Method and apparatus for determining critical pressure of variable air volume heating, ventilating, and air-conditioning systems
A strategy for determining the critical supply duct pressure in variable-air-volume heating, ventilating, and air-conditioning systems that compensates for duct leakage and variable loads, enabling its use during normal system operation. The strategy consists of a static pressure sensor, an airflow sensor, a supply fan, a fan modulating device, a controller coupled to the static pressure sensor and the airflow sensor, and a data processing algorithm for analyzing results from a function test using these components. The functional test involves changing the supply duct pressure setpoint, waiting for equilibrium, recording pressure, flow, and time, then changing the supply duct pressure setpoint to the next setting in the sequence.
“This invention was made with State of California support under California Energy Commission Grant number 02-03. The Energy Commission has certain rights to this invention.”
1. Field of the Invention
The following invention relates to controls for variable-air-volume heating, ventilating, and air-conditioning (HVAC) systems, specifically to supply duct static pressure control.
2. Description of Prior Art
Modern buildings typically have complex heating, ventilating, and air-conditioning systems to control indoor temperature, pressure, ventilation rate, and other variables in a way that makes efficient use of energy. One way to conserve energy in these systems is to use a so-called variable-air-volume design. Key components of a variable-air-volume system are a supply fan and terminal units. The supply fan is a prime mover that causes air to move. A terminal unit contains a throttling damper that regulates an amount of air supplied to a space in a building that it controls in order to regulate temperature and ventilation in that space.
In a variable-air-volume system, a flow rate of conditioned air supplied to a building is adjusted so that no more air than necessary is used. Variable flow is achieved using controls on or near the supply fan and by the use of controls on the terminals. The supply fan controls adjust the speed of the fan, an angle of the fan blades, an angle of guide vane at an inlet or outlet of the fan, or by adjusting a damper upstream or downstream of the fan that throttles the flow. The controls on the terminals determine how much air flows through each terminal.
The most common control strategy for the supply fan of variable-air-volume systems is to regulate a static pressure in a supply duct at a point downstream of the supply fan. This strategy seeks to keep the static pressure at a measurement point constant at all times. Control strategies based on a constant static pressure in the supply duct have been proposed in U.S. Pat. No. 4,437,608 to Smith (1984) and U.S. Pat. No. 6,227,961 to Moore et al. (2001). U.S. Pat. No. 4,836,095 to Wright (1989) describes a variant of this strategy for systems that have multi-speed fans rather than fans in which the speed is continuously variable. A rule of thumb for this strategy is to locate the pressure sensor two-thirds of the distance from the supply fan to the end of the supply duct. A problem with this strategy is that it is inefficient at part-load conditions, when the supply flow rate is significantly lower than a design flow rate, which is the flow rate at which the system should operate when the fan is running at full speed.
A control strategy that overcomes the problem of constant static pressure control is one in which a static pressure setpoint is reset based on a position of a terminal damper that is most open. Control strategies that reset the static pressure based on the position of the terminal damper that is most open have been proposed in U.S. Pat. No. 4,630,670 to Wellman and Clark (1986) and U.S. Pat. No. 5,863,246 to Bujak (1999). An objective is to keep this damper nearly open or completely open. Doing so keeps the supply duct pressure near the critical pressure, reducing throttling losses at part-load conditions. The critical pressure is the lowest supply duct pressure at which all of the terminal dampers are still controlling. When the supply duct pressure is below the critical pressure one or more terminal dampers will be fully open yet unable to get enough air.
A report published by the California Energy Commission (CEC publication number P500-03-052F, 2003) showed that the critical supply duct pressure is correlated with the supply airflow rate. This fact is exploited in U.S. Pat. No. 6,719,625 to Federspiel (2004), which describes a static pressure reset strategy that adjusts the static pressure setpoint based on the supply airflow rate. This strategy overcomes many of the problems of static pressure reset strategies that rely on terminal damper position measurements. However, it requires some knowledge of how the critical supply duct pressure is related to the supply airflow rate.
Accordingly, a need exists for a strategy that will allow the relationship between critical supply duct pressure and a supply flow rate to be determined so that the static pressure reset strategy based on supply airflow rate can be optimized.
SUMMARY OF THE INVENTION
In accordance with the present invention, a strategy for determining the critical supply duct pressure of a variable-air-volume heating, ventilating, and air-conditioning system comprises the supply fan, a fan modulating device, a static pressure sensor, an airflow sensor, and a controller coupled to the static pressure sensor. The controller is commanded to a sequence of static pressures. Supply airflow at each static pressure setpoint is recorded, and the data are processed using a model-based analysis technique that determines the critical supply duct pressure, the leakage coefficient, and the rate of change of the load at the test condition.
OBJECTS OF THE INVENTION
Accordingly, a primary object of the present invention is to provide a strategy for determining the critical supply duct pressure of variable-air-volume heating, ventilating, and air-conditioning systems so that a static pressure reset strategy can be configured and optimized.
Another object of the present invention is to provide a strategy for determining the critical supply duct pressure of variable-air-volume heating, ventilating, and air-conditioning systems that can be implemented during normal system operation.
Another object of the present invention is determine the leakage rate of the supply air duct in variable-air-volume heating, ventilating, and air-conditioning systems.
Another object of the present invention is to provide a strategy for determining the critical supply duct pressure of variable-air-volume heating, ventilating, and air-conditioning systems that can compensate for load changes that occur while the strategy is implemented.
Other further objects of the present invention will become apparent from a careful reading of the included drawing figures, the claims, and detailed description of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
REFERENCE NUMERALS IN DRAWINGS
DESCRIPTION OF THE PREFERRED EMBODIMENT
Determination of the critical supply duct pressure involves implementing a functional test on the air-handling unit, then processing the data from the functional test using a model-based procedure. The data processing uses a dual-mode model of a variable-air-volume air-handling system. The two modes are “controlling” and “starved”. The supply fan in most variable-air-volume air-handling systems is used to regulate the static pressure at a point in the supply duct. The static pressure should be sufficiently high that all terminals served by the air-handling unit get enough air to meet their load. If it is too high, then even the most-open variable-air-volume terminal will be throttling considerably, and energy will be wasted. The critical supply duct pressure occurs when the most-open variable-air-volume terminal is 100% open and just meeting the load because this condition minimizes throttling losses while keeping the system in control. When the supply duct pressure is high enough that all of the terminals are meeting the load, the system is operating in the controlling mode. When one or more terminal dampers are 100% open and not meeting the load, the system is in the starved mode. The lowest supply duct pressure that keeps all the terminals in control is called the critical pressure.
The controlling-mode model contains three terms. The first is a constant term that represents the cumulative flow rate through the dampers at the beginning of the functional test used to determine the critical pressure. The second is a term to account for duct leakage, which can be very significant in some systems. The third is a time-dependent term that accounts for the fact that the loads, and therefore the supply flow, may change over the course of the functional test if it is conducted during normal operation. Mathematically, the controlling model is as follows:
where Qc is the total supply airflow rate when the system is in control, Cp is the leakage coefficient, and Ct is the rate of change of the supply airflow rate due to changing load conditions. The first term on the right-hand side of Equation 1 is the controlled cumulative terminal flow (cumulative flow through the terminal dampers) at the start of the functional test. The second term is leakage flow, and the third is the time-varying component of the controlled cumulative terminal flow.
When Ct=0, Q0 is held constant as long as the terminal dampers can change the system flow coefficient according to the following relation:
where CQ is the system flow coefficient.
When the supply duct pressure drops below the critical pressure (starved mode), the relationship between flow coefficient and pressure in Equation 2 no longer holds. The flow coefficient becomes less that that of Equation 2, and Q0 becomes a function of the pressure. In the starved mode, the flow coefficient is modeled a quadratic function of pressure as follows:
where the polynomial coefficients c0, c1, and c2 must be determined empirically. The starved-mode model is as follows:
The starved-mode model has three additional parameters besides the three parameters of the controlling-mode model (Equation 1). The term CtT/Q0 compensates for the fact that only a fraction of the terminal flows (those of unstarved terminals) may be changing with time in response to changing loads.
The preferred functional test procedure for determining the critical supply duct pressure involves the following sequence of operations:
- 1. start at a sufficiently high supply duct pressure setpoint
- 2. wait for the terminals to reach equilibrium (e.g., 2 minutes for laboratory experiments, 15 minutes for field experiments)
- 3. take a reading of supply flow, static pressure, and time
- 4. reduce the supply duct static pressure setpoint by a small amount (e.g., 0.1 in. w.c.)
- 5. wait for the terminals to reach equilibrium again
- 6. take a reading of supply flow, static pressure, and time
- 7. repeat steps 4-6 until the supply flow is less than a pre-determined limit (e.g., 70% of the starting flow)
- 8. increase the pressure by a small amount (e.g., 0.1 in. w.c.)
- 9. wait for terminals to reach equilibrium again
- 10. take a reading of supply flow, static pressure, and time
- 11. repeat steps 8-10 until the pressure equals the starting pressure
The preferred analysis procedure for determining the critical pressure from the functional test data is as follows:
- A. Assign the first N high-pressure points at the beginning of the test and the M low-pressure points at the end of the test to the controlling-mode model. Estimate the coefficients of the controlling-mode model with least squares. Determine if the time-dependent term can be dropped from the model using a t-test with a decision probability of 0.02.
- B. Assign the remaining data points to the starved-mode model. Estimate the three coefficients of the starved-mode model using the coefficients determined from the controlling model.
- C. Compute the variance of the combined residuals.
- D. Repeat steps 1-3 for all allowable values of N and M.
- E. Choose the values of N and M that produce the lowest variance
- F. Determine the pressure at which the flow predicted by the starved model equals the flow predicted by the controlling model.
FIG. 2is a graph showing the functional test data and results of the analysis procedure for a test conducted on a laboratory air-handling unit. The gradual slope of controlling-mode model 22 is due to duct leakage. Starved-mode model 21 shows a rapid decrease in pressure below the airflow rate corresponding to critical supply duct pressure 23, which is caused by terminals becoming starved. Experiments conducted over a wide range of conditions demonstrate that the standard error of values from the preferred embodiment is 6% of the true critical supply duct pressure.
Conclusion, Ramifications, and Scope
Accordingly, the reader will see that the critical pressure determination strategy of this invention has a number of advantages including the following:
- (a) It can be implemented during normal system operation,
- (b) It can determine duct leakage,
- (c) It can compensate for time-varying loads.
This disclosure is provided to reveal a preferred embodiment of the invention and a best mode for practicing the invention. Having thus described the invention in this way, it should be apparent that various different modifications can be made to the preferred embodiment without departing from the scope and spirit of this disclosure. Thus the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.
1. An apparatus for determining a critical supply duct pressure of a variable-air-volume heating, ventilating, and air-conditioning systems comprising in combination:
- said supply fan;
- a fan modulating device coupled to said supply fan;
- a static pressure sensor;
- at least one airflow sensor;
- a supply fan controller coupled to said static pressure sensor and said fan modulating device, said supply fan controller configured to regulate static pressure to a static pressure setpoint;
- a calculator configured to determine a critical supply duct pressure.
2. The apparatus of claim 1 wherein said airflow sensor is located upstream of said supply fan.
3. The apparatus of claim 1 wherein said airflow sensor is located downstream of said supply fan.
4. The apparatus of claim 1 wherein said calculator uses data from said airflow sensor to compute said critical supply duct pressure.
5. The apparatus of claim 1 wherein said calculator uses data from said static pressure sensor to compute said critical supply duct pressure.
6. The apparatus of claim 1 wherein said calculator uses said static pressure setpoint to compute said critical supply duct pressure.
7. The apparatus of claim 1 wherein said calculator is configured to use a controlling-mode model.
8. The apparatus of claim 7 wherein said model of the controlling system behavior includes a leakage term.
9. The apparatus of claim 7 wherein said controlling-mode model includes a time-dependent term.
10. The apparatus of claim 1 wherein said calculator is configured to use a starved-mode model.
11. The apparatus of claim 1 wherein said calculator uses a least squares data fitting procedure.
12. A method for determining a critical supply duct pressure of a variable-air-volume heating, ventilating, and air-conditioning system, the method including the steps of:
- commanding a supply duct setpoint to a setting;
- waiting for equilibrium;
- measuring a supply airflow rate after equilibrium is reached;
- repeating said commanding, waiting, and measuring steps for a sequence of said supply duct setpoint settings;
- processing measured data with a calculator configured to determine a critical supply duct pressure from said data acquired.
13. The method of claim 12 further including the step of measuring a supply duct static pressure after equilibrium is reached and including said supply duct static pressure in said processing step.
14. The method of claim 12 further including the step of measuring a time at which equilibrium is reached and including said time at which equilibrium is reached in said processing step.
15. The method of claim 12 wherein said calculating step uses a controlling-mode model.
16. The method of claim 15 wherein said controlling-mode model includes a leakage term.
17. The method of claim 15 wherein said controlling mode model includes a time-dependent term.
18. The method of claim 12 wherein said calculating step uses a starved-mode model.
19. The method of claim 12 wherein said calculating step uses a least squares data fitting procedure.
Filed: Dec 1, 2004
Publication Date: Jun 1, 2006
Inventor: Clifford Federspiel (El Cerrito, CA)
Application Number: 11/001,369
International Classification: F24F 7/00 (20060101); F24F 11/00 (20060101);