Andre Luiz Diniz

A Four-Dimensional Model of Hydro Generation for the Short-Term Hydrothermal Dispatch Problem Considering Head and Spillage Effects

The generation of a hydroelectric plant is a nonlinear function of the turbined outflow, storage and sometimes also of the spillage. Other aspects, such as forbidden operating zones and individual turbine efficiency curves, are also important. Although for the self-scheduling of a hydro plant a precise integer modeling of the hydro power production function (HPF) is convenient, in the security constrained short-term hydrothermal dispatch problem for large-scale systems a strategy which best balances an accurate representation with an acceptable computational burden is required. In this paper, a detailed review of different approaches to model the HPF is presented, and a new four-dimensional piecewise linear model is proposed. This model takes into account the water head as a function of forebay and tailrace levels and considers spillage effects. Nonconcave regions of the HPF are approximated by using convexification and regression techniques. A major advantage of this approach is to consider the influence of storage, turbined outflow and spillage in a single function that can be used in a straightforward way, instead of deriving several curves for different heads. Numerical results show the applicability of this approach to the day-ahead network constrained short-term hydrothermal dispatch problem of the large Brazilian system.

Short-Term Hydrothermal Dispatch With River-Level and Routing Constraints

Summary form only given. Recently, there has been a growing need to consider issues related to multiple uses of water-such as navigation, fishing, or recreation-in the operation planning of electrical power systems, specially in predominantly hydro systems. In short-term models, it is of particular importance to consider maximum/minimum values and ramp limits for the stream level of a river. However, in order to properly represent such constraints, it is also necessary to model in detail the river routing, i.e., the water wave propagation along the channels that connect reservoirs in cascade. This paper proposes a linear programming model to represent river stream-level constraints and river-routing effects in the short-term hydrothermal dispatch problem. Results show the high accuracy of the proposed approach to represent maximum hourly and daily river-level variations as well as the impacts of taking into account a detailed representation of river routing in the operation of hydrothermal systems.

A New Nested Benders Decomposition Strategy for Parallel Processing Applied to the Hydrothermal Scheduling Problem

Several optimization strategies are suitable for parallel processing, such as mathematical-programming based decomposition strategies, like Lagrangian relaxation and two-stage Benders decomposition, and evolutionary programming-like algorithms. In such cases, most subproblems can be solved independently by different processors. However, parallel processing is not suitable for some problems solved by nested Benders decomposition, due to the hierarchy between subproblems related to different time steps. In particular, for the deterministic case, parallel programming has been restricted to thread processing in lower-level machine computation and optimization solver codes. This paper proposes a new nested Benders decomposition strategy that is suitable for parallel processing, where time-coupled stages are solved simultaneously and an alternative procedure is employed to share initial conditions for the next stages as well as Benders cuts for the previous stages. The methodology is applied to the deterministic short term hydrothermal scheduling problem for the real large-scale Brazilian system, where the advantages of the proposed approach become more evident. In order to show the applicability of the method in low-budget and small parallel environments, the case study was processed with up to 24 process on multi-core computers.

A local branching approach for network-constrained thermal unit commitment problem under uncertainty

This paper addresses the day ahead network constrained thermal unit commitment problem under uncertainty. In this problem the electrical network is considered by a DC power flow model with phase angles represented directly into the model and the associated flow limit constraints dynamically introduced through an iterative process. The uncertainty regards to the stochastic demand to be supplied by thermal plants, possibly due to a configuration with high wind penetration. Two main contributions are presented: the first is a new compact mixed-integer formulation for unit commitment constraints such as minimum up/down times, by defining “multi-node constraints” that comprise integer variables related to all nodes in given sub-trees of the original scenario tree. The second is the application of a local branching strategy instead of a standard branch-and-cut algorithm to solve the problem. Computational experiments are carried out with an IEEE 118 buses system, assuming severe constraints on transmission lines capacities, in two scenarios trees for a 24 hour period.

An exact multi-plant hydro power production function for mid/long term hydrothermal coordination

The generation of a hydroelectric power plant is a nonlinear function of its storage and turbined outflow. Nonlinear, mixed-integer or linear programming models have been proposed to approximate this function in the context of hydrothermal coordination, usually with one function for each plant. This paper proposes a new exact “Multi-plant hydro production function (MHPF)”, which depends on the storage and discharge of a given reservoir power plant and comprises not only its generation but also the power output to all subsequent run-of-the-river plants until the next reservoir. Based on this function we build a piecewise linear model that can be embedded in stochastic linear programs for optimal hydrothermal coordination. We illustrate the proposed MHPF approach for real sets of cascaded hydro plants of the Brazilian System.

A decomposition scheme for Short Term Hydrothermal Scheduling problems suitable for parallel processing

This paper presents the application of the multi-stage Benders decomposition methodology to solve the Short Term Hydrothermal Scheduling problem with a smart definition of stages. The transmission network is represented in detail by a DC-linear model with losses, where the voltage phase angles are included directly in the optimization problem. The decomposition approach allows the application of parallel processing. Two cases are presented: the first one based on the IEEE 118 buses system, in order to assess the consistency of the methodology, while the second one is the actual Brazilian System, for performance analysis. The CPU time is reduced with the proposed methodology as compared to traditional Benders decomposition, while obtaining the same optimal solution for system operation.