Numerical application

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Regarding the feeder power forecasting, the same FFNN configuration of the day-ahead forecast can be used.

2.1.4. Numerical application

In this section, the proposed two-step procedure is applied to a distribution substation supplying both commercial and domestic loads. A one-year period of substation power measurements was available in the form of mean values evaluated at time steps of ∆t =10 min. In this application, to perform the load leveling service, a 6 MW-5 hours BESS is supposed to be connected to the secondary side of the transformer. The BESS efficiency is considered 90% in charging and 93% in discharging operations, and the admissible DOD is 80% [24]. In order to maximize the BESS lifetime and to avoid capacity reduction, charge and discharge power cannot exceed the BESS rate [15].

In the most general case, the feeder power forecasting depends upon factors such as substation power values and weather conditions (temperature, humidity, pressure, etc.). However, in this application only the substation power historical data were available and were selected as input and target to train the FFNN. Eleven neurons and four delays were chosen for the FFNN configuration. In all the experiment days, a mean absolute percentage error (MAPE) resulted whose values were within 1.0-8.7%.

The optimal two-step strategy shown in previous section was applied to several days. In the following subsections, for the sake of conciseness, only the results will be shown with reference to a single day of the year, in particular, December 1, 2010. Similar results were obtained when considering other days.

Day-ahead scheduling results

With the aim of evaluating the accuracy of the forecast, in figure 2.4 the day ahead forecasted feeder power profile and the values of the actual measurements are reported, with reference to a time interval of 10 minutes.

Figure 2.4: Day-ahead forecasting (feeder power).

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Hour

Feeder power (MW)

Day-ahead forecasting Actual data

MAPE resulted in 5.20% with a maximum percentage error of about 14%. In figure 2.5 the forecasted feeder power and the forecasted substation power are reported. Obviously, in cases of absence of BESS, these power profiles would assume the same values. The leveling value of the power requested to the transmission network resulted equal to 8.74 MW, whereas the maximum value of the forecasted feeder power was 11.52 MW.

In order to verify the satisfaction of the BESS constraints, the charging/discharging pattern resulted from the day ahead procedure is shown in figure 2.6, whereas in figure 2.7 the energy stored during the day is reported. The start of the battery-charging period resulted at 9:40 p.m.

Figure 2.5: Day-ahead scheduling (feeder and substation powers).

Figure 2.6: Day-ahead scheduling (BESS power).

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Feeder and substation power (MW)

Feeder, day-ahead forecasting Substation, day-ahead forecasting

Charging stage Discharging stage

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Hour

BESS power (MW)

Charging stage Discharging stage

Figure 2.7: Day-ahead scheduling (BESS energy).

Very short time predictive control results

Very short time predictive control procedure was applied to all the time intervals of the day.

The MAPE between power forecasted and actual measured values is about 3%, while the maximum percentage error resulted 12%. In order to reduce the effect of the maximum forecasting error on the load leveling procedure, the BESS reference signals were calculated every 20 minutes instead of every 10 minutes. It is calculated based on average value of the two very short time optimized BESS powers at time intervals i and i+1. For example, when the forecasted powers for time intervals i and i+1 are 5 kW and 10 kW, respectively, then average forecasted power of the two sequential time intervals will be 7.5 kW. More accurate BESS reference signals were experimented in this way.

Figure 2.8 shows the day-ahead forecasted (output of the day ahead scheduling) and the very short time predictive control forecasted substation power (output of the very short time predictive procedure). In order to verify the satisfaction of the constraints, the resulting charging/discharging patterns are shown in figure 2.9 whereas the energy stored during the day is reported in figure 2.10. To verify the effectiveness of the proposed procedure, in figure 2.11 the very short term predictive forecasted substation power profile is compared with its actual profiles with and without BESS (the power without BESS is equal to the actual profile of the actual feeder power).

Figure 2.8: Very short term predictive control (substation power).

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BESS energy (MWh)

Discharging stage Charging stage

BESS capacity

Depth of discharge

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Substation Power (MW)

Very short time forecasting Day-ahead forecasting Leveling power

Figure 2.9: Very short term predictive control (BESS power).

Figure 2.10: Very short term predictive control (BESS energy).

Figure 2.11: Very short term predictive control (substation power).

In table 2.1 the peak value and the load factor of the substation power without BESS and with BESS (day-ahead forecasting, real-time forecasting and actual values) are reported.

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BESS power (MW)

Discharging stage Charging stage

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BESS energy (MWh)

BESS capacity

Depth of discharge

Discharging stage Charging stage

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Substation power (MW)

with BESS - Very short time forecasting with BESS - Actual

without BESS

Case study Peak value (MW) Load factor

Without BESS 11.52 0.730

With BESS, Day-ahead 8.74 0.981

With BESS, Very short time 9.07 0.941

With BESS, Actual values 9.72 0.888

Table 2.1: Peak value and load factor of the substation power with and without BESS.

The analysis of the results reported in figure 2.11 and table 2.1 clearly reveals: (i) a decrement of the peak power of about 15%; (ii) an improvement of the load factor of about 20% (the ideal load factor is 1); (iii) a not negligible influence of the feeder power forecasting errors both in day-ahead and in real-time stages; and (iv) that the negative influence of the forecasting errors is concentrated at only a few points around the leveling power. Then, the proposed two-step procedure shows clear good performance and further improvements are expected in the presence of most performance forecasting of feeder power.

2.2. An advanced optimal operation strategy for demand response under