# Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - title

**Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC**

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - setup

**Simulation Setup & Configurations**

**Author / organization: **A. Engelmann and T. Faulwasser / KIT

**Objective Function of Simulation:**

**Simulation Duration:**Depending on the length of the weather forecasts, the computational power, and the desired closed-loop performance, different horizon lengths ?? in can be chosen. A long horizon leads in to larger optimization problems which are in general harder to solve. We perform open-loop and closed-loop simulations for an exemplary winter week in this document. Full-year simulations are also available

**Key Performacne Indicator: **

- Comfort Level
- Fluctuation in Energy Demand
- Thermal Peak Consumption

**Initial Simulation State: **

- All temperatures are initialized with 21°C

**Stopping Criteria of Simulation: **

** --**

**Start Point: **

- As the resulting OCP is a convex quadratic program which is commonly easy to solve numerically, we initialize the states and inputs with all zero
- As initial condition ??(??) for closed-loop simulation, we use 21°C for all room and wall temperatures

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - short description

**Short Description of simulation Results **

We have to distinguish two types of results here: In each time step, we get an open-loop optimal trajectory which is the solution to OCP solved at this time instant.

The first step of this solution is then applied to the system. After the next sampling period, a new OCP with new initial condition and new weather forecast is solved. Recording the resulting sequence of states yields a closed-loop trajectory.

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - input

**Simulation Input **

**Test Data**

**Link to test data:**Here**Storage of Data:**SmILES data format

**Test System Model used for Simulation: **

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - best practice

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## Nested Applications

## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - long description

**Results Description of Simulation -- KIT.TC1.TS1 FlexOffice Thermal MPC**

Figure 3 shows an open-loop optimal trajectory, which is the solution of OCP for one time instant with temperature tracking MPC. Figure 4 shows the resulting trajectories for a constant input of ??? =[0 10 0 10 0 13] ???? for all ??. One can see, that the indoor temperatures fluctuate quite heavily depending on the outdoor temperature and the solar irradiation.

Figure 5 shows closed-loop trajectories with temperature tracking MPC. Here one can see that the desired temperature of 21°C is tracked accurately except for days, where the outdoor temperature is quite high. This comes from the fact that FlexOffice has no cooling capabilities, hence, there is no way for the controller of avoiding this behavior. Figure 6 shows the corresponding inputs. One can see that strong spikes occur in the heating powers of the concrete core activation and the radiators. This leads to high peak-loads in the district heating and electricity grid, which we would like to avoid.

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## Simulation Results of KIT.TC1.TS1 FlexOffice Thermal MPC - long description2

Figure 7 shows closed-loop trajectories, where we use a formulation quadratically penalizing the input. The resulting indoor temperatures stay closer to the lower bound of the indoor temperature which is 19°C here. Furthermore, on can see that the input spikes are much smaller than in the temperature tracking case which can be observed in Figure 8.