wmpy-power 1.0.0

Estimates hydropower generation accounting for operating constraints and electricity grid operations.

wmpy_power

wmpy_power is a hydropower generation simulation model that uses a physically-based representation of hydropower generation. The model parameterizes production using physically-meaningful parameters that are calibrated using a reference generation dataset.

To Do List

• Write automated tests
• Example batch jobs for parallel BA

Documentation

Introduction

wmpy_power simulates hydropower generation using a physically-based representation of hydropower generation (Zhou et al., 2018). Hydropower generation is simulated using timeseries of inflow and storage, and plant characteristics including nameplate capacity, average head, and reservoir storage capacity (where applicable). Model parameters are calibrated to a reference monthly hydropower generation dataset - typically historical generation - using the shuffle complex evolution algorithm (SCE; Duan et al., 1993). A two-stage calibration is performed: first at the balancing authority (BA) scale, and second at the facility scale.

The model is designed to work with inflow and storage simulated by the mosartwmpy routing and water management model (Thurber et al., 2021), however is agnostic to the source of these data.

Calculations

wmpy_power uses a simple hydropower generation formula to calculate hydropower generation:

$$ P=\rho ghQ \eta \ (1) $$

Variable	Variable in Code	Definition	Units	Value
ρ	lumped in with gravitational acceleration; 9800	density of water	kg m-3	1000
g	lumped in with density of water; 9800	gravitational acceleration	m3s-2	9.81
h	plant_head_m	gross hydraulic head of the hydropower facility	m	plant-specific
Q	flow	turbine flow rate	m3s-1	plant-specific timeseries
η	not directly used; see below	non-dimensional efficiency term	–	plant-specific

This general formulation (equation 1) is modified for use in the model to accommodate parameters being calibrated, and to accommodate two cases of hydropower generation, run-of-river (ROR) plants, and plants associated with reservoirs. For both cases of generation, the non-dimensional efficiency term (η) is replaced with a combined efficiency and bias correction factor f_b:

$$ P=\rho ghQf_b \ (2) $$

Variable	Variable in Code	Definition	Units	Value	Range
fb	efficiency_spill	non-dimensional efficiency term and bias correction factor	–	balancing authority-specific; calibrated in step one	0.5-1.5

This efficiency term is calibrated at the BA level in step one of the calibration. NOTE: alternative groupings of plants can be used in place of BAs; the BA variable is used by the code, but values can be replaced with other grouping identifiers, for example HUC4 basins.

Q is adjusted to account for both plant-specific maximum flow limits and spill. Maximum flow limits are imposed by limiting Q to a maximum value using Q_max where:

$$ Q_{max} =S_f \ (3) $$
$$ Q =min(Q, Q_max) \ (4) $$

Variable	Variable in Code	Definition	Units	Value	Range
Qmax	max_discharge	density of water	kg m-3	1000
S	nameplate_capacity_MW	nameplate capacity	W	plant-specific; from PLEXOS
fm	efficiency_penstock_flexibility	penstock intake scale factor	–	plant-specific; calibrated in step two	0.5-1.5
g		gravitational acceleration	m3s-2	9.81
h	head	hydraulic head of the dam	m	plant-specific

Q is adjusted for spill by month using plant-specific monthly spill correction factors developed in step two of the calibration. These spill correction factors are applied as:

$$ Q_sc,m =Q_m(1 -f_f,m); m = {1,2, ..., 12} \ (5) $$

Variable	Variable in Code	Definition	Units	Value	Range
fs,m	monthly_spill	monthly spill correction factors	–	plant-specific; calibrated in step two	0-1
fp	penstock_flexibility	penstock flexibility of handling max flow	–	plant-specific; calibrated in step two	0.5-1.5

Run-of-River (ROR) Facilities

Generation for ROR plants is calculated using the hydropower generation formula and setting the head (h) to a fixed value equal to the dam height.

Reservoir Facilities

Generation for hydropower plants with reservoirs is calculated using the hydropower generation formula, with the head estimated using simulated volumetric storage, total volumetric capacity, and assuming that the shape of the reservoir is a tetrahedron:

$$ h=H^3\sqrt{\frac{v}{v_{max}}} \ (6) $$

Variable	Variable in Code	Definition	Units	Value
h	height	hydraulic head of the dam	m	plant-specific
H	plant_head_m	dam height	m	plant-specific
V	storage	reservoir storage	m3	plant-specific timeseries
Vmax	storage_capacity_m3	reservoir volumetric capacity	m3	plant-specific

Shuffled Complex Evolution (SCE) Implementation

SCE is used to implement a two-step multiscale calibration that produces the inputs required for the hydropower generation formula (equation 2). Step one of the calibration is to address the errors in annual hydro-meteorological biases at the scale of hydrologic regions. The objective function used in step one is to minimizes the mean absolute error between annual observed potential generation and annual simulated potential generation at the BA level:

$$ PG_{BA,sim} = \sum_{i=1}^n \rho gh_i Q_i f_{b,i} \ (6) $$ $$ PG_{BA,obs} = TL_{2010} \times 0.04 + \sum_{i=1}^n G_{obs,i} \ (7) $$ $$ MAE_{PG} = \sum_{i=1}^n \lvert PG_{BA_{sim,i}} - PG_{BA_{obs,i}} \rvert \ (8) $$

Potential generation is computed as:

$$ PG = G + R \ (10) $$ $$ R = 0.04TL \ (11) $$

Variable	Definition	Units	Value
PG	potential generation	MWh	computed at the BA scale
G	actual generation	MWh	input at the plant scale
R	operating reserve	MWh	calculated as 4% of the TL
TL	total load	MWh	mean of annual generation of years provided

The operating reserve percentage is set to as default to 4% of total load in model.py (operating_reserve_percent). This can be changed in model configuration.

Step two of the calibration seeks to reflect the complexity in monthly multi-objective reservoir operations and daily generation constraints. It works to improve seasonal variation for each power plant by calibrating a penstock flexibility factor (fp) and monthly spill correction factors (fs,1, fs,2,…, fs,12). The objective function used in step two is to minimize the Kling-Gupta Efficiency between simulated monthly power generation and observed monthly power generation at the plant level:

$$ KGE=1-\sqrt{(r-1)^2 + \left(\frac{sd(G_{sim})}{sd(G_{obs})}\right)^2 + \left(\frac{mean(G_{sim})}{mean(G_{obs})}\right)^2}\ (12) $$ $$ r = cor(G_{sim}, G_{obs}) \ (13) $$

Variable	Definition	Units	Value
Gsim	simulated monthly generation	MW	computed at the plant scale
Gobs	observed monthly generation	MW	input at the plant scale

Model Setup

The model repository contains documentation and example code for setting up and running the model. It is built as a Python package and the scripts can be imported into a Python environment.

Model Inputs

Model inputs are specified in the run script.

Input		Description	Format
daily simulated flow and storage	simulated_flow_and_storage_glob	daily simulated flow and storage, typically from a MOSART simulation, for each hydropower plant	.parquet
observed monthly power generation	observed_hydropower_glob	observed monthly hydropower generation for each hydropower plant	.parquet
reservoir and plant parameters	reservoir_parameter_glob	reservoir and hydropower plant static parameters	.parquet

Many configuration options are available for running the model. These options can be specified in a configuration yaml file or passed directly to the model initialization method, or both (the latter takes precedence). Most options have sensible defaults, but a few are required as discussed below. For the full list of configuration options, see the config.yaml file in the repository root.

Dependencies are listed in the setup.cfg file. To install dependencies, run pip install -e . from the root directory of this repository.

There are two ways to run the model. The simplest is to provide a configuration file and run the model directly:

config.yaml

# first year of calibration data
calibration_start_year: 1984
# last year of calibration data
calibration_end_year: 2008
# balancing authority or list of balancing authorities to calibrate
balancing_authority:
  - WAPA
# glob to files with simulated daily flow and storage for plants in the balancing authorities
simulated_flow_and_storage_glob: ./inputs/**/*flow*storage*.parquet
# glob to files with observed monthly hydropower for plants in the balancing authorities
observed_hydropower_glob: ./inputs/**/*monthly*obs*.parquet
# glob to files with reservoir/plant parameters for plants in the balancing authorities
reservoir_parameter_glob: ./inputs/**/*PLEXOS*.parquet

python wmpy_power/model.py config.yaml

Alternatively, the model can be invoked from a python script or console:

from wmpy_power import Model

# you can initialize the model using the configuration file:
model = Model('config.yaml')
# or directly:
model = Model(
  calibration_start_year=1984,
  calibration_end_year=2008,
  balancing_authority=['WAPA'],
  simulated_flow_and_storage_glob='./inputs/**/*daily*flow*storage*.parquet',
  observed_hydropower_glob='./inputs/**/*monthly*obs*.parquet',
  reservoir_parameter_glob='./inputs/**/*PLEXOS*.parquet',
)
# or both (keyword arguments take precedence)
model = Model(
  'config.yaml',
  balancing_authority=['CAISO'],
  output_type='csv',
)

# run the model (this will write the calibrations to file but also return a DataFrame
calibrations = model.run()

# plot each plant's modeled hydropower versus observed hydropower
model.plot(calibrations)

# get modeled generation for the calibrations and write to file
generation = Model.get_generation(
  './**/*_plant_calibrations.csv',
  './inputs/*reservoir_parameter*.parquet',
  './inputs/**/*daily*flow*storage*.parquet',
)

By default, the model writes the calibrated parameters to a parquet file per balancing in the current working directory, but this behavior can be overridden using the output_path and output_type configuration options. So far only "csv" and "parquet" formats are supported.

Input Files

Daily flow and storage parquet files are expected to have these columns:

column	example	units
date	1980-01-01	date
eia_plant_id	153	integer
flow	461.003906	m^3 / s
storage	1.126790e10	m^3

Monthly observed hydropower parquet files are expected to have these columns:

column	example	units
year	1980	integer
month	1	integer
eia_plant_id	153	integer
generation_MWh	38221.193	MWh

Reservoir/plant parameter parquet files are expected to have these columns:

column	example	units
eia_plant_id	153	integer
balancing_authority	WAPA	string
name	1980	integer
nameplate_capacity_MW	1	MW
plant_head_m	5123.3	m
storage_capacity_m3	1.5e10	m^3
use_run_of_river	True	boolean

Notebook

The tutorial.ipynb file provides a Jupyter notebook illustration of running the model and plotting results.

Working with Parquet files

It's easy to read and write parquet files from pandas, just pip install pyarrow or conda install pyarrow, then:

import pandas as pd
df = pd.read_parquet('/path/to/parquet/file.parquet')
df['my_new_column'] = 42
df.to_parquet('/path/to/new/parquet/file.parquet')

Legacy Files

wmpy_power was originally developed in MATLAB. The model provides a utility to convert Excel and MATLAB files to parquet files. This functionality can also be used to build inputs in Excel and convert them into parquet.

from wmpy_power import Model

Model.update_legacy_input_files(
  daily_flow_storage_path='/path/to/flow/storage/matlab/file.mat',
  reservoir_parameters_path='/path/to/plexos/parameters/excel/file.xlsx',
  monthly_observed_generation_path='/path/to/observed/generation/excel/file.xlsx',
  daily_start_date='1980-01-01', # for daily flow/storage, since this isn't mentioned in the file itself, have to assume a start date
  monthly_start_date='1980-01-01', # for monthly observed hydro, since this isn't mentioned in the file itself, have to assume a start month
  output_path=None, # defaults to the same place as the input files, but with the .parquet extension
  includes_leap_days=False, # whether or not the daily data includes entries for leap days (Tian's files don't)
)