hydro system having 10 generating units and results are presented. Time to Failure and Time to Repair for outage events were obtained and checked for annual trends, seasonality and correlations. Outages of units were also evaluated for homogeneity. The impacts of planned outage on forced outages were quantified and suitable probabilistic distributions were developed to represent frequency and duration of outages. Three different scenario generation algorithms were developed using Markov/Semi-Markov based processes and Monte Carlo Simulation. It was found that Semi-Markov based scenario generation algorithm that comprehensively accounts for impacts of planned outages on forced outages is best suited to generate scenarios of forced outages for energy studies and operational planning models.

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This thesis presents a Stochastic Dynamic Programming (SDP) modeling algorithm to model six hydropower plants in British Columbia (BC), Canada. The main output of the algorithm is the water value function for the two biggest reservoirs in BC, Williston and Kinbasket reservoirs. The AMPL programming language was used to implement the algorithm. Extensive testing has shown that the program is able to solve the problem producing acceptable water value and marginal value functions up to a problem size of ~ 164 million states per time step using the computing resources available on one of the BC Hydro’s servers.The objective of the work presented here was to assess the sensitivity of solution efficiency and precision for several storage state and decision space discretizations. The impact of introducing a storage state-space corridor, as an alternative of the traditional fixed storage state-space, was investigated. In addition, the sensitivity of the modeling results to different spill penalty values was analyzed. It was found that finer state-space increments give more precise results but the granularity was limited to the computing resources available. Introducing the storage state-space corridor provided several advantages; nevertheless, care should be taken in the design of such corridors so that the solution efficiency and accuracy are not jeopardized. Also, recommendations on the use of suitable spill penalty value are provided.Flexibility is one important feature of the modeling algorithm. This flexibility is a result of optimizing the algorithm and the organization of the code, which provided control over the increment of the state-spaces and the storage corridor, the ability to run the problem for one storage reservoir while fixing the state of the other storage reservoir and the ability of the user to run the model either directly on a personal computer/server using the command prompt or by using a scheduling program to optimize the use and sharing of computing assets.Further enhancements of the algorithm will enable the model developed in this thesis to handle much larger problems but will likely still suffer from the limitations due to the inherent curse of dimensionality in modeling using the SDP algorithm.

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Wind power is gaining popularity around the globe mainly because of its advantages such as its renewability and its low environmental impact. However, wind power has some operational disadvantages. Wind power is uncertain, variable, and non-dispatchable. These three properties add cost on wind power producers and electric utilities. In this thesis, stochastic optimization (SO) is applied to minimize the cost of day-ahead (DA) wind forecast uncertainty.SO requires the statistical properties of an uncertain parameter to be accurately represented. In this thesis, scenarios were used to represent the wind forecast error (WFE). To generate WFE scenarios that properly characterize the wind forecast uncertainty, first the statistical properties of the DA WFE was investigated. Then two competing scenario generation algorithms, one based on Markov chain (MC) and the other based on autoregressive moving average (ARMA), were proposed and tested. Both models were successful in generating representative WFE scenarios, but the ARMA-based model was found to be better at recreating the statistical properties of the WFE. These two algorithms required the generation of numerous scenario to confidently capture the WFE probability distribution. Since using all the generated scenarios in a SO problem was infeasible, a scenario reduction algorithm based on probability distance was applied to reduce the number of scenarios while preserving the information they contain.The scenarios obtained after the reduction process were used as inputs into a two-state linear SO model. The results of the optimization showed that, under normal operating conditions, SO can reduce the cost of DA wind forecast uncertainty by up to 70%. The SO models were also found to be better at avoiding load shedding and wind power curtailment. When comparing the two scenario generation algorithms with respect to cost savings, the MC-based model resulted in higher cost savings because the scenarios it generated were better at capturing extreme WFEs, which led to less load shedding events. Sensitivity analysis conducted by varying input assumptions showed that the savings from SO vary considerably based on the modeling assumptions and that care should be taken when designing a cost savings evaluation strategy.

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The need to establish electricity storage in British Columbia is brought by a regional and global shift towards the development of renewable electricity generation. The integration of renewable sources of power is challenging for system operators due to their inability to be dispatched. Energy storage enables a time lag between generation, transmission, and consumption. The unique characteristics of British Columbia, namely abundance of water and mountainous terrain, are well suited for the development of Pumped Hydro Storage (PHS). The goal of this thesis is to investigate the value of the integration of a PHS plant in the BC Hydro system at a high level of planning. BC Hydro’s Generalized Optimization Model, used for medium to long term planning, was modified to include PHS plants. The benefits of the PHS plant were considered as the incremental increase of the objective function of this optimization model compared to a base case. A method was developed to value PHS plants based on projected benefits and costs. A case study was performed using various configurations of PHS plants; including closed loop plants and one extension of an existing hydropower plant. Sensitivity analysis was performed to test the response of NPV over a number of inputs. As the capacity and storage of the closed loop plants increased, the usage also increased. Benefits were not uniform across the set of water years reflecting the characteristics of each year’s conditions and configuration of the BC Hydro system. The yearly benefit is highest for the extension of the existing hydropower plant. For the closed loop projects, the NPV is highest for the least amount of storage for each capacity. The NPV of all projects was most sensitive to the variation of construction costs. Complete cost recovery of these plants using revenues consisting of trade revenues and increased overall system is unlikely. Additional sources of benefits and revenue streams should be identified and included in future studies of PHS projects. This research can be extended to projects with more certain estimates of characteristics and costs.

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Electric utilities engaging in integrated resource planning face a variety of uncertainties which complicate the development of robust plans. These uncertainties occur in variables such as demand growth, energy price, green house gas regulations, and water inflows for hydroelectric-dominated utilities, just to name a few. This study examines the current planning methods in use among (largely North American) utilities with a particular focus on the features of each method that manage or mitigate uncertainty. The two most common planning methods (portfolio-based and scenario-based planning) are analysed and their advantages, disadvantages, potential alterations, and circumstances of best application are evaluated. These findings are then applied to the case of BC Hydro, one of the largest electric utilities in Canada, with recommendations for changes to their current planning process.

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The BC Hydro and Power Authority is the largest electric utility in the province of British Columbia, Canada. With a generating capacity of more than 12,000 MW, it serves almost 2 million customers in the province. It operates 31 hydroelectric facilities, most of them located in multi-reservoir systems. In order to facilitate the operation of these reservoirs, BC Hydro developed an in-house application called the Operations Planning Tool (OPT), a deterministic Linear Programming (LP) model that provides the optimal operation of the multi-reservoir systems considering multiple purposes. The objective of this research was to investigate, develop, incorporate and test additional modeling features that would expand the current capabilities of the OPT. This included developing a formulation for the analysis of units’ maintenance outages and changing the optimization model to consider inflow uncertainty and avoid the use of weight coefficients and penalty functions. The formulation developed for the analysis of units’ maintenance outages is based on a two-stage algorithm. In the first stage, a pre-processor defines all the possible outage solutions given some initial configurations. In the second stage, a modified OPT model is run to find an outage solution that optimizes the objectives using a Mixed-Integer Linear Programming (MILP) algorithm. The formulation was tested using the Bridge River system in British Columbia, Canada. An alternative OPT model was also developed to consider the uncertainty in the reservoir’s inflow and modify the formulation of the objective function. It was desired to avoid the use of weight coefficients and penalty functions due to the limitations that they present. The proposed alternative was based on the development of a linear decision rule and the use of chance constraints. The linear decision rule is an operating rule that defines the spillway releases and forebay elevation as a linear function of the inflow, the turbine releases and a deterministic decision variable. The chance constraints were used to consider the probability of the spillway releases and forebay elevation not being within a preferred range of values established by the user. The developed formulation was tested using the Stave Falls system.

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The reservoir operations model developed in this thesis is a stochastic dynamic programming decision support tool for the optimization of the operation of snowmelt-driven reservoirs with small storage flexibility hydropower systems during the spring freshet. The model operates under the objective of maximizing the value of electricity generation through electricity trading over a short-term planning period. Project and watershed data, stochastic inflows, and estimated electricity prices are used to calculate optimal expected turbine release policies over a short-term planning period. Results are used to provide decision support to operators in the form of a daily expected optimal turbine release volume and marginal value of energy of the reservoir. Including stochasticity in the model allows for inflow probabilities, which may not be easily evaluated by an operator, to be reflected in an operation decision. A combination of forecast, historical, and current state of the system data is included in the model to reflect the most up-to-date view of uncertain conditions. Case studies indicate that although operators may deviate from the expected optimal policy to meet other interests and requirements in real-time, the model provides an optimal expected policy during the freshet period and has shown in a case study to increase the value of a single reservoir’s operations by 6% during one three-month freshet period.

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We present the implementation of a Sampling Stochastic Dynamic Programming (SSDP) algorithm to maximize water value, while meeting consumer demand for the BC Hydro hydroelectric system in British Columbia, Canada. The implementation includes power generation facilities on the Columbia and Peace River systems.Variability of natural streamflow into a reservoir is a major source of uncertainty when developing reservoir operation policies and determining the value of water within a system. This study investigates SSDP model performance with various hydrologic inputs. Sixty years of historical data are used to generate hydrologic scenarios comprised of inflow and forecast sequences as input to the SSDP model. Scenario types studied include historical record data, inflows and forecasts generated from an autoregressive lag-1 model, and BC Hydro ensemble streamflow prediction forecasts.We present results of our implementation of the SSDP algorithm including a discussion on improved reservoir operation policy and the future value of water with various hydrologic inputs. We also present our investigation of the marginal value of water with the evolution of forecasts. Results indicate that forecasts are most valuable in determining the value of water during the early freshet, and the value added from updating future forecasts diminishes as the time in which the forecast is made progresses through the melting period.

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A wide variety of factors make reservoir operation a complex and dynamic problem, including multiple operational objectives, hydrological uncertainties and dam safety considerations. Concerns have grown in recent years regarding reliability of existing hydropower storage and discharge facilities, as many of these facilities are aging and their failure could significantly impact reservoir operations and pose threats to dam safety. A number of reliability methods were investigated in this study and a formal reliability analysis process has been adopted to assess the reliability of water release facilities using censored failure data. The nonparametric product-limit estimation method was used to analyze the time-dependent reliability of different types of spillway gates and hydropower turbines, and parametric model fitting techniques were subsequently applied to fit reliability functions. Failure and repair events were simulated using Monte Carlo simulation, which provided random variables to capture the uncertainty of availability for hydro facilities. The reliability analysis process was integrated into a simulation-optimization operations planning model to develop a reliability-based modeling framework that quantitatively treats risk and uncertainties in hydro operations. A specific reservoir system in British Columbia was selected as to illustrate the model application. Results and analyses provided guidelines for evaluating and comparing alternative reservoir operating plans that incorporate reliability assessment and failure simulation. It is demonstrated that dam overtopping is more likely to occur due to a simultaneous occurrence of high inflow events and spillway gate failures than being caused by an extreme inflow event. The presented work highlights the needs to systematically collect and archive reliability data and to conduct reliability analysis for hydropower water release facilities whenever new information and data become available.

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Operating hydropower reservoirs with small storage capacity is a challenging task due to the fact that in a watershed system there usually exist multiple stakeholders with different and conflicting preferences and values. Consequently the process of planning for reservoir operation must be carried out with consideration of several, usually competing, objectives. This process becomes even more challenging during a high inflow or flooding event for three main reasons. First, the objective of minimizing adverse consequences of such an event is added to the set of objectives that the operator must deal with. Second, inflow forecast uncertainty-driven risks are highly intensified due to the high sensitivity of the outcomes to inflow forecasts. And third, the available time for making a decision is very short while comprehensive analysis is a necessity in order to make an informed decision regarding the best operational alternative. Under these circumstances, the best approach to confront this challenge could be developing a Risk-Informed Decision Making (RIDM) framework that provides operation planning engineers with a solid and pre-designed guideline to deal with the task of identifying the best operational alternative in an efficient and timely manner.The current study is an attempt to apply the virtual structure of a RIDM framework for the Cheakamus River system in British Columbia. The framework is a coherent assembly of a number of methods and tools we have either developed or utilized from the existing widely used methods and techniques in practice. The product of our work is an example of the necessary tools that need to be used to develop recommendations for operating Daisy Lake reservoir during a high inflow event in a manner that all the operational objectives are served in the best possible way. This is done while taking into account making trade-offs among competing objectives. We illustrate the practical applicability and merits of the framework through applying it to a historical high inflow period in October 2003. The outcome is near real-time decisions with less dependency on only planners’ judgement and more dependency on thorough and systematic analysis with consideration of human judgement and possible risk tolerances.

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Canada built and operates three large dams and the U.S. built and operates one dam in the Columbia River based on the Columbia River Treaty (CRT) which was signed in 1961 and ratified in 1964. Annual Operating Plan developed by two Entities does not include non-power requirements, unless they are mutually agreed upon by both Entities. Supplemental Operating Agreements (SOA) have been negotiated and implemented since the 1990s to meet the U.S. and the Canadian power, fish, wildlife and/or recreation needs. The objective of this research was to develop a multi-objective optimization model to deal with multiple and conflicting objectives. The Columbia River Treaty Model (CRTM) developed by BC Hydro was modified by this research to incorporate three non-power requirements that are agreed upon by both Entities. The new model, which utilized the Goal Programming technique to solve the multi-objective reservoir optimization problem, was used to perform a number of case studies in order to investigate the impacts of incorporating different non-power requirements onto the BC Hydro system. Specific minimum outflow at the border in January affects the level of fulfillment of three non-power requirements. The first requirement is the Flow Augmentation requirement to aid in the downstream migration of Salmon in the U.S. The second requirement is the flow requirements below the Arrow reservoir to protect Whitefish eggs during the spawning and hatching periods. The third requirement is the specific flow requirement to provide enough water cover for the Trout spawning downstream of Arrow. The model uses three prioritized objectives of which the Flow Augmentation and Whitefish are of highest priority followed by the Trout Spawning and the maximization of BC Hydro revenues. Four Arrow minimum flow scenarios were compared with the Treaty operation. The study results show that lowering the minimum Arrow flow limit in January increases the satisfaction level of the Flow Augmentation and Whitefish non-power requirements. However, it may be in conflict with the power requirement of meeting Pacific North-west winter peak loads. Unless additional flow is required for Flow Augmentation during April, it has no effect on Trout spawning.

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Hydro system operators are often confronted with a myriad of conflicting and challenging decision situations. In particular, managing hydroelectric facilities during high inflow or unusual events can be complex, time consuming and challenging. Most high inflow events that challenge operational planners are driven by hydrology, with either too much or too little water being available. Other factors such as unusual electricity market conditions, dam safety or equipment concerns also drive decision making. In a typical case operators try to balance multiple, and at times, competing objectives during high inflow events. In the case of high inflow subject flood events, Operation Planning Engineers are usually under time pressure to make decisions when the potential outcomes of different management options are highly uncertain. In such situations, planners must quickly make critical and important decisions taking into account the current state of the system and latest available information and forecasts. Their decisions can have environmental, social and financial consequences.The purpose of this research is to develop an effective tool for the Operation Planning Engineers in Generation Resource Management of BC Hydro (British Columbia Hydro and Power Authority), which can be quickly and efficiently used during high inflow events at some of BC Hydro facilities. We describe the process that we have developed to build a tool to implement a Structured Decision Making Framework for a typical BC Hydro facility. The tool addresses the inflow uncertainties associated with high inflow floods and includes multiple objectives that are difficult to measure by means of a common unit, which necessitated the development of utility functions and required a trade-off analysis to be carried out. In this paper we also describe a methodology to do the tradeoff analysis among the objectives.We present the results of the analysis for a flood event in the Cheakamus River, October, 2003. At the end of the project decisions made in real-time will be less dependent on the planner’s own risk tolerance and more aligned with corporate risk tolerances that are acceptable to senior management.

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The main objective of reservoir operation planning is to determine the amount of water releasedfrom a reservoir and the amount of energy traded in each time step to make the best use ofavailable resources. This is done by evaluating the trade-off between the immediate and thefuture profit of power generation. A set of constraints have to be met in operating a reservoirsystem such as the continuity equations, transmission limits, generation and reservoir limits,flood control limits and load resource balance. Another important issue that needs to beaddressed in these problems is uncertainty, which comes from lack of knowledge or certaintyabout the exact amount of an input parameter because of its spatial and temporal variability,inherent nature of a problem or parameter, errors in measurement due to human or technologyinaccuracy and other errors in modeling due to simplification or ignorance.This research successfully implements a Reinforcement Learning (RL) optimization algorithmincorporating some of the operating rules and flood control constraints of the Columbia RiverTreaty. It considers the main sources of uncertainty in operating a large scale hydropowersystem: market prices and inflows by using a number of scenarios of historical data on inflowand energy prices in the learning process. The RL method reduces the time and computationaleffort needed to solve the operational planning problem and can be used to determine the valueof water and marginal value of water for the BC Hydro system. The results suggest that the RLalgorithm can incorporate a typical flood control rules for multireservoir optimization problemsof this type.

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In the next few years, the province of British Columbia will experience the installation of significant amounts of wind power as part of BC Hydro calls for clean renewable energy resources. The inherent variability and uncertainty of wind power will impact the operation of the BC Hydro system. If the system loses some of its flexibility in the process of integrating more wind power, there are costs that need to be assessed and recognized. Of particular interest are the costs associated with incremental wind reserves to manage wind variability and the cost associated with foregoing day-ahead market opportunities due to the wind forecast error. Pumped-storage hydro systems have been proposed as a good technology to complement wind generation due to their ability to manage wind energy imbalances over time. This research investigated the feasibility of expanding an existing hydropower system by installing a pumped-storage hydro system to mitigate the impacts of integrating wind in a large scale hydro system. This study proposed the installation of an additional pump station, equipped with automatic generation control capabilities.Two optimization models were developed to assess the benefits of the pumped-storage hydro system and the impacts of wind integration: A long-term mixed integer optimization, and a short-term stochastic linear optimization models to simulate BC Hydro short-term operations considering different load and wind stochastic scenarios. Both models are an extension of the BC Hydro Generalized Optimization Model (GOM), which is a deterministic linear optimization model that has been used to assess many capital investments and water use planning studies for the BC Hydro system. The model proposed in this research included a stochastic extension of GOM.Optimization runs of the BC Hydro’s hourly system operation for one year, with and without the pumped-storage hydro system were carried out and their outcomes were compared to estimate the overall benefits of the pump-storage system. The results indicated that there are benefits of installing a pumped-storage hydro system in the BC Hydro system to manage and to reduce wind power integration impacts. The benefits increased as more wind power is installed in the BC Hydro system.

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