The zero "hour" and its influence on the Incremental and Cumulative Energy until specific hour

Question

Dear colleagues, 
 
 In the Scenario Energy Cost there is a column (Figure 1) with name Energy Used Incremental. For a specific hour it is equal to the Wire Power ( the time step is one our) of the previous hour. 
 The problem for me is when the Cumulative Energy uses this incremental value. In the example the cumulative energy for the first two hours of the day in the table is 7kWh. 
 But I don't agree, because: 
 During the first hour the Wire Energy is 3.1 kW, during the second hour the Wire Energy is 3,1kW. It means that if time step is exactly 1 hour, then the cumulative energy for these two hours will be 6.2 kWh. 
 Am I wrong, and where? 
 I suppose that the explanation is somehow hidden in the first ( very useless in my opinion ) row, The Zero Hour. 
 So the second question is what is the purpose of the first row, where in the column Time (hours) is written 0,00? Can I remove it? 
 I have this zero hour also in the context results table. For a day (EPS) with 24 hours, a have 25 rows. Figure 2.

Thank you in advance

Wayne Hartell · Accepted Answer

Hi Boyan, 
 I've taken a quick look at this and believe that the results displayed in WaterGEMS are indeed correct as Jesse states. 
 You state that the flow for the first hour is 2.17 (2.168) L/s, but actually that is not correct and this is the basis of your calculation differences, I think. 
 From the tables you pasted into this thread, both the scenario energy cost table and the pipe flex table indicate the flow is 2.71 L/s. Using this value of 2.71 L/s the calculated wire power, and both incremental and cumulative energy values seem correct to me. 
 These energy costs are calculated based on the underlying EPS (extended period simulation), so I think it's worth covering that for a moment so we can properly understand what the values at time 0, 1, 2 etc really mean. For every extended period simulation there is an initial hydraulic analysis at time 0. This generates the initial hydraulic conditions in the system, based on initial element settings such as tank levels, pump statuses, valve statuses and so on. Since this is at time 0 though, no time has passed and therefore no energy has been consumed, no water has been pumped, no tank levels have changed etc. 
 Next, the simulation will calculate the next time step. The time of the next time step can change depending on the configuration of the network such as controls, tank levels and sizes, but in the simplest case, the next time step is 0 + hydraulic time step. So if the hydraulic time step is 1 hour, time step 1 is 1 hour (or 3600 seconds). 
 Now at the next time step (so precisely at 3600 seconds) we calculate the new system steady state condition. This will likely result in different flow rates and adjusted tank levels and so on. 
 But how do we know how much to change the level in a tank, for example? We assume that for the whole previous hour (that is, from time 0 seconds right up to but not including 3600 seconds) (i.e., as close to 3600 as is possible without triggering the final decimal place, so 3599.9999999999 seconds say) had the same steady state conditions as that which was calculated at time 0. Thus if the flow in a pipe into a tank at time 0 was 1L/s, we calculate that 3600L entered the tank in the first hour (1L/s * 3600 s = 3600L). 
 So when thinking about energy (e.g., wire power) if the wire power was 3.9kW at time 0, then the cumulative energy at time 0 is also 0 (no time has passed) and at time 1 hour, the cumulative energy is 3.9kW * 1hr = 3.9 kWhr since 1 hour passed with an average usage of 3.9kW. 
 The same logic applies at time 24 hours. Your calculations show a wire power of 3.9kW and a cumulative energy of 3.9kWhr, but actually this is not correct since the hydraulics calculated at time 24, have no time to have any effect (hour 24 is the end of the EPS simulation). For the hydraulics at time 24 hours to have any effect on energy used, the EPS simulation would have to be extended past time 24 hours. 
 I hope this helps. 
 Regards, 
 Wayne.

Jesse Dringoli · Answer

Hello Boyan, 
 It appears that this is working as designed. 
 Using your example, the first row in the table indicates that the wire power between zero (start of the simulation) and 1.0 hours is 3.9 KW. Between 1.0 and 2.0 hours, the wire power is 3.1 KW. This means at the end of hour 2.0, the total is 7.0 KWh, hence the cumulative energy used in the 2.00 hr row shows as 7.0. 
 Basically the wire power indicates the power used within that timestep (from that one until the start of the next timestep), whereas the cumulative energy used column indicates the total energy used up until the beginning of that timestep. 
 In other words, the wire power column is showing what happens during that timestep and the cumulative energy used is showing what happened up until that timestep. 
 So for example if you want to see how much wire power the pump was using at hour 3.0 (which is essentially 3.0 through 4.0 since the time step is set to 1.0 hour), you would look at the wire power for the hour 3.0 row whereas if you want to see the amount of energy used up until hour 3, you would look at the cumulative energy column for the hour 3.0 row. 
 If the cumulative energy were not done in this way, then the cumulative energy shown at the end of the simulation (last timestep) would not be quite right. Meaning, if the cumulative energy referred to the energy used at the end of the given timestep, then the 24.0 row (assuming a simulation duration of 24 hours) would actually show the energy used in 25 total hours. (because again, the 24.0 row indicates what happens between 24.0 hours and 1.0 hours later). On the other hand, with the way it currently works, the cumulative energy cost for the last row (24.0 hr) shows the energy used in 24 hours (because it accounts for the wire power from the previous, 23.0 hr timestep, which is the power used from 23 to 24 hours) 
 I have added some of this clarification to the wiki article: Using the Scenario Energy Cost tool in SewerGEMS, SewerCAD and CivilStorm 
 Regarding the purpose of the first, 0.00 hr row: think of the Time column as representing what is happening between that time and the next time. The program is performing a series of steady state simulations one after the other (which we call EPS). This means that the conditions are assumed to be constant throughout that time step increment, which in this case is 1.0 hours (and changes in demands, controls, storage volume, etc are tracked between the timesteps). So, the data shown for that 0.00 hr row describes what happens between the very first moment of the simulation, and 1.0 hr into the simulation. The exception of course is statistical results like the aforementioned cumulative energy used, which as mentioned is showing the energy used up until that time step. 
 So, continuing with the same example, the wire power of 3.9 KW for the 0.00 hr row essentially indicates that the average energy used between 0.00 and 1.00 hr is 3.9 KW. The cumulative energy used for the 0.00 hr row shows as zero because it refers to the beginning of that timestep, where nothing has happened yet (0.00 hours).

The zero "hour" and its influence on the Incremental and Cumulative Energy until specific hour

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