A General control algorithm for cooling towers in cooling plants with electric and/or gas-driven chillers.Received September September: see month. 13,2006; accepted February February: see month. 23, 2007INTRODUCTION A chiller chill·er n. 1. One that chills. 2. A frightening story, especially one involving violence, evil, or the supernatural; a thriller. chiller Noun 1. plant often consists of multiple chillers, multiple condenser condenser Device for reducing a gas or vapour to a liquid. Condensers are used in power plants to condense exhaust steam from turbines and in refrigeration plants to condense refrigerant vapours, such as ammonia and Freons. water pumps, and multiple cooling towers as depicted de·pict tr.v. de·pict·ed, de·pict·ing, de·picts 1. To represent in a picture or sculpture. 2. To represent in words; describe. See Synonyms at represent. in Figure 1. In some situations, it is economical to employ a mix of chillers that are "powered" by electricity and natural gas (e.g., absorption absorption [Lat.,=sucking from], taking of molecules of one substance directly into another substance. It is contrasted with adsorption, in which the molecules adhere only to the surface of the second substance. or engine-driven). This is termed a hybrid chiller plant. The major advantage of using natural gas chillers in hybrid central chiller plants is a reduction in peak electrical demand and on-peak energy usage, which can reduce overall operating costs operating costs npl → gastos mpl operacionales . The electric demand cost can often account for about half of the total air-conditioning air-conditioning Control of temperature, humidity, purity, and motion of air in an enclosed space, independent of outside conditions. In a self-contained air-conditioning unit, air is heated in a boiler unit or cooled by being blown across a refrigerant-filled coil and then bill. [FIGURE 1 OMITTED] Proper control of cooling tower fans in cooling plants can have a significant impact on operating costs. For all electric plants, optimal control of cooling fans has been shown to result in significant (e.g, 5%--15%) savings in plant energy costs as compared with typical strategies that are employed (see Sud [1984], Lau et al. [1985], Hackner et al. [1985], Klein Klein , Melanie 1882-1960. Austrian-born British psychoanalyst who first introduced play therapy and was the first to use psychoanalysis to treat young children. et al. [1988], Braun Braun , Eva 1912-1945. German lover and later wife of Adolf Hitler. They began living together in 1936, but the liaison was kept secret, and she was never seen in public with him. They were married hours before their double suicide on April 30, 1945. [1988], Braun et al. [1989a, 1989b], ASHRAE ASHRAE American Society of Heating, Refrigerating & Air Conditioning Engineers [2003]). The savings for plants employing absorption chillers can be even larger because of higher heat rejection requirements. For instance, Koeppel et al. (1995) simulated optimal control of tower fans and condenser pumps for a cooling plant having a double-effect absorption chiller and determined a 20% reduction in costs compared to using fixed speeds with a tower bypass In communications, to avoid the local telephone company by using satellites and microwave systems. control to maintain a constant cooling tower water supply. Although there is a large body of literature related to supervisory control Supervisory control is a general term for control of many individual controllers or control loops, whether by a human or an automatic control system, although almost every real system is a combination of both. for all-electric plants, there is very little literature on supervisory control of absorption, engine-driven, and hybrid chiller plants. Braun and Diderrich (1990) developed an algorithm algorithm (ăl`gərĭth'əm) or algorism (–rĭz'əm) [for Al-Khowarizmi], a clearly defined procedure for obtaining the solution to a general type of problem, often numerical. for cooling tower fan control for all-electric plants that is included in the 2003 ASHRAE Handbook--HVAC Applications (ASHEAE 2003). However, this strategy is not appropriate fro hybrid plants hybrid plant, n the creation of a new plant from natural or artificial fertilization between two species. The letter x in the middle of the plant name indicates its hybrid status. because it is based on minimizing input energy usage rather than cost. Koeppel et al. (1995) developed a simplified sim·pli·fy tr.v. sim·pli·fied, sim·pli·fy·ing, sim·pli·fies To make simple or simpler, as: a. To reduce in complexity or extent. b. To reduce to fundamental parts. c. strategy for cooling tower fan control for absorption cooling plants that involves the determination of a linear relationship between a setpoint Setpoint may refer to:
Field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics. results were used to determine a simple linear model for a case study involving a single double-effect absorption chiller. The application of the simple strategy resulted in savings that were nearly identical to the optimization results. However, it's it's 1. Contraction of it is. 2. Contraction of it has. See Usage Note at its. it's it is or it has it's be ~have not obvious how linear control relationships would be determined in practice and how to apply this method to hybrid plants. This paper develops a general algorithm for control of cooling tower fans for cooling plants that have any combination of electric and natural-gas chillers. The development follows an approach that is similar to the development of Braun and Diderrich (1990). The control method is evaluated through comparisons with optimal control for a range of different cooling plants and operating conditions using a simulation tool. Optimal control means that the control is based on minimization min·i·mize tr.v. min·i·mized, min·i·miz·ing, min·i·miz·es 1. a. To reduce to the smallest possible amount, extent, size, or degree. b. Usage Problem To reduce. See Usage Note at minimal. of an operating cost function that incorporates perfect information about the plant. A nonlinear A system in which the output is not a uniform relationship to the input. nonlinear - (Scientific computation) A property of a system whose output is not proportional to its input. optimization was performed to determine the performance for the benchmark A performance test of hardware and/or software. There are various programs that very accurately test the raw power of a single machine, the interaction in a single client/server system (one server/multiple clients) and the transactions per second in a transaction processing system. optimal control using the simulation tool. The development of the near-optimal control algorithm used several simplifying assumptions and heuristics heu·ris·tic adj. 1. Of or relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem: in order to determine analytical expressions In mathematics, an analytical expression (or expression in analytical form) is a mathematical expression, constructed using well-known operations that lend themselves readily to calculation. for cooling tower control. In this context, near-optimal control implies that the strategy has performance that is close to that associated with optimal control. DEVELOPMENT OF A NEAR-OPTIMAL COOLING TOWER CONTROL ALGORITHM Chiller plants, such as that depicted in Figure 1, typically have multiple cooling towers with fans that have multiple speeds of operation. In general, optimal control of cooling tower fansresults from a trade-off in the cost of operating the chillers and cooling tower fans. The energy consumption of a chiller is sensitive to the condenser water temperature, which is affected by the cooling tower control. Increasing the tower airflow reduces the chiller energy requirement but at the expense of an increase in fan power consumption. For a given set of conditions, an optimal tower control exists that minimizes the sum of the chiller and cooling tower fan power. Braun and Diderrich (1990) described how the determination of optimal tower fan control can be separated into two parts: tower sequencing and optimal airflow. For a given total tower airflow, optimal tower sequencing specifies the number of operating cells and the fan speeds that give the minimum fan power consumption. Once the tower sequencing is specified, then the optimal airflow can be determined by analyzing the trade-offs between the costs of operating the chiller and the fan. This section presents the development of an algorithm for near-optimal control of cooling towers that is based upon a combination of heuristic rules Noun 1. heuristic rule - a commonsense rule (or set of rules) intended to increase the probability of solving some problem heuristic, heuristic program for tower sequencing and an open-loop control equation derived de·rive v. de·rived, de·riv·ing, de·rives v.tr. 1. To obtain or receive from a source. 2. from a detailed analysis. Optimal Fan Sequencing Simple relationships exist for the best sequencing of cooling tower fans for towers having multiple cells as capacity is added or removed. When additional tower capacity is required, Braun et al. (1989a, 1989b) have shown that in almost all practical cases, the speed of the tower fan operating at the lowest speed (including fans that are off) should be increased first. Similarly, for removing tower capacity, the highest fan speeds are the first to be reduced. This leads to the following general rules for sequencing of tower fans: 1. All Variable-Speed Fans: Operate all cells with fans at equal speeds. 2. Multi-Speed Fans: Increment To add a number to another number. Incrementing a counter means adding 1 to its current value. lowest-speed fans first when adding tower capacity. Reverse for removing capacity. 3. Variable/Multi-Speed Fans: Operate all cells with variable-speed fans at equal speeds. Increment lowest-speed fans first when adding tower capacity with multi-speed fans. Add multi-speed fan capacity when variable-speed fan speeds match the fan speed associated with the next multi-speed fan increment to be added. Criteria criteria (krītēr´ē  ),n. for Optimal Tower Airflow Most cooling towers utilize single-or two-speed Two´-speed` a. 1. Adapted for producing or for receiving either of two speeds; - said of a power-transmitting device. fans, such that the optimization problem In computer science, an optimization problem is the problem of finding the best solution from all feasible solutions. More formally, an optimization problem  is a quadruple is discrete A component or device that is separate and distinct and treated as a singular unit. rather than continuous. However, for
the purpose of estimating the control parameters Control parametersIn a nonlinear dynamic system, the coefficient of the order parameter; the determinant of the influence of the order parameter on the total system. See: Order Parameter. , it is sufficient to consider the flow as being continuously adjustable. Consider the problem of determining the optimal tower control for continuously adjustable tower airflow. The minimum combined chiller and tower fan cost occurs at a point where the rate of change of cost with respect to changes in tower airflow is equal to zero, or [dC.sub.twr]/[d[gamma].sub.twr] = [dC.sub.ch]/[d[gamma].sub.twr], (1) where [C.sub.twr]and [C.sub.ch] instantaneous in·stan·ta·ne·ous adj. 1. Occurring or completed without perceptible delay: Relief was instantaneous. 2. energy costs for the cooling tower fans and chillers and defined as ratio of the airflow to the maximum possible airflow with all cells operating at maximum speed. In order to solve for the optimal tower control, it is necessary to develop a functional relationship for the sensitivities of chiller and cooling tower costs to tower airflow. Chiller Cost Sensitivity to Tower Airflow The rate of change of chiller cost with respect to tower airflow may be expressed as [[dC.sub.ch]/[d[gamma].sub.twr]] = [[dC.sub.ch]/[dT.sub.cwr]].[[dT.sub.cwr]/[d[gamma].sub.twr]], (2) where [T sub.cwr] is the condenser water return temperature. The rate of change of total chiller cost with respect to condenser water return temperature is [[dC.sub.ch]/[dT.sub.cwr]] = [[N.sub.ch].[summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (i-1)] [ER.sub.i]].[[dE.sub.[ch,i]]/[dT.sub.cwr]], (3) where [E sub [ch,i]] is the rate of energy input and [ER.sub i] is cost per unit energy input (heat or electricity) for the ith chiller. The rate of change of energy input with respect to condenser water temperature written as [[dE.sub.[ch,i]]/[dT.sub.cwr]] = [[S.sub.[c,h,i]].[COP COP In currencies, this is the abbreviation for the Colombian Peso. Notes: The currency market, also known as the Foreign Exchange market, is the largest financial market in the world, with a daily average volume of over US $1 trillion. .sub.[rated,i]]/[COP.sub.i].[E.sub.[ch,rated,i]]], (4) where COP is the chiller coefficient of performance The coefficient of performance, or COP (sometimes CP), of a heat pump is the ratio of the output heat to the supplied work or (ratio of cooling to energy input), [COP.sub.rated] is the chiller COP at the chiller design conditions, [PLR PLR pupillary light reflex. .sub.ch] is the chiller part-load ratio (load relative to rated capacity), and [S.sub.ch] is the sensitivity of the chiller input energy to changes in condenser water temperature given as [S.sub.[ch,i]] = 1/[[E.sub.[ch,i]].[dE.sub.[ch,i]]]/[dT.sub.cwr]., (5) For the purpose of determining tower airflow, it is reasonable to assume that the factor [S.sub.ch]([COP.sub.rated] /COP) is constant for a given chiller over different operating conditions. With this assumption, Equation 4 can be simplified to [[dE.sub.[ch,i]]/[dT.sub.cwr]] = [[S.sub.[ch,rated,i]].[PLR.sub.[ch,rated,i]].[E.sub.[ch,rated,i]], (6) Where [S.sub.[ch,rated,i]] is evaluated at the chiller design conditions. The next step is to develop a relationship for the effect of the tower control on the condenser water return temperature. From an effectiveness model for the thermal performance of a cooling tower (Braun et al. 1989c), the condenser water return temperature may be expressed as [T.sub.cwr][equivalent][T.sub.wd]+[[Q.sub.twr]/[[epsilon].sub.[a,twr]][m.sub.[a,twr]][c.sub.s]], (7) where [T.sub.wb] is ambient wet-bulb temperature, [Q.sub.twr]. is the cooling tower heat rejection rate, [m.sub.[a,twr]] is the tower air mass flow rate, [epsilon.sub.[a,twr]].is the an air-side effectiveness for heat and mass transfer within the tower, and [C.sub.s] is a property of the air-water vapor vapor /va·por/ (va´por) pl. vapo´res, vapors [L.] 1. steam, gas, or exhalation. 2. an atmospheric dispersion of a substance that in its normal state is liquid or solid. mixture termed the saturation saturation, of an organic compound saturation, of an organic compound, condition occurring when its molecules contain no double or triple bonds and thus cannot undergo addition reactions. specific heat. Equation 7 is simplified by relating the performance to design conditions, assuming that the tower effectiveness and saturation specific heat Equation 7 is are constants and utilizing the definitions for relative tower airflow, and tower approach and range. [T.sub.cwr] = [T.sub.wb] + [Q.sub.twr]/[[epsilon].sub.[a,twr]][m.sub.[a,twr]][c.sub.s] [[epsilon].sub.[a,twr,rated]][m.sub.[a,twr,rated]][c.sub.[s,rated]](T.sub.[cwr,rated]-[T.sub.[wb,rated]])/[Q.sub.[twr,rated]] = [T.sub.wb] + [Q.sub.twr]/[m.sub.[a,twr]]/[m.sub.[a,twr,rated]][Q.sub.[twr,rated]] [[epsilon].sub.[a,twr,rated]][c.sub.[s,rated]]/[[epsilon].sub.[a,twr]][c.sub.s]([a.sub.[twr,rated]] + [r.sub.[twr,rated]] ~[T.sub.wd] + 1/[[gamma].sub.twr] [Q.sub.twr]/[Q.sub.[twr,rated]](a.sub.[twr,rated] + r.sub.[twr,rated]), (8) where [a.sub.[twr,rated]] and [r.sub.[twr,rated]]. are the tower approach and range evaluated at the rating condition with the tower operating with maximum tower airflow at the chiller design load. The approach is the difference between the condenser water supply and ambient wet-bulb temperatures ([T.sub.cws]-[T.sub.wb]), whereas the range is the difference between the condenser water return and supply ([T.sub.cwr] - [T.sub.cws]). The ratio of the tower heat rejection to the design heat rejection can be approximated as [Q.sub.twr]/[Q.sub.[twr,rated]] = [N.sub.ch].[summation over (i=1)][PLR.sub.[ch,i]].[f.sub.[twr,rated,i]], (9) Where [f.sub.[twr,rated,i]] = [Q.sub.[cw,rated,I]]/[Q.sub.[twr,rated]], (10) and where [Q.sub.[cw,rated,i]] is the heat rejection from ith chiller to the condenser water at the rating condition. Equations 8 and 9 lead to [MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression. NOT REPRODUCIBLE re·pro·duce v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es v.tr. 1. To produce a counterpart, image, or copy of. 2. Biology To generate (offspring) by sexual or asexual means. IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ] (11) Combining Equations 2, 3, 6, and 11 results in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12) Cooling Tower Fan Cost Sensitivity to Tower Airflow The sensitivity of the tower fan costs to changes in control depends upon the type of fans and motors employed. For variable-speed drives and with each tower cell operating at equal flows, the fan power varies approximately ap·prox·i·mate adj. 1. Almost exact or correct: the approximate time of the accident. 2. with the cube cube, in geometry, regular solid bounded by six equal squares. All adjacent faces of a cube are perpendicular to each other; any one face of a cube may be its base. The dimensions of a cube are the lengths of the three edges which meet at any vertex. of the airflow. For multi-speed fans and with an optimal sequencing strategy, the fan power varies as a piecewise linear function In mathematics, a piecewise linear function
where V is a vector space and that approaches the variable-speed relationship as the number of speed settings increases. For single-speed fans, the fan power increases as a single linear function of the total tower airflow. For a system with discrete tower fan settings, it is adequate to assume a continuous variation in order to perform the optimization and determine the discrete control that is closest to the estimated control. For single-speed fans, the power is assumed to be a continuous linear function. For two-speed fans, performance data suggest that a squared relationship for power consumption as a function of airflow is adequate. For three-speed (or more) fans, a cubic variation in power consumption with airflow is sufficient. Thus,for varible-speed or three-speed fans, the sensitivity of the fan power consumption to control is assumed to be [dC.sub.twr]/[d[gamma].sub.twr] = 3.[[gamma].sub.twr.sup.2].[ER.sub.e].[P.sub.[twr,rated]], (13) While for two-speed fans [dC.sub.twr]/[d[gamma].sub.twr] = 2.[[gamma].sub.twr].[ER.sub.e].[P.sub.[twr,rated]], (14) and for single-speed [dC.sub.twr]/[d[gamma].sub.twr] = [ER.sub.e].[P.sub.[twr,rated]], (15) where E[R.sub.e]. is cost per unit electricity input and [P.sub.[twr,rated]] is the rated fan power with the fans running aT capacity. Optimal Tower Airflow Substituting Equations 12 and 13 into Equation 1 and solving for [[gamma].sub.twr] gives the following relationship for near-optimal control of cooling towers with three-speed or variable-speed fans. [[gamma].sub.twr] = [{1/3([a.sub.[twr,rated]] + [r.sub.twr,rated]) [[N.sub.ch].summation over (i = 1)] ([PLR.sub.ch,i][f.sub.[twr,rated,I]])[[N.sub.ch].summation over (i=1)]([PLR.sub.[ch,I]][S.sub.[ch,rated,i]) [[ER.sub.i][E.sub.[ch,rated,i]]]/[[ER.sub.e][P.sub.[twr,rated]]])}.sup.[1/4]], (16) For two-speed fans, Equation 14 is used instead of Equation 13 and the near-optimal control [[gamma]sub.twr] = [{1/2([a.sub.[twr,rated]] + [r.sub.[twr,rated]]) [[N.sub.ch].summation over (i=1)] ([PLR.sub.[ch,i]][f.sub.[twr,rated,i]])[[N.sub.ch].summation over (i=1)] ([PLR.sub.[ch,i]][S.sub.[ch,rated,i]] [[ER.sub.i][E.sub.[ch,rated,i]]]/[[ER.sub.e][P.sub.[twr,rated]]])}.sup.[1/3]], (17) while for single-speed fans, [[gamma].sub.twr] = [{([a.sub.[twr,rated]] + [r.sub.[twr,rated]]) [[N.sub.ch].summation over (i=1)] ([PLR.sub.[ch,i]][f.sub.[twr,rated,i]])([PLR.sub.[ch,i]][S.sub.[ch,rated,i]] [[ER.sub.i][ER.sub.[ch,rated,i]]]/[[ER.sub.e][P.sub.[twr,rated]]])}.sup.[1/2]], (18) The relative tower airflow is the ratio of airflow to the rated airflow with all fans operating at maximum speed. The factors that affect the optimal relative tower airflow are (1) the part-load ratio for each chiller, PL[R.sub.[ch,i]]; (2) the ratio of the operating costs per unit time for each chiller at its rating conditions to the rated cooling tower operating costs per unit time, (E[R.sub.i][E.sub.[ch,rated,i]])/(E[R.sub.e][P.sub.[twr,rated]]); (3) the sensitivity of individual chiller input energy requirement to changes in condenser water temperature at the chiller rating conditions, Sch,rated,i; (4) the ratio of the ith chiller heat rejection rate at its rating condition to the rated cooling tower heat rejection rate, [f.sub.[twr,rated,i]]; and (5) the sum of the tower approach and range at the tower rating condition ([a.sub.[twr,rated]] +[r.sub.[twr,rated]]). All of the factors in these expressions, except chiller part-load ratio and utility rates, are based on design information and do not require measurements. The design approach to wet-bulb, [a.sub.[twr,rated]] is the temperature difference between the tower sump water and the ambient wet-bulb for the tower operating at its air and water flow capacity at the tower rating conditions. The rated range, [r.sub.[twr,rated]] is the water temperature difference across the tower at these same conditions. The sum of [a.sub.[twr,rated]] and [r.sub.[twr,rated]] is the temperature difference between the tower inlet inlet /in·let/ (-let) a means or route of entrance. pelvic inlet the upper limit of the pelvic cavity. thoracic inlet the elliptical opening at the summit of the thorax. and the wet-bulb and represents a measure of the tower's capability to reject heat to ambient relative to the system requirements To be used efficiently, all computer software needs certain hardware components or other software resources to be present on a computer system. These pre-requisites are known as (computer) system requirements and are often used as a guideline as opposed to an absolute rule. . A small temperature difference results from a high tower heat transfer effectiveness or high water flow rate and yields lower condenser water temperatures with lower chiller energy consumption, resulting in a lower optimal tower airflow. Typical values for the design approach and range are 7[degrees]F and 10[degrees]F. Chiller part-load ratio measures the load for each chiller and influences the optimal tower airflow in two ways. First, chiller loading influences the total heat rejection requirements of the cooling tower, which affects the optimal airflow. The optimal tower airflow increases with heat rejection requirement. The first summation on the right-hand side right-hand side n → derecha right-hand side right n → rechte Seite f right-hand side n → lato destro of Equations 16--18 characterizes this effect. The factor [f.sub.[twr,rated,I]] weights the individual chiller loadings according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. their effect on the total heat rejection and is larger for chillers having greater design cooling capacity or lower design COP (e.g., absorption). The chiller loading also influences the chiller to cooling tower cost ratio along with the cost ratio at the rating conditions. As the ratio of chiller to tower cost increases, it becomes more beneficial to operate the tower at higher airflows. If the tower airflow were free, then the best strategy would be to operate the towers at full capacity independent of the load. The cost ratio is typically higher for hybrid cooling plants than for all-electric plants because of lower chiller COPs and higher heat rejection requirements for gas-driven chillers. The chiller sensitivity factor, Sch, is the incremental Additional or increased growth, bulk, quantity, number, or value; enlarged. Incremental cost is additional or increased cost of an item or service apart from its actual cost. increase in chiller operating cost for each degree increase in condenser water temperature as a fraction of the power, or (change in chiller input energy rate) [S.sub.ch] = [(change in chiller input energy rate)/[(change in condenser water temperature) . (chiller input energy rate)] , (19) If the chiller input energy rate increases by 2% for a 1 degree increase in condenser water temperature, then S is equal to 0.02. A large sensitivity factor means that the chiller input energy then S is equal to 0.02. A large sensitivity factor means that the chiller input energy rate is very sensitive to the cooling tower control, favoring favoring an animal is said to be favoring a leg when it avoids putting all of its weight on the limb. A part of being lame in a limb. operation at higher airflows. The sensitivity factor should be evaluated at design conditions using chiller performance data. Typically, the sensitivity factor is between 0.01 and 0.03[degrees][F.sub.-1] PERFORMANCE EVALUATION Performance evaluation The assessment of a manager's results, which involves, first, determining whether the money manager added value by outperforming the established benchmark (performance measurement) and, second, determining how the money manager achieved the calculated return The performance of the near-optimal control algorithm was evaluated through comparisons with optimization results for typical hybrid cooling plants that were simulated using a tool described by Braun (2006). A brief review of the modeling approach and plant characteristics is provided in this section along with the performance evaluation. Chiller Plant Modeling The cooling plant simulation tool neglects energy storage effects and determines hourly costs cooling for a specified combination of chillers, condenser water pumps, and cooling any given hour, the cost of energy associated with operating the chiller plant is [C.sub.pl] = ([P.sub.twr] + [P.sub.cwp])[ER.sub.e] + [[N.sub.ch].summation over (i = 1)] [E.sub.[ch,i]][ER.sub.i], (20) where [P.sub.twr] is cooling tower fan power, [P.sub.cwp] is condenser water pump power, [E.sub.[ch,i]] is the rate of energy usage for the ith chiller (gas or electric), [N.sub.ch] is the total number of chillers (gas and electric), [ER.sub.e] is the cost per unit of electrical energy, and [ER.sub.i] is the cost per unit energy input (heat or electricity) for the ith chiller (gas or electric). The rate of energy consumption for the ith chiller is determined as consumption for the ith chiller is determined as [E.sub.[ch,i]] = [[gamma].sub.[ch,i]].[PLF Noun 1. PLF - a terrorist group formed in 1977 as the result of a split with the Popular Front for the Liberation of Palestine; became a satellite of al-Fatah; made terrorist attacks on Israel across the Lebanese border .sub.i].[Q.sub.[ch,rated,i]]/[COP.sub.[rated,i]], (21) where [[gamma].sub.[ch,i]] is a control variable (0 or 1) that indicates whether the chiller is operating or not, [Q.sub.[ch,rated,i]] is the rated chiller capacity, [COP.sub.[rated,i]] is the rated chiller COP, and [PLF.sub.i] is the part-load factor, defined as the ratio of energy usage to the value at the rating condition. The chilled-water supply temperature and condenser water flow rate are assumed to be constant, and the chiller part-load factor is correlated cor·re·late v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates v.tr. 1. To put or bring into causal, complementary, parallel, or reciprocal relation. 2. in terms of the chiller load and entering condenser water supply temperature. Figures 2--5 show part-load factors (PLF) as a function of chiller part-load ratio (PLR) and entering condenser water temperature ([T.sub.cws]) for the four different chillers considered within the simulation tool: (1) electric centrifugal centrifugal /cen·trif·u·gal/ (sen-trif´ah-gal) efferent (1). cen·trif·u·gal adj. 1. Moving or directed away from a center or axis. 2. chiller with variable-speed motor, (2) electric centrifugal chiller with fixed-speed motor and inlet guide vane Vane , John Robert 1927-2004. British pharmacologist. He shared a 1982 Nobel Prize for research on prostaglandins. vane the membranous or main part of the contour feather in birds as distinct from the shaft. capacity control, (3) single-effect absorption chiller, and (4) engine-driven centrifugal chiller. These figures were generated by using correlations to manufacturers data. The PLR is the ratio of chiller load to a rated capacity. Not surprisingly, the variable-speed electric chiller has the best part-load performance, whereas the fixed-speed electric has the worst. [FIGURE 2 OMITTED] [FIGURE 3 OMITTED] [FIGURE 4 OMITTED] [FIGURE 5 OMITTED] In order to simulate simulate - simulation a cooling plant, rated cooling capacities ([Q.sub.[ch,rated]]) and COPs ([COP.sub.rated]) are specified for each chiller. The model assumes that all of the energy input to the chillers is rejected to the condenser water loop. The temperature of water leaving the condenser is determined from an energy balance on the condenser. Individual condenser pumps are assumed to be dedicated to individual chillers and to provide rated flow rates. The total condenser flow rate and pump power are simply the sums of the rated values for the chillers that are operating. Water flows and power are scaled with chiller cooling capacity according to user-specified rating values for volumetric flow rate In fluid dynamics and hydrometry, the volumetric flow rate, also volume flow rate and rate of fluid flow, is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m3 s-1 per unit rated cooling capacity (gpm/ton or L/s?kW) and pump power per unit volumetric flow rate (W/gpm or W?s/L). An effectiveness model presented by Braun et al. (1989c) is used to represent the performance of cooling tower cells. The model considers the impact of air and water flow rates on heat and mass transfer rates using characteristics that are representative of commercial cooling towers. For simplicity in developing and evaluating control strategy heuristics, the cooling tower is modeled as a single cell having continuously variable airflow rate. The performance of a cooling tower that has multiple cells that are operating identically (e.g., same flows) is equivalent to the performance of a single larger cooling tower having the same total water and airflow rates. There are two limiting cases that are considered for estimating the cooling tower fan power: (1) variable-speed fans and (2) single-speed staged fans. These two cases represent the upper and lower bounds This article is about order theory and lattice theory. For analysis of algorithms in computational complexity, see Big O notation. In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P for performance associated with a particular tower design. For variable-speed fans, the fan laws are employed and the power varies with the cube of the airflow. This characterizes the behavior of either a single large tower with a variable-speed fan or multiple smaller tower cells with variable-speed fans all operating at the same speeds. For staged fans, it is assumed that the fan power varies linearly with airflow. This characterizes the behavior of multiple tower cells having single-speed fans that are staged on and off. The cooling tower size and design fan airflow rates and power consumption are scaled according to the plant heat rejection requirements. Rated airflows and power are specified in terms of volumetric volumetric /vol·u·met·ric/ (vol?u-met´rik) pertaining to or accompanied by measurement in volumes. vol·u·met·ric adj. Of or relating to measurement by volume. airflow rate per unit condenser heat rejection rate at design (cfm/ton or L/s kW) and fan power per unit volumetric flow rate (W/cfm or W s/L). For given cooling load, ambient air conditions, and plant control variables, the cooling plant model iteratively determines the condenser entering and leaving water temperatures that balance condenser and tower heat rejection. The primary ambient condition that influences plant cooling performance is the air wet-bulb temperature, whereas the dry-bulb temperature The dry-bulb temperature is the temperature of air measured by a thermometer freely exposed to the air but shielded from radiation and moisture. In construction, it is an important consideration when designing a building for a certain climate. has a minor effect. The control variables are the sequencing and relative loadings for individual chillers and the relative tower fan speed or airflow. Overall Plant Characteristics Table 1 gives parameters used in system simulations to evaluate the performance of the near-optimal tower control algorithm. The design ambient conditions, performance ratings See benchmark. , and embedded Inserted into. See embedded system. component performance characteristics were used along with a specification of the number, type, and cooling capacities of chillers to determine the cooling tower design airflow and fan power requirements. For all cases considered in this study, two 500-ton chillers were employed. All six possible combinations of two different chillers were chosen from the four available types: (1) fixed-and variable-speed electric, (2) fixed-speed electric and absorption, (3) fixed-speed electric and engine, (4) variable-speed electric and absorption, (5) variable-speed electric and engine, and (6) absorption and engine. For each of these chiller combinations, all other combinations of cooling tower fan types, utility rates, plant part-load ratios (ratio of load to total chiller capacity), and ambient conditions given in Table 1 were considered, leading to 768 operating points (6 X 2 X 2 X 2 X 4 X 4) for evaluation of the control algorithm.
Parameter Value
Design conditions
Wet-bulb temperature 80[degrees]F
Dry-bulb temperature 95[degrees]F
Electric chillers
Motor Fixed or variable-speed
Rated COP 6.0
Condenser-water flow rate 3 gpm/ton
Condenser-water pump power 15 W/gpm
Absorption chiller
Rated COP 1.0
Condenser-water flow rate 4 gpm/ton
Condenser-water pump power 15 W/gpm
Engine-driven chiller
Rated COP 1.5
Condenser-water flow rate 3 gpm/ton
Condenser-water pump power 15 W/gpm
Cooling tower
Motor Staged or variable-speed
Rated airflow 200 cfm/ton
Rated fan power 0.4 W/cfm
Utility costs
Electrical energy 0.05 or 0.15 $/kWh
Gas energy 0.40 or 1.20 $/therm
Plant operating conditions
Plant part-load ratio 0.25, 0.5, 0.75, 1.0
Wet-bulb temperature 50[degrees]F, 60[degrees]F, 70[degrees]F,
80[degrees]F
Dry-bulb/wet-bulb difference 15[degrees]F
Figure 6 shows the effect of tower airflow and electric chiller part-load ratio on plant energy costs per ton of cooling provided for a plant that utilizes equally sized electric (variable-speed) and absorption chillers with an overall plant part-load ratio of 0.5 at the design ambient conditions ([T.sub.wb] = 80[degrees]F, [T.sub.db] = 95[degrees]F). Lines of constant plant costs are shown over the range of about 0.0.085 to 0.125 $/ton for the entire range of tower airflow (20% to 100% of the design tower airflow) and electric chiller part-load ratios (0.1 to 0.8). [FIGURE 6 OMITTED] Figure 6 indicates that the optimal tower airflow for this operating condition is about 50% of the design airflow and relatively independent of the relative chiller loadings. Greater airflow results in improved chiller performance but at the expense of increased fan power. Lower airflow results in lower fan power but with higher chiller energy input requirements. The optimum results from these trade-offs, which depends on the total plant load. The penalty associated with operating the cooling tower at the design airflow as compared with the optimal flow would be about 15% for these operating conditions if the electric chiller is heavily loaded. Although the penalty is much smaller if the absorption chiller loading is maximized, the optimal chiller policy for this case is to maximize loading on the electric chiller. Benchmark Comparisons The performance of the cooling tower control algorithm was evaluated using the simulation tool. Simulated plant costs for the simple control algorithm were compared with those for optimal tower airflow. The bechmark optimal results were determined by minimizing the plant costs of Equation 20 with respect to tower airflow using a one-dimensional one-di·men·sion·al adj. 1. Having or existing in one dimension only. 2. Lacking depth; superficial. one-dimensional Adjective 1. having one dimension 2. golden-section search algorithm In computer science, a search algorithm, broadly speaking, is an algorithm that takes a problem as input and returns a solution to the problem, usually after evaluating a number of possible solutions. applied to the plant model. The comparisons were performed for the systems and operating conditions described in the previous section (Table 1) and assuming that the multiple chillers were loaded evenly. The comparisons were insensitive in·sen·si·tive adj. 1. Not physically sensitive; numb. 2. a. Lacking in sensitivity to the feelings or circumstances of others; unfeeling. b. to whether the chillers were loaded evenly or not. Figure 7 shows comparisons between the cooling plant costs for optimal and near-optimal control when applied to the hybrid, all-electric, and all-gas-driven chiller plants. Overall, the near-optimal control algorithm gives performance that is within 1% of the minimum power consumption. The method worked extremely well in all cases considered. [FIGURE 7 OMITTED] CONTROL STRATEGY IMPLEMENTATION The cooling tower control algorithm involves determination of a relative tower airflow using Equations 16, 17, or 18. The different equations are for different fan types and give tower airflow relative to the maximum tower airflow if all tower fans were operating at the highest fan speed. As a result, the maximum relative airflow must be constrained con·strain tr.v. con·strained, con·strain·ing, con·strains 1. To compel by physical, moral, or circumstantial force; oblige: felt constrained to object. See Synonyms at force. 2. to 1. There are additional constraints CONSTRAINTS - A language for solving constraints using value inference. ["CONSTRAINTS: A Language for Expressing Almost-Hierarchical Descriptions", G.J. Sussman et al, Artif Intell 14(1):1-39 (Aug 1980)]. on the temperature of the supply water to the chiller condensers, which are necessary to avoid potential chiller maintenance problems. Some chillers have a low limit on the condenser water supply temperature that is necessary to avoid lubrication lubrication, introduction of a substance between the contact surfaces of moving parts to reduce friction and to dissipate heat. A lubricant may be oil, grease, graphite, or any substance—gas, liquid, semisolid, or solid—that permits free action of migration from the compressor compressor, machine that decreases the volume of air or other gas by the application of pressure. Compressor types range from the simple hand pump and the piston-equipped compressor used to inflate tires to machines that use a rotating, bladed element to achieve . A high temperature limit is also necessary to avoid excessively high pressures within the condenser, which can lead to compressor surge See power surge. SURGE - Sorter, Updater, Report Generator, Etc. IBM 704, 1959. Sammet 1969, p.8. . If the condenser water temperature falls below the low limit, then it is necessary to override An arrangement whereby commissions are made by sales managers based upon the sales made by their subordinate sales representatives. A term found in an agreement between a real estate agent and a property owner whereby the agent keeps the right to receive a commission for the sale of the open-loop tower control and reduce the tower airflow to go above this limit. Similarly, if the high limit is exceeded, then the tower airflow should be increased as required. At each decision interval (e.g., five minutes), the following steps can be executed to determine the setpoint for the relative cooling tower airflow: 1. Evaluate the time-averaged values of the condenser water supply temperature and overall plant cooling load over a fixed time interval (e.g., five minutes). 2. If the condenser water supply temperature is less than the low limit, then reduce the setpoint for the relative tower airflow by a fixed increment and exit the algorithm. Otherwise go to step 3. For fans with discrete settings, the setpoint increment should be chosen so that a single fan changes speed by a single step. 3. If the condenser water supply temperature is greater than the high limit, then increase the setpoint for the relative tower airflow by a fixed increment and exit the algorithm. Otherwise go to step 4. 4. If the chilled-water load has changed by a significant amount (e.g., 10%) since the last control change, then go to step 5. Otherwise exit the algorithm. 5. Use the current measured cooling load to estimate the PLR (load relative to rated capacity) for each chiller. 6. Use individual chiller part-load ratios, performance information at rating conditions for the chillers and cooling tower, and utility energy rates for the current rate period to determine a relative cooling tower airflow setpoint using Equation 16, 17, or 18. The relative tower airflow must be converted to a specific set of tower fan settings. The total cooling tower airflow is approximately linear with individual tower cell fan speed and the number of fans operating, such that [[gamma.sub.twr] = 1/[N.sub.twr] [[N.sub.twr].summation over (i - 1)] [[gamma].sub.twr,i], (22) where[[gamma].sub.twr,i]is fan speed control function (0 to 1) for the ith cooling tower cell fan and [N.sub.twr] isthe number of cooling tower cells. Equation 22 can be used to determine the required fan settings for a given total relative airflow. However, first it is necessary to have specific sequencing rules for the order in which fans should be turned on and off. As previously discussed, the best fan settings for a given airflow result from operating the maximum number of fans at the lowest possible speeds. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke" put differently , the fans operating at the lowest speeds should be incremented first when adding fan capacity. For fans with discrete speed settings, this means that all tower fans should be operating at low speed before any fan speeds are increased to the next speed increment. Fan capacity should be removed in the reverse order in which it was added. The process for converting from relative tower airflow setpoint to specific fan settings depends on the type of fan as described below: 1. Fans with Discrete Speed Settings. For multiple cells having fans with discrete speed settings (e.g., two-speed), Equation 22 and the sequencing rules can be used to construct a table relating airflow to fan-speed settings for individual cooling tower cells. The minimum tower airflow would be that associated with a single cell operating at its minimum fan setting (e.g., half-speed). The next increment of airflow would be associated with two cells operating at their minimum speed and so on. The conversion process between a relative airflow setpoint and the discrete fan control involves choosing the set of discrete fan settings from the table that produces a tower airflow closest to the desired flow, assuming that airflow is proportional proportional values expressed as a proportion of the total number of values in a series. proportional dwarf the patient is a miniature without disproportionate reductions or enlargements of body parts. to fan speed. In general, it is better to have greater rather than less than the optimal airflow. A good rule of thumb is to choose the set of discrete fan controls that results in a relative airflow that is closest to, but not more than 10% less than, the target relative airflow. 2. Variable-Speed Fans. If the cooling tower cells have only variable-speed fans, then all operating fans should be set at identical speeds. If possible, all tower cells should be operated unless the required fan speed would fall below a minimum allowable setting (e.g., 0.2). According to Equation 22, the fan-speed setting if all cells are operating is equal to the relative airflow setpoint. If the calculated setting for this case is below the minimum allowable setting, then the number of operating cells should be reduced by one and Equation 22 should be used to determine the required setting. This process should be repeated as necessary until the calculated fan setting is above the minimum allowable. 3. Discrete and Variable-Speed Fans. If the cooling tower cells have a mix of fans with variable-speed and discrete settings, then the goal is to operate the fans as close to the same speed as possible. For the discrete fans, Equation 22 and the sequencing rules can be used to construct a table relating airflow to fan-speed settings for individual cooling tower cells (see step 1). The first entry in the table should be for all discrete fans turned off. Then, for each entry in the table, the required fan control settings for the variable-speed fans that give the required relative airflow are determined using Equation 22, assuming that all the variable- speed fans operate at the same speed (see step 2). Then, the fan settings are selected from the table using the criteria that the variable-speed setting should be closest to, but less than, the maximum discrete fan setting. COOLING TOWER CONTROL EXAMPLE Consider an example plant consisting of one variable-speed electric and one engine-driven chiller, each having a rated cooling capacity of 500 tons (Transparent Optical Networking Services) A marketing term for providing dark fiber to a customer. The customer is responsible for generating the transmission signal and interpreting it at the other end. See dark fiber. . The rated COP for the electric chiller is 6, resulting in a rated electrical power input requirement of [E.sub.ch,rated,E-1] = [Q.sub.ch,rated,E-1]/[COP.sub.rated,E-1] = 500 tons/6 . 3.517 kW/ton = 293.1 kW . The rated COP for the engine-driven chiller is 1.5. Then, the rated requirement for energy input to the gas chiller is [E.sub.ch,rated,G-1] = [Q.sub.ch,rated,E-1]/[COP.sub.rated,E-1] = 500 tons/1.5 . 3.517 kW/ton = 1172 kW . The cooling tower has two cells, each having two-speed fans. The tower design approach range from manufacturers' data are 7[degrees]F and 10[degrees]F. The rated airflow and fan power 200 cfm/ton and 0.4 W/cfm. Therefore, the fan power for the total rated plant cooling capacity is [P.sub.twr,rated] = 200 cfm/ton . 0.0004 kW/cfm . 1000 tons = 80 kW . 596 HVAC&R RESEARCH From energy balances on the chillers operating at rated capacities and COPs, the fraction of the cooling tower heat rejection associated with each chiller is: [f.sub.[twr,rated,E-1]] = [Q.sub.[ch,rated,E-1]](1 + [1/[COP.sub.[rated,E-1]]])/[Q.sub.[ch,rated,E-1]](1 + [1/[COP.sub.[rated,E-1]]]) + [Q.sub.[ch,rated,G-1]](1 + [1/[COP.sub.[rated,G-1]]]) = 500(1 + 1/6)/500(1 + 1/6) + 500(1 + 1/1.5) = 0.412 [f.sub.[twr,rated,G-1]] = 1 - [f.sub.[twr,rated,E-1]] = 0.588 From the characteristics given in Figures 2 and 4, it is found that the rated sensitivity factor for chiller input energy with respect to changes in condenser water temperature is about 0.015[degrees][F.sub.-1] for both chiller types. This is a relatively typical value for chillers. Consider a time during the on-peak period where the total plant load is 700 tons, electrical energy costs are $0.1/kWh, and gas energy costs are $0.80/therm. If the chillers are equally loaded, then both chillers have a part-load ratio of 0.7 under these conditions. For two-speed fans, the relative tower airflow is then determined using Equation 17 so that [[gamma].sub.twr] = [{1/2([a.sub.[twr,rated]] + [r.sub.[twr,rated]])([N.sub.ch].summation over (i=1)]([PLR.sub.[ch,i]][f.sub.[twr,rated,i]]))[[N.sub.ch].summation over (i=1)]([PLR.sub.[ch,i,rated,i]] [[ER.sub.i][E.sub.[ch,rated,i]]]/[[ER.sub.e][P.sub.[twr,rated]]])}.sup.[1/3]] = [{1/2(7F + 10F])(0.7 x 0.411 + 0.7 x 0.588)}.sup.[1/3]] x [{[0.7 x 0.015]/[0.1 $/kWh x 80 kW](0.1 $/kWh x 293.1 kW + 0.80 $/therm x 0.03412 therm/kWh x 1172 kW)}.sup.[1/3]] = 0.784 . At this load, the cooling tower fans should operate at approximately 78% of the maximum tower airflow. In order to convert [[gamma].sub.twr] into a specific tower control, it is necessary to define the tower sequencing. Table 2 gives this information in a form that specifies the relationship between [[gamma].sub.twr] and tower control for this example. For a specific chilled-water load, the fan control should be the sequence of tower fan settings from Table 2 that results in a value of [[gamma].sub.twr] that is closest to, but not more than, 10% less than the value computed with Equation 17. For this example, sequence number 3 would represent the best choice.
Sequence Number [[gamma].sub.[twr]] Tower Fan Speeds
Cell #1 Cell #2
1 0.25 Low Off
2 0.50 Low Low
3 0.75 High Low
4 1.00 High High
CONCLUSIONS The algorithm developed in this paper is similar in nature to the approach developed by Braun and Diderrich (1990) for all-electric plants that appears in the 2003 ASHRAE Handbook--HVAC Applications (ASHRAE 2003). However, the current algorithm is general for cooling plants that incorporate any combination of electric and gas-driven chillers. The control algorithm determines cooling tower fan settings in response to loadings on individual chillers. Parameters of the algorithm are evaluated using design information for the chillers and cooling tower fans. In addition to reducing operating costs, use of the open-loop control strategy simplifies the control and improves the stability of the tower control compared with the use of a constant condenser water supply or approach to wet-bulb. ACKNOWLEDGMENTS See About this product. The financial support of ASHRAE under RP-1200 and the technical support provided by the Project Monitoring Subcommittee sub·com·mit·tee n. A subordinate committee composed of members appointed from a main committee. subcommittee Noun that included Jay Kohler Kohler, village (1990 pop. 1,817), Sheboygan co., E Wis., on the Sheboygan River; inc. 1912. The Kohler plumbing-fixtures plant there, which still produces its famous stainless-steel products, has been the scene of some of the longest and most bitter labor disputes , Paul Paul, 1901–64, king of the Hellenes (1947–64), brother and successor of George II. He married (1938) Princess Frederika of Brunswick. During Paul's reign Greece followed a pro-Western policy, and the Cyprus question was temporarily resolved. Sarkisian, and Dharam Punwani are greatly appreciated. NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc. binomial nomenclature [a.sub.twr] = cooling tower approach to wet-bulb temperature ([T.sub.cws]--[T.sub.wb]) [C.sub.ch] = instantaneous cost of operating chillers [C.sub.twr] = instantaneous cost of operating cooling tower [COP.sub.i] = coefficient of performance for the ith chiller [E.sub.ch,i] = rate of energy input for ith chiller (gas or electric) [ER.sub.e] = cost per unit of electrical energy [ER.sub.i] = cost per unit energy input (heat or electricity) for the ith chiller (gas or electric) [f.sub.twr,i] = fraction of cooling tower heat rejection associated with ith chiller [N.sub.ch] = total number of chillers (gas and electric) [N.sub.twr] = number of cooling tower cells [P.sub.cwp] = total condenser water pump power [P.sub.twr] = total cooling tower fan power [PLF.sub.i] = part-load factor for ith chiller defined as the ratio of energy usage to the value at the rating condition [PLR.sub.[ch,i]] = part-load ratio for ith chiller (gas or electric)--load relative to rated chiller capacity [PLR.sub.plt] = part-load ratio, plant--total cooling load relative to rated cooling capacity for plant [Q.sub.ch,i] = cooling load for ith chiller [Q.sub.twr] = cooling tower heat rejection rate [r.sub.twr] = cooling tower range ([T.sub.cwr]--[T.sub.cws]) [S.sub.ch,i] = sensitivity of ith chiller input energyto changes in condenser water temperature [T.sub.cwr] = condenser water return temperature [T.sub.cws] = condenser water supply temperature [T.sub.db] = ambient dry-bulb temperature [T.sub.wp] = ambient wet-bulb temperature [[gamma].sub.[ch,i]] = control function that determines whether the ith chiller (gas or electric) is on or off (0 or 1) [[gamma].sub.twr] = control function that specifies the relative airflow for the cooling tower [[gamma].sub.[twr,i]] = control function that specifies the relative fan speed or airflow for an individual cooling tower cell Additional Subscript (1) In word processing and scientific notation, a digit or symbol that appears below the line; for example, H2O, the symbol for water. Contrast with superscript. (2) In programming, a method for referencing data in a table. rated = evaluated at rating conditions REFERENCES ASHRAE. 2003. 2003 ASHRAE Handbook--HVAC Applications, Chapter 41, "Supervisory Control Strategies and Optimization," pp. 41.1--41.39. Atlanta Atlanta (ətlăn`tə, ăt–), city (1990 pop. 394,017), state capital and seat of Fulton co., NW Ga., on the Chattahoochee R. and Peachtree Creek, near the Appalachian foothills; inc. 1847. : American American, river, 30 mi (48 km) long, rising in N central Calif. in the Sierra Nevada and flowing SW into the Sacramento River at Sacramento. The discovery of gold at Sutter's Mill (see Sutter, John Augustus) along the river in 1848 led to the California gold rush of Society of Heating, Refrigerating re·frig·er·ate tr.v. re·frig·er·at·ed, re·frig·er·at·ing, re·frig·er·ates 1. To cool or chill (a substance). 2. To preserve (food) by chilling. and Air-Conditioning Engineers, Inc. Braun, J.E. 1988. Methodologies for the design and control of central cooling plants. PhD dissertation dis·ser·ta·tion n. A lengthy, formal treatise, especially one written by a candidate for the doctoral degree at a university; a thesis. dissertation Noun 1. , University of Wisconsin--Madison. Braun, J.E., S.A. Klein, J.W. Mitchell Mitchell, city (1990 pop. 13,798), seat of Davison co., SE S.Dak.; inc. 1881. Mitchell is a trade, distribution, and shipping center for a dairy and livestock area. , and W.A. Beckman Beckman or Beckmann may refer to:
Braun, J.E., S.A. Klein, J.W. Mitchell, and W.A. Beckman. 1989b. Methodologies for optimal control of chilled-water systems without storage. ASHRAE Transactions 95(1):652--62. Braun, J.E., S.A. Klein, and J.W. Mitchell. 1989c. Effectiveness models for cooling towers and cooling coils. ASHRAE Transactions 95(2):164--74. Braun, J.E., and G.T. Diderrich. 1990. Near-optimal control of cooling towers for chilled-water systems. ASHRAE Transactions 96(2):806--13. Braun, J.E. 2006. Optimized operation of chiller equipment in hybrid machinery rooms and associated operating and control strategies, ASHRAE RP-1200 final report. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Hackner, R.J., J.W. Mitchell, and W.A. Beckman. 1985. HVAC (Heating Ventilation Air Conditioning) In the home or small office with a handful of computers, HVAC is more for human comfort than the machines. In large datacenters, a humidity-free room with a steady, cool temperature is essential for the trouble-free system dynamics System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. and energy use in buildings--Part II (RP-321). ASHRAE Transactions 91(1B):781--95. Klein, S.A., D.R. Nugent Nugent may refer to one of the following:
A machine for generating mechanical power in rotary motion from the energy of steam at temperature and pressure above that of an available sink. By far the most widely used and most powerful turbines are those driven by steam. driven chiller. ASHRAE Transactions 94(1):627--43. Koeppel, E.A., J.W. Mitchell, S.A. Klein, and B.A. Flake flake an epidermal scale. flake Cocaine, see there . 1995. Optimal supervisory control of an absorption chiller system. HVAC&R Research 1(4):325--42. Lau, A.S., W.A. Beckman, and J.W. Mitchell. 1985. Development of computer control--Routines for a large chilled-water plant. ASHRAE Transactions 91(1B):766--80. Sud, I. 1984. Control strategies for minimum energy usage (RP-253). ASHRAE Transactions 90(2A):247--77. James James, person in the Bible James, in the Gospel of St. Luke, kinsman of St. Jude. The original does not specify the relationship. James, rivers, United States James. E.Braun, PhD Fellow ASHRAE James E. Braun is a professor of mechanical engineering, Ray W. Herrick Laboratories, Purdue University Purdue University (pərdy  `, -d`), main campus at West Lafayette, Ind. , West Lafayette West Lafayette, city (1990 pop. 25,907), Tippecanoe co., W Ind., a suburb of Lafayette, on the Wabash River; inc. 1924. A primarily residential city, it is the seat of Purdue Univ. , IN.(ASHRAE
2003). However, this strategy is not appropriate for hybrid plants
because it is based on minimizing input energy usage rather than cost.
|
|
||||||||||||||||||
,
Printer friendly
Cite/link
Email
Feedback
Reader Opinion