Multiperiod Integrated Ultra-Supercritical Power Plant

The Multiperiod Integrated Ultra-Supercritical Power Plant is an example model to determine the optimal schedule and operation of a pulverized coal-fired ultra-supercritical power plant integrated with thermal energy storage system (TES) for given electricity prices over a time horizon. The multiperiod model uses the Integrated Ultra-Supercritical Power Plant model for each period in the horizon. A more detailed description of the model is given in the sections below.

Model Structure

The multiperiod power plant model is developed by creating multiple instances of Integrated Ultra-Supercritical Power Plant model, where every instance is indexed by a time period, along with two coupling variables to link each time period. These coupling variables are: the optimal power produced by the power plant and the amount of storage material available at the end of each time period. A scheme showing how the multiperiod model is constructed is shown in the figure below:

../../_images/multiperiod_integrated_ultra_supercritical_powerplant.png

Degrees of Freedom

The multiperiod model has a total of 4 \(n\) degrees of freedom, where \(n\) represents the number of time periods. The degrees of freedom for each time period are listed below:

  1. Boiler feed water flow (\(boiler.inlet.flow_-mol\)),

  2. Steam flow to charge heat exchanger (\(HXC.inlet_-1.flow_-mol\))

  3. Condensate flow to discharge heat exchanger (\(HXD.inlet_-2.flow_-mol\)),

  4. Cooler enthalpy at outlet (\(cooler.outlet.enth_-mol\))

Notable Variables

Variable Name

Description

\(NetPower_t\)

Net power out from the power plant at each time period in MW

\(SaltInventory_t\)

Solar salt inventory at each time period in kg

Notable Constraints

  1. Power plant ramping is limited by including the following equations for a given \(ramp_-rate\):

\[NetPower_{t-1} - ramp_-rate \leq NetPower_t\]
\[NetPower_{t-1} + ramp_-rate \geq NetPower_t\]

  1. The salt inventory \(SaltInventory\) is given by the hot salt and total salt material balances, the latter involving a fixed amount of salt \(total_-salt\). The material balances are shown in the following equations:

\[HotSaltInventory_t = HotSaltInventory_{t-1} + F^{charge}_{salt, outlet} - F^{discharge}_{salt, inlet}\]
\[total_-salt = HotSaltInventory_t + ColdSaltInventory_t\]

Note that the notable constraints and variables in the multiperiod model also consider the notable variables and constraints given in Integrated Ultra-Supercritical Power Plant.