Abstract
Using wind-availability forecasts in day-ahead unit commitment can require expensive real-time operational adjustments. We examine the benefit of conducting interim recommitment between day-ahead unit commitment and real-time dispatch. Using a simple stylized example and a case study that is based on ISO New England, we compare system-operation costs with and without interim recommitment. We find an important tradeoff—later recommitment provides better wind-availability forecasts, but the system has less flexibility due to operating constraints. Of the time windows that we examine, hour-20 recommitment provides the greatest operational-cost reduction.
WIND generation increases supply variability and uncertainty, which requires changing power-system operations to ensure real-time balance between energy supply and demand [
The literature studies means of mitigating operational wind-integration costs. One approach uses synergistic technologies, e.g., demand response [
Alternatively, operational wind-integration costs can be reduced by modifying power-system operations. Such adjustment can be done using a stochastic, robust, or distributionally robust approach to modeling unit commitment [
Operational planning with explicit uncertainty characterization presents challenges. For one, market operators have a short time window following gate closure to provide day-ahead operating schedules and prices to market participants. The capabilities of optimization software and computational hardware are considerably greater than those available at the advent of stochastic unit commitment [
As such, operational models with explicit uncertainty characterization see limited use today by any market operator. Instead, most market operators rely on deterministic models [
Our case study shows reduced operational wind-integration costs with recommitment compared to having only day-ahead and real-time market operations. Among the time windows that we examine, hour-20 recommitment minimizes operational wind-integration costs, suggesting that hour 20 balances wind-forecast quality with operational flexibility of the system. However, this result is specific to our case study.
Our work makes two contributions to the extant literature. First, we propose a comprehensive approach to modeling market operations that can be applied to studying the benefits of introducing recommitment to reduce operational wind-integration costs. The models that we use are not novel. The novelty of our work is in implementing these models in a realistic manner that mimics real-world power-system operations. As such, our approach can be applied to other systems with different resource mixes and load, and weather patterns. Second, our case study demonstrates the tradeoff between forecast quality and generator flexibility. If market operators intend to introduce recommitment, our modeling approach and metrics could be employed to optimize the timing of the processes.
The remainder of this paper is organized as follows. Section II provides our model formulation. Section III details the simulation approach. Section IV provides the data that underlie and results of an illustrative example. Section V summarizes data for our comprehensive case study. Sections VI and VII provide case-study results and conclude, respectively.
1) Sets and indices: we model system operations at hourly time steps over the ordered set, , of hours in the optimization horizon and define as the time index. is the index for buses, which are in the set, . We define sets, and , of non-wind and wind generators, respectively, and let be the generator index. We define as the set of generators that are located at bus . We define a set, , of transmission lines and let be the transmission-line index. Non-wind generators are modeled as having an ordered set, , of start-up types, which correspond to how long the unit has been offline when it is started, and we let denote the start-up type index.
2) Parameters and functions: non-wind generators are assumed to have a three-part cost structure. is the fixed no-load cost ($/h) of having non-wind generator online. gives the output-dependent cost function ($) of non-wind generator . is the cost ($/start-up) of non-wind generator incurring a type- start-up. For all , non-wind generator incurs a type- start-up if it has been offline between and hours when it is started up. If non-wind generator has been offline or more hours when it is started up, then it incurs a type- start-up. Wind generators are costless to operate.
Non-wind generator must produce between MW and MW while it is online and must produce MW while it is offline. In addition, generator ’s output can decrease by MW at most and increase by MW at most between one hour and the next. Non-wind generator can provide up to MW and MW of non-spinning and spinning reserves, respectively. In addition, non-wind generator must be offline a minimum of hours after it is shutdown and must be online a minimum of hours after it is started-up. Wind generator has a MW nameplate capacity and is its p.u. hour- availability factor.
There is MW of load at bus during hour . is the p.u. load-based reserve requirement and is the p.u. spinning-reserve requirement. Transmission line has an -MW flow limit and is the p.u. bus-/transmission-line- shift factor. is an arbitrarily large constant.
3) Variables: we represent the status of non-wind generators using four sets of binary variables. equals if non-wind generator is online during hour and equals otherwise. equals if non-wind generator is started-up during hour and equals otherwise. In addition, equals if non-wind generator incurs a type- start-up during hour and equals otherwise. equals if non-wind generator is shutdown at time and equals otherwise. Two additional sets of binary variables capture the operation of non-wind generators vis-à-vis the provision of operating reserves. equals if non-wind generator is the largest hour- contingency (which prevents it contributing towards the hour- reserve requirement) and equals otherwise. equals if non-wind generator cannot provide hour- non-spinning reserves due to a minimum-down-time constraint and equals otherwise.
gives generator ’s hour- power output (MW) and and represent hour- non-spinning and spinning reserves (MW), respectively, that are provided by non-wind generator . Wind generators are disallowed from providing operating reserves. gives the number of hours that non-wind generator is offline as of the beginning of hour and measures the number of hours beyond that non-wind generator is offline as of the beginning of hour . represents the actual start-up cost ($) that is incurred by non-wind generator during hour .
Each hour’s total reserve requirement is the sum of a p.u. proportion of the hourly system-wide load and the largest contingency of the system during the hour. These reserve requirements are based on current practice of California Independent System Operator, which manages a system with relatively high renewable-energy penetrations. represents the hour- contingency-based reserve requirement (MW). and represent hour- non-spinning and spinning reserves (MW) that are curtailed, respectively. measures curtailed hour- load at bus (MW). measures hour- net power (MW) that is withdrawn from the transmission network into bus .
We model system operations using the mixed-integer linear optimization problem:
(1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
(8) |
(9) |
(10) |
(11) |
(12) |
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
(20) |
(21) |
(22) |
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
(29) |
(30) |
(31) |
(32) |
(33) |
(34) |
Objective function (1) minimizes system-operation costs. We model non-wind generators as having three-part operating costs—start-up, no-load, and output-dependent variable costs. The variable costs, , are convex piecewise-linear functions of the , meaning that (1) is linear in the . The final term in (1) penalizes load and reserve curtailments.
Constraints (2) and (3) ensure bus-level and system-wide load balance, respectively. Constraint (4) enforces flow limits on transmission lines.
Constraints (5)-(9) impose spinning- and non-spinning-reserve requirements. Constraint (5) defines the values of the . Constraints (6) and (7) determine the generator that is the largest contingency during each hour, which is ensured by (19) and (20) not to supply reserves. Constraint (8) ensure that the total hourly reserve requirements are met. Constraint (9) ensures that a p.u. portion of the total reserve requirement is met by spinning reserves.
Constraint (10) ensures that each wind generator produces between zero and its maximum operating point, which depends on its hourly capacity factor ( wind conditions). Constraints (11)-(13) impose the minimum and maximum production limits on non-wind generators. Constraints (12) and (13) account for additional power that is provided if reserves are called. Constraints (14) and (15) enforce ramping limits on each non-wind generator, accounting for reserves in determining upward ramping.
Constraints (16)-(20) restrict the provision of reserves. Constraints (16) and (17) ensure that no generator provides more reserves than it is capable of providing. and are included on the right-hand sides of (16) and (17), respectively, to ensure that generators provide spinning reserves only while they are online and that a generator does not provide non-spinning reserves if it is unable to start-up due to a minimum-down-time constraint. Constraint (18) determines the values of based on the number of hours that generators are scheduled to be offline and their minimum down time.
Constraints (21)-(23) define the number of hours that each non-wind generator is offline. If , (23) forces to equal zero. Otherwise, if , (22) forces to equal . Constraints (24)-(27) compute start-up costs. Constraints (24) and (25) determine the type of start-up that occurs during a given hour, based on the duration of time that a given unit has been offline. Constraint (26) ensures that exactly one start-up type is incurred each time that a unit is started and (27) computes the corresponding cost.
Constraints (28) and (29) enforce the minimum-up-time and minimum-down-time restrictions, respectively. Constraint (30) defines the values of and based on intertemporal changes in . Constraints (31) and (32) impose integrality restrictions and (33) and (34) impose non-negativity.
We use a rolling-horizon approach to model system operations one hour at a time. In doing so, we distinguish two processes. The first, to which we refer as unit commitment, determines the commitment schedule of non-wind generators for the following day as well as system operations for the current hour. The second, to which we refer as economic dispatch, determines current-hour system operations.

Fig. 1 Illustration of rolling-horizon modeling approach, assuming hour-12 and -18 unit commitment.
The first set of horizontal lines shows that unit commitment takes place during hour of day . This process determines the real-time operation of the system during hour of day , as well as day-() unit commitments. These decisions are illustrated by hours that are covered by the thick lines. The thin line indicates that these decisions are made using a -hour optimization horizon through hour of day . These additional hours beyond day are included to ensure that sufficient generating capacity is kept online at the end of day to serve the day-() load [
Following the unit commitment that is conducted during hour of day , the decision-making process rolls forward sequentially through hours - of day , conducting economic dispatch. These economic-dispatch processes determine system operation during each of these hours, using a rolling -hour optimization horizon. These economic-dispatch processes are followed by unit commitment during hour of day , which determines system operation during hour of day and can adjust day-() unit-commitment decisions. These hourly optimization processes continue sequentially to simulate system operations over the full year.
When modeling unit commitment, we impose the constraints:
(35) |
(36) |
where is the final hour of the current day; is non-wind generator i’s minimum notification time (h); and and are the values of hour- start-up and commitment decisions, respectively, of non-wind generator that have been fixed during previous decision-making processes. Constraint (35) restricts the system operator’s ability to shutdown the units that are committed to be online by a previous unit commitment. Specifically, a unit that is scheduled to shutdown during the current day or before its minimum-notification time can be instructed instead to remain online as opposed to shutting down. Constraint (36) allows a unit to be started-up during the current or next day, so long as its minimum-notification time is respected.
We impose (36) and (37) on economic-dispatch processes.
(37) |
Constraint (37) is stricter variant of (35)—the only adjustment to unit-commitment instructions that (37) allows is the starting-up unit without the option of shutting-down units.
The decision-making process that is conducted in Lines 15-21 depends on whether is an hour during which unit commitment or economic dispatch is conducted. (cf. Line 15) represents the set of hours during which unit commitment is conducted. In the former case, the optimization is conducted including (35) and (36) in the model and the commitment decisions are fixed (cf. Lines 17 and 18). In the latter case, the optimization is conducted including (36) and (37) in the model and no commitment decisions are fixed. Line 22 adds the operational cost that is incurred during hour of day to . Lines 23-30 update the ending state of each non-wind generator after the current decision-making process. This information is used in Lines 6-13 of the following iteration.
in Lines 16 and 20 represents an optimal decision-variable vector. Optimal decision-variable values are used in fixing unit-commitment decisions in Lines 17 and 18, computing operational cost in Line 22, and updating the state of non-wind generators in Lines 23-30.
This section presents a stylized two-day example, which demonstrates the tradeoffs in the timing of conducting recommitment.

Fig. 2 Modeled load and actual wind availability during the second day of the example from Section IV and day-ahead wind-availability forecasts produced during hours , , , and of the first day.
The remaining rows of
Our case study is based on ISO New England, from which conventional-generator and transmission-network data are obtained directly. Previous research works [
Hourly historical year- load data for the eight load zones in ISO New England are obtained from a public repository (cf. https://www.iso-ne.com/isoexpress/web/reports/load-and-demand/). The system-wide load ranges between GW and GW and averages GW across the year.
We model the cases with two wind penetrations— GW and GW of nameplate capacity, which are % and %, respectively, of peak load. These cases correspond to wind serving % and %, respectively, of annual load (absent wind curtailment). Wind capacities (i.e., the value of ) for the two wind-penetration levels are apportioned to the eight load zones in proportion to their co-incident peak loads.
Actual hourly wind availability and forecasts (i.e., the values of ) are modeled using the data from Wind Integration National Dataset (WIND) Toolkit [
We employ a two-step process to model . First, each set of modeled actual and forecasted wind-availability data are averaged across each of the eight load zones to determine a zonal-average capacity factor. We do this by computing the simple average of the capacity factors reported in WIND Toolkit for the sites that are in each of the eight zones. Next, the modeled actual and forecasted wind-availability data are used to determine the values of . For a given instance of (1)-(34), the values of are set equal to the corresponding zonal-average modeled actual capacity factor for the hour. For the remaining hours, , we use zonal-average forecasted capacity factors. WIND Toolkit provides -, -, -, and -hour-ahead forecasts of wind availability. We use weighted averages of these forecasted capacity factors to set values of . For instance, the value of is set equal to the -hour-ahead forecasted wind availability for the corresponding hour, whereas the value of is set equal to the weighted average of the - and -hour-ahead forecasted wind availabilities for the corresponding hour, with weights of and , respectively. Values of are set equal to the -hour-ahead forecast.
One peculiarity of WIND Toolkit, which is summarized in
We focus on the impacts of recommitment on operational wind-integration costs. Thus, we model wind availability as the sole source of uncertainty. This uncertainty is reflected by the values of being updated iteratively as operational decisions are made (cf. Line 14 of
In addition to considering the cases with two wind-penetration levels ( GW and GW), we consider the cases with base and low levels of generator flexibility. Base flexibility uses the values of that are reported in the ISO New England dataset. Low flexibility uses doubled values of .
We contrast a case in which unit commitment is conducted during noon of each day to the cases in which unit commitment is conducted during noon and during some combinations of hours , , and , giving seven combinations total.

Fig. 3 Modeled actual system-wide wind availability during the first hours of January , and corresponding day-ahead forecasts produced during hours , , and of January , assuming GW of wind for case study from Section VI.
System operations differ, depending on whether only a noon day-ahead unit commitment is conducted or recommitments is conducted. With only noon day-ahead unit commitment, assuming base generator flexibility, the energy-supply shortfall that arises in real time from actual wind production being lower than the noon forecast is addressed by committing fast-start generators in real time (beginning during hour of January , ), which operate for a total of hours between them. These fast-start units have high operating costs, which increases operating cost for the day.
Conducting hour- or hour - recommitment reduces the total number of hours that the fast-start units are operated to and hours, respectively. These fast-start units are replaced by lower-cost units that require advanced notification to start-up.
We illustrate the high cost of fast-start units by computing (38), which is the average output-dependent cost of each unit, if it operates at its nameplate capacity.
(38) |
If conducting only a noon day-ahead unit commitment, the system relies heavily on the units with advanced-notification times of four hours or less to meet the wind-availability deficit. This reliance stems from the inability to commit lower-cost units with longer advanced-notification times. Conversely, with hour- recommitment, these most expensive units can be substituted to some extent by lower-cost units that have higher advanced-notification times.
To illustrate this tradeoff, we focus on the operation during the first hours of January , of three units, the cost and flexibility characteristics of which are summarized in
Tables
First, if conducting a single recommitment, an hour- recommitment yields the greatest cost reductions. This result keeps with our finding a tradeoff between forecast accuracy and generator flexibility. Conducting three recommitments yields further cost reduction and two recommitments yields cost reductions in most cases. With low generator flexibility, hour- recommitment yields slightly lower costs compared to hour- or hour- recommitments. This result stems from the combined impact of relatively (to hour-) inaccurate hour- wind-availability forecasts and the system having limited operational flexibility during hour .
Tables
This paper examines the benefits of recommitment in reducing operational wind-uncertainty costs. To do so, we develop a detailed operational model that mimics many of the costs and constraints for which system operators account in their operational models. Nonetheless, our model is not an exact replica of that used by any market operator. We develop a rolling-horizon algorithm to simulate hourly system operations that consist of unit commitment and economic dispatch. The key distinction between these processes is the extent to which the system operator can adjust commitment decisions relative to previous decisions and which decisions are binding.
We demonstrate our model and draw important conclusions regarding the use of recommitment with a comprehensive case study, which is based on ISO New England, and a stylized example. Both the example and case study demonstrate the cost impacts of wind uncertainty, which are increasing in wind penetration and generator inflexibility. We also demonstrate the benefits of introducing recommitment, which raises a fundamental tradeoff between forecast accuracy and operational flexibility. For our example and case study, hour- recommitment offers the most cost reductions. Other systems may benefit from the recommitment being conducted at different time and the methodology that we develop could be used to examine the tradeoffs therein.
We adopt an hourly timescale for all of our modeling. Hourly timescales are used in nearly all wholesale electricity markets for day-ahead and reliability unit commitment. With few exceptions, sub-hourly timescales are used for economic-dispatch modeling. We use an hourly timescale for our economic-dispatch modeling, due to the computational cost that sub-hourly timescales would entail. Modeling economic dispatch at sub-hourly timescales could reveal more load and wind-availability variability (compared to hourly timescales). However, our fundamental results regarding the tradeoffs in introducing and the timing of recommitment likely would continue to hold.
Our model does not allow wind generators to provide reserves, if their output is curtailed. An area of future study could examine the benefits of using curtailed wind in this manner. Another area of future work would be to compare the benefits of recommitment to a modeling paradigm that represents uncertainty explicitly, e.g., stochastic, robust, chance-constrained, or distributionally robust optimization. We do not consider explicit uncertainty representation, because no wholesale market employs such a model today [
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