Hydropower is an important renewable energy resource. It is low-carbon, emits nearly no
particulate pollution, can ramp quickly, and is capable of storing energy across many hours or
days. While it is a very valuable resource by itself, hydropower can also serve as a key enabler
for the increased penetration of non-dispatchable renewable energy resources like wind and solar
power.
This project focused on developing an optimization-based coordinated control framework for a
hydropower cascade. It consisted largely of two parts. The first is the development of the
coordination scheme. The second is the simulation and state estimation tools that were developed
to allow comparisons between historical operations and the operations dictated by the
coordination scheme.
The coordinated control scheme that we developed is based on a control technique known as
Model Predictive Control (MPC), wherein a linear state space model is designed to model the
hydraulics of a hydropower cascade. Here, the hydraulics model describes how water flows in a
hydropower cascade change the reservoir elevations behind each hydropower plant. The model
accounts for the delay between water discharged from the upstream plant affecting the forebay
elevation of the downstream plant.
The control scheme also accounts for the non-linear character of tailrace elevations. There is an
obvious relationship between the amount of water discharged into the tailrace and the tailrace
elevation. Our modeling work takes that a step further by identifying the conditions that lead to
encroachment and modeling encroachment. Encroachment is when the downstream forebay
backs up into the upstream tailrace, causing the tailrace elevation to be higher than it would be
otherwise.
The optimization scheme also accounts for the relationship between turbine discharge, hydraulic
head, and powerhouse generation in a hydropower plant. Turbine discharge and hydraulic head
are mapped to a corresponding amount of powerhouse generation using a three-dimensional
piecewise planar function. This function is fit to historical operations data. Since the relationship
between the three variables can be represented using a set of linear functions, the model for
hydropower production can be integrated into a linear or quadratic program. This results in an
optimization model that is both fast and accurate, an improvement over other coordinated control
schemes that are based on nonlinear or mixed-integer programming.
The objective function was formulated to minimize the sum of the squared turbine discharge and
spill for each hydropower plant. The weights were chosen such that water was preferentially
discharged from large surface area reservoirs to small surface area reservoirs. This allocates a
certain volume of water such that it results in the maximum total hydraulic head. Weighting
turbine discharges in this way is unique in the hydropower optimization literature.
We tested the coordinated control scheme on the Mid-Columbia hydropower system. The MidColumbia consists of seven dams on the Columbia River in Eastern Washington State. Historical
data on system operations allowed us to benchmark the performance of our coordination scheme
with actual system operations. Further data was provided that allowed us to properly calibrate the
parameters of our model, including forebay and tailrace curves, travel times, and hydropower
production functions.
Simulations were conducted for a five-day period with five-minute time resolution. The results
of our simulations, in brief, can be condensed into four areas.
1. The hydraulic potential of the system (H/K) increased steadily over the course of the
simulations. At the end of the simulation period, the total system H/K was 0.6% higher
than in the historical case. This translates to several feet of additional hydraulic head.
2. The net energy stored in the cascade increased. Overall, the net energy benefit was 1708
MWh, or 0.33% of the total energy generated during the simulation period. In general,
Grand Coulee ran an energy deficit (i.e., its forebay was lower in the optimized case than
the historical case) and the remaining hydropower plants ran an energy surplus.
3. Ramping was reduced substantially. Quantitative measures indicated that ramping
decreased substantially at every hydropower plant besides Grand Coulee. Qualitatively,
the discharge profiles were much smoother in the optimized case than in the historical
case. This method of operation could have substantial (but uncertain) benefits to
hydropower plant owners and operators due to less unit cycling and ramping, which
results in lower maintenance and repair costs.
4. System constraints were satisfied. The Mid-Columbia system is constrained at many
times of the year due to environmental limits on turbine discharge, spill, and flow
ramping. These limits are designed to ensure the health of salmon runs on the Columbia
River and the spawning areas in the Hanford Reach downstream of Priest Rapids. One of
the primary benefits of doing coordinated control in an optimization framework is that
system constraints can be explicitly obeyed. This ensures that regulatory and legal
bounds on system operations are satisfied completely.
The second part of the research involved the development of a state estimation procedure for a
hydropower cascade. Evaluating the coordinated control scheme necessitated developing a state
estimation procedure to reconcile measured values of turbine discharge, spill, and forebay
elevation. In lieu of being able to test the outputs of the coordinated control scheme on the actual
Mid-Columbia system or on a high-fidelity simulator, an inherently inaccurate computer model
must be used. This model will contain some modeling errors. Likewise, the measured flows and
forebay elevations can be biased and noisy.
These biases and noise levels are unknown and, a priori, we do not know which values can be
trusted and to what extent. The state estimation procedure takes these values and the hydraulic
model, and adjusts the measurements such that the model is open-loop stable and the estimated
measurements are consistent with each other. The general idea is that one flow measurement is
assumed to be the true flow through the system, and the other flows (upstream and/or
downstream) are adjusted to reduce the residual error between the estimated flow and the
measured flow. Constraints are added to the procedure to ensure that the estimated flow profile is
similar to the measured flow profile. Results are given demonstrating the practical efficacy of the
proposed state estimation method.
