Editor's note: This is the fifth article in a five-article series.

The first four articles in this series^1,2,3,4 considered only plant load in the modeling of central-chiller-plant performance. This article adds building and air-handler loads to the mix. A system serving a 1,672,000-sq-ft, one-shift facility is modeled over a 24-hr period for both design-day and fall-day weather conditions.

The system simulation modeling used in preparation of this article consists of a set of simultaneous equations that obey the laws of physics and thermodynamics and includes the nonlinear performance characteristics of plant equipment, air-side equipment, and buildings, always arriving at energy equilibrium after a change in steady-state condition.

Air-Handler Leaving-Water-Temperature Control
Figure 1 illustrates the improvement in plant performance resulting from the control of distribution-pump power to provide air-handler leaving-water temperatures of 51°F and 54°F. The top chart gives primary/secondary- (P/S-) plant performance, while the bottom chart gives primary-only- (P-only-) plant performance. The chillers maintain a supply-water temperature of about 44°F. Implementing this control in a system experiencing low-load delta-T likely would result in complaints of excessive heat, requiring cleaning, parts replacement, and, possibly, water- and air-distribution-system modifications before 54°F air-handler leaving-water temperature could be maintained. Figure 1 shows little difference in plant performance between the two pumping approaches.

Base System
Figure 2 illustrates a P/S system operating at a peak plant design load of 4,902 tons. The lighting load of 1.7 w per square foot and plug load of 0.8 w per square foot are consistent with a 1980s-era system.

Equal load on each of the chillers in operation is assumed. Air-handler response is the average of the 75 units. Article 1¹ gives the performance characteristics of the chiller and tower. The plant in Figure 2 is the same one depicted in Figure 4 of Article 1¹.

The electricity demand of each of the plant's 75 fans at design load is:

cfm × (dh) ÷ [6,356 × (E_fan-ASD)]

39,253 cfm × 3.91 in. ÷ (6,356 × 0.547) = 44.15 hp

0.746 kw per hp × 44.15 hp = 33 kw (Figure 2)

Each air handler includes a fan-powered terminal drawing 24.1 kw. Also included in Figure 2 are return-air and fresh-air fans. The chilled-water and tower pumps circulate water at a rate of 2,400 gpm and 3,000 gpm, respectively. The variable-speed secondary pump is at energy equilibrium at the conditions of Figure 2. The primary chiller pump is operating at 16 kw based on efficiency of 0.81 and head of 28.6 ft. The tower pump is operating at efficiency of 0.83 and head of 55.6 ft.

Energy in = Energy out
"Energy in equals energy out" is a condition of a real system, assuming change in internal energy is zero. Energy exits a system at the towers, exhausted to the atmosphere. For Figure 2, energy to the tower can be determined by the first law of thermodynamics:

Tons = gpm × delta-T ÷ 24 = 3,000 gpm × (81.87°F – 72.65°F) ÷ 24 = 1,152.5 tons

With the addition of tower-fan power (35 kw ÷ 3.517 = 9.95 tons), the total energy out is 1,163 tons for each tower, or 5,817 tons for all five. Note the building load of 3,513 tons is 5,817 tons when exhausted at the towers, a 65-percent increase attributed to the air handler and plant equipment.

Energy into the system in Figure 2 consists of the building loads plus the heat generated by the electricity required to drive the air-handler fans, pumps, and chillers/towers. Pump loading is modeled as a function of pump efficiency. All other electricity to the system, air handlers, chillers, and towers is modeled as fully loading the system.

Ein = (q_s-ton) + (q_solar) + (FA_ton) + (q_p-ton) + (light)_ton + (plug)_ton + (AHU)_kw ÷ 3.517 + (P_heat)_kw ÷ 3.517 + (FA_heat)_kw ÷ 3.517 + (P_sec-kw × E_sec) ÷ 3.517 + (P_c-kw × E_c × Pc#) ÷ 3.517 + (chiller_kw × chiller#) ÷ 3.517 + (P_t-kw × E_t × P_t#) ÷ 3.517 + (fan_t-kw × Tower#) ÷ 3.517

Ein = 1,422 tons + 501.8 tons + 178 tons + 222.4 tons + 808.7 tons + 380.5 tons + (4,883 kw ÷ 3.517) + 0 + 0 + (699.9 kw × 0.803 ÷ 3.517) + (16 kw × 0.81 × 5 ÷ 3.517) + (451.7 kw × 5 ÷ 3.517) + (37.8 kw × 0.83 × 5 ÷ 3.517) + (35 kw × 5 ÷ 3.517)

Ein = 3,513.4 + 1,388.4 + 159.8 + 18.42 + 642.2 + 44.6 + 49.8 = 5,817 tons

These relations are an integral part of the set of simultaneous equations and, therefore, hold for all figures and curves presented in the five articles in this series. The system always is at energy equilibrium. All data and curves meet the requirements of “energy in equals energy out” and the first law of thermodynamics. Any data point in any figure in any of the five articles in this series can be shown in a form similar to Figure 2.

24-hr Operation
The remaining figures in this article will consider the 24-hr operation of the system in Figure 2.

The top chart in Figure 3 shows the design-day ambient dry bulb and wet bulb, while the bottom chart shows the resulting building loads. The facility is assumed to be a one-shift operation; therefore, "on" control of lights and plug loads occurs from 8 a.m. to 6 p.m. The building-shell and fresh-air loads are set by outside temperature, while solar load is assumed as shown in the bottom chart.

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