Question 9.5: Inverse problem with several anomalies. Heating and DHW inst......

Since 13 components have been considered, 13 characteristic curves must be defined. For achieving this, the different Types existing in TRNSYS v 17 were used, the characteristic curves of two of these components having been shown in the two previous examples (Example E.9.4 , Example E.9.3). The simulation of the installation was carried out hour by hour, with the demand profiles that have been represented in Fig. E.9.2. The cumulative values of the exergy of the flows in the reference conditions and for the state with the two anomalies introduced in the equipment described above are presented in Table E.9.6. In order not to include external induced anomalies (such as control inter-vention, changes in external conditions, etc.), the reference state coincides with the free condition.
When there are several anomalies in an installation, the anomaly in one of the i-th components leads to the unit consumption variation in the component itself \Delta k_{i,i n t} (intrinsic malfunction) and in the rest of the j-th equipment (j = 1,n, j ≠ i) it leads to induced malfunctions \Delta k_{j,i nd} as well as a variation in its products \Delta P_{j} (dysfunctions). The objective is to discriminate between these induced malfunctions and dysfunctions, in order to evaluate the increase in the resources consumption due to the intrinsic mal-function of the i-th component. By using the MD method, the extra consumption of resources associated with the increase in the products of the j -th equipment can be obtained through the dysfunctions D F_{ji} but additional information is needed to eval-uate the effect of the other induced malfunctions.
Complementing the MD diagnosis with that of the CC diagnosis, the component with the most important intrinsic malfunction can be identified, that which causes the greatest impact on fuel. Once this intrinsic malfunction is eliminated, the analysis is carried out again by applying the MD method a second time. The impact on fuel calculated in the first analysis \Delta F_{T}^{1} less the impact on fuel made in the second \Delta F_{T}^{2} (when the main anomaly has been eliminated) is the fuel saving obtained when that anomaly has been eliminated, that is to say

On the other hand, this fuel saving is the sum of the intrinsic malfunction M F_{i,i n t}^{1^{st}} plus the effects induced in that first analysis \left(\sum_{j}D F_{j i}^{1^{st}}+\sum_{j}M F_{j i}^{i n d,1^{st}}\right) plus the total product variation of the plant \Delta P_{s}^{1,2} and the dysfunction that is generated between both states. In this way, induced malfunctions can be calculated. The method can be repeated as many times as intrinsic malfunctions exist and the inverse diagnosis problem solved, see Fig E.9.12. For more details of the method see Picallo et al. 2016 [E.1].
The values obtained are presented in Table E.9.8. This table refers to the first anal-ysis, which contains the two malfunctions, and then the second is presented, which has the most influential malfunction removed. In column M F_{i n t}^{1^{st}} the intrinsic malfunctions are represented, while column M F_{i nd}^{1^{st}} represents the values of the induced malfunc-tions, as the characteristic curves of the components are not represented by horizontal lines. The sum of both columns corresponds to the total malfunctions of each compo-nent, while the last column represents the dysfunctions. In view of the table we can make the following comments:

•  The method of the characteristic equations allows us to distinguish between the intrinsic mal-functions and the induced malfunctions. Thus, the table shows that the components with the intrinsic malfunctions are \left[M F_{6,i n t}^{1^{st}}=323\,M J\right] and \left[M F_{10,i n t}^{1^{st}}=1212\,M J\right] corresponding to the HX and RS components, respectively.
• However, this methodology does not allow for the identification of the origin of each of the dysfunctions, since only the total dysfunctions DF_{i}^{1^{st}} can be calculated for each component.

Since we identify two components with intrinsic malfunctions, the next step is to eliminate the intrinsic malfunction of greatest weight (that of RS). Once that intrinsic malfunction has been eliminated, and this component is brought back to the reference conditions, we perform the simulation again, in order to evaluate the decrease in the impact on fuel between the first and the second simulations.
Table E.9.9 shows the results obtained by applying the method of characteristic equations to this second simulation. In view of the table we can make the following comments:

• Since the anomaly in RS has been eliminated, only the anomaly in HX is present, highlighting the malfunction in the heat exchanger M F_{6,i n t}^{2^{nd}}=317\,M J. As we can see, this intrinsic anom-aly varies slightly with respect to the previous situation, as the operating conditions of the equipment are slightly modified.
• {D}F_{i,0}^{2^{nd}} is still important. In fact, since the fault is in HX, the final DHW production is still lower than the reference state, and this has an impact on the consumption reduction \Bigr(\sum_{i}{ D}F_{i,0}^{2^{nd}}\;=\;-\,792\:M\!J\Big).
• Since the number of intrinsic anomalies has been reduced, the total production variation \Delta P_{s_{DHW}}^{2^{nd}} is closer to zero.
• The impact on fuel due to the existence of the two intrinsic anomalies is \Delta F_{T}^{2^{nd}}\,=\,-\,590\,M J.
• In short, the saving obtained by the elimination of the anomaly in RS is: \Delta F_{sav}^{}\,=6886\,M J.

The general results corresponding to the anomalies which were deliberately caused are collected in Table E.9.10. The rows M F_{i n t},\sum_{}^{}M F_{i n d},\mathrm{and}\sum D F are the intrinsic and induced malfunctions and the dysfunctions of the components with anomalies; while row D F_{0}+\Delta P_{s} indicates the effects of the anomalies on the final production. Finally, D F_{anomaly} summarizes the impact on fuel of each anomaly.

Thus, the anomaly in RS generates an extra consumption of 6886 MJ of which 7599 MJ are due to the anomaly proper, and the remaining -714 MJ are due to the decrease in the final product. On the other hand, the anomaly in HX generates an over-consumption of -590 MJ (underconsumption in this case), of which 277 MJ are due to the anomaly in the heat exchanger and the remaining -867 MJ are explained by the reduction in the DHW production.