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Fault-tolerant supervisory control of building condenser cooling water systems for energy efficiency.

Introduction

Fault-tolerant control (FTC) is a control that can accommodate system faults and is capable of maintaining acceptable stability and good performance, not only when the system is fault-free but also when the system suffers from some faults or malfunctions (Patton 1997; Mahmoud et al. 2003). According to the approaches of control systems to respond the faults, FTC can be broadly classified into passive FTC and active FTC (Patton 1997; Niksefat and Sepehri 2002; Jiang 2005). Passive FTC is based on the theory of robust control to ensure that the control system is robust enough to absorb possible faults that may happen in the system (Blanke et al. 2006; Silva et al. 2006). Active FTC, on the other hand, is based on the active response to any possible fault. The recovery of faulty measurements and reconfiguration of control systems are needed when the degree of faults is significant (Jiang 2005; Yu et al. 2005).

FTC has been an active area of research in the control engineering for many years (Hopkins 1971; Koczela 1971; Patton 1997; Niksefat and Sepehri 2002; Mahmoud et al. 2003; Jiang 2005; Yu et al. 2005; among others). However, the related research for building HVAC systems was relatively late, and only a limited number of studies are available in the open literature. In 1985, Takahashi and Shiraishi (1985) presented a fault-tolerant scheme for the airflow pressure control in ventilation systems. It could be the very beginning effort in the HVAC field to apply FTC to enhance system operational performance and control robustness.

In the last 15 years, more efforts have been undertaken to develop FTC strategies for building HVAC systems thanks to the growing interest in FDD (Lee et al. 1997; Du et al. 2007, 2008; Zhou et al. 2009; Talukdar and Patra 2010; among others). Since the sensor fault is one of the typical faults commonly occurred in HVAC systems, sensor fault detection, isolation, and reconstruction for FTC have been studied in a number of publications (Lee et al. 1997; Wang and Chen 2002; Hao et al. 2005; Du and Jin 2007). The central idea covered in these studies is that a reconstruction scheme was used to recover the faulty measurement once a sensor fault was identified. The recovered data rather than the faulty measurements were then used for control and optimization. Fault diagnosis and temperature sensor recovery for an air handling unit were studied by Lee et al. (1997). A two-stage artificial neural network was used for fault diagnosis, and a regression equation was employed to recover an estimate of the supply air temperature when the supply air temperature sensor fails. Wang and Chen (2002) presented a supervisory control scheme that adapts to the presence of the measurement faults in outdoor airflow rate control. Three neural network models were used to detect and identify the faults in the control system and to recover the measurement of the outdoor air or supply airflow sensor when the fault occurs. There are several studies using the principal component analysis (PCA) method to detect and diagnose sensor faults and to reconstruct faulty sensors (Wang and Chen 2004; Hao et al. 2005; Jin and Du 2006; Du and Jin 2007; among others). The results obtained from simulation tests showed that the PCA method is capable of recovering the faulty measurements of sensors with good performance. Therefore, it can be used for achieving FTC.

Besides the research on sensor fault detection and recovery, efforts have also been made on the design of robust strategies that are able to tolerate system performance degradations and malfunctions of control logics. Fargus and Chapman (1997) discussed the tolerance to faults and auto-configuration of neural network parameters in the implementation of a hybrid proportional-integral-neural controller for building HVAC systems. Liu and Dexter (2001) described a fuzzy-model-based supervisory control scheme for variable air volume (VAV) air-conditioning systems that can adapt to the presence of performance degradations. The fuzzy models were used to predict the performance of the air-conditioning system for particular values of the set-points, operating conditions, and sizes of the faults. Silva et al. (2006) presented an FTC strategy for HVAC terminal units based on multiple models. Multiple models were used for modeling the system performance in the presence of different faults and in different operating conditions. The models were then used to tune different controllers in order to maintain the required performance in the presence of faults. Talukdar and Patra (2010) presented a dynamic model-based FTC strategy for a VAV air-conditioning system. A state space model was used to detect, isolate, and estimate stuck faults of the damper vanes of air handling units. Fault identification was implemented by an adaptive interactive multiple observer scheme. An input modification scheme was used to prevent the convergence of the observer corresponding to the functional VAV box. Katipamula and Brambley (2007) presented a general model for automated continuous commissioning of HVAC systems. The automated commissioning was achieved based on automated proactive fault isolation and automated reconfiguration of controls. Ma and Wang (2011) presented online fault detection and robust control of chillers and cooling towers in building central chiller plants. The faults considered were the component performance degradations. The control system was reconfigured by tuning model parameters and/or changing the search ranges of control variables once a fault was detected.

Since the operation of HVAC systems is vulnerable to various faults, and the occurrence of any fault may increase system running cost and/or affect indoor thermal comfort, it is therefore necessary to ensure that the control system is robust enough to tolerate major possible faults that may happen during the routine operation of air-conditioning systems. This article presents a fault-tolerant supervisory control strategy for building condenser cooling water systems. In this strategy, an FDD scheme is embedded into the control system and used to monitor whether the critical sensors, major components, and control logics work in a healthy condition. Once a fault is detected, prompt corrective action is then taken to allow the system to continuously operate with acceptable performance despite the presence of the fault. The performance of this strategy is tested and evaluated against a simulated virtual system representing the actual condenser cooling water system in a super high-rise building in Hong Kong.

[FIGURE 1 OMITTED]

Description of the system and instrumentation

Figure 1 illustrates the schematic of the condenser cooling water system concerned in this study. There are six identical centrifugal chillers with the capacity of 7230 kW (24,669,784 BTU/h) and nominal power consumption of 1270 kW (4,333,420 BTU/h) each at design condition used to supply the chiller water at 5.5[degrees]C (41.9[degrees]F). Each chiller is interlocked with a constant-speed condenser water pump and a constant-speed primary chilled water pump. A total of 11 evaporative cooling towers with 2 different types (named CTA towers and CTB towers, respectively) are used for heat rejections. All cooling towers are an in-house type with crossover flow and equipped with variable-speed axial fans. Each of the CTA towers has a heat rejection capacity of 5234 kW (17,859,149 BTU/h) and a nominal power consumption of 152 kW (518,646 BTU/h) at design conditions. Each of the CTB towers has a heat rejection capacity of 4061 kW (13,856,707 BTU/h) and a nominal power consumption of 120 kW (409,457 BTU/h) at design conditions.

The main instrumentation installed in this system is illustrated in Figures 1 and 2. As shown in Figure 1, at the main supply and return pipelines, both in the primary chilled water loop and condenser cooling water loop, temperature sensors and flow meters are installed to measure the total building cooling loads and heat rejections, respectively. In each individual chiller and cooling tower, water flow meters, temperature sensors, and power meters are installed to monitor their operational status (see Figure 2). It is worth pointing out that not all cooling towers in this system are equipped with the inlet air dry-bulb temperature sensor and relative humidity sensor. Only 3 of them (out of a total of 11) are installed with both sensors to monitor ambient air status.

Fault-tolerant supervisory control strategy

For practical applications, it is almost impossible and also unnecessary to consider all possible faults that may happen in the routine operation of air-conditioning systems. A reasonable application of FTC is to detect and diagnose the critical faults that have significant impact on the system operational performance and then to take appropriate actions to handle and tolerate the faults to ensure that the system still operates with good performance.

Outline of fault-tolerant supervisory control strategy

Figure 3 illustrates the flowchart of the fault-tolerant supervisory control strategy developed for condenser cooling water systems. It mainly consists of a fault detection and diagnosis (FDD) scheme, a fault accommodation and tolerant (FAT) scheme, and a model-based predictive control (MPC) scheme. The FDD scheme is used to detect and diagnose the faults in critical sensors, physical components, and control logics. When a fault is detected and diagnosed, the FAT scheme is then employed to accommodate and tolerate the fault by using certain methods in order to regain control as far as possible. The MPC scheme is utilized to predict the system energy performance and response to the changes of control settings and then to identify the best control settings for the local process controllers to minimize the total energy consumption of chillers and cooling towers. To accommodate the variations of the raw data with noise, outliers, and high-frequency fluctuations, a measurement filter is used to preprocess the online measurements collected from the real process of the condenser cooling water system. The measurement filter utilizes the measurements both in previous time steps and the current time step to derive more reliable values, which are then used for fault detection and control optimization.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

FDD scheme and FAT scheme

As shown in Figure 3, FDD is implemented through several series steps, including sensor fault detection, system-level fault detection, component-level fault detection, sequence control fault detection, and fan speed control fault detection. According to the fault types and fault severities, the FAT scheme then uses different methods to accommodate and tolerate the faults in order to minimize their negative impact on the system operational performance. Table 1 summarizes the major accommodation and tolerant methods used for different types of faults. The details of each method are presented below along with the description of each fault detection step in the FDD scheme.

Sensor fault detection and recovery

Accuracy of sensor measurements is essentially important for reliable control, especially when the sensor measurement is used as a feedback point in the process controller. Since the condenser water supply temperature is one of the important control settings in the operation of condenser cooling water systems, the fault in the condenser water supply temperature sensor is therefore considered in the FDD scheme. This sensor fault is detected through monitoring the deviations between the measured temperatures and the corresponding temperatures derived from the energy balance equation, as shown in Equation 1. When the deviations in a time window (e.g., 1 h) defined continuously exceed the threshold (e.g., [+ or -] 1.0%), the FDD scheme will consider that the condenser water supply temperature sensor fails to provide reliable measurements. In this condition, the faulty measurement will be recovered by using the temperature derived from equation 1. The recovered data rather than the faulty measurements are then used for performing the fan speed control. It is worthwhile to point out that this sensor fault detection and recovery is established based on an assumption that the other sensors and flow meters in the system are fault-free. since the data were all collected from the simulated virtual system, this assumption could be easily satisfied:

[T.sub.rec] = [T.sub.w,cd,out] - [[[summation].sup.l.sub.i=1][c.sub.p,w][M.sub.w,ev,i]([T.sub.w,ev,in,i] - [T.sub.w,ev,out,i]) + [[summation].sup.l.sub.i=1][W.sub.ch,i]] / [[c.sub.p,w][M.sub.w,cd,tot]], (1)

where T is the temperature; M is the water flow rate; W is the power consumption; c is the specific heat; l is the number of chillers in operation; and subscripts rec, ev, cd, ch, w, in, out, p, and tot represent recovery, evaporator, condenser, chiller, water, inlet, outlet, pressure, and total, respectively.

System-level fault detection

After the sensor fault detection and recovery, system-level fault detection is then used to monitor whether the overall system operates in a healthy condition. This is achieved by using a system-level performance index (PI), as shown in Equation 2. since the constant-speed condenser water pumps are used in the system studied and the faults in these pumps are not considered, the power consumption of the condenser water pumps is therefore not involved in this PI. This system-level PI is called the overall system coefficient of performance (SCOP). It is directly related to the system energy consumption. A previous study has demonstrated that this PI is effective in identifying whether the operation of condenser cooling water systems suffers from the performance degradations at the system level (Ma and Wang 2011a). As shown in Figure 4, through monitoring the residuals between the system-level PI calculated by using online measurements and the corresponding PI predicted by the MPC scheme, the FDD scheme can determine whether the system operational performance is acceptable. If the system operational performance is acceptable, the FDD scheme then considers that there is no fault or the fault can be tolerant. Therefore, the FDD process is terminated, and there is no further action needed to update the control system or change the control modes. Otherwise, the FDD scheme will start the component-level fault detection:

SCOP = [Q.sub.tot,rej] / [W.sub.tot] = [[[summation].sup.l.sub.i=1][c.sub.p,w][M.sub.w,ev,i]([T.sub.w,ev,in,i] - [T.sub.w,ev,out,i]) + [[summation].sup.l.sub.i=1][W.sub.ch,i]] / [[[summation].sup.l.sub.i=1][W.sub.ch.i] + [[summation].sup.m.sub.j=1][W.sub.CT A,j] + [[summation].sup.n.sub.k=1][W.sub.CT B,k]], (2)

where SCOP is the overall coefficient of performance; Q is the heat transfer rate; subscripts CTA, CTB, and rej indicate CTA tower, CTB tower, and rejection, respectively.

[FIGURE 4 OMITTED]

Component-level fault detection and fault tolerance

Component-level fault detection is established based on the component-level PIs. The fan power consumption is selected as the PI of the cooling towers. The compressor power consumption is selected as the PI of the chillers. These two PIs have been proven to be valid in detecting the faults in cooling towers and chillers (Ahn et al. 2001; Zhou et al. 2009). It is worth noticing that, at the component level, the FDD scheme is only used to identify which component suffers from the faults. It is not used to identify the specific fault in cooling towers and chillers, such as cooling tower fill packing fouling, fan motor degradation, chiller condenser fouling, compressor motor degradation, etc. As shown in Figure 4, FDD is achieved based on the comparison of the calculated PIs by using online measurements and the predicted PIs by using the reference models. The reference models used are the same models as used in the MPC scheme, which will be presented in the section entitled "MPC scheme."

If not all residuals of the component-level PIs are well within the thresholds during the time window defined, the FDD scheme then concludes that the system component suffers from some faults. According to the residuals of each individual PI, the FDD scheme also determines which component is subject to the fault(s). If the corresponding residuals significantly exceed the threshold, the FDD scheme will consider that the system component suffers from a significant degree of performance degradation. In this condition, an alarm will be sent out and a repair will be requested. Meanwhile, the manual control mode will be required to replace the automatic control. since the performance of cooling towers or/and chillers is reduced greatly, more cooling towers are therefore suggested to be used to increase the heat transfer performance of cooling towers. The manual control mode I, as briefed in Table 1, can be used. If the fault is not serious, the control system of the MPC scheme will be reconstructed by updating the model parameters and changing the search ranges of control variables. The model parameters will be updated by using previous 24-h historical data with no fault or a lesser degree of fault. If all residuals of the component-level PIs are well within the thresholds defined, the FDD scheme will move to detect and diagnose the faults in control logics.

Control fault detection and fault tolerance

In the cooling tower system control, a sequence controller is used to control the number of cooling towers in operation and also to control which cooling tower is in operation. A proportional-integral controller is used to adjust the cooling tower fan speed to control the outlet water temperature of cooling towers at the desired set-point. The number of cooling towers in operation and the condenser water supply temperature set-point (i.e., cooling tower outlet water temperature set-point) are systematically optimized by the MPC scheme that will be presented in the section entitled "MPC scheme."

In practice, the ON/OFF of cooling towers is controlled by using modulating valves. Cooling towers may not be sequenced properly due to the malfunction of the modulating valves. The fault in the cooling tower sequence control can easily be detected based on monitoring the actual water flow rate in each cooling tower. Once the fault is detected, an alarm will be sent out and a repair will be requested. The manual control mode as described in Table 1 will be used since such a fault cannot be handled automatically in most cases.

If there is no fault in the cooling tower sequence control, the FDD scheme then starts to detect the fault in the fan speed control. The fan speed controller may work improperly if the parameters of the proportional value and integral value are not selected properly or both parameters cannot continue to provide proper response after working over a long period. The fault in the cooling tower fan speed control can be detected by using the logics presented in Figure 5. The fault detection is mainly achieved by comparing the measured condenser water supply temperature with the corresponding set-point together with the monitoring of the fan operating frequency. Within the time window defined, if the condenser water supply temperature cannot be controlled at the desired set-point while the operating towers are not operating at their maximum or minimum allowed frequencies, the FDD scheme then concludes that the fault occurred in the fan speed control. In this condition, an alarm will be sent out and a repair will be requested. The manual control mode will be used as well.

If there is no fault in the cooling tower fan speed control, the FDD scheme will consider that the MPC scheme fails to provide reliable estimates. This may happen in practice. For instance, for a given condition, if significantly fewer cooling towers than the actual desired are predicted by the MPC scheme, it may result that the operating cooling towers run at their maximum allowed frequency while the condenser water supply temperature cannot still be controlled at the desired set-point. In this condition, all components and sensors may be fault-free and the process controllers may work properly. However, the overall system operational performance is unacceptable. The FDD scheme, therefore, will consider that the MPC scheme suffers from the "fault." In order to ensure that the system can still work properly, an alternative control strategy will be used to replace the MPC scheme. In the meanwhile, an alarm will be sent out to inform the operators that the MPC scheme is subject to a fault and the alternative control strategy is being used for practical control. The alternative control strategy used is a traditional strategy commonly used in practice. In this alternative strategy, the condenser water supply temperature set-point is determined by using the fixed approach control method. In this method, the cooling towers are controlled to maintain a constant temperature difference between the condenser water supply temperature and ambient air wet-bulb temperature. The operating number of cooling towers is controlled based on the operating number of chillers. For the CTA and CTB towers, their operating numbers can be determined by using Equations 3 and 4, respectively:

[N.sub.CT A] = INT ([min(2 x [N.sub.ch] + 2, [N.sub.ct,tot]) + 1] / 2), (3)

[N.sub.CT B] = INT (min(2 x [N.sub.ch] + 2, [N.sub.ct,tot]) / 2), (4)

where N is the operating number of equipment, INT is the integral function, and subscript ct indicates cooling tower.

[FIGURE 5 OMITTED]

MPC scheme

In the fault-tolerant supervisory control strategy, the MPC scheme is used to identify the optimal control settings that can minimize the total energy consumption of chillers and cooling towers. The MPC scheme used in this study is an optimal control strategy developed previously. It is called the hybrid quick search (HQS)-based strategy (Ma et al. 2009). The HQS-based strategy was developed by using a model-based approach, in which a simplified chiller model and a simplified cooling tower model are used to estimate system energy performance and response to the changes of control settings. The HQs method is used as the optimization tool to search for optimal control settings for the local process controllers. To ensure that the system operates properly, a lower limit of 18.0[degrees]C (64.4[degrees]F) is imposed on the condenser water supply temperature set-point. The search range of the cooling tower operating number is constrained by Equation 5.

The simplified chiller model used is developed based on the fundamental principles of thermodynamics and the heat transfer processes in the chiller (Ma et al. 2009). The overall heat transfer coefficients of the evaporator and condenser are simulated using the classical heat exchanger efficiency method and represented empirically by Equations 6 and 7, respectively. A fictitious refrigeration cycle is assumed to simplify the complicated thermodynamic processes in the refrigeration system. Based on the fictitious refrigeration cycle, the power consumption of the chiller is predicted by using an empirical polynomial, as in Equation 8, through utilizing the fictitious power consumption determined from the fictitious refrigeration cycle.

The cooling tower model utilized is the so-called "Toolkit model" (Lebrun 1993), in which the cooling tower is modeled as an equivalent heat exchanger. Since both the airflow rate and water flow rate flowing through the cooling towers can be varied, the heat transfer coefficient is therefore modified and computed by using Equation 9. The fan power consumption is modeled using Equation 10, which is a third-order polynomial in terms of the airflow rate flowing through the cooling tower.

The optimization tool of the HQs method is developed based on the effective combination of the fixed approach control method and the exhaust search method. In the HQS method, the near-optimal setting generated by the fixed-approach control method is used as the search center to define a relatively narrow search range, as shown in Equation 11. Based on this narrow search range defined, the exhaustive search method is then used to seek the global optimal control settings with a proper increment (e.g., 0.1 K). The details of the HQS-based strategy together with the details of the models and the HQS method can be found in Ma et al. (2009).

min(2 x [N.sub.ch], [N.sub.ct,tot]) [less than or equal to] [N.sub.ct] [less than or equal to] min((2 x [N.sub.ch] + 2), [N.sub.ct,tot]), (5)

[C.sub.1][M.sup.-0.8.sub.w,ev] + [C.sub.2][Q.sup.-0.745.sub.ev] + [C.sub.3] = 1/[UA.sub.ev], (6)

[C.sub.4][M.sup.-0.8.sub.w,cd] + [C.sub.5][([Q.sub.ev] + [W.sub.ch]).sup.1/3] + [C.sub.6] = 1/[UA.sub.cd], (7)

[W.sub.ch] = [a.sub.0] + [a.sub.1][W.sub.fic] + [a.sub.2][W.sup.2.sub.fic], (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[W.sub.ct] = [d.sub.0] + [d.sub.1][M.sub.a] + [d.sub.2][M.sup.2.sub.a] + [d.sub.3][M.sup.3.sub.a], (10)

[T.sub.w,set,fix] - [DELTA]T [less than or equal to] [T.sub.w,set] [less than or equal to] [T.sub.w,set,fix] - [DELTA]T, (11)

where UA is the heat transfer coefficient; [C.sub.1]-[C.sub.6], [a.sub.0]-[a.sub.2], [b.sub.0]-[b.sub.2], and [d.sub.0]-[d.sub.3] are coefficients; and subscripts fic, fix, des, set, and a represents fictitious, fixed approach, design, set-point, and air, respectively.

Faults modeling, PI selection, and residual formulation

As presented earlier, the faults considered in the fault-tolerant supervisory control strategy include sensor faults, component performance degradations, and malfunctions of control logics. Usually, sensor faults can be categorized into hard failure and soft failure. Since the hard failure can easily be detected by using value limitations widely adopted in the Building Management System (BMS) as an alarm trigger, only the bias error is considered in this study. The fault in the condenser water supply temperature sensor is introduced by adding a fixed bias to model the sensor soft fault.

The component faults commonly include step fault and ramp fault. Since the ramp fault is closer to the real process of gradual performance degradations of system components, only the ramp fault is considered. In this study, four typical faults commonly encountered in cooling towers and chillers are considered. They include cooling tower fan motor degradation, cooling tower fill packing fouling, chiller motor degradation, and chiller condenser fouling. As presented in the section entitled "FDD scheme and FAT scheme," the power consumption of cooling towers and the power consumption of chillers are selected as the PIs of the cooling towers and chillers, respectively. In the tests, the faults are introduced using the methods summarized in Table 2, through multiplying different factors into the corresponding equations within the chiller model and cooling tower model to represent different degrees of fault severity.

The cooling tower sequence control fault is introduced through operating fewer cooling towers than desired to represent that the cooling towers are not sequenced properly. The fan speed control fault is introduced by changing the proportional and integral values in the fan speed controller. The MPC control fault is introduced through deliberately reducing the cooling loads by 20% during the MPC predictive process. The detailed modeling methods of the above faults, PIs used, and residual formulations as well as thresholds used are summarized in Table 2. It is worth noticing that the thresholds used are determined by considering the sensor measurement errors and model predictive errors.

Results and validation

Setup of the tests

The performance of the proposed strategy is tested and validated against a simulated virtual system previously developed (Ma and Wang 2011b). This simulated virtual system was constructed based on the platform of TRNSYS. In the tests, the building cooling loads simulated using Energy Plus and weather data in the typical year of Hong Kong were used as the test conditions. The chilled water supply temperature set-point and the number of chillers in operation were not optimized. The constant temperature set-point and the total cooling load-based sequence control strategy were used.

The parameters in the chiller model and cooling tower model were trained using the normal test data in four summer days. A previous study has demonstrated that both models have satisfactory performance in prediction (Ma and Wang 2011a). For conciseness, the model validation results are not presented.

Figure 6 shows the building cooling load profiles and ambient air temperatures used to test the performance of the fault-tolerant supervisory control strategy. In the tests, the faults were introduced progressively at the beginning of the second day and continued until the end of the test. For component performance degradations, the faults were also introduced at the beginning of the second day and linearly increased to 130% of the values of the fault-free conditions when the test was finished.

[FIGURE 6 OMITTED]

Test the effects of different faults on system performance

Different faults may have different impacts on the overall system performance. The effects of the faults on the system operational performance are therefore tested and validated first. In this study, a total of seven cases, as listed in Table 3, are tested and evaluated. These test cases can cover most operating conditions (i.e., fault-free and with different faults) that may be encountered in the routine operation of condenser cooling water systems. The tests were carried out based on the fault severities presented in Table 2.

Table 4 summarizes the energy consumption of the chillers and cooling towers under different test cases. It can be found that additional energy will be consumed by the condenser cooling water system when the fault was introduced. Compared to Case 1 with no fault, Case 2 with a +0.5[degrees]C (32.9[degrees]F) sensor bias consumed about 3917.0 kWh (12.39%) more energy of the cooling towers and 2096.5 kWh (0.59%) less energy of the chillers. The energy saving of the chillers was mainly achieved due to the use of lower condenser water supply temperature as a result of the sensor bias. The total energy consumption of the chillers and cooling towers increased 1820.5 kWh(0.47%).

When the operation of the condenser cooling water system suffers from the component performance degradations (Cases 3 and 4), the energy consumption of both chillers and cooling towers will increase compared to that with no fault condition. The fault(s) in one component (i.e., cooling towers) has an impact on the performance of the other component (i.e., chillers), but the effect is not significant. The test results show that about 5.35% and 4.86% total energy of the chillers and cooling towers was wasted when the faults happened in the cooling towers and chillers, respectively.

In Case 5, two fewer cooling towers than desired were used to simulate the malfunction of the modulating valves (i.e., sequence control fault) in the cooling towers. In order to maintain the desired condenser water supply temperature set-point, the operating cooling towers must speed up to increase the airflow rate and thus to increase the heat transfer performance of the cooling towers. This will increase the energy consumption of the cooling towers. However, the energy consumption of the chillers maintained almost constant since the condenser water supply temperature can still be controlled at the intended settings in most working conditions. The total energy penalty due to this sequence control fault is 8792.6 kWh (2.29%) as compared to that with no fault condition.

In Case 6, with fan speed control fault, significantly more energy of the cooling towers was consumed while a certain amount of chiller energy was saved. Due to the malfunction of the fan speed control, the actual condenser water supply temperature result was significantly lower than the desired values. In the meanwhile, during most high cooling demand periods, the cooling towers operated at their maximum allowed frequencies, which will be shown later in Figure 13.

In Case 7, due to wrong information used by the MPC scheme, the actual working condition of the condenser cooling water system was significantly different from that used by the MPC scheme. Therefore, the control settings identified by the MPC scheme were not the real optimal settings for the real process of the condenser cooling water system. In this particular case studied, the cooling towers consumed 5163.9 kWh (16.33%) more energy, while chillers saved 1034.6 kWh (0.29%) energy. The total energy consumption of the chillers and cooling towers increased 4129.3 kWh (1.07%) when compared with the system operated at the healthy condition.

The above studies show that any fault in condenser cooling water systems will deteriorate the overall system operational performance. The effect of some faults is serious, while the effect of some faults is less significant. The results also show that the effects of different faults on the performance of chillers and cooling towers are also different. Some faults, i.e., chiller faults, tower faults, etc., can degrade the performance of both chillers and cooling towers. However, some faults, such as fan speed control fault and the MPC fault particularly studied, only have significant negative impact on the performance of cooling towers.

Test the performance of the FDD scheme

In this section, the performance of the FDD scheme is tested and validated. Figure 7 shows the fault detection results under the fault-free condition (Case 1). It can be found that both the system-level PIs (SCOP) and component-level PIs were well within the thresholds defined when the condenser cooling water system operated at the healthy condition. Due to the model prediction errors, small differences existed between the predicted values and measured values.

Figure 8 shows the fault detection result when the condenser water supply temperature sensor suffered from +0.5[degrees]C (32.9[degrees]F) sensor bias (Case 2). The fault can be detected immediately once the sensor fault was introduced. Figure 9 shows the comparison between measured and predicted power consumptions of the chillers and cooling towers under this sensor fault condition. It can be observed that the measured power consumption of the chillers was less than that predicted by the MPC scheme, while the measured power consumption of the cooling towers was significantly higher than the predicted values. This is because, due to the sensor bias, the actual condenser water supply temperature resulted was lower than the intended set-point. However, the overall system operational performance was still acceptable in terms of the SCOP (see Figure 8). This demonstrates that sensor faults should be detected first in the FTC strategy.

[FIGURE 7 OMITTED]

Figure 10 shows the fault detection result when the cooling towers were subjected to fan motor degradation and fill packing fouling (Case 3). It can be observed that the faults can be detected early on the third day (i.e., around the 52nd hour) in terms of the SCOP when the degree of the cooling tower performance degradations increased to 11.7%. The FDD scheme also detected that the faults happened in the cooling towers since the residuals of the cooling tower PI significantly exceeded the thresholds defined. However, the residuals of the chiller PI were well established within the thresholds; even the degree of the cooling tower performance degradations was significant. It is worth noticing that, due to the relatively smaller energy consumption of the cooling towers than that of the chillers, the overall system operational performance was still acceptable, while the cooling tower performance degraded greatly at the early stage of the performance degradations (i.e., from the 30th hour to the 52nd hour).

Figure 11 shows the residuals of the system-level PIs and component-level PIs under the chiller motor degradation and condenser fouling condition (Case 4). The fault was detected at the end of the second day in terms of the SCOP when the degree of the chiller performance degradations increased to 10.0%. The FDD scheme also detected that the faults happened in the chillers, while the cooling towers can still maintain the acceptable performance, since the residuals of the cooling tower PI were well within the thresholds defined.

[FIGURE 8 OMITTED]

Figure 12 illustrates the fault detection result when the operation of the condenser cooling water system suffered from the cooling tower sequence control fault (Case 5). It can be observed that the system operational performance was unacceptable during some time periods in terms of the SCOP, while the chillers and cooling towers can still maintain acceptable performance. The FDD scheme, therefore, further detected whether the fault occurred in the control logics. As shown in Figure 12, the residuals of measured cooling tower water flow rates were significantly higher than the values predicted by the MPC scheme, since the residuals were positive. The FDD scheme therefore identified the fault happened in the cooling tower sequence controller.

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

Figure 13 illustrates the residuals of different PIs under the cooling tower fan speed control fault. Similar to the cooling tower sequence control fault, the overall system performance was not acceptable during high cooling demand periods when the fault was introduced. However, the PI residuals of the chillers and cooling towers were still well within the thresholds defined. By using the logics presented in Figure 5, the FDD scheme further detected the fault that occurred in the fan speed controller.

The fault detection result with the MPC fault is not provided for conciseness. The fault can be detected in terms of the SCOP, while the system components and local process controllers can still work properly. Therefore, the FDD scheme can detect the fault that happened in the MPC scheme.

The above results show that the FDD scheme developed is capable of detecting the sensor faults, physical component performance degradations, and malfunctions of control logics in condenser cooling water systems. Therefore, it can be embedded into the supervisory control strategy to achieve FTC.

Test the performance of the fault-tolerant supervisory control strategy

In this section, the performance of the fault-tolerant supervisory control strategy is tested and evaluated. For the sake of brevity, only the test results with two chiller faults, a fan speed control fault, and an MPC fault are presented.

Test results with two chiller faults

Figure 14 shows the test results when the system operated under the two chiller faults (Case 4) and the control system of the MPC scheme was reconstructed through tuning the model parameters together with the increase of the upper limit of the search range defined in Equation 5 by allowing two more cooling towers in operation. The model parameters were updated at the 48th, 64th, 68th, 72nd, and 86th hours, respectively. It is worth noticing that the model parameters in the reference models were updated as well. Compared to the results in Figure 11 with the same faults but without using the FAT scheme, the system can be almost re-controlled within the acceptable range in terms of the SCOP once the control system was reconstructed. In the meanwhile, the performance of the chillers was also acceptable, since the residuals of the chiller PI were re-established within the thresholds.

[FIGURE 11 OMITTED]

Table 5 summarizes the energy consumption of the chillers and cooling towers when the control system was reconstructed once the fault was detected. Compared to that without using the FAT scheme, about 275.7 kWh of energy of the cooling towers and 465.6 kWh of energy of the chillers were saved due to the update of the control system. The energy saving of the chillers was achieved due to the use of lower condenser water supply temperature set-point. The energy saving of the cooling towers was mainly achieved due to the use of more cooling towers with lower fan frequency although the use of lower condenser water supply temperature set-point deteriorated the heat transfer efficiency of the cooling towers. However, the total energy saving is very limited. Only about 0.18% total energy of the chillers and cooling towers can be saved. Compared to the system operated at the healthy condition, significant more energy was still wasted. Therefore, once a fault is detected in chillers, proper actions should be taken immediately to handle the fault to allow the chillers to operate at good efficiency.

[FIGURE 12 OMITTED]

Test results with cooling tower fan speed control fault

Table 6 summarizes the energy consumption of the chillers and cooling towers when the operation of the condenser cooling water system suffered from a fan speed control fault, and manual control mode II, as described in Table 1, was used once the fault was detected. Since the fan speed controller cannot continue to adjust the fan operating frequency properly, the fixed operating frequency was therefore used in the manual control. Compared to the system with the same fault but without using the manual control mode, about 31,094.4 kWh of energy can be saved from the cooling towers while about 9676.2 kWh more energy will be consumed by the chillers when the FAT scheme was used. The total energy savings were 21,418.2 kWh (5.23%).

[FIGURE 13 OMITTED]

Test results with the MPC fault

Table 7 presents the energy consumption of the chillers and cooling towers when the MPC scheme failed to provide reliable estimates and the alternative control strategy, as presented in Table 1, was used to replace the MPC scheme once the fault was detected. Since the local process controllers can still work properly, the alternative control strategy rather than the manual control mode was therefore used for automatic control. Compared to that without using the FAT scheme, the use of the alternative control strategy helped save about 2649.4 kWh (0.68%) total energy of the chillers and cooling towers. Most of the above energy savings were from the cooling towers. The energy saving of the chillers was only about 298.3 kWh.

[FIGURE 14 OMITTED]

The above results show that a certain amount of energy of the condenser cooling water system can be saved through using the proposed FAT methods once the fault was detected. The actual energy savings by using the proposed strategy will be different for different types of faults and different fault severities. However, compared to the system operated at the healthy condition, significant more energy of the condenser cooling water system was still wasted even if the FAT methods were used to handle the faults.

Conclusions

This article presented a fault-tolerant supervisory control strategy for building condenser cooling water systems. The proposed strategy employs different methods to accommodate and tolerate the sensor faults, physical component performance degradations, and malfunctions of control logics that may happen in the routine operation of condenser cooling water systems to achieve FTC.

The proposed strategy was tested and evaluated against a simulated virtual system representing the actual condenser cooling water system in a super high-rise building in Hong Kong. The results show that the FDD scheme embedded into the control system is effective in identifying whether the system operates in a healthy condition and also can identify which component or which controller suffers from the faults. Compared to the system operated with no faults, about 0.47%-6.48% more energy of the chillers and cooling towers will be wasted when the operation of the system suffered from the faults studied. The results also show that about 0.18%-5.23% energy of the chillers and cooling towers can be saved by using the proposed fault-tolerant supervisory control strategy under the fault conditions studied, as compared to that using the same control strategy but without using the FAT scheme. This part of energy savings was achieved through using the fault-tolerant supervisory control strategy only and without adding any additional cost. The total energy saving percentage is relatively small when recognizing the modeling mismatch, and the performance benefits, in practice, might likely be hard to measure. However, it could be expected that this strategy can save more energy in practice when the degree of faults is significant. Meanwhile, it can help identify the early faults and malfunctions and therefore can avoid the faults to be developed into complete faults to cause emergency shutdown of HVAC systems.

DOI: 10.1080/10789669.2011.568320

Acknowledgment

The research work presented in this article was financially supported by a grant of the National 11-5 program of PRC and a grant from The Hong Kong Polytechnic University as well as the support from Sun Hung Kai Real Properties Limited.

Nomenclature

[a.sub.0]-[a.sub.2], [b.sub.0]-[b.sub.2] = coefficients

c = specific heat, kJ/(kg K)

[C.sub.1]-[C.sub.6] = coefficients

[d.sub.0]-[d.sub.3] = coefficients

f = frequency, Hz

INT = integral function

M = mass flow rate, L/s

N = operating number of equipment

Q = heat transfer rate, kW

SCOP = overall system coefficient of performance

T = temperature, [degrees]C([degrees]F)

UA = heat transfer coefficient, kW/K

W = power consumption, kW

Greek symbols

[epsilon] = PI residual

Subscripts

a = air

cd = condenser

ch = chiller

ct = cooling tower

CTA = CTA tower

CTB = CTB tower

des = design

ev = evaporator

fic = fictitious

fix = fixed approach

in = inlet

m = measured

out = outlet

p = pressure

pred = predicted

rec = recovery

ref = reference

rej = rejection

seq = sequence

set = set-point

tot = total

w = water

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Received December 30, 2010; accepted February 22, 2011

Zhenjun Ma, PhD, is Lecturer. Shengwei Wang, PhD, CEng, Member ASHRAE, is Chair Professor

Zhenjun Ma (1,2) * and Shengwei Wang (1)

(1) Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong

(2) The Sustainable Buildings Research Centre (SBRC), Faculty of Engineering, University of Wollongong, Australia

* Corresponding author e-mail: zhenjun@vow.edu.au
Table 1. Fault types considered and their accommodation and
tolerant methods.

Fault types Faults in FAT actions

Sensor fault Condenser water Sensor fault recovery
 supply
 temperature
 sensor

Component Chillers and Reconstruction of the
 performance cooling MPC scheme (if
 degradation towers faults are not
 serious)

 Manual control mode I
 (if faults are
 serious)

Malfunction of Cooling tower Manual control mode II
 control logics sequence
 control

 Cooling tower Manual control mode II
 fan speed
 control

 MPC scheme Alternative control
 strategy

Fault types Brief of the methods used

Sensor fault Recover the faulty
 measurements by using the
 temperatures derived from
 Equation 1

Component Update model parameters and
 performance change the search ranges
 degradation of control variables

 Cooling towers are sequenced
 by using one more cooling
 tower than values determined
 by Equations 3 and 4; fan
 operating frequency is fixed
 at 35 Hz

Malfunction of Cooling tower operating
 control logics numbers are determined by
 using Equations 3 and 4;
 fan operating frequency is
 fixed at 35 Hz

 Using fixed-approach control
 method for fan speed
 control; cooling tower
 operating numbers are
 determined by using
 Equations 3 and 4

Table 2. Faults modeling, PIs used and residual formulations.

No Typical faults Fault modeling Fault severities

1 Sensor fault Add a fixed bias to +0.5[degrees]C
 the sensor (32.9[degrees]F)
 measurements bias

2 Cooling tower Decrease the Ramp fault (0%-30%)
 fan motor airflow rate
 degradation

3 Fill packing Decrease the heat Ramp fault (0%-30%)
 fouling transfer
 coefficient

4 Chiller motor Increase the Ramp fault (0%-30%)
 degradation electromechanical
 power loss

5 Chiller Decrease the heat Ramp fault (0%-30%)
 condenser transfer
 fouling coefficient

6 Cooling tower Operate fewer Two fewer cooling
 sequence cooling towers towers
 control than actual
 fault desired

7 Fan speed Change the -
 control proportional and
 fault integral values
 in the fan speed
 controller

8 MPC fault Reduce building 20% reduction
 cooling load in
 the predictive
 process

9 Overall SCOP

No Typical faults PIs used

1 Sensor fault [T.sub.w,cd,in]

2 Cooling tower [W.sub.ct,tot]
 fan motor
 degradation

3 Fill packing
 fouling

4 Chiller motor [W.sub.cho,tot]
 degradation

5 Chiller
 condenser
 fouling

6 Cooling tower [M.sub.w,ct]
 sequence
 control
 fault

7 Fan speed [T.sub.w,cd,in]
 control and f
 fault

8 MPC fault -

9 SCOP

No Typical faults Residual formulations Thresholds

1 Sensor fault [[epsilon].sub.sensor] = [+ or -]1.0%
 [[[T.sub.w,cd,in,m] -
 [T.sub.rec]] / [T.sub.rec]]
 x 100%

2 Cooling tower [[epsilon].sub.ct] = [+ or -]10.0%
 fan motor [[[W.sub.ct,tot,m] -
 degradation [W.sub.ct,tot,ref]] /
 [W.ct,tot,ref]] x 100%

3 Fill packing
 fouling

4 Chiller motor [[epsilon].sub.ch] = [+ or -]4.0%
 degradation [[[W.sub.ch,tot,m] -
 [W.sub.ch,tot,ref]] /
 [W.sub.ch,tot,ref]] x 100%

5 Chiller
 condenser
 fouling

6 Cooling tower [[epsilon].sub.ct,seq] = [+ or -]10.0%
 sequence [[[M.sub.w,ct,m] -
 control [M.sub.w,ct,pred]] -
 fault [M.sub.w,ct,pred]] x 100%

7 Fan speed [[epsilon].sub.ct,speed] = [+ or -]1.0%
 control [[[T.sub.w,cd,in,m] -
 fault [T.sub.w,set]] /
 [T.sub.w,set]] x 100%

8 MPC fault - -

9 [[epsilon].sub.scop] = [+ or -]3.0%
 [[[SCOP.sub.m] -
 [SCOP.sub.pred]] /
 [SCOP.sub.pred]] x 100%

Table 3. List of different test cases considered.

Test Test conditions
cases

Case 1 Normal operation with no fault
Case 2 Condenser water supply temperature
 sensor fault
Case 3 Cooling tower fan motor degradation and
 fill packing fouling
Case 4 Chiller motor degradation and condenser
 fouling
Case 5 Cooling tower sequence control fault
Case 6 Cooling tower fan speed control fault
Case 7 MPC fault

Table 4. Energy consumption of chillers and cooling towers
under different test cases.

 Energy consumption

 [W.sub.ct,tot], [W.sub.ch,tot], [W.sub.tot],
Test cases kWh kWh kWh

Case 1 31,624.7 353,043.2 384,667.9
Case 2 35,541.7 350,946.7 386.488.4
Case 3 51,222.6 354,029.2 405,251.8
Case 4 32,117.7 371,238.7 403,356.4
Case 5 40,398.2 353,062.3 393,460.5
Case 6 66,048.0 343,532.7 409,580.7
Case 7 36,788.6 352,008.6 388,797.2

 Energy difference

 [W.sub.ct,tot] [W.sub.ch,tot]

Test cases kWh % kWh %

Case 1 - - - -
Case 2 3917.0 12.39 -2096.5 -0.59
Case 3 19,597.9 61.97 986.0 0.28
Case 4 493.0 1.56 18,195.5 5.15
Case 5 8773.5 27.74 19.1 0.01
Case 6 34,423.3 108.85 -9510.5 -2.69
Case 7 5163.9 16.33 -1034.6 -0.29

 Energy difference

 [W.sub.tot]

Test cases kWh %

Case 1 - -
Case 2 1820.5 0.47
Case 3 20,583.9 5.35
Case 4 18,688.5 4.86
Case 5 8792.6 2.29
Case 6 24,912.8 6.48
Case 7 4129.3 1.07

Table 5. Energy consumption of the system with and without the FAT
scheme-two chiller faults condition.

 Energy consumption

 [W.sub.ct,tot], [W.sub.ch,tot],
Operation modes kWh kWh

Without the FAT scheme 31,117.7 371,238.7
With the FAT scheme 31,842.0 370,773.1

 Energy Energy saving
 consumption

 [W.sub.tot], [W.sub.ct,tot] [W.sub.ch,tot],
Operation modes kWh

 kWh % kWh %

Without the FAT scheme 403,356.4 - - - -
With the FAT scheme 402,615.5 275.7 0.86 465.6 0.13

 Energy saving

 [W.sub.tot],
Operation modes

 kWh %

Without the FAT scheme - -
With the FAT scheme 741.3 0.18

Table 6. Energy consumption of the system with and without the
FAT scheme--fan speed control fault condition.

 Energy consumption

 [W.sub.ct,tot], [W.sub.ch,tot], [W.sub.tot],
Operation modes kWh kWh kWh

Without the FAT 66,048.0 343,532.7 409,580.7
 scheme
With the FAT 34,953.6 353,208.9 388,162.5
 scheme

 Energy saving

 [W.sub.ct,tot] [W.sub.ch,tot]

Operation modes kWh % kWh %

Without the FAT - - - -
 scheme
With the FAT 310,94.4 47.08 -9676.2 2.82
 scheme

 Energy saving

 [W.sub.tot]

Operation modes kWh %

Without the FAT - -
 scheme
With the FAT 21,418.2 5.23
 scheme

Table 7. Energy consumption of the system with and without the
FAT scheme--MPC fault condition.

 Energy consumption

 [W.sub.ct,tot], [W.sub.ch,tot], [W.sub.tot],
Operation modes kWh kWh kWh

Without the 36,788.6 352,008.6 388,797.2
 FAT scheme
With the FAT 34,437.5 351,710.3 386,147.8
 scheme

 Energy saving

 [W.sub.ct,tot] [W.sub.ch,tot] [W.sub.tot]

Operation modes kWh % kWh % kWh %

Without the - - - - - -
 FAT scheme
With the FAT 2351.1 6.39 298.3 0.08 2649.4 0.68
 scheme
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Date:Jan 1, 2012
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