Mixed-Integer Program Logic for LT

The Long-Term (LT) Capacity Expansion functionality in Aurora includes the option to use a Mixed-Integer Program (MIP) to make the resource build and retire decisions.

There are two MIP methods that provide different options in how the dispatch of generators are represented in the optimization and which information is used from the chronological solve. The MIP methods differ from the Traditional LT logic in several ways.

First, there are significant advantages to using one of the two MIP methods, including:

Faster convergence
A solution that gives lower total system cost to meet the requirements
Improved stability, especially in Energy Only LTs
Better handling of complex build and retire constraints

The general iterative methodology is the same for all LT methods. During each LT iteration an updated set of candidate new resource options and retirements are placed in the system and the model performs the standard chronological commitment and dispatch logic with that configuration. The model tracks the performance of all new resource options and resources available for retirement, tracking the resource costs and value based on the market prices developed in the iteration. At the end of each iteration the LT logic decides how to adjust the current set of new builds and retirements, or it determines that the model has converged and writes the final RMT with the decisions to the input database. The LT methods differ in how they determine the adjustment to the current mix of resources in the system each iteration.

In the two MIP methods (Chronological and LDC), Aurora formulates a Mixed-Integer Program to make the resource selection. The decisions are done on a pool level if Operating Pools are being used. Both methods include constraints to honor these user-specified criteria:

Annual Min/Max and Overall Min/Max Limits - Aurora adds new resource constraints to ensure that both annual and overall min/max criteria on both a new resource as well as a new resource group basis are honored.
Reserve Margin Targets - Aurora ensures that the zone and pool based reserve margin constraints defining the minimum capacity that must be available for reliability are met.
Retirement Limits - Aurora adds constraints to ensure that the model retires units only within the time frame specified in the Resources table. It also ensures that the total annual retirements are limited by the limit specified for each pool. Because pools are solved individually, the global retirement limit may not be honored, but the model will ensure that it is met for each pool individually.
LT Energy Min Constraints - If the user has defined minimum energy constraints for the LT in the Constraint table, Aurora will add these to the MIP to optimize the selection of resources in order to satisfy the target values.
Retrofit Constraints - Constraints are added to the model to facilitate the analysis of retrofit units. These constraints ensure that only one of the options (the original resource or a retrofitted resource in a given year) is available to the system at any point in time.
Dependent Constraints - Constraints are added to the model to limit build decisions based on other build options like Limiting New Resource, Prerequisite New Resource constraints, and the other LT constraints that can be specified in the Constraint table.

If any constraints are deemed infeasible (e.g., The reserve margin cannot be met with the available resources) the model will use intelligent in-feasibility handling to relax those constraints as little as possible.

Chronological

Chronological is generally the recommended method. For this method, the dispatch of all of the resources in the most recent iteration forms the basis for the valuation of the candidate and existing resources. This allows the effect of complex dispatch constraints - such as commitment that cannot be modeled directly in the LDC method because of computational limitations - to influence the LT decisions through the chronological valuation that is used. This valuation consists of a total Net Present Value (NPV) metric which is determined for all resources whose status can be changed by the optimization, and the logic seeks to build the most valuable resources to the system. The valuation is based on the cumulation of fixed and variable costs as well as energy revenue from the hourly dispatch for the whole simulation period, and the values will change each iteration as the mix of resources actually in the system is adjusted.

The MIP formulation also includes extra constraints to limit the amount of changes in system capacity that can happen between each iteration. These include a limit on the change in total capability in the system in each zone, a limit on the number of changes to retirement decisions, and a limit on the number of new resource candidate that can be removed from the system from iteration to iteration. These constraints are dynamically updated to help guide Aurora to an optimal solution and promote convergence.

When typical planning reserve margin targets are being used Aurora will normally not build significantly past the input reserve margin, but it may if there are many valuable resources options. If that behavior is not desired for a specific pool, a reserve margin maximum can also be entered in the Operating Pools table.

In general, the Chronological method produces similar results to the Traditional LT Logic when using reserve margin targets, but it will do a better job at evaluating complex sets of constraints such as the impact of simultaneous RPS and reserve margin targets. For Energy Only runs the convergence is typically much faster with the Chronological method than the Traditional LT logic.

LDC

The Load Duration Curve (LDC) method focuses on simulating the actual dispatch in the optimization solve itself and uses less information from the chronological dispatch than the other method. LDC is recommended when the primary goal of the LT Plan is ensuring enough capacity is built to serve load (i.e., Unserved energy is not acceptable) or when capacity needs to be built to serve competing needs of energy and ancillary service requirements.

For the LDC method, the formulation also includes the following constraints:

Energy Targets - The dispatch of resources are explicitly modeled in the optimization problem using a load duration curve approach with aggregate load constraints. As such, the approximate cost of dispatch and serving the load is directly modeled in the optimization problem as opposed to assuming the dispatch from the chronological solution. The number of dispatch intervals used each year depends on the LT Study Precision setting and are as follows: 4 if using Low, 7 for Medium, and 10 for High. The data that defines each of these intervals is based on average demand, resource costs and capabilities, and other values from the sampled dispatch hours in the chronological that map to the LDC intervals.
Curtailment Constraints - During each iteration of the LT, the model tracks the usage of Demand Curtailment units. For each hour that curtailment resources are utilized, or the demand is relaxed, Aurora will add a constraint that ensures there is sufficient non-curtailment capacity available to meet that hour’s demand.
Ancillary Constraints - The contribution to ancillary services is directly represented by variables in the optimization so that enough capacity is built to serve both energy and ancillary requirements.

The objective is formulated as the total Net Present Value (NPV) of the production, fixed, and build costs to meet all of the above requirements. The MIP searches to find the mix of resources (both existing and new build/retrofit options) over time that satisfies all energy and demand requirements while minimizing the total NPV.

Convergence is deemed to have been met when the total cost objective from successive iterations has only changed within a tolerance amount as dictated by the precision chosen for the LT study. When using the LDC method, convergence will generally be much faster than the Chronological method, but each individual MIP will potentially take significantly longer to solve.

Simulation Logic

Mixed-Integer Program Logic for LT