Physics Based Models

White-box or physics based models are based upon the knowledge of the processes occur- ring in either a particular component, room, or building. Physics based models have been been developed for fans (Wemhoff & Frank 2010), AHUs (Tashtoush et al. 2005), individ- ual zones (Oldewurtel et al. 2012) and multizone buildings (May-Ostendorp et al. 2011, Mendoza-Serrano & Chmielewski 2012). Table 2.2 summarises some of the key studies which have utilised physics based models for control.

Dynamic first-order models have been used to represent thermal processes in buildings (Oldewurtel et al. 2012, Mendoza-Serrano & Chmielewski 2012, May-Ostendorp et al. 2013). These models are analogous to electrical RC network, using thermal capacitance and thermal resistance to calculate thermal conditions or energy usage.

More extensive dynamic thermal simulation tools such as EnergyPlus (May-Ostendorp et al. 2011) and TRNSYS (Henze et al. 2005) have also being used as predictive mod- els for MPC of HVAC systems. These simulation tools are commonly used for forecasting building energy consumption and thermal conditions. However, they are not ideally suited to control. This is in part due to the amount of computation required and also the diffi- culties involving with integrating the software within a control scheme. The key difficulty is linking the control software with simulation tools. Tools such as MLE+ and BCVTB (Bernal et al. 2012, Wetter 2008) make communication between the two disparate systems

24 2.6. Prior Applications of Model Predictive Control to Buildings

simpler, yet to the authors knowledge this has not been commercially implemented for the control of a real building. Some studies have utilised the more comprehensive simulation tools to facilitate the development of simplified models to use for control. For example, Candanedo & Athienitis (2011) used data obtained from an EnergyPlus simulation to de- velop a state-space model of both radiant floor heating and a solar heat pump. In previous studies researchers have used simpler models for the development of the controller; while utilising the more comprehensive models to evaluate the performance of the controller (Ma et al. 2012).

In one of the seminal papers on the application of MPC to building systems, Oldewurtel et al. (2012) made use of physics based models as part of a stochastic model predictive control strategy (SMPC), to control a range of HVAC systems. SMPC takes into account uncertainty in the model inputs, for example in this case weather predictions. It also allows constraints to be enforced based upon a predefined probability. This would allow constraints upon internal environmental conditions to be defined in a similar manner to that used by building standards (CIBSE 2013). In most commercial applications and in the previous studies discussed here deterministic model predictive control (DMPC) is used. Unlike SMPC, DMPC does not take into account the uncertainty in model inputs, it assumes that all inputs are correct.

Oldewurtel et al. (2012) made use of a thermal RC network to model the thermodynamics of the buildings. Five different variations of HVAC system were investigated, with varying building types and weather conditions.

One of the interesting elements of the paper by Oldewurtel et al. (2012) is the method used to evaluate the performance of the MPC control strategy. In the majority of papers, the performance of the proposed control strategy is compared with more commonly used techniques, such as RBC. However, Oldewurtel et al. (2012) make use of a theoretical benchmark which they term the performance bound. The authors define the performance bound as the optimal control which can be achieved with perfect knowledge of both the dynamics of the system and of all future disturbances which can act upon the system. To calculate the performance bound, Oldewurtel et al. (2012) used a DMPC algorithm with perfect weather (i.e. observed weather) predictions. In computing the performance bound a prediction horizon of seven days and a control horizon of three days was used. Hence, the performance bound can be thought of as the performance limit of DMPC.

Oldewurtel et al. (2012) found that both DMPC and SMPC outperformed RBC both in terms of Non-Renewable Primary Energy (NRPE) usage and thermal comfort statistics. SMPC was found to outperform DMPC, however the performance is dependent upon the quality of the weather forecast.

May-Ostendorp et al. (2011) utilised an EnergyPlus model as the predictive model in an MPC system to control windows in a mixed-mode building. While the building being in- vestigated was mixed-mode, the MPC controller only controlled the automated windows. This makes the paper of particular relevance to this thesis. The goal of the MPC controller was to minimise the energy usage whilst preserving thermal comfort. In summer the re-

Chapter 2. Ventilation: Theory and Control 25

sulting control is essentially a night ventilation strategy. With the automated windows being opened during cooler nighttime periods. This passive technique, whereby the ther- mal mass of the building is cooled, reduced the daytime cooling loads. The optimiser used in the MPC controller reached this solution with no expert knowledge and with minimal constraints. The initial cost function was simply a minimisation of the cooling energy with a penalty for the number of transitions between window states to prevent excessive switching. Despite this the solution mimics a heuristic approach, which is used in many naturally ventilated and mixed-mode buildings.

The simple cost function used by May-Ostendorp et al. (2011) did result in a significant reduction in energy used for cooling against a reference control scheme, the details of which are unclear. However, the night cooling also resulted in overcooling the space, sometimes below the heating setpoint. To overcome this heating energy was included in the cost function. With the new cost function the savings in the cooling energy were decreased. However, overall energy usage and thermal comfort were improved.

A number of practitioners who make use of physics based models often justify dismissing the data driven alternatives due to problems with insufficient input excitation (Afram & Janabi-Sharifi 2014). This is certainly a valid concern. However, it must be stressed that by their nature the physics based models will always be a model of what is believed to be happening within a building or system. The performance gap between energy simulations and real building performance is a well documented problem (De Wilde 2014, Demanuele et al. 2010, Attia et al. 2013). Some of the uncertainties which contribute to this gap are present predominantly at the design stage. For example, changes in the building design and specifications or uncertainty regarding how the building will be used by the eventual occupants. However, even when building a model to describe a building which is already built and occupied, there is still a great deal of uncertainty. For example, without extensive testing it is difficult to know how airtight a building is or the level of insulation. While reasonably accurate information should be available for recently built or prospective buildings, this is unlikely to be the case for older buildings. To have a significant impact on UK Carbon Dioxide emissions, the ability to be applied in a retrofit scenario should be essential for a potential controller.

Beyond issues relating to the fabric, the stochastic nature in which occupants make use of a building can be hard to quantify, even in the case of a currently occupied building. Attempting to more accurately simulate occupancy patterns in buildings is a current active area of research (Gunay et al. 2013, Rijal et al. 2008, Page et al. 2008). However, this is the cutting edge of building simulation and the techniques used are not established within the building services community.

Studies which compare physics based models to empirical options are of particular interest. Neto & Fiorelli (2008) compared the ability of EnergyPlus and neural network models to forecast building energy consumption. Despite energy forecasting being the primary function of tools such as EnergyPlus, both types of models had a similar error range. The authors concluded that either method would be suitable for energy forecasting. Ruano et al. (2006) compared the performance of EnergyPlus and neural networks to predict

26 2.6. Prior Applications of Model Predictive Control to Buildings

zone air temperature. Radial Basis Function (RBF) neural networks were trained using multi-objective genetic algorithms. The neural networks outperformed the EnergyPlus simulation. A sliding window adaptive methodology was also demonstrated. This adjusted the neural network model’s parameters to allow adaption to recent conditions.

Chapter 2. Ventila tion: Theor y and Contr ol 27

Study Problem Description Predictive Model

Main Aim Findings and Comments Building System Element Con-

trolled May- Ostendorp et al. (2011) Simplified office building in Boul- der, Colorado (simulated in EnergyPlus) Mixed-mode building

Window position Physics based model using Ener- gyPlus

Demonstrate an MPC approach to window control in a mixed- mode building. Additionally present a rule extraction method using generalised linear models (GLMs)for control.

Results for specific location showed a potential en- ergy saving of above 40%. The GLM approach achieved between 70-90% of the optimiser energy savings, but at a fraction of the computational ex- pense. Mendoza- Serrano & Chmielewski (2012) Theoretical building of 100 rooms, each subdivided into 4 zones

HVAC with ther- mal energy stor- age (TES) and chiller

Heat flow to the chiller and TES

White-box physics- based linear model

Apply economic model predic- tive control (EMPC) in con- junction with TES to time-shift power consumption away from periods of high demand to peri- ods of low energy cost.

Energy costs were reduced through the use of EMPC. The use of short control horizons gave similar operational costs with large computational savings compared with the longer horizons.

Neto & Fiorelli (2008) * Administration Building, Uni- versity of S˜ao Paulo HVAC with window-type and split air conditioners

N/A EnergyPlus and neural network

Comparison between neural net- work model and physics based model (EnergyPlus) for forecast- ing building energy consump- tion.

Results showed that both methods are suitable for energy forecasting and had a similar error range.

Oldewurtel et al. (2012) Four differ- ent European buildings Five variants, primarily me- chanically venti- lated Multiple possibil- ities depending on HVAC sce- nario Thermal Resistance- Capacitance (RC) network

The development and analysis of a stochastic model predic- tive control (SMPC) strategy for building climate control that takes into account the uncer- tainty due to weather predictions

SMPC was shown to outperform RBC, in terms of Non-Renewable Primary Energy (NRPE) usage, thermal comfort statistics and in terms of advan- tageous room temperature dynamics.

Ruano et al. (2006) * Secondary school building located in the south of Portugal

Air conditioned Air conditioner ON/OFF state

EnergyPlus and RBF neural net- work

Design models for prediction of inside air temperature predic- tion.

The neural network models were shown to achieve better results than the EnergyPlus simulations. Simple control technique was demonstrated for the purpose of validating the models. Predictive con- trol was stated as the preferred usage for the mod- els developed.

Table 2.2: Summary of key studies on application of MPC to building control systems using physics based models. * Relevant studies which investigated different control methodologies or were limited to system identification.

28 2.6. Prior Applications of Model Predictive Control to Buildings