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Currently in China, energy conservation and emission reduction are important initiatives for society. Because of its large proportion of building energy consumption, several methods for building energy conservation have been introduced for central air conditioning. This paper presents a hybrid system for a modelling and control approach. By analysing the cooling capacity transfer process and the electromagnetic properties of pumps, the modelling is performed in a hybrid system framework. Pumps are classified as fixed-frequency pumps, variable-frequency pumps, and switchable pumps; a switch control strategy is used in the chilled water system for supplying cooling capacity. In order to adjust indoor temperature and save electrical energy, the cooling capacity allocation and average temperature methods are presented, which satisfy the goal of optimal control of real-time energy consumption. As a numerical example, the temperature variation and cold regulation processes are simulated. Three rooms are the control objects that lower the setting points, and pumps waste as little electrical energy as possible. The results show 49.4% of water pump power consumption when compared with constant water volume technology. The modelling and control approach is more advantageous in ensuring the success of reconstruction projects for central air conditioning.

Currently, China is facing a series of ecological problems, such as climate change, environmental degradation, and increases in energy consumption. According to the “China Statistical Yearbook 2015”, the levels of energy utilization and features of energy consumption remain in a backward predicament of high energy consumption, low efficiency, and serious waste. In 2013, for example, the average power consumption was 148.5 million kWh every day, and the transfer efficiency was 43.12% [

Central air conditioning accounts for a great proportion of building energy consumption and has considerable opportunities for energy conservation and emission reduction. Thus, research on energy savings for central air conditioning has a significant impact. There are several methods for building energy conservation: manual dispatching based on management view, optimized control schemes based on sample statistics, and technical renovation based on variable water/air volume. In the perspective of management, Liang et al. [

Because of uncertain cold loading, variable water/air volume has the advantages of instantaneous adjustment of cooling capacity and energy consumption. Compared with building a new system, technical innovation avoids massive cost and long projects. Moreover, in the air conditioning system, up to 70% of the power consumption is due to pumps and fans [

Many investigation reports in the literature show that variable water volume technology is a current focus in our research. There are several optimization methods that can effectively address these problems. These methods are the analytical approach [

Control strategies include temperature difference and pressure difference control methods. Wang and Burnett [

Moreover, some experimental and applicable results show advantages towards the method of technical renovation. Anderson et al. [

In these studies, pure continuous or discrete control systems are used for the control of the entire air conditioning system. However, the constant frequency pumps, variable-frequency pumps, and switching pumps in the chilled water system constitute a hybrid system. The frequency conversion operation and switching action of the pumps reflect the continuous and discrete dynamics, respectively. Therefore, the methods can hardly reflect the accuracy and applicability of the system structure and control process, nor an ideal energy saving effect. In addition, the electromagnetic properties of pumps are elided normally, although the hydraulic and thermodynamic characteristics are considered. Because the mathematical model of a pump motor is a high-order, nonlinear multivariable system with strong coupling effects, the variable-frequency, quadratic regression empirical formulas or simple proportional expressions cannot reflect the dynamics of motor appropriately. Compared with the pressure difference control strategy, the temperature difference control method is superior in energy saving.

In this paper, a hybrid model was used in the modelling of the chilled water system in a central air conditioning system. Variable-frequency pumps and switchable pumps denote continuous and discrete control inputs, respectively. Based on the model, a hybrid dynamical control strategy was proposed for variable volume control and better energy saving performance. This model reflects the actual working conditions of central air conditioning water systems, especially in aspects of pump movement and water flow change characteristics. Problems such as time variability, multivariable, nonlinearity, and uncertainty are considered, and the energy saving performance of the proposed control method is exhibited.

The modelling and controlling of the system are shown as follows: first, an optimized pump model of speed adjustment based on vector control was developed, which prefers electromagnetic properties and the torque response effect. In addition, considering the load characteristics of the water system, we regulate the water volume of pumps by vector control instantaneously. Second, the cooling capacity transfer process is described, with thermodynamic properties throughout the framework. The measure of constant temperature difference is used in the model. Third, we use switching control strategy, cooling capacity allocation, and average temperature methods in order to obtain the hybrid dynamical property by volume adjusting and pump switching (on/off). Thus, we not only realise variable volume control, but also satisfy the energy saving requirement. Finally, a numerical example illustrates the control process and situation of energy savings.

This paper is organized as follows. In Section

The hybrid system is described by

for_{i} denotes constant vector, and _{i} and_{i} are state matrices;_{i} is input matrix.

In the air conditioning system, the cooling capacity transfers from chiller unit to chilled water system by evaporator. The pumps drive water as cycle in the chilled water system, and send cooling capacity to air condition unit for exchanging from chilled water system to air system. After mixing with fresh air, the cold air is sent to air conditioning room to drop the temperature. In the process of temperature change in air conditioning room, the heat balance is influenced by several aspects: cold air, random heat of occupants and equipment, latent heat inside, and heat transfer from building structure. The processes of the cooling capacity transfer and temperature change is shown in Figure

Cooling capacity transfer and temperature change processes.

This paper uses constant air volume and variable water volume/constant temperature difference measures to transfer cooling capacity. In chilled water system, switching and variable-frequency behaviours of pumps adjust the flow for saving energy, which denote the discrete and continuous time process, respectively. So we give an equation to show the heat balance as follows:

The description of the symbol can be seen in the subsequent chapters and in Nomenclature.

Towards motor model of variable-frequency pump, we use a direct torque control model to build and design the closed-loop control of torque and flux linkage; but for constant frequency pump, we use constant to describe it. By building relationship of torque with water flow volume, we get equations of state space for the whole process of the model at last.

It is known that the cold load of central air conditioning is affected by factors such as the structure and materials of a building, outdoor weather parameters, indoor lighting, radiating equipment, and number of occupants. In order to describe the dynamic process, we consider the area

The dynamic thermal balance equation in a room is

In the cooling capacity transfer process, some of the cold is lost; we set the transfer efficiency as

Because of the return air rate

According to the three kinds of pumps, the water flow volume is expressed as

Most variable-frequency pumps are asynchronous AC motors in air conditioning systems. We use a stator flux-oriented direct torque control-space vector pulse width modulation (DTC-SVPWM) model to build and design the closed-loop control of torque and flux linkage. The features of DTC-SVPWM are that the controller computes the suitable stator voltage vector, and the method of SVPWM modulation generates the voltage vector to control torque and flux linkage. The structure is shown in Figure

Motor model.

The_{e}. We obtain

The simplified equations of stator voltage and torque are

Torque control loop.

We use an integral controller for torque adjustment.

In general, the water volume

State space.

Thus, the coefficients of the state space equation are

According to the electromagnetic property of a variable-frequency pump, the output mechanical power of the pump is

The power of a fixed pump is

The goal of optimal control for central air conditioning is to minimise the power of the chilled pumps; further, the inside temperature _{0},_{1}_{1},_{2}_{f}_{i}, and the switching law_{i} and_{i} are one-to-one correspondence.

Equation (_{0},_{f}]; (ii) the function is divided into several parts, and we calculate the integration on each time interval; (iii) the sum of all integration terms is the minimum of the objective function.

Switching law is state-independent, so the length of each time interval is not the same.

We simply consider the requirement of energy saving, and the humidity is not concerned in this work.

Variable water flow is realised by variable-frequency regulation of variable-frequency pumps and switching control of switchable pumps. For the water flow volume of the variable-frequency pump, the feedback closed loop can be used in the system for accurate adjustment. For the switching pumps, we propose an algorithm for deployment. According to the changing cold load, we set the switching condition and orientation. The switching law is a simple and economic mode in reconstruction engineering that avoids complex processes and computing time. It is shown in Figure

Control strategy of switching pumps.

The switching strategy is based on state dependence. The switching behaviour occurs simply by satisfying the state judgement. In other words, once the real-time sampling value is beyond the setting threshold value

The maximum number of switching pumps is

The minimum number of switching pumps is 0. If a nonswitching pump is operating, the system is close to optimal energy saving.

Whether switching is on or off, the system obeys one pump at a time. The switching behaviour triggers only one pump.

For a whole building, the framework is modelled with a switching control strategy. In real system, with many rooms with different areas, the cooling capacity requirement and temperature setting need an adaptive method to match. For allocation of cooling capacity, we adopt a weighting factor according to the proportion of thermal capacity in each room. This is a quantitative criterion on the demand side; on the supply side, there is a measure to balance different inside temperatures. The average temperature difference as a feedback signal is used to control the pumps. The switching condition

Cooling capacity allocation and average temperature methods.

Obviously, these are based on the quantitative criterion, whatever the average temperature difference or weighting factor.

In view of allocating cooling capacity by weighting factor, the computing method of average temperature difference actually involves the average temperature per cubic meter.

Heat capacity

In this section, we present numerical results from simulations of the chilled water system. Three different rooms are the simulation objects; the cold air is sent to the rooms for reducing the inside temperatures. The supply side uses pumps for sending cold water to the air system by the switching control strategy and cooling capacity allocation method. We use one variable-frequency pump, four switching pumps, and two fixed pumps to transfer chilled water and adjust cooling capacity. The cooling capacity transfer mode of variable water volume and constant air volume is presented. The purpose of the variable water volume is accuracy control and energy saving, via our model and control strategy. The parameters are listed in Table

Thermal parameters.

Parameter | Value | Remark |
---|---|---|

| 67.725, 90.3, 158.025 | Rooms A, B, and C, respectively |

| 0.02 | |

| 0.013 | |

| 0.655, 0.655, 0.655 | Rooms A, B, and C, respectively |

| 0.025 | |

^{2}) | 36, 8, 0 | Room A |

^{2}) | 52, 9, 0 | Room B |

^{2}) | 66, 12, 6 | Room C |

| 1010 | |

| 4180 | |

| 0.214, 0.286, 0.5 | Rooms A, B, and C, respectively |

| 0.2 | |

| 0.0037, 0.286, 0.0026 | Rooms A, B, and C, respectively |

| -0.061 | Whole system |

^{2} | 0.049, 0.051, 0.05 | |

| 19, 28, 31 | Rooms A, B, and C, respectively |

| 0.82 | |

| 5 | |

| 0.86 | |

| 30, 30, 30 | Rooms A, B, and C, respectively |

| 25, 25, 25 | Rooms A, B, and C, respectively |

| 35, 35, 36 | Room A |

| 35, 35, 36 | Room B |

| 35, 35, 36 | Room C |

| 25.8, 26.1, 25.9 | Rooms A, B, and C, respectively |

Simulink 2007 was used for simulating the whole process, where the simulation time was 5000 s. The switching sample time

The inside temperatures of the three rooms started at 30°C, and the system began at full capacity; in other words, all pumps were operating at rated power at the very start. Some curves were introduced into rooms as inside random cold loads; the surface temperatures of the wall space, window, and roof are set at constant values. The sending air volume was the same as the three rooms and was constant.

Figure

Inside temperature.

Random cold loads.

Total temperature difference.

Water flow volume.

Considering the electromagnetic properties, the speed of a pump starts from zero to a stable value with a smooth curve (Figure

Electromagnetic parameters.

Parameter | Value | Remark |
---|---|---|

| 2 | variable-frequency pump |

| 2.5 | variable-frequency pump |

^{2}) | 0.0012 | variable-frequency pump |

| 2.8 | variable-frequency pump |

| 1.5 | |

| 1.6 | |

^{2}) | 22 | variable-frequency pump |

| 2 | |

| 0.9 | variable-frequency pump |

Speed of pump.

Electromagnetic torque.

By the power models of the pumps, the energy consumption was simulated (Figure

Power consumption.

Power consumption comparison.

The performance of systems controlled by hybrid dynamic control strategy and constant water volume technology (all the pumps work at rated power and the chilled water system works without using our control strategy), respectively, is shown in Figure

A hybrid dynamical approach to modelling and control is used in central air conditioning, which is a suitable approach for energy saving reconstruction in contemporary China. By analysing the cooling capacity transfer process from the chilled water system to the air system, the framework is built. By involving a direct torque control measure, the electromagnetic property is considered. For optimal hybrid control, the switching control strategy is developed; the cooling capacity allocation and average temperature methods are presented. On the basis of mathematical power models of pumps, the goal of accurate control and energy saving is realised. By simulation, a numeral example shows a hybrid control process and situation of energy savings. The approach saves 49.4% of water pump power consumption when compared with constant water volume technology. The modelling and control of multihybrid systems and their applications in refrigeration systems will be investigated in future works.

Current

Amount

Mass

Speed

Number of pole-pairs

Flow volume

Resistance

Voltage

Area

Specific heat

Thermal capacity

Factor of cooling capacity allocation

Amount

Constant

Rotating inertia

Feedback coefficient (a room)

Feedback coefficient (total system)

Heat transfer coefficient

Power

Heat

Returned air rate

Switch status signal

Electromagnetic torque

Load torque

Heat transfer efficiency

Factor

Temperature difference

Temperature

Surface temperature

Flux linkage

Angular speed

Rated

Air

Variable-frequency pump

Fresh air

Filter time

Fixed-frequency pump

Initial

Integral time

Surface (wall space, window, and roof)

Latent heat

Random

Return

Stator

Sending air

Setting value

Switchable pump

M-axis of stator flux-oriented

T-axis of stator flux-oriented

Water

Total

Sensible heat

Busbar

Flux linkage.

No data were used to support this study.

The authors declare that they have no conflicts of interest.

The research was supported by the National Natural Science Foundation of China (no. 40761104181).