Distribution Factors in Generator Interconnection
Definitions and implications
The application of distribution factors in power system analysis is well-understood and a well-established practice. There are many resources available to understand these DC power flow-based calculations (linked here and here are some good high-level overviews), but with the number of projects in interconnection queues blooming across ISOs and utilities across the United States, we feel it is worthwhile to take a closer look at these calculations in the context of renewable energy development and generator interconnection.
The implications associated with distribution factors are far-reaching and, at times, controversial. In this article, we’ll explain why they play such significant roles in interconnection, and share ideas on mechanisms which could help developers better understand and factor them into project decision-making.
Distribution factors: Determination and system upgrade cost allocation
Estimating how much a certain quantity changes in response to a change in another quantity is a fundamental exercise in all disciplines, from engineering to economics to social sciences. In the context of interconnection studies, this exercise generally takes the form of determining how much a given generation project impacts the power flow through an overloaded line. Asked another way, how much does that project contribute to the overload? A distribution factor (DF) is how that question is answered mathematically. Generally, DF values describe, on a percentage basis, the relationship between changes in the system to various grid-connected elements. A variety of terms are used to refer to DFs in this context (note this is not an exhaustive list of all DF types):
PTDF - Power Transfer Distribution Factor
Captures nodal power transfer sensitivities on network elements under system-intact conditions
LODF - Line Outage Distribution Factor
Captures branch power redistribution sensitivities on network elements due to a branch outage
OTDF - Outage Transfer Distribution Factor
Captures nodal power transfer sensitivity of network elements under branch outage conditions
Other generic terms for DFs
Shift factor (e.g., injection shift factor, generator shift factor)
A benefit of using DFs is, once calculated, they can actually tell us a lot about a given system under certain conditions very quickly without having to solve large numbers of equations every time. There are numerous types of DFs that may be calculated depending on the applicable analysis. In an interconnection studies context, DFs are most often associated with power injection-based sensitivities, with implications being driven primarily by the extent to which a project’s power output at its point of interconnection (POI) contributes to or exacerbates an identified system reliability criteria violation. Put more simply, these DF calculations describe how a unit of electric power will transfer from one point to another, with percentage flows of that power being determined according to other elements (i.e., generators) and the network topology. The network topology will inherently vary in this study context, considering both system-intact and contingency/outage conditions, and appropriate DFs are employed to consider this variation.
Interconnection studies include performing an extensive contingency analysis to understand the impacts of new projects on the bulk transmission system. The analysis ensures ISOs and utilities identify any necessary mitigations to maintain future system reliability. Both AC- and DC-based contingency analysis are leveraged to determine mitigations, and their usage is dependent upon the ISO or utility’s established interconnection process. Projects are modeled and evaluated against a baseline (i.e., pre-project) analysis, and any violation shown to be associated with that project being on-line and delivering power has mitigations proposed and cost allocated on a percentage basis of its impact, often referred to as the project’s MW impact. In other words, assuming the project were to move forward to construction and energization, if the project contributes to a violation to system reliability, the project’s fractional contribution to this violation is determined, and a corresponding fractional cost of the network upgrade to mitigate the violation is assigned to the project’s owner. This fraction is dependent on the DF value determined during cost allocation stages in an interconnection study, and this is the sole purpose for DF determination in an interconnection study.
Further, because DFs are determined in a DC power flow context, which assumes uniform bus voltages across the system, they can only be used to cost allocate mitigations on overloaded transmission lines and transformers. Voltage violations are not accounted for – this is not the intention of transfer DFs. Thermal loading mitigations tend to be the most expensive, so their accuracy in DF determination is very important. Even small DF values can make or break a renewable or storage project’s ability to move forward towards construction. While DFs are common in cost allocation procedures, their applicability and associated criteria may vary from organization to organization. In project development, understanding the nuances associated with performing a study in a particular region, the violation definitions, and the cost allocation process are critical to making well-informed judgments in building and executing a project portfolio. Most ISO and utilities make public their interconnection study practices in manuals and other documentation, which outline the details of their criteria and cost allocation practices.
DFs in generator interconnection: An example
Consider the small power system shown in Figure 1 below, with a 100 MW project seeking interconnection onto the grid at bus 1 (Gen 1) and a 75 MW project seeking interconnection at bus 2 (Gen 2). Let’s also assume that during the contingency analysis for both projects, it was found that an outage of the line from bus 1 to bus 4 as shown caused a thermal overload violation on the line from bus 3 to bus 4, prompting a $10,000,000 reconductoring upgrade. To cost allocate the network upgrade, we can determine the DF for this line for both projects under the contingency condition (also known as an Outage Transfer Distribution Factor, or OTDF), calculate their respective MW impact on the line showing the violation, and allocate that cost on a percentage basis according to the results. As mentioned above, cost allocation can vary between ISOs and utilities. For simplicity, we’ll assume that the cost of the line upgrade will be proportional to the sum of each project’s MW impact, i.e., Gen MW impact = DF * (Gen MW Dispatch).
Because DF calculations are determined via DC power flow, we can utilize simplified power balance equations at a Bus k in the network, where branch flows are determined by the branch susceptance b and the difference in voltage angles at either end. The sum of those flows would determine the net injection (or withdrawal) at Bus k.
For the example network, these become the following:
Assuming a voltage angle of 0° at Bus 1 as a reference, we can represent this system of equations as follows:
Note that the system is symmetric, i.e.,
Plugging in the parameter values in the grid model, we can solve for the bus voltage angles to then determine the power flows. To calculate the DFs for a generator at Bus 2 sinking to the load, we’ll assume a 1 MW injection at Bus 2 and a corresponding 1 MW withdrawal at Bus 4.
To obtain DF values for each branch under these conditions, we’ll use the calculated angle values to determine the branch power flows. Here, D_kj represents the transfer DF from Bus k to Bus j:
With bus 1 and bus 2 as candidate generator buses, bus 4 as the sink, and all line reactances equivalent at 1 p.u., we determine the DFs for generators at bus 1 and bus 2 to be 0.54 and 0.64 (calculated separately), respectively. To cost allocate the upgrade, we can calculate the MW impacts of the two generators as follows, along with their respective cost responsibilities for the upgrade:
Gen 1 MW impact = 0.54 * (100 MW) = 54 MW
Gen 2 MW impact = 0.64 * (75 MW) = 48 MW
Total MW impact = 54 MW + 48 MW = 102 MW
Gen 1 impact percentage = 54/102 = 52.94%
Gen 2 impact percentage = 48/102 = 47.06%
Gen 1 upgrade cost allocation = 52.94% * $10,000,000 = $5,294,000
Gen 2 upgrade cost allocation = 47.06% * $10,000,000 = $4,706,000
DF evaluation in renewable and storage project development scenarios
Considering the link between cost allocation and DF determination, it is of interest to project developers to have advance understanding of their project’s contribution to potential thermal violations when building a project portfolio. To make matters more complicated, often the cost allocation for one project is influenced by that of another nearby. For example, if a project with a higher MW Impact opts to not move forward when cost allocations are published by the ISO or utility, the cost allocation is recalculated based on the remaining projects MW Impact and nearby projects whose share may have been relatively minor may have a recalculated cost allocation that is now higher.
Due to the nature of generator interconnection model development and the extent of analysis required to ensure accurate results, developers often rely on their judgment of prior study results, some limited analysis using specialized software, and engineering expertise to inform decision-making. Ideally, developers would be able to accurately assess (i.e., via AC and/or DC contingency analysis) any number of scenarios that consider their project’s location and size, inclusion/exclusion of other developers’ projects, and ISO/utility-determined mitigation inclusion/exclusion, among other modeling considerations, to more accurately understand prospective projects’ influence on the grid prior to entering into the interconnection queue.
Distribution factors are useful in a variety of analyses, and are commonly used in cost allocation for assigned upgrades to mitigate thermal violations in interconnection studies.
Distribution factors reflect a project’s contribution to a violation on a percentage basis, and assigned costs can make or break a project’s ability to move to construction.
The ability to perform scenario evaluations would help developers in decision-making prior to submitting a project to an interconnection queue.
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