Energy Consumption Forecast of Photo-Voltaic Comfort Cooling Using UPPAAL Stratego

Abstract

To balance the fluctuations of renewable energies, greater flexibility on the consumption side is required. Moreover, solutions are required to handle the uncertainty related to both production and consumption. In this paper, we propose a probabilistic extension to FlexOffers to capture both the interval in which a given energy resource can be operated and the uncertainty that surrounds it. Probabilistic FlexOffers serve as a support for a method to forecast energy production and consumption of stochastic hybrid systems. We then show how to generate a consumption strategy to match a given consumption assignment within a given flexibility interval. The method is illustrated on a building equipped with solar cells, a heat pump and an ice bank used to feed the air conditioning system.

Appendices

A Thermodynamics

Constants from Sect. 4.

$$\begin{aligned}&A_s = \left\{ \begin{array}{ll} 80 &{} \text { if } s \le 25\\ (s-25) \cdot 120 &{} \text { o.w} \end{array} \right. \\&B_s = \left\{ \begin{array}{ll} 0 \cdot s &{} \text { if } s \le 25\\ 2000 &{} \text { o.w } \end{array} \right. \\&COP _s = \left\{ \begin{array}{ll} 0.16 \cdot s &{} \text { if } s \le 25\\ 4 &{} \text { o.w } \end{array} \right. \\&H_{ HVAC } = \dot{M}_{ air } \cdot C_{ air }\\&T_{ HVAC } = 18\,^{\circ }\text {C}\\&D = \frac{1}{M_{ air } \cdot C_{ air }}\\&A_{ eff }= \frac{6\,\text {m}^2}{10}\\&H_{ env } = \frac{1}{0.0093}\\&IB _{ full } = 55 \\&IB _{ empty } = 0 \end{aligned}$$

where

• $\dot{M}_{ air } = 1 \frac{\text {kg}}{\text {s}}$ is the HVAC air flow rate.

• $C_{ air } = 1005.4 \frac{\text {J}}{\text {kg}\cdot \text {K}}$ is the specific heat capacity of air.

• $M_{ air } = 7113.5\,\text {kg}$ is the mass of air in the building.

• $M_{ ice } = 1500\,\text {kg}$ is the total mass of ice within ice bank.

• $C_{ ice } = 2108\,\frac{\text {J}}{\text {kg}\cdot \text {K}}$ is the specific heat capacity of ice.

B Model Specifics

Figure 8 depicts the Uppaal-stratego model used for on-line controller synthesis. It consists of two location Choose_speed and Wait. The solid edge from Choose_speed to Wait encodes a non-deterministic choice between the available heat pump settings i.e. the controllable modes in the stochastic hybrid game. When the next controllable mode is set, update_irr() computes the next uncontrollable mode, i.e. the irradiance forecast. apply_flow() then updates each variable according to the flow functions of the corresponding stochastic hybrid game, as seen in Listing 1.1. To this end, numeric integration using the Euler method is implemented in each update_X() function call, for numSteps number of steps. Finally, update_kWh() updates the energy consumption/production for this period. Invariant $x \le 1$ in the Wait location and guard $x == 1$ on the clock x together encode the period. The dotted edge encodes a reset to a new period and is considered uncontrollable by Uppaal-stratego for control strategy synthesis.

Fig. 8.

Uppaal-stratego model for on-line controller synthesis.