电气工程与自动化专业暖通空调系统中英文资料外文翻译文献

暖通空调系统中英文资料外文翻译文献

外文文献：

HV AC system optimization––condenser water loop Abstract

This paper presents a model-based optimization strategy for the condenser water loop of centralized heating, ventilation and air conditioning (HV AC) systems. Through analyzing each component characteristics and interactions within and between cooling towers and chillers, the optimization problem is formulated as that of minimizing the total operating cost of all energy consuming devices with mechanical limitations, component interactions, outdoor environment and indoor cooling load demands as constraints. A modified genetic algorithm for this particular problem is proposed to obtain the optimal set points of the process. Simulations and experimental

results on a centralized HV AC pilot plant show that the operating cost of the condenser water loop can be substantially reduced compared with conventional operation strategies.

Keywords: Centralized HV AC system; Condenser water loop; Model-based optimization; Genetic algorithms;Simulations and experiments

1. Introduction

A typical centralized heating, ventilation and air conditioning (HV AC) system is comprised of a condenser water loop and chilled water loop that, together with chillers and indoor air loops,provide a comfort environment for the conditioned space. The process of a condenser water loop consists of chiller condensers, pumps, cooling towers and fans [1]. The schematic diagram of a condenser water loop is shown in Fig.

1. Chiller condensers transfer the indoor cooling load and the heat generated by the compressors into the condenser water. Pumps provide the energy to circulate water between the chiller condensers and the cooling towers. The heat is rejected to the ambient air through heat transfer and evaporation by the cooling towers.

Since the condenser water loop is a main function block of HV AC systems, its energy consumption contributes significantly to the overall operating cost. Efficient operation of individual devices as well as the whole condenser water loop has been intensively studied in recent years. Among many published research results, Cassidy and Stack [2] showed that varying the speed of cooling tower fans can reduce energy consumption at part load conditions. Braun and Doderrich [3] proposed a systematic approach to find a near optimal variable speed drive (VSD) fan speed based on parameters estimated from design data. This method was further extended by Cascia [4] to simplify the component model and provide equations for determining the set points of near optimal control. However, all these methods were based on the assumption that the condenser water flow rate is unchanged. By considering the effects of condenser water flow rate on the performance of the chiller condensers and cooling towers, Shelton and Joyce [5] recommended a fixed condenser water flow rate (1.5 gpm/ton) as a rule of thumb for system operation. Later, Kirsner [6] showed that high condenser water flow rate (3 gpm/ton) has good performance at full load

condition, while low condenser water flow rate (1.5 gpm/ton) has advantages at part load conditions. Unfortunately, systematic determination of the water flow rate under different out-door environment and cooling loads is still an open question. Another important variable to be considered in condenser water loop optimization is the condenser water supply temperature. Schwedler [7] used several examples to demonstrate that the lowest possible leaving tower water temperature does not always conserve system energy. Nevertheless, his results were not conclusive as only half speed and full speed fan conditions were considered.

In this paper, a novel optimization strategy for the condenser water loop is presented. Our objective is to minimize the total energy consumption of the condenser water loop. Based on the mathematical models of related components, the operating characteristics of cooling towers, the effects of different ambient environment and the interactions between chillers and cooling towers,the energy efficiency of the condenser water loop can be maximized by both variable water flow rate and air flow rate. A modified genetic algorithm is used to search for optimal values of the independent variables. Simulation and experimental results on a centralized HV AC pilot plant demonstrate that a significant operating cost can be saved by the proposed method.

2. Problem formulation

In the condenser water loop, there are three types of devices which consume energy, namely chillers, pumps and fans. Therefore, the objective function is to minimize the

total energy consumption of these devices.

fan pump chiller total P P P P ++=min

The power consumptions of the chillers, pumps and fans are given, respectively. )()(,,,i adj adji i nom i

i cap chiller Temp PLR COP Q P ???=∑

CWS

CHWS CHWS CHWS CHWS CHWS i adj i i cap i i cap i adj T T c T c T c T c T c c Temp Q Q b Q Q b b PLR where

52432210,2

,2,10,)()(+++++=++=∑∑

))()()(

())()()(

(3,,,32,,,2,,,10,,3,,,32,,,2,,,10,,k

nom a k a k nom a k a k k nom a k a k nom fan fan j

nom w j w j nom w j w j nom w j w j nom pump j pump m m e m m e m m e e P P m m d m m d m m d d P P and

+++=+++=∑∑ Note that the performance of the condenser water loop is a ?ected by several factors, such as the physical limitations of individual components, interactions among them and the outdoor environment. These factors have to be considered in solving the optimization problem. The mathematical formulations and physical explanations of these constraints are given below.

2.1. Mechanical constraints

As P pump and P fan are influenced by m w;j and m a;k monotonically, the physical limitations for m w;j and m a;k

are Constraint (1)

2.2. Cooling tower constraint

The cooling tower constraint is given as [10]

Constraint (3)

where K is the total number of operating cooling towers and m w;k is the water flow

rate to each cooling tower. Without loss of generality, in analyzing the cooling tower performance, it is assumed that the condenser water is evenly distributed in each cooling tower

There are two factors affecting cooling tower performance in Constraint (3), one is m w;j vs. m a;k and the other is T CWR vs. T w b . To simplify the analysis, it is assumed that T CWR and T w b are constants in discussing the effect of m w;j vs. m a;k . Fig. 2 shows five curves of equal heat rejection rate [11], where the x-axis is percentage of water flow rate at full load and the y-axis is percentage of air flow rate at full load. These curves of equal heat rejection rate are divided into three portions. ?Portion (1): the air flow rate is very small and the water flow rate must be very big in order to achieve a given heat rejection rate. In this case, the air flow rate is too small to exchange heat efficiently with the condenser water. The outlet air flow wet bulb temperature is almost the same as that of the inlet water.

?Portion (2): the air flow rate is very big, while the water flow rate is very small, the heat ex-change is saturated and the outlet water temperature is nearly equal to the ambient air wet bulb temperature.

?Portion (3): the heat rejection rate of the cooling tower increases with either increased air flow rate or increased water flow rate and vice versa.

Apparently, the energy efficient operating range must lie inside Portion (3). In this portion, a reduced air flow rate leads to a lower fan power consumption, but the water flow rate has to be increased, resulting in an increased pump power consumption. Similarly, a reduced water flow rate lowers the pump power consumption but results in an increased fan power consumption. Constraint (3) limits the value of m w;j and m a;k due to the cooling tower characteristics.

The term T CWR T wb in Constraint (3) reflects the effect of T wb on the cooling tower performance. Assuming the cooling tower heat rejection rate and condenser water supply temperature are kept constant, the optimal operating point of cooling towers changes if T wb changes. Fig. 3 gives an example where the cooling tower heat rejection rate is assumed to be a fixed value for different wet bulb temperatures of ambient air, 20 and 25 LC, respectively. The optimal operating points are labeled as pentagons to indicate the corresponding power consumption of the fans and pumps. While the curves of fan power consumption are the same for different wet bulb temperatures, the condenser water flow rate changes with changing air flow rate and

outdoor environment for a constant cooling tower heat rejection rate.

The optimal air flow rate is 85% of the full load at 25 ℃ and 50% at 20 ℃. For an optimal operating point, the power consumption is 12% of the full load at 20 ℃ wet bulb temperature. If the air flow rate is kept at 85% of the full load at 20 ℃ instead of 50%, the combined power consumption of the fan and pump is 19% of the full load. Compared with 12% of the full load at the optimal point, almost 7% of the energy of the full load could be saved with varying the mass flow rates of water and air.

2.3. Interaction constraints

The variable T CWS influences both the chiller power consumption and the cooling tower performance.

Constraint (4)

This temperature is also restricted by boundaries that are often provided by chiller manufacturers for safe operation of the chillers.

It has been generally acknowledged [3,5–7,12–16] that a decreasing T CWS results in an increasing COP and lower energy consumption of the chillers. However, a lower T CWS leads to a smaller T CWR and then higher m a;k and m w;k for fixed Q and T wb. As m a;k and m w;k increase, the fan power and condenser water pump power increase cubically. Fig.

4 illustrates the trade-off between the chiller and cooling tower fan power associated with an increasing tower air flow rate [2]. Here, a fixed condenser water flow rate is assumed. As the air flow rate increases, the fan power increases. At the same time, there is a reduction in the condenser water supply temperature, resulting in a lower chiller power consumption.

On the other hand, T CWR, in turn, affects the heat exchange efficiencies in the cooling towers. When the condenser water supply temperature decreases, the condenser water return temperature also decreases for the same cooling load. This

results in lower efficiencies of the cooling tower under the same ambient wet bulb temperature, as the enthalpy difference between ambient air and condenser water becomes smaller. The optimal operating point occurs at a point where the rate of power increase in the fans and pumps is equal to the rate of power reduction in the chillers.

3. Optimization algorithm

In the optimization problem, i, j, k, m a;k and m w;j are independent variables, T wb, T CHWS, T CHWR and m CHW are variables that can be measured and Q, T CWS and T CWR are variables to be deter-mined by constraints.

As this optimization problem is a combinatorial optimization problem with non-linear constraints and contains both continuous and discrete variables, conventional gradient based optimization methods cannot be applied directly. An exhaustive search method or an exhaustive search method combined with conventional gradient based methods can be applied to find the optimal solutions, even though it is impractical in real time applications for such a complicated problem due to its time consuming nature. Genetic algorithms for problem solving are not new, but it is only very recently that they are implemented in industry applications [17–20]. The genetic algorithm is more attractive than other optimization algorithms in several aspects:

?It can handle problem constraints by simply embedding them into the chromosome

encoding procedure.

?It is feasible to solve multi-model, non-differentiable, non-continuous problems etc., since it is independent of the function gradient.

?It is very easy to understand and involves very little mathematics.

?It has implicit parallel computation features, which make it more efficient than the exhaustive search methods.

The implementation of a modified genetic algorithm for this particular problem can be divided

into four phases: encoding, construction of fitness function, evolution and termination.

3.1. Encoding

The first step for a genetic algorithm is encoding. It is a process of transforming a series of problem inputs into a serial of codes that can be easily interpreted and used in evaluating the information it represents by the fitness function. In this application, both discrete variables (i, j, k) and continuous variables (m a;k , m w;j) are converted into binary strings and are connected together to form a chromosome.

For the discrete variables, each bit represents the status of each component. For example, ‘‘1’’ stands for either a chiller, a pump or a fan being staged on, while ‘‘0’’ is for off.

For the continuous variables, such as the mass flow rates of air and water, the upper and lower bounds of their binary strings stand for minimum and maximum values in Constraint (1). The lengths of the binary strings are determined by the control precision of the corresponding variables: the more precise set point control, the longer binary string.

3.2. Construction of fitness function

In order to fulfill Constraints (2)–(5), penalty functions are commonly used to penalize an in feasible solution. In this step, a penalty function is added if any constraint cannot be fulfilled. The fitness function is expressed in the following equation.

where v1, v2and v3are the penalty multipliers, which should be large positive numbers. With this fitness function, the minimal system power consumption without violating any constraints has the maximum fitness value. The fitness values will be used as guides for evolution.

3.3. Evolution

The evolution consists of three major functions: selection, crossover and mutation [17]. These functions are performed for each generation to produce the next generation with improved fitness values.

?Selection is the process of determining the number of times that a particular individual is chosen for reproduction. The ‘‘roulette wheel’’ selection method [17] is adopted in the application based on linear scaled fitness values.

?Crossover is a basic function to produce new individuals which have some parts of both parents genetic material. A single point crossover method is adopted here and shown by the following example.

Parent 1: 1 1 1 1 1 1 ‘‘crossover at the second bit’’ New individual 1: 1

1 0 0 0 0 Parent 2: 0 0 0 0 0 0 ) New individual 2: 0 0 1 1 1 1

?Mutation is a random process where one bit of a binary string is flipped to produce a new individual. Single bit mutation is used in the example below.

Original individual: 1 1 1 1 1 1 ‘‘mutation at the fifth bit’’

New individual: 1 1 1 1 0 1

The crossover and mutation points are all selected randomly in each generation.

The probability of crossover and mutation are selected according to the recommendations in Refs.

T he evolution procedure of the modified genetic algorithm is illustrated in Fig. 5. The major differences with the simple genetic algorithm given in Ref. [17] are:

1.To restrict the searching space by knowledge from the previous optimization. The

reduced searching space reduces computing time.

2.To keep the individual with the best fitness value in each generation. This operation prevents the optimal results from being lost in the subsequent evolutions.

The parameter settings in the modified genetic algorithm are listed as follows: ?Number of individuals in a generation: 100;

?Maximum number of generations: 500;

?Precision of each continuous variable: 28;

?Generation gap: 0.9;

?Probability of crossover: 0.7;

?Probability of mutation: 0.01.