3.2.5. Reduction Estimation of Ancillary Services for TSO

The exact amount of ancillary services provided to TSO and, consequently, the relative amount of incomes for the BESS owners may appear not directly dependent on the location of the BESS in the distribution network. However, being the storage devices connected to a given distribution network, their operation can be limited by the risk of violation of distribution system technical constraints. Indeed, if all these resources contribute simultaneously to an FCR request, they cause high momentary power flows that may exceed the maximum allowed overcurrent or cause excessive voltage deviations. The provision of secondary frequency control can also originate the same technical issues, even exacerbated because both services can be provided simultaneously. From this point of view, these services can depend indirectly on the position of BESS in the distribution network.

In order to assess these network limitations, the following procedure has been implemented. In normal operating conditions (Figure 4), for each hour of the typical day, a first probabilistic load flow (PLF) is executed without considering the provision of TSO ancillary services (but with the BESS typical scheduling). If the risk of technical constraints violation is greater than the acceptable one (*RTOT* > *RA*), the TSO ancillary services are suspended, and the virtual battery reserved to DSO is systematically used to solve or limit the network contingencies. In the other case, two additional PLFs are solved, by assuming that all the BESS installed are generating/absorbing their nominal powers simultaneously. If *RTOT* ≤ *RA*, the TSO ancillary services can be freely provided, limited only by the respect of the DSO semi-bands and by the power exchanged for arbitrage (BESS scheduling). Otherwise, the TSO ancillary services are suspended again. To simplify the analysis, it has not been calculated the maximum amount of TSO services that can be provided without causing any network contingency. Still, the verification of technical constraints is always performed assuming the full provision of the available flexibility.

**Figure 4.** Identification of existing limitation in providing TSO services due to technical constraints violation in ordinary operating conditions.

In emergency configurations, the virtual battery is used to solve (or limit) possible contingencies during the repair of the faulted component, while the TSO ancillary services are not considered, because it is assumed that during emergency configurations of the distribution network, they are always suspended.

Once all these limitations have been identified, the total amount of flexibility for TSO services is estimated by summing in the typical day all the available regulation semi-bands Δ*Pf*. The result is finally compared with the same amount of flexibility calculated without considering the limitation introduced by the distribution network and the virtual battery of the DSO. In this way, it has been possible to estimate the reduction of the potential flexibility available for the TSO ancillary services, due to the DSO needs. Some examples of this procedure are depicted in Figure 5, that considers the storage device of Figure 2, with the assumption of *rFCR* = 1/3 (i.e., one-third of the available band of flexibility in each hour is dedicated to FCR and two-third to aFRR) and Δ*t aFRR* = 2 h.

**Figure 5.** Examples of available flexibility for TSO services (*rFCR* = 1/3 and Δ*t aFRR* = 2 h).

The first case of calculation refers to the preliminary estimation of the available flexibility for TSO without considering DSO limitation. Because the SoC in the fifth hour of the day remains constant (*Pf BESS*

= 0), the semi-band coincides with the nominal power of the battery (*Pn* = 1000 kW). Thus, the flexibility for FCR is ±333 kW, and for aFRR is ±667 kW.

The second case (10th hour of the day) considers the presence of the virtual battery dedicated to the DSO. The SoC is still constant (*Pf BESS* = 0). However, the proximity of the upper bound limits the available regulation semi-band to Δ*Pf* = (Cmax\_DSO − *SoC10*)/Δ*t* = (3600 − 2800)/1 = 800 kW (<*Pn*). Thus, the flexibility for FCR is ±267 kW, while the flexibility for aFRR should be ±533 kW. However, because secondary control has to be guaranteed for 2 h, this flexibility is further reduced to Δ*Pf aFRR* = (Cmax\_DSO − *SoC10*)/Δ*t aFRR* = (3600 − 2800)/2 = 400 kW.

The third case (18th hour of the day) is partially influenced by the presence of the two hours (19th and 20th) during which, in ordinary conditions, the TSO services are suspended due to technical constraints violations. Because the aFRR has to last for two hours, it cannot be provided from the 18th to the 20th hour. Instead, the FCR can be provided in the 18th hour, while it is suspended in the 19th and 20th hour. The available flexibility for FCR, in this case, is limited by the discharge of the battery (*Pf BESS* = 200 kW), resulting in ±800 kW.

## **4. Case Study and Discussion**

The proposed case study describes a real application of the approach for finding optimal BESS installation projects in a small network of the Italian distribution system (Figure 6).

**Figure 6.** Test network.

Twenty-two MV nodes (9 trunk nodes and 13 lateral nodes), that supply energy to both MV and LV end-users (total rated power 13.8 MW), are fed by the bulk grid, via two primary substations, and by five RES generators: one 5 MW wind turbine (WT, in node 14) and four photovoltaic generators (PV, 0.5 ÷ 3.5 MW, in the nodes 8, 11, 16, 21). Loads and generators are modeled with typical daily curves. Two kinds of daily load profiles have been assumed for representing the residential customers (74%) and the

agricultural ones (26%); the standard deviation adopted for the loads is equal to 0.05 pu. Figure 7 shows the used load patterns. Furthermore, the load and generation uncertainties are modeled with a normal probability distribution. The WT output power has been modeled with a constant mean value (0.50 pu), greater than zero, and a high and constant standard deviation (0.15 pu) during the day. While the PV generation, characterized by high production during the day and no output during the night, has been assumed with a standard deviation variable hourly (i.e., small at the sunrise and sunset, and significant, 0.03 pu, in the central hours of the day). The network is radially operated, but it is provided by some tie connections, usually open, that can be closed during emergency conditions. The test network may be considered located in a prevalently rural ambit since it is constituted by long overhead lines (fault rate equal to 12 fault/(year·100 km)) and the extended lateral branches. More details on the network characteristics are provided in the Appendix A. As a consequence of these characteristics, this network is electrically weak, and voltage regulation problems or overloads may occur due to the non-homotheticity between production and load demand.

**Figure 7.** Case study: load profiles.

Table 1 reports the main parameters adopted in the case study, inherent to:


Regarding the main parameters of the optimization algorithm, a general rule often adopted for the genetic algorithm is that population size and number of generations have to increase with the dimension of the optimization problem (DOP—number of variables to be optimized simultaneously). Considering that the solution coding adopted uses 28 genes for each BESS (Figure 1), and that the optimization has been limited to three storage devices, then DOP = 84. From sensitivity analyses performed on the specific case study, population size and number of generations have been chosen equal respectively to 500 individuals and 50 iterations, representing a good compromise between quality of the results and calculation time. Indeed, it has been observed that the population size should be 5 ÷ 6 times DOP in order to achieve a high accuracy of the Pareto-optimal solutions set. Instead, the Pareto front does not improve significantly with the growth of generations after a minimum number of iterations (0.5 · DOP).

All nodes are eligible for BESS, but not more than 3 BESS are considered for each possible configuration. The threshold adopted for BESS owners CBA allows feasible solutions with a payback time comparable with the BESS lifespan (i.e., 12 years as in Table 1). Figure 8 shows the energy price daily pattern adopted for the monetization benefits.


**Table 1.** Main parameters used for the study.

**Figure 8.** Case study: daily energy prices.

For validating the effectiveness of the procedure, the comparison between the optimal solutions and a base case, that does not use the support of the BESS, has been considered. In the base case (without any BESS installed), network congestions occur during the evening (peak load, Figure 7) in the first branch of the B area (link 1–4, Figure 6), both in normal operations (network configuration showed in Figure 6) and in some emergency conditions. The total yearly overcurrent duration is equal to 735 h/year. For solving these contingencies, network upgrading would be necessary.

By applying the proposed optimization, the two OFs are calculated for each examined configuration. As a result of the optimization, the Pareto set is constituted by individuals that differ for the three BESS positions along the network, the nominal rates, and the daily schedules of charging/discharging cycle. The Pareto optimal front obtained for the proposed case study is shown in Figure 9.

**Figure 9.** Case study: Pareto optimal front.

By analyzing the resulting optimal siting, a tendency of locating the BESS close to the 3.5 MW PV generator (Figure 6, A area) can be recognized. In that location, the BESS presence does not increase the risk of technical limit violations, due to the strength of the network (relatively short electric distance from the primary substations), in opposition to the majority of the nodes in the other part of the network (i.e., B area). Therefore, in the A area of the system, the BESS can be successfully exploited for providing TSO ancillary services (the frequency services), with negligible impact on the distribution network operation. For the BESS located in the B area, the suitable BESS reservation rate for the DSO use permits to provide ancillary services to the distribution network, with a valuable contribution to relieve the contingencies. Recurrent BESS size in the optimal solutions is in the range 0.1 ÷ 1.3 MW with duration 1 ÷ 7 h; the most recurrent size is 1 MW/2 MWh.

In the Pareto front, diverse types of solutions can be seen:


Starting from this classification, by analyzing each configuration, some comments arise:

• In the S-a solutions, some BESS mainly dedicated to distribution networks are located in the B area of the system; the other BESS are small in size and, in some cases, too small to offer the FCR/aFRR services in a profitable manner. The arbitrage service is not profitable due to the very narrow band in the daily energy prices during the day (Figure 8). For these reasons, the CBA ratio has the maximum value (1.569 vs. a risk equal to zero), in the S-a solutions. For this type of solution, the BESS in the A area can offer 100% of services to TSO, while for the BESS in the B area, the services are limited to the 72 ÷ 81% of the total capacity. Globally, the overall solution can offer to the TSO a quantity in the range 83 ÷ 92%;


To investigate the impact of the BESS cost in the analysis, the CBA ratio in the Pareto front showed in Figure 9 has been calculated considering an expected 20% reduction of the BESS cost in the next years. It is important to remark that this sensitivity analysis does not modify the size and the type of solutions in the Pareto front but only the numerical values for the CBA ratio, because the BESS cost affects only the above mentioned OF. In the new conditions, the profitability threshold for the BESS owners (CBA = 1) is raised, and the new "compromise solution" can be identified with the red star in Figure 9, for which the total yearly overcurrent duration is equal to 102 h/year. In other words, following the expected reduction for the BESS cost in the next years, the proposed approach can identify a good compromise solution between BESS owners and DSO. For the DSO's point of view, it is essential to highlight that the BESS installation allows a partial risk reduction that can be completed by exploiting the flexibility from other local resources (active generators and loads). Moreover, even if not considered in the paper, BESS has also the potential to provide reactive support to the distribution network. Therefore, if local markets of ancillary services will be implemented, the profitability of BESS investment and the benefits for DSO operation can both get larger.

In Figure 10, the average daily schedules for the different BESS in the two areas of the network have been reported. In the A area, the BESS can be dedicated only to the owner profits because the DSO does not need support in this part of the network; the BESS change their SoC by maintaining an average energy level around 50%, to guarantee adequate support to the frequency service in upward e downward (TSO services). This assumption is confirmed by some sensitivity analyses for the frequency service remunerative prices; in particular, the simulation highlights that an increase in the remuneration (+15%) has similar effects of the BESS cost reduction, discussed above. On the contrary, the same reduction (−15%) in the remuneration for the frequency services jeopardizes the profitability of BESS investment because only the S-d solutions remain in a region where the NPV of the incomes are greater than the BESS cost (CBA ratio < 1).

The BESS size, in the A area, is limited to avoid technical violations during the feasibility check for the frequency control participation. On the contrary, in the B area, the energy pattern mainly follows the DSO needs: indeed, the BESS discharge from the 19th hour to the 21st hour covers the peak load during the evening, when the power congestion occurs.
