Cascaded Hydro Systems Research Articles

Insights from a Comprehensive Capacity Expansion Planning Modeling on the Operation and Value of Hydropower Plants under High Renewable Penetrations

This paper presents a quantitative assessment of the value of hydroelectric power plants (HPPs) in power systems with a significant penetration of variable renewable energy sources (VRESs). Through a capacity expansion planning (CEP) model that incorporates a detailed representation of HPP operating principles, the study investigates the construction and application of HPP rule curves essential for seasonal operation. A comparative analysis is also conducted between the proposed rule curve formulation and alternative modeling techniques from the literature. The CEP model optimizes installed capacities per technology to achieve predefined VRES penetration targets, considering hourly granularity and separate rule curves for each HPP. A case study involving twelve reservoir hydropower stations and two open-loop pumped hydro stations is examined, accounting for standalone plants and cascaded hydro systems across six river basins. The study evaluates the additional generation and storage required to replace the hydropower fleet under high VRES penetration levels, assessing the resulting increases in total system cost emanating from introducing such new investments. Furthermore, the study approximates the storage capabilities of HPPs and investigates the impact of simplified HPP modeling on system operation and investment decisions. Overall, the findings underscore the importance of reevaluating hydro rule curves for future high VRES penetration conditions and highlight the significance of HPPs in the energy transition towards carbon neutrality.

Short-Term Scheduling of Expected Output-Sensitive Cascaded Hydro Systems Considering the Provision of Reserve Services

The integration of large-scale wind and solar power into the power grid brings new challenges to the security and stability of power systems because of the uncertainty and intermittence of wind and solar power. This sensitive expected output has real implications for short-term hydro scheduling (STHS), which provides reserve services to alleviate electrical perturbations from wind and solar power. This paper places an emphasis on the sensitive expected output characteristics of hydro plants and their effect on reserve services. The multi-step progressive optimality algorithm (MSPOA) is used for the STHS problem. An iterative approximation method is proposed to determine the forebay level and output under the condition of the sensitive expected output. Cascaded hydro plants in the Wujiang River are selected as an example. The results illustrate that the method can achieve good performance for peak shaving and reserve services. The proposed approach is both accurate and computationally acceptable so that the obtained hydropower schedules are in accordance with practical circumstances and the reserve can cope with renewable power fluctuations effectively.

Stochastic daily hydrothermal scheduling based on decomposition and parallelization

This paper studies the stochastic short term hydrothermal scheduling of systems that have a significant contribution from controllable reservoirs, focusing on the reservoirs’ operation policy when non-linearity and deployment of supplementary reserves at the real operation stage are modeled. Wind power and forced outages of power plants and transmission lines are treated as stochastic variables, and the total reserve is an endogenous variable to the model. The problem includes cascaded hydro systems with head-sensitive plants, a DC power flow representation with nonlinear transmission losses, and four types of operating reserves; and it aims at pre-positioning generation and reserves schedules in the light of the expected deployment of operating reserves throughout the day. To solve the optimization problem, a hybrid scheme elaborated from outer approximation and Benders decomposition is applied. The proposed solution method is tested in a real-size system, where its effectiveness, in terms of computational speed and accuracy, is demonstrated.The main nomenclature used is presented next. Other auxiliary variables, coefficients, dual variables and scalars are detailed within the section they are mentioned.

Dynamic incorporation of nonlinearity into MILP formulation for short-term hydro scheduling

Optimization tools are widely used for solving the short-term hydro scheduling (STHS) problem in a cascaded hydro system. In a mixed integer linear programming (MILP)-based formulation, the nonlinear and non-convex hydropower production function (HPF) is represented by piecewise linear approximation. However, instead of using a set of predefined curves with static breakpoints or a preprocessing phase to define the complete relationship between the power output, the net head, and the water discharge, this paper proposes a novel method in which the breakpoints in the linearization are determined dynamically, taking into account the time-varying head effect, intake loss, penstock loss, tailrace loss, and head-dependent turbine efficiency. Only one binary variable is needed to indicate the on/off status and power generation of a unit per period. Furthermore, there are few studies available on how to represent the HPF precisely for the hydraulic system where penstocks are shared by multiple generating units. In this paper, we investigate three heuristics to explicitly incorporate the nonlinear and state-dependent power loss in shared penstocks into the STHS problem. The method and heuristics have been implemented in an operational STHS tool used by many hydropower producers in Nordic countries. We use a simple hydro system to illustrate the method and heuristics and a real hydro system in Northern Norway to study calculation efficiency and solution quality. The numerical results indicate that the proposed method can precisely represent the head-dependent and nonlinear operating characteristics of the generating units. The accurate modeling of a system with multi-level shared penstock configurations is crucial for obtaining the optimal unit commitment. The heuristics can effectively handle the power loss in shared penstock in various operating conditions.

An efficient stochastic algorithm for mid-term scheduling of cascaded hydro systems

Due to the stochastic and correlated attributes of natural inflows, the mid-term generation scheduling problem for cascaded hydro systems is a very challenging issue. This paper proposes a novel stochastic optimization algorithm using Latin hypercube sampling and Cholesky decomposition combined with scenario bundling and sensitivity analysis (LC-SB-SA) to address this problem. To deal with the uncertainty of natural inflows, Latin hypercube sampling is implemented to provide an adequate number of sampling scenarios efficiently, and Cholesky decomposition is introduced to describe the correlated natural inflows among cascaded stations. In addition, to overcome the difficulties in solving the objectives of all the scenarios, scenario bundling and sensitivity analysis algorithms are developed to improve the computational efficiency. Simulation results from both two-station and ten-station systems indicate that the proposed method has the merits in accuracy as well as calculation speed for the mid-term cascaded hydro generation scheduling. The consideration of natural inflow correlation makes the formulated problem more realistic.

A risk dispatching model with Muskingum constraints for cascaded hydro systems

A risk dispatching model for short‐term cascaded hydro scheduling during high‐water season is proposed in this paper taking into consideration of uncertainty factors and the process of water flow. The uncertainty of natural inflow and market price is simulated by the multi‐scenarios method. The conditional value at risk (CVAR) is introduced to quantify the risk caused by these uncertainties. In the objective function, the added CVAR represents the risk preference of the hydropower producer. Based on the degree of risk aversion of the producer, the generation profit and risk are coordinated. In addition, the Muskingum model is used to formulate the process of water flow between upstream and downstream stations. A mixed‐integer linear programming model of short‐term cascaded hydro system scheduling in the high‐water season is developed and solved. Numerical studies demonstrate that the proposed approach can balance the risk and generation profit in the high‐water season and the model with the Muskingum constraint is more refined. © 2018 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A successive approximation approach for short-term cascaded hydro scheduling with variable water flow delay

In cascaded hydro systems, water delay time is a very important factor that requires coordination between upstream and downstream reservoirs. Due to the nonlinear characteristics of the water delay time, modeling and solving short-term cascaded hydro scheduling (STCHS) is a very challenging task. This paper proposes a novel STCHS model with continuous variation of water delay time to describe real-world operations in detail. The proposed model includes a nonlinear function related to water delay time. A successive approximation (SA) approach is developed to address the nonlinearity by iterative calculation, making the problem tractable. The proposed model and method are validated with two-reservoir and ten-reservoir systems. Numerical results demonstrate that the proposed method produces more realistic results than existing methods when dealing with STCHS problems.

Strategic bidding for price-maker producers in predominantly hydroelectric systems

This paper proposes an equilibrium model to determine price and quantity strategic bids for generation companies participating in a day-ahead electricity market, with predominantly hydroelectric generation. Each agent aims to maximize its profit by solving a bi-level optimization problem, where the upper level represents the producer revenue maximization problem, while the lower one consists of minimizing the cost of system operation, faced by the independent system operator. Price-maker companies operating both hydro and thermal plants are considered in a cascade hydro system with reservoirs managed by different owners. Consequently, a novel approach is proposed to decouple the first and second levels of the problem. We present an individual plant modeling, where the main constraints related to a hydrothermal system are considered. Through the utilization of the Karush–Kuhn–Tucker optimality conditions, the bi-level optimization model is converted to a single level nonlinear problem, known in literature as a mathematical program with equilibrium constraints (MPEC). To face the difficulties of this nonlinear, nonconvex, multi-stage problem, the MPEC complementarity conditions are replaced by the strong duality condition. Moreover, competition among several leaders is modeled as an iterative procedure, and the methodology is applied in two systems with data and configurations derived from the Brazilian hydrothermal system.

Optimal Hydro-Wind Power Generation for Day-Ahead Pool Market

Wind power production is uncertain. The imbalance between power committed and delivered on pool markets produces increased costs on the system, which must be paid by defaulting producers, decreasing their revenues. In order to invert this situation wind producers may submit their bids join with hydro resources, due to their availability. This paper proposes an optimization technique regarding the maximum benefit for both producers, taking into account the wind unpredictability. A cascaded hydro system is considered.

Risk-Constrained Scheduling and Offering Strategies of a Price-Maker Hydro Producer Under Uncertainty

This paper presents a stochastic mixed-integer linear programming (SMILP) approach to maximize total expected profit of one price-maker hydro producer in a pool-based electricity market. Head dependence, commitment decisions, discharge ramping, startup costs and forbidden zones are all effectively handled in our approach. Uncertainty about the competitors' offers is adequately represented by residual demand curves (RDCs) scenarios. The management of risk is suitably addressed by conditional value-at-risk (CVaR) to provide the efficient frontier, i.e., the solutions set for which the expected profit may not be augmented without enlarging the variance of profit. Appropriate offering strategies to the pool are also developed, consisting of supply functions built for different risk levels. A representative cascaded hydro system with 7 reservoirs is considered to analyze and compare risk-neutral versus risk-averse results.

Risk-averse profit-based optimal operation strategy of a combined wind farm–cascade hydro system in an electricity market

There is a trend toward direct participation of wind farms in electricity markets. However, wind power is inherently intermittent and cannot be accurately predicted even in short time; thus increasing the imbalance costs paid by wind farm owners. To cope with these problems, some techniques have been proposed in literature including wind farm coupling to hydro units, energy storage facilities, and constructing a virtual power plant (VPP). This paper presents a stochastic profit-based model for day-ahead operational planning of a combined wind farm–cascade hydro system. The generation company (GenCo) that owns the VPP considers a portion of its hydro plants capacity to compensate the wind power forecast errors. The proposed optimization problem is a mixed integer linear programming (MILP), formulated as a two-stage stochastic programming model. The day-ahead scheduling is a here and now decision and the optimal operations of facilities are resources variables. In order to protect the GenCo against low price scenarios and wind power variation, the conditional value at risk (CVaR) is used as the risk aversion criterion. The proposed model is successfully applied to a real case study and the results are presented and discussed. The results are illustrated varying in the risk aversion level and the penalty coefficients for negative/positive imbalances. It is shown that the bidding strategy of the GenCo varies significantly depending on the chosen penalty market mechanism.

Application of Chaotic Univariate Marginal Distribution Algorithm to Economic Dispatch Control of Cascade Hydropower Plants

The economic dispatch control of cascade hydropower plants is a large scale non-linear constrained optimization problem, which plays an important role in cascade reservoirs daily optimal. This paper proposes a chaotic univariate marginal distribution algorithm (CUMDA) to solve the economic dispatch problem of cascade hydropower plants. In the proposed method, a chaotic search is integrated with univariate marginal distribution algorithm (UMDA) to effectively avoid premature convergence, chaotic sequences combine with adaptive approach are applied to help algorithm escape from local optimal trap. The feasibility of the proposed method is demonstrated for economic dispatch control of a test cascade hydro system. The simulation results show that the proposed method can obtain higher quality solution.

Scheduling of a hydro producer considering head-dependency, price scenarios and risk-aversion

In this paper, a mixed-integer quadratic programming approach is proposed for the short-term hydro scheduling problem, considering head-dependency, discontinuous operating regions and discharge ramping constraints. As new contributions to earlier studies, market uncertainty is introduced in the model via price scenarios, and risk aversion is also incorporated by limiting the volatility of the expected profit through the conditional value-at-risk. Our approach has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, requiring a negligible computational time.

Optimal hydro scheduling and offering strategies considering price uncertainty and risk management

Hydro energy represents a priority in the energy policy of Portugal, with the aim of decreasing the dependence on fossil fuels. In this context, optimal hydro scheduling acquires added significance in moving towards a sustainable environment. A mixed-integer nonlinear programming approach is considered to enable optimal hydro scheduling for the short-term time horizon, including the effect of head on power production, start-up costs related to the units, multiple regions of operation, and constraints on discharge variation. As new contributions to the field, market uncertainty is introduced in the model via price scenarios and risk management is included using Conditional Value-at-Risk to limit profit volatility. Moreover, plant scheduling and pool offering by the hydro power producer are simultaneously considered to solve a realistic cascaded hydro system.

Mixed-Integer Nonlinear Programming Approach for Short-Term Hydro Scheduling

This paper is on the problem of short-term hydro scheduling, particularly concerning a head-sensitive hydro chain. A novel mixed-integer nonlinear programming approach is proposed for optimizing power generation efficiency. The proposed approach considers not only the nonlinear dependence between power generation, water discharge and head, but also start-up costs for the hydro units and discontinuous operating regions, in order to obtain more realistic and feasible results. Numerical results based on one of the main Portuguese cascaded hydro systems illustrate the proficiency of the proposed approach.

Scheduling of head-dependent cascaded reservoirs considering discharge ramping constraints and start/stop of units

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning head-dependent reservoirs under competitive environment. We propose a novel method, based on mixed-integer nonlinear programming (MINLP), for optimising power generation efficiency. This method considers hydroelectric power generation as a nonlinear function of water discharge and of the head. The main contribution of this paper is that discharge ramping constraints and start/stop of units are also considered, in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve two case studies based on Portuguese cascaded hydro systems, providing a higher profit at an acceptable computation time in comparison with classical optimisation methods based on mixed-integer linear programming (MILP).

Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to earlier studies, we model the on–off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas. Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper. Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement.

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.

Scheduling of Head-Sensitive Cascaded Hydro Systems: A Nonlinear Approach

In this paper, we propose a novel nonlinear approach to solve the short-term hydro scheduling problem under deregulation, considering head-dependency. The actual size of hydro systems, the continuous reservoir dynamics and constraints, the hydraulic coupling of cascaded hydro systems, and the complexity associated with head-sensitive hydroelectric power generation still pose a real challenge to the modelers. These concerns are all accounted for in our approach. Results from a case study based on one of the main Portuguese cascaded hydro systems are presented, showing that the proposed nonlinear approach is proficient.

Nonlinear optimization method for short‐term hydro scheduling considering head‐dependency

AbstractThis paper is on the problem of short‐term hydro scheduling, particularly concerning head‐dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head‐dependency is considered on short‐term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head‐dependency. Copyright © 2008 John Wiley & Sons, Ltd.