Evaluation of Energy Saving Potential using Stochastic Model Predictive Control for Stand Alone Air

Conditioning Units A Study in Indian Scenario

Presented by: Sandeepan Majumdar Department of Power Engineering, Jadavpur University

Tiyasa Ray, Sandeepan Majumdar, Sumit Mukherjee

Paper ID: 127

Introduction

Need for Control of HVAC Systems

Buildings account for over 40% of total energy consumptionMost of it is consumed by HVAC systemsSevere need to minimize wastage of energy due to increasing demand

Difficulty in modeling buildings accuratelyFitting into existing infrastructuresDeveloping a robust yet energy minimizing control strategyDecrease model dependency

Challenges

Model Predictive Control Widely used for control of HVAC systemsCould be modified to optimize for energy efficiency, thermal comfort, cost etc. Savings depend on model accuracy Number of optimization parameters could be large for a large system

Stochastic Model Predictive Control

Why Stochastic Model Predictive Control?

To Use a Stochastic Dynamical Model of the process to Predict it’s possible future states and choose the best control action

•In many control problems decision must be taken under uncertainty.•Robust Control approaches do not model uncertainty only assumes that it is bounded and considers the worst case. •Stochastic Models provide additional information about uncertainty.

In this work a novel approach to control all these air conditioning units using a centralized controller based on Stochastic Model Predictive Control (SMPC) has been presented. The SMPC takes into account the predicted weather to reduce energy consumption while maintaining the comfort level of the occupants. A sample office space has been modeled and performance of the algorithm has been studied for weather conditions of large cities of India.

Building Model

The electrical analogy of heat transfer is becoming increasingly popular due to its simplicity and relatively accurate performance. There are many possible wall models that could be used but we adopt a standard 3R2C model.

R denotes the thermal resistance (K/W). thermal mass is denoted by C and has the unit J/K.

A single room is modeled as a thermal capacitor (representing the thermal storage of air in the room)and a wall as a combination of R and C components

Here the capacitors C1 and C2 are wall capacitances, while Ca1 and Ca2 are air capacitances

each standalone unit comprises of an air conditioner that draws air from the outside through a quality controlled vent (we assume there is 50% fresh air intake), which is then cooled to the supply air temperature(chosen by the user) at the air conditioner and injected into the room.

Now, an undirected graph is constructed for the thermal system comprising of N nodes and L links, where N is equal to the number of thermal capacitances and L is equal to the number of thermal resistances.

where C is a diagonal, matrix consisting of the thermal capacitances, R is a diagonal, matrix consisting of the thermal resistances, D is the incidence matrix for the undirected graph constructed from the thermal

network, B0 is a column vector whose non-zero elements are the thermal conductance of nodes

connected to the ambient, T∞ is the outside ambient temperature, u is the heat input into each room, Pd is the heat generated at each room due to occupancy, B is the corresponding input matrix and y is the matrix of room temperatures.

Building Model

Air Conditioner Model

For the purposes of simplicity we assume that the time scale of the dynamics of the cooling process is very fast and can be ignored. We also assume that the energy consumption due to the fan drawing in the air is negligible in comparison to the energy required for cooling. where, Tr,i is the re-circulated air temperature,

yi is the room temperature, ms,i is the mass flow rate, Cp is the specific heat capacity, Tsup,i is the supply air temperature (controlled by the user) Qi is the energy consumed.

For all of these quantities the i subscript is used to denote ith room/zone

Cost Function Formulation

Where, Tr,i(k) is the return air temperature for the kth sample,

Tpeak,i(k) is the peak supply air temperature,Toff,i(k) is the off peak supply air temperature, Speak is the set of all samples starting from the present sample

that lie in the peak periods, Soff is the set of all samples starting fromthe present

I(:) denotes the indicator function, Ti(k) is the temperature of the ith zone, Tmax,i is the maximum preferred temperature of the zone, Tmin,i is the minimum preferred temperature of the zone, Ak,i is the event that Ti(k) >Tmax,i and Bk,i is the event that Ti(k)

<Tmin,i, p isa weighting constant and Sall is the set of all samples

beginning from the present to the time the office is closed

Implementation of Stochastic MPC to the Cost Function

Hour. Occupant MeanZ1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9

08:00 4 2 1 2 2 3 4 2 209:00 5 3 1 3 3 4 5 3 310:00 8 4 2 4 4 5 8 4 411:00 8 4 2 4 4 5 8 4 412:00 8 4 2 4 4 5 8 4 413:00 5 3 1 3 3 2 5 3 314:00 8 4 2 4 4 5 8 4 415:00 8 4 2 4 4 5 8 4 416:00 8 4 2 4 4 5 8 4 417:00 8 4 2 4 4 5 8 4 418:00 8 4 2 4 4 5 8 4 419:00 8 4 2 4 4 5 8 4 4

Hour. Occupant Standard DeviationZ1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9

08:00 2 1 1 1 1 1 2 1 109:00 2 1 1 1 1 1 2 1 110:00 4 3 2 3 3 2.

54 3 3

11:00 4 3 2 3 3 2.5

4 3 3

12:00 4 3 2 3 3 2.5

4 3 3

13:00 2.5 1.5

4 1.5

1.5

2 2.5

1.5

1.5

14:00 4 3 2 3 3 2.5

4 3 3

15:00 4 3 2 3 3 2.5

4 3 3

16:00 4 3 2 3 3 2.5

4 3 3

17:00 4 3 2 3 3 2.5

4 3 3

18:00 4 3 2 3 3 2.5

4 3 3

19:00 4 3 2 3 3 2.5

4 3 3

The initial temperature of the building, i.e. room temperature at the start of the simulation is assumed to be equal to the ambient temperature at the start of the simulation for all the cases.

We assume that the mean and standard deviation of the occupancy values for each zone are available apriori (but not the exact values) and weather forecasts for the 12 hour period is also available.

Appropriate values of Tr,i are obtained by Minimizing J while supply air constraints are satisfied.

Base Case is evaluated with a fixed room temperature of 24 Degree Celsius.

Percentage Energy Saving is Computed.

Building Model Used of Simulation

The office space in consideration comprises of 9 zones, consisting of a reception, two conference halls, 5 office rooms, a pantry and

a store room. The dimensions are marked in the figure.

Results

Ahmedabad

Allahbad

Aurangabad

Balmer

Bhagalpur

Bhubaneshwr

Chennai

Dehradun Go

a

Gwalior

Hydrabad

Indore

Jagdelpur

Jaiselmer

Jodhpur

Kolkata

Kurnool

Mangalore

Nagpur

New DelhiPatna

Raipur

Ramagundam

Ratnagiri

Saharanpur

SholapurSurat

Trichi

Veraval

00.51

1.52

2.53

3.54

Percentage Saving

Energy Saving Varies significantly with location however it is clear that there is a potential for saving as high as 3.5%

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