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Energy modeling is a field that is conceptually and mathematically very rich. In this section of the Documentation, we discuss and clarify topics and concepts that are related to modeling energy systems in general, and we provide detailed mathematical derivations for all equations and mathematical formulations used in SAInt.
The purpose is to help users understand how they can use SAInt most effectively, and to be transparent about the mathematical treatment used in SAInt so that users can understand exactly what their results mean.
The Scenario Analysis Interface for Energy Systems (SAInt) is a software platform to model, plan, and operate energy networks and markets, including electricity and gas. SAInt advances energy planning by allowing users to model coupled energy networks and to analyze the challenges and synergies at their interface.The user can run simulation and/or optimization to quantify the trade-offs between costs and reliability and to study the intersection of markets and physical systems.
A SAInt project is subdivided into three model layers, namely, network, scenario and solution. The network layer is a description of the different facilities and components forming the network model, their static properties (e.g., name, diameter, length, elevation, resistance, reactance, etc.) and how they are connected and related to one another. The scenario layer is a description of a case study performed on the facilities and components in the network model. A scenario is characterized by a scenario type (SteadyGas, SteadyACPF, QuasiDynamicACOPF, DCUCOPF, etc.), a time window (start time and end time), and the definition of settings, controls, and constraints and how they change over time (described by events and profiles). Every scenario type has an underlying mathematical model derived from (physical) laws governing the behavior of and interactions between the facilities and components in the network model. The solution layer is a description of the results obtained from solving the mathematical model of a scenario.
The goal of this document is to provide a description of the mathematical models for the different scenario types in SAInt.
After reading this document you will be able to answer the following questions:
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How are the facilities and components of each network type modelled for different scenario types?
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What are the relevant parameters and variables considered for each mathematical model describing a scenario type?
Either electric network or gas network can be described as a directed graph, consisting of a set of nodes and a set of branches. A branch connects two nodes and is assigned with a direction [1]. Both node and branch are called object in SAInt and this document. Besides, there is another category of objects, external, which injects/withdraws electricity/gas from/to the network. It connects one and only one node. So, there are three categories of objects in a network.
All the different objects are discussed based on such three categories for electric network (\cref{sec:ElecNet}) and gas network (\cref{sec:GasNet}). Each object can be described by several equations and constraints. There are three types of equation/constraint:
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Network equation. It is only related to individual object in the network. The constant are specified by individual object in network-editing mode and cannot be updated by set-point event nor constant-updating event.
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Set-point equation. It directly specifies value of variable, and the user must provide one and only one value for each equation. The default values of constants are given by individual object in network-editing mode, and the constants can be modified by set-point events.
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Constraint. The default value is given by individual object in network-editing mode, and the value can be modified by constant-updating events. It only makes an impact in optimal power flow, but the violation of constraint will issue warning in power flow simulation.
A simulation/optimization problem takes all the equations and constraints of all the objects into consideration and solve/optimize them simultaneously.