# Primary Chilled Water System Control Optimization Integrated with Secondary System Linearization--Part I: Theoretical Analysis and Simulation.

INTRODUCTIONBuilding heating, ventilation, and air-conditioning (HVAC) systems are designed and operated to ensure that conditioned spaces have an accurate and desirable supply air temperature, relative humidity, air flow rate, and air distribution rate to ensure comfort in the space. Chilled water systems in particular provide cooling for many air-conditioning and industrial processes. Regardless of its size or complexity, every chilled water system has cooling equipment, pumps, a distribution system, cooling loads, and control valves. The chilled water system can be defined as a primary system that includes chillers and pumps, and a secondary system comprised of the cooling coil and control valves. The secondary system consists of a supply air temperature control system with an air-water coil, control valve, and supply air temperature sensors. The distribution system is a piping network that transfers chilled water between the primary and secondary systems.

The most widely used proportional and integral (PI) control is designed for a linear time invariant system (Astrom et al. 1995). Most HVAC systems exhibit highly non-linear behavior (Dexter and Haves, 1989), and PI control parameters have to be tuned to guarantee their performance and stability. Poor control performance was observed using conventional adaptive control for HVAC systems with nonlinearities, dynamics and multiple operating modes (Dexter and Haves, 1989). Most common control problems are hunting issues which are defined as a periodic oscillation in the controlled function of any feedback control system. Hunting issues cause energy waste and also control device wear-out and thermal comfort complaints. The fundamental reasons for the hunting issue include wrong controller gain value or ratio of proportional and integral gains, wrong system control and operation and constant gain control for nonlinear systems. Figure 1 shows the impacts of coil control hunting issues on the zone supply air temperature from a real project case study. When the temperature is over the set point, additional cooling is needed to cool the air. When the temperature is below the set point, additional heating is needed to warm up the air, Therefore, when hunting issue occurs, there is an energy waste due to compensation of the temperature fluctuation.

The constant-primary variable-secondary flow system quickly became the standard for larger systems and was presented as such in HVAC textbooks and industry handbooks (ASHRAE 2000). By the late 1990s, there was growing support among chiller manufactures, system designers, and building owners and operators for the variable primary flow system (Schwedler and Bradley 2000, 2003). The variable primary flow system is often perceived to be more complicated than the primary-secondary system. Different pump speed control methods are developed in the past which does not consider the secondary system nonlinearities into controls. This paper presents the theoretical model and simulation on traditional control methods and an innovative integrated control linearization approach. The model integrates the primary chilled water pump head and water loop differential pressure under differing load distributions. Characterization of the secondary system was conducted through theoretical modeling and simulation to reveal the key control characteristics and the impacts of such characteristics on the control and energy performance of the integrated system.

LITERATURE REVIEW

Current primary system pump speed control options include the constant DP set-point control method, DP reset based on the valve position, and the DP reset based on the water flow rate. Controlling the speed of the variable speed pump so that it maintains a constant pressure differential between the main chilled water supply and the return pipelines is a common practice dating back to the 1990s. In fact, current guidelines, such as the 2008 ASHRAE Handbook, still recommend this procedure. Ahmed (1989) presented the cost-effectiveness of using a constant DP control for a direct-return system. Ahmed (1991) proposed a DDC-based pump control method for a direct-return hydraulic system by measuring and calculating the water flow rate for each coil-valve branch. However, in practice, it is too complicated and expensive to install flow sensors and differential pressure sensors in all of the coils. Moreover, it is not applicable in fields to measure the water flow rate for each coil. Rishel (1998) was the first to propose resetting the differential pressure set point based on the coil valve position. However, it was only the general idea instead of a practical method. Moore and Fisher (2003) were also interested in resetting the differential pressure so that at least one control valve remained 90% open in an arbitrarily chosen range. The authors pointed out the disadvantages of the method, namely, the pump hunting issues, problems related to unstable operation, and the fluctuating discharge air temperature.

Nonlinearity was defined as the distance between a closed loop with a nonlinear process/linear controller and a suitably defined ideal linear closed loop. Multiple linear time-invariant process models are used and validated around a steady state process. The authors address questions concerning when linear control should be applied and whether linear control is adequate for a nonlinear process. Underwood (2000) developed a simplified nominal linear model for a fresh-air heating and room space temperature control system comprising a hot water heating and chilled ceiling system. In his paper, controller robustness is analyzed under chiller plant operating conditions. Control system components are modeled in detail to capture the underlying dynamics of the nonlinear HVAC plant. Closed-loop plant simulations agree with the experimental data (Underwood, 2000). Zheng (2007) investigated the ratio of P and I gains and find out a new tuning algorithm. This algorithm adjust controller gain ratios according to control valve positions to tune a PI loop is a method of integrating control tuning and system operations, which is superior to both one-and two-dimensional tuning methods. However, the author noted that this method is intended for a system that has a known or constant loop pressure. The author also suggests integrating the system operations with the tuning of the controller.

PRIMARY SYSTEM MODELS

To fully understand the system pressure and flow characteristics, the system models are developed to investigate the hydronic system friction pressure loss distribution, flow characteristics of the chilled water piping network and the chilled water pumps. First of all, a water system network pressure drop model is developed to characterize the pressure drop on each individual component such as chiller, pump, and coil and control valve. Secondly, the pump head curve and system curves are fully investigated to find out the key influential parameters. For different water system configurations, the water system network model could be significantly different. The chilled water system with variable primary pumps could be one of the most representative systems. The similar model could be applied for the secondary system side for a variable primary-secondary system. Therefore, a water system network pressure drop model is presented for variable primary flow chilled water system here.

Definition of System Flow Resistance

Similar to the concept of electrical resistance, the system flow resistance S is defined as the ratio of pressure drop over the square of volumetric water flow rate corresponding to the pressure drop. The volumetric water flow rate is used because it is easily measured for application and also the water density changes slightly when the chilled water temperature changes from 40[degrees]F to 60[degrees]F.

Pressure drop caused by the friction of a fluid flowing in a pipe may be described by the Darcy-Weisbach equation (1):

[mathematical expression not reproducible] (1)

Eq. (1) shows that pressure drop in a hydronic system (pipe, fittings, and equipment) is proportional to the square of the fluid velocity. Experiments show that pressure drop is more nearly proportional to between [V.sup.185] and [V.sup.19], or a nearly parabolic curve (ASHRAE Handbook, 2008). The design of the system (including the number of terminals and flows, the fittings and valves, and the length of pipe mains and branches) affects the magnitude of the flow resistance.

Equation (2) may also be expressed by introducing system flow resistance S as

[mathematical expression not reproducible] (2)

A centrifugal pump is usually selected to work at its highest efficiency under the design condition. Therefore, the design system resistance can be calculated based on the design water flow rate and design pump head. The pump works at its highest efficiency for any operation point along the polynomial curve of the design system resistance.

Water System Network Pressure Drop Model

Figure 3 shows the schematic diagram of a direct-return variable primary chilled water system with three representative loads for secondary system.

Nearly all cooling system consists of water-filled closed piping system. Figure 4 illustrates the schematic diagram of the water system network for a variable primary chilled water system with ith cooling coils. The network includes circuits for which the coil, valve, chiller and pipes are the components. The variable primary pumps provide the pressure differential needed to distribute the water flow to each terminal unit which is cooling coils in this model. There is head loss due to viscous friction along the flow direction. S represents system flow resistance for each pipe between two nodes. CS denotes the system resistance of each branch including branch pipe, coils and control valves.

The pump head is determined as the pressure differential across the most resistant circuit with the control valve fully open. Denote the flow ratio of each branch as [mathematical expression not reproducible], the pump head can be further deduced as Eq. (3).

[mathematical expression not reproducible] (3)

To illustrate the difference of pump head due to load distribution factors, the simulation results of pump head based on the water system network pressure drop model is illustrated in Figure 5. One pump and one chiller are assumed in operation under all conditions.

As shown in Figure 5, the starting pump head at no flow is 48 kPa which is the minimum controlled differential pressure at the remote coil for constant differential pressure set point control. The real system flow curve requires no pressure drop at zero flow. The area bounded by the pump head curves for different loads include the possible operation points when the remote differential pressure is constant at the design. The system curve is steeper if steadily heavy loads are closer to the pumps. This means the pump head is the highest if the heavy loads are closer to the pumps compared to the uniform load distribution or heavy loads at remote. The system curve is flatter if steadily heavy loads are far away from the circulation pumps.

SECONDARY SYSTEM MODELS

The analysis is based on a typical valve-cooling-coil control system. The control block diagram is shown in Figure 6.

To investigate the impacts of the primary system parameters on the secondary system, there is a characteristic to link the valve to the primary system, termed the installed characteristic [psi](x)(Underwood, 1999). Equation (4) presents the expression of the new installed characteristic, which links the primary loop pressure with the water flow.

[mathematical expression not reproducible] (4)

Where P = P/[P.sub.d] as the ratio of the loop pressure differential to the design loop pressure differential.

As shown in Figure 7, a typical control valve with authority 0.5 and let-by 0.01 (ASHRAE, 2000 and Underwood, 1999) is used to demonstrate the relationship between loop pressure and water flow rate through the valve. Both loop pressure and water flow are the ratio of actual value over the design value at valve full open position. It can be seen that the water flow rates decreases when the loop pressure differential decreases at the same valve position.

The dimension less time constant and steady state gain can be expressed when the input is water flow.

[mathematical expression not reproducible] (5)

[mathematical expression not reproducible] (6)

Figure 8 shows the time constant under the different fluid flow rates. As shown in the figure, the time constant is not a constant under different water flow rates, which means it is not a constant in the full valve operation range. The seemingly one curve shows that time constant is almost a constant under certain water flow rate, which implies that the airflow rate has very little impact on the coil time constant although airflow ratio as an impact factor shows in the expression of the coil time constant. The less the water flow rate, the longer the time constant is. Briefly, the water flow rate has significant influence on the time constant and the impact of the airflow rate is approximately negligible.

The water flow rate is related to the valve position, valve authority and differential pressure on the valve. Among the influential parameters, the loop pressure differential is the only parameter affected by the control and operation. Thus the impacts of loop pressure differential on the coil time constant are simulated. Figure 9 demonstrates the coil time constant profiles with the valve position for typical equal-percentage valve which is widely used in valve-coil control system.

Figure 10 shows the coil gain under the different inlet water temperature given design airflow and inlet air temperature. The seemingly one curve shows that coil gain is almost a constant under certain water flow rate, which implies that the inlet water temperature has very little impact on the coil gain although inlet water temperature as an impact factor shown in the expression of the coil gain. The lower the inlet water temperature, the smaller the coil gain is. The smallest gain is 20 which occur at the full water flow.

CONCLUSION

This paper presents the theoretical model and simulation on traditional control methods and an innovative integrated control linearization approach. The model integrates the primary chilled water pump head and water loop differential pressure under differing load distributions. Characterization of the secondary system was conducted through theoretical modeling and simulation to reveal the key control characteristics and the impacts of such characteristics on the control and energy performance of the integrated system. PI control is designed for a linear time invariant system so the system gains vary with the operating parameters like loop pressure and water temperature. The study concludes that the differential pressure in the primary chilled water loop substantially impacts the control performance and stability of the secondary system. The nonlinear characteristics can be dynamically reduced through an integrated approach, resetting the water supply temperature and pressure control.

NOMENCLATURE

[DELTA]P = head loss through friction in a pipe, lb. /[ft.sup.2] (Psi)

[??] = fluid density, lb. /[ft.sup.3] (kg/[m.sup.3])

C= is the specific heat, Btu/(lb-[degrees]F) (J/kg-[degrees]C) .

D = inside diameter of pipe, ft. (m).

f = friction factor, dimensionless

L = pipe length, ft. (m).

V = fluid average velocity, ft. /min (m/s)

g = gravitational acceleration, 32.2 ft. /[min.sup.2] (9.78 m/[s.sup.2])

S = System flow resistance, ft. /GP[m.sup.2] (m/ [([m.sup.3]/s).sup.2]).

m = Volumetric water flow rate, GPM for water or CFM for air ([m.sup.3]/s)

M is the total mass of the coil including water and tubes, lb. (kg).

[mathematical expression not reproducible]

x = valve position, %

Subscripts

pmp = pump; ch = chiller; w = chilled water; a = air

REFERENCES

Ahmed, O. 1989. Cost Effectiveness of Direct Return Hydronic System. Proceedings of 12th World Energy Engineering Conference, Atlanta, Georgia, 1989:431-436.

Ahmed, O. 1991. DDC Applications in Variable-Water-Volume Systems. ASHRAE Transactions, Vol. 97(1): 751-758.

Dexter A.L., and Haves, P. 1989. Robust Self-Tuning Predictive Controller for HVAC Applications. ASHRAE Transactions, Vol. 95(2): 431-438.

Astrom, K.J., and Hagglund, T. 1995. PID Controllers: Theory, Design, and Tuning, 2nd edition. North Carolina: Instrument Society of America/Research Triangle Park, 1995.

Rishel, J. B. 1998. System Analysis vs. Quick Fixes for Existing Chilled Water Systems. HPAC Engineering. 70(1): 131-134. ASHRAE. 2000. ASHRAE Handbook--HVAC Systems and Equipment. 23:1-23:5.

Schwedler, M. and B. Bradley. 2000. Variable-Primary-Flow Systems: An Idea for Chiller-Water Plants the Time of Which Has Come. HPAC Engineering. 72 (4): 41-44.

Schwedler, M. and B. Bradley. 2003. Variable Primary Flow in Chiller-Water Systems. HPAC Engineering. 75(3): 37-45.

Underwood, C. P. 2000. Robust Control of HVAC Plant II: Controller Design. Chartered Institution of Building Services Engineers, Vol. 21(1): 63-71.

Zheng, Bin. 2007. Analysis and Auto-Tuning of Supply Air Temperature PI Control in Hot Water Heating Systems. January, 2007. Dissertation of University of Nebraska.

Lixia Wu, Ph.D.

MEMBER ASHRAE

Mingsheng Liu, Ph.D., PE

Member ASHRAE

Dr. Lixia Wu, ASHRAE member, Technical committee TC7.9 PCM, is a director of Engineering at Bes-Tech, Inc., King of Prussia, PA. Dr. Mingsheng Liu, ASHRAE member, is the president and CTO at Bes-Tech, Inc., Omaha, NE.

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Author: | Wu, Lixia; Liu, Mingsheng |
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Publication: | ASHRAE Conference Papers |

Date: | Dec 22, 2014 |

Words: | 2750 |

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