This paper explores potential changes in reservoir operating rules for a series of five peaking hydropower facilities on the Connecticut River undergoing FERC relicensing that should complete in 2019. This paper evaluates the trade-offs between two primary goals: maximizing revenues from hydroelectric power generation and returning the river to a more natural flow regime. These trade-offs are assessed using the Connecticut River Hydropower Operations Program (CHOP), a linear programming (LP) optimization model applied at an hourly time-step to capture the sub-daily effects to the flow regime. The model objective function is formulated to maximize hydropower revenues with respect to historical regional energy price data and is demonstrated to accurately mimic hydropeaking operating conditions and match historical power generating rates.

A case study compares modeled hydropower operating conditions between current hydropeaking operations and a strict run-of-river condition, where dam inflows must be directly released as outflows at all times. Analysis suggests that the run-of-river condition would result in a total economic loss of 7-9% of average annual revenues at the four mainstem facilities and as much as 17% at the larger, pumped-storage facility. However, an exploration of operating revenue losses at the pumped-storage facility suggests that there is potential for reoperations within the run-of-river operating condition to substantially reduce these losses. The run-of-river operation is demonstrated to improve the Connecticut River’s flow regime on the sub-daily time scale, with significant reductions in rates of change in flows to levels that approach those observed at a nearby unaltered location. The modeled improvements to the flow regime demonstrate the merit of this run-of-river condition as a potential reoperation for the hydropower system.

]]>The minimize energy and MINIMAX formulations were applied to four test models: a confined, homogeneous aquifer with two wells; a confined, homogeneous aquifer with 20 wells; a confined, heterogeneous aquifer with 20 wells; and an unconfined, homogeneous aquifer. The MINIMAX formulation produced the same results as the minimize energy formulation when the non-pumping lifts were the same. As the non-pumping lifts varied, the MINIMAX formulation deviated from the minimize energy formulation.

A case study of the Lancaster subbasin of Antelope Valley, California, was used to further test the minimize energy and MINIMAX formulations. Two minimize energy formulations were examined, the first lifting water to the ground surface elevation at each well and the second lifting the water to a single reference elevation that took the value of the maximum ground surface elevation that was used in the first formulation. The MINIMAX formulation was applied to the case where the water was lifted to the reference elevation. The difference in total energy between the MINIMAX and minimize energy formulations was less than 10%, but the distribution of pumping among the wells varied greatly.

]]>This work introduces a new type of variable to GWM, called a state variable, which is defined as either a hydraulic head or streamflow type variable. The value of the state variables are entirely dependent on the flow-rate variables and are calculated using the response matrix approach. State variables may be included in the objective function and summation constraints in this new MF2005-GWM version 2.0. The mathematical formulation, implementation, and sample problems are included to describe the theory and use of state variables.

Additional functionality is added to GWM in a Beta version for the capability to solve quadratic programming problems. In version 1.1.1 of GWM, the objective function must be a linear sum of decision variables. The addition of the state variable package in version 2.0 expands the definition of the objective to allow linear sums of state variables. The expanded capability to quadratic terms in the objective is motivated by the desire to represent energy costs, which are a function of the product of hydraulic head (a type of state variable) and flow-rate variables. This report includes the motivation, mathematical development, implementation, verification and a sample problem for a version of GWM including quadratic objective terms.