By Mark Parrish
The study discussed in this article focuses on quantifying the consequences of an asset’s failure. The goal is to produce estimated daily costs of outages partitioned annually by month to better understand average and seasonal consequences for 54 of the U.S. Army Corps of Engineers’ hydropower facilities. In recognition that each plant and region has different access and quality of data available, the scope of the effort also includes a need to develop methodology that is consistent and reliably available across the nation.
In 2011, the Corps developed the Hydropower Modernization Initiative (HMI) to establish priorities for appropriated funding across the regions covered by the Western Area Power Administration, Southwestern Power Administration and Southeastern Power Administration. Projects in the Bonneville Power Administration region are funded directly through rates, rather than appropriations, for power-specific investments. This study considers plants included in the HMI program but is generally applicable to all Corps plants.
The study considers energy replacement value, greenhouse gas (GHG) emissions and the social cost of GHG emissions, all of which are consequences of unit outages. Energy replacement value is the cost to produce energy from alternative generating resources, and GHG emissions describe emissions generated from the fossil-fueled facilities used to replace the hydropower generation. The social cost of GHG emissions is an attempt to monetize the consequences of GHG emissions.
Factors related to unit outages
A unit outage may induce two outcomes: A loss in total generation or a shift from peak to off-peak generation. For hydropower systems, the consequence of unit outage is a function of a plant’s operating strategy, water availability, regional generation mix and regional electricity demand. These factors act together in determining unit outage magnitude and economic impact.
Hydropower plants can be referred to as run-of-river, peaking or semi-peaking. For run-of-river plants, a unit outage would most likely result in loss of generation. For peaking and semi-peaking plants, where storage is available, a unit outage may result in a shift from peak to off-peak generation.
A hydropower plant is either water- or capacity-constrained, and a unit outage tightens the capacity constraint. If water availability exceeds the capacity constraint, this would result in a consequence from a unit outage. If, however, water availability is below the capacity constraint, a unit outage would result in no consequences. Water availability is seasonal, which implies that unit outage consequences are also seasonal.
Regional generation mix
Regional generation mix reflects what generating resource would most likely be used to replace the generation lost because of a unit outage at a hydro plant. This affects the economic value of electricity and the possible environmental consequences from additional GHGs.
Regional electricity demand
As electricity demand increases in a region, more expensive generating units are used. This increases the value of generation lost as a result of a unit outage (i.e., if water availability was the same, a unit outage may have less economic impact in spring when compared to summer months, when electricity demand is higher). Similar to water availability, electricity demand is also seasonal.
The nearest representative optimization function takes as input daily average flow and reservoir elevations from historical data. From a set of representative flows, the optimization function looks to find the closest historical daily record that matches the input values.1
Methodology and modules
To take into consideration all of the factors listed above, four modules are developed. The first module takes historical daily flow and reservoir elevation data and shapes it into hourly flow distributions using current representative operating strategies. The second uses plant-level characteristics to apply outage constraints on the hourly flow and consequently hourly generation. The last two modules, energy replacement value and the social cost of carbon, provide the environmental and economic impacts of outages, taking into consideration regional energy demand and the regional generation mix.
Modules require the following data:
- Average daily hydrology — At least 15 years of average daily flow and reservoir elevations;
- Current representative hourly flow distributions — At least three years of hourly flow data out of the powerhouse to represent high, average and low water years;
- Plant level characteristics — Turbine types and size, turbine efficiency tables, and maximum and minimum plant hydraulic capacity;
- Regional emissions — Rate for 1 MWh of generation;
- Energy pricing — At least three years of historical hourly locational marginal pricing (LMP) values and current Energy Information Administration (EIA) forecast.
Modeling current hourly generation operations
To quantify the expected consequences of unit outages across a large ensemble of hydrologic conditions and current plant operation, at least 15 years of historic average daily flow and reservoir elevations were collected for each plant. Figure 1 shows average daily flows sectioned into hourly flow distributions using current operations. Tables are used to convert hourly flow into hourly generation using a power equation with generalized turbine efficiency.
The flow simulation model focuses on shaping the average daily flow values to hourly flow values. This model takes as input a daily average flow value and a daily average reservoir elevation. A historical representative hourly flow distribution is then matched to the average daily flow value using an exhaustive optimization algorithm that seeks to minimize the difference between the modeled flow and reservoir elevations from a set of historical values. Once the representative hourly flow distribution is applied to the average daily flow value, plant-level constraints (i.e., minimum and maximum hourly flow values) are enforced.
Applying hourly flow distribution and plant level constraints
Once the nearest representative day is matched to the modeled data, an hourly flow distribution is assigned to the modeled average flow. The representative flow distribution is the percent of average daily flow calculated over the 24-hour time period. This distribution is then applied to the input modeled daily flow.
Maximum powerhouse flow values are usually defined by the hydraulic capacity of the powerhouse, and minimum hourly flow constraints are generally required to satisfy environmental purposes and are generally seasonal.
Conditioned on meeting the minimum flow values, flow is sent through the powerhouse to meet the power demands of customers and these demands vary greatly throughout the day. The method of applying plant-level constraints keeps this variability by taking water from lower flow values (e.g., hours 23 and 24) to satisfy minimum flow constraints and adding surplus water that exceeds maximum hourly flow values to higher flow values (e.g., hours 16 and 17). The first step in accomplishing this task is sorting the flows from high to low, producing an hourly flow ranking.
Once the flow values are ranked, the model finds the first hourly flow ranking that does not satisfy the minimum flow requirement. If a flow ranking does not meet the minimum flow value, it looks for available water — water that exceeds minimum hourly flow constraint — moving down the hourly flow ranking.
The process is similar for hourly flow rankings that exceed the maximum flow values. Starting at hourly flow ranking No. 1, if a flow ranking exceeds the maximum flow constraint, it moves up the flow ranking until it finds a flow ranking that can utilize the surplus water.
Modeling changes in generation due to outage constraints
A unit outage may result in two different types of consequences; lost generation or shifts from higher valued peak generation, to lower valued off-peak generation. This can simulated by applying a capacity constraint on the modeled flow.
Logical unit refers to the average unit size for a particular plant. Corps hydropower plants often contain more than one family of turbines. These different families could cause a difference in capacity, efficiency and time in use between all of the plant’s units. In this regard, the value of some units may be higher than the value of others. This level of modeling would require greater detail, such as hourly unit scheduling, which are beyond the scope of this study.
A simplifying assumption is that unit outages are based on the concept of a logical unit. A single unit outage would be modeled as the reduction of the capacity of one logical unit, while a two-unit outage would be modeled as reduction of two logical units.
The redistribution of generation under capacity constraints from unit outages follows the assumption that generation follows the greater system demand. Plant operators will therefore redistribute water to those hours with available capacity and the next-highest market price.
Modeling shifts in hourly generation due to unit outages
The procedure in enforcing unit outages follows the same procedure discussed above in enforcing maximum hydraulic capacity. However, for this procedure the maximum hydraulic capacity is reduced by a number of logical units corresponding to the number of unit outages. The hourly generation is also computed as before, only this time using the constrained flows.
Calculating unit outage energy replacement value
This section describes the steps in assigning a monetary value to calculating unit outage replacement value using LMP to estimate marginal hourly energy prices. LMP is a computational technique that determines a shadow price (the estimated price of a good or service) for which no market price exists for an additional MWh of demand. Conversations with representatives of the plant’s power marketing agencies suggested the proper LMP hub for specific plants.
Because LMP values are only historical, other sources are required to develop energy price forecasts. Each year, EIA publishes an Annual Energy Outlook (AEO) that lists 30-year generation energy costs and contains forecasts for different electric market modules. The AEO also lists actual energy prices for the immediate three years prior to the forecast.
A unique shaping ratio should be defined to reflect hourly, weekly and seasonal variability. To reflect hourly variability, daily LMP values can be sorted from high to low (see Figure 2), similar to the sorting on hourly generation producing hourly ranked shaping ratios. Weekly variability is considered by computing shaping ratios for weekends and weekdays. Finally, seasonal variability is taken into account by computing shaping ratios for each month. These shaping ratios are computed as averages among dates with like hourly rankings, month, and weekday classification.
The procedure to align the hourly generation with the hourly energy price follows the assumption that the highest generation periods correspond to the highest energy prices, but this may not always be the case. A plant may also generate energy to satisfy environmental constraints or customer needs not aligned with system demand.
With this assumption, the procedure to calculate daily energy value is simply the product of the generation and its associated energy price. The daily energy replacement value for a unit outage is calculated as the difference between the all-units energy value and the corresponding unit outage energy value.
Quantifying outage GHG emissions and the social cost of carbon methodology
Avoiding emissions from fossil fuels is a major environmental benefit associated with hydropower generation. Quantifying avoided emissions depends on the generating resource mix of the power that is displaced by the hydropower project. Although monetizing the value of these increased emissions is wrought with uncertainty, it does provide a way to compare consequences of unit outages across different regions and to compare the addition of both financial and environmental consequences.
Because different regions have different generating resource mixes, this factor is regionally dependent. This factor may also be seasonally- or even hourly-dependent as different mixes of generating resources are required to meet demand.
The EPA’s eGrid is a comprehensive database of environmental attributes of electric power systems, incorporating data from several federal agencies. One field of data stored in the eGrid database is emission rates defined as pounds per MWh for three GHG: Carbon dioxide, methane and nitrous oxide among 26 eGrid sub-regions. These regions are constrained within a single Nuclear Energy Regulatory Commission region with similar emissions and generating resource mixes. These are further divided into baseload and non-baseload generating resources. Because hydropower is often used to replace the generating resources on the margin, this study uses the non-baseload emission rates.
Social cost of carbon
The social cost of carbon is an attempt to monetize the consequences of an incremental increase in carbon emissions for a given year. This estimate was developed by the Interagency Working Group on Social Cost of Carbon for the U.S. government with the intent to include this cost in cost-benefit analyses. Consequences included in this valuation include net agricultural productivity, human health, property damages from increased flood risk and the value of ecosystem services due to climate change.
The aging infrastructure of the Corps’ hydropower facilities coupled with financial and resource constraints makes the prioritization of hydropower investments imperative. The study’s methodology allows for objective measurements of consequences that sometimes defy initial intuition. For example, due to hydraulic capacity constraints a unit outage of a baseload plant may have much more severe consequences than a peaking plant, although its overall operations seem less lucrative. This objective approach allows for a more accurate representation of a plant’s overall risk. This study is updated annually to include current price forecast and hydrologic conditions as a part of a successful HMI program that has motivated both public and customer funding.
Mark Parrish is a mathematician for the U.S. Army Corps of Engineers’ Hydroelectric Design Center.
1View the original paper and full sets of mathematical equations and factors discussed in this article at http://bit.ly/2hrxvsG.
Additional Information on Quantifying The Cost of Unit Outages
Mark Parrish discussed the details of this study and what the future holds with regard to implementing the process with associate editor Gregory B. Poindexter. To listen to this audio file, log on to https://pennwell.box.com/v/UnitOutage.