Problem formulation and solving procedure

Let us consider the system shown in figure 2.1, where a distribution substation with HV/MV transformers connects the HV transmission grid to some MV feeders (for the sake of conciseness, in figure 2.1 only one feeder is shown); the feeders supply MV loads, MV/LV distribution transformers and distributed generation units. A BESS is connected to the MV bus of the HV/MV transformers.

The control center performs an optimal strategy consisting of BESS charging/discharging power control in order to level the power exchanged with the HV grid¹. We propose to perform the optimal strategy on the basis of following two multi-period optimization steps:

 Day-ahead scheduling: that identifies an optimal profile of the substation power whose peak value has been minimized; this profile is obtained thanks to an optimal day-ahead scheduling of the BESS charging/discharging powers.

 Very short time predictive control: that predicts a few minutes ahead BESS charging/discharging power with the aim of approaching the substation power to the optimal profile obtained in the day-ahead scheduling.

The figure 2.2 provides a flowchart of the two-step procedure. The multi-period optimization problems are discussed in the next subsections. In both steps, a single-objective constrained minimization problem is formulated as (2.1).

Figure 2.2: Flowchart of the two-step procedure.

The day is split in time intervals of length ∆t. During each time interval, the feeder power is assumed constant and equal to its mean value. The choice of the time interval length depends on a compromise between accuracy and computational efforts. In order to maximize the BESS lifetime, a control on the number of charge/discharge cycles is imposed. Here, without loss of generality, this number is limited to one cycle/day and divide the day into two contiguous time periods: the discharging period and the charging period. Moreover, for the sake of clarity it is assumed that the first time interval is the beginning of the discharging

1 Hereinafter the difference between the load demand and DG production will be referred to as “feeder power.” The total power of the Neural Network

Day-ahead forecasting

Multi-period optimization Feeders

power forecasted

data Feeders

power data

Charge/Discharge storage system

power Day-ahead procedure

Forecasted substation power

Feeders power data

Neural Network Short-time forecasting

Feeders power forecasted

data

Multi-period optimization

Very short time predictive procedure

period and the last time interval is the end of the charging period. Thus, the time intervals of are the indices associated to the first and last time intervals, respectively, in which the BESS is allowed to discharge (charge).

Day-ahead scheduling

As previously evidenced, the day-ahead scheduling is performed once a day for the next day, with the aim of identifying an optimized profile of the substation power imported from the transmission network in the next day.

Input data of the scheduling are the BESS state of charge at the beginning of the day and the forecasted daily profile of the feeder power. The BESS state of charge at the beginning of the day is the output of the procedure applied in the preceding day while the forecasted daily profile of the feeder power is obtained through a FFNN trained by historical data.

Output of the scheduling is the profile of the substation power in the next day, which is the input of the very short time predictive control algorithm (figure 2.2). Hereinafter, this quantity will be referred to as day-ahead forecasted substation power.

The day-ahead scheduling is based on the solution of a linear multi-period optimization problem. The linear optimization problem aims to minimize the upper value of the substation power. This is obtained by considering a theoretical leveling value (Plev) (figure 2.3) and assuming that when the requested power is greater than P_lev the BESS can discharge the stored energy, and when the requested power is lower than Plev the BESS can charge. In this way, the expected daily profile of the substation power is leveled.

Figure 2.3: Load leveling schematic view.

Then, the objective function (2.1) to be minimized is:

lev da

obj P

f  (2.3)

Equality constraints refer to the BESS state of charge at the beginning of the day and at the end of the charging stage. In more detail, the BESS state of charge at the end of the charging stage has to reach a specified value:

sp

where ^da

i ,

P is the day-ahead BESS power at time interval i, b _ch (_dis) is the BESS efficiency during the charge (discharge) mode, C^sp_finis the specified value of the BESS charge when the charge ends and C_in^sp is the BESS state of charge at the beginning of the day. In a typical day the two states of charge (C_in^spandC^sp_fin) should have the same value. However, due to particular events, the expected load demand can be very different from the forecasted one and, consequently, different values for the states of charge could be suitable. Obviously, C_in^spand

sp

Cfin cannot exceed the battery size.

The value of n can be either fixed or dynamically evaluated. In the first case an opportune _in^ch time of the day can be chosen on the basis of specific needs of the application. In the second case, the multi-period optimization is repeatedly performed until the value of n_in^ch, corresponding to the minimum value of P_lev, is found. Also a genetic algorithm (GA) can be used for evaluating,n_in^ch, which is a discrete variable.

The inequality constraints impose that the BESS can have only one charge/discharge BESS power rate, the ramp rate constraint could be also considered [15].

A further inequality constraint imposes that the state of charge cannot be lower than a minimum value (based on the admissible depth of discharge) during the discharge stage, that is²:

where C_min is the admissible minimum value of the state of charge.

Finally, an inequality constraint is imposed on the day-ahead forecasted substation power (

da i ,

Psub ) which has to be bounded by the minimized leveling power (P ); this result in: _lev



t



P is the day-ahead forecasted feeder power. l

With reference to the feeder power forecasting, a FFNN with delay lines and one hidden layer is used to implement the NARX model [17, 18]. To have proper forecasting, different network

2 It should be noted that a further inequality constraint should be included to impose that the state of charge cannot exceed the size of the

configurations were tried by varying the number of hidden neurons and the number of delays as well as various percentages of samples for training, validation and test.

Very short time predictive control

The very short time predictive control procedure is repeatedly performed at all the time intervals of the day. The main output of the procedure is the BESS charge/discharge power for each control intervali



1,...,n_t



. Aim of the procedure is to minimize the difference between the substation power calculated at this step and that evaluated in the previous step (i.e. the day-ahead forecasted substation power).

Input data of the procedure performed at each time interval i-1 are the forecasts of the feeder power (output of a FFNN) from the i^th time interval to the last time interval of the day, the day-ahead forecasted substation power values obtained in the day-ahead scheduling, and the BESS state of charge at the beginning of the i^th time interval (output of the optimization performed in the previous time interval).

Outputs of the procedure are the charge/discharge power and the state of charge at the end of the i^th interval (input for the next time interval).

The very short time predictive procedure is based on the solution of a non-linear multi-period optimization problem. The objective function (2.1) of the multi-period optimization for the i^th control interval is: procedure (hereinafter referred as very short time forecasted substation power).

The first equality constraint to be satisfied refers to the power balance at each time interval:



_t



of the feeder power, both at time interval j.

Moreover, relationship (2.4) is modified according to the considered control interval: when the control interval falls into the discharging stage it is:



^disfin



control interval falls into the charging stage, it is:



^chfin



The inequality constraints (2.5) and (2.6) are still considered, while constraint (2.7) is modified as follows:



^disfin



dis in min

n

i j

vst

dis

i t P C , i n ,...,n

C

dis fin

j ,

b  

 







1 (2.13)

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

In document Optimal Integration of Battery Energy Storage Systems in Smart Grids. (Page 46-50)