In this section, two case studies are performed and the obtained results are discussed. In the first case study, the VB operation of the controller is analysed. This study demonstrates the accurate behaviour of the controller. Later, in a second case study, the residential VB charging capacity, discharging capacity, maximum charging power, and maximum discharging power of each Spain climate area are obtained along a natural year, concluding maximum power ratios and TCL contribution percentages. For this study, a VB controlled by the new developed controller has been used.
4.1. Case Study: VB Controller Operation
The control system developed in
Section 2 was implemented in MATLAB [
39] and its performance is studied for a VB of 1000 TCLs classified as follows: 125 reversible heat pumps (cold), 125 cold pumps, 125 reversible heat pumps (heat), 125 non-reversible heat pumps, 250 refrigerators, and 250 electric water heaters. The parameters of each TCL have been randomly selected by using a Gaussian probability distribution centered on the mean values given in
Table 3 and a standard deviation of
. The simulation covers 200 time instants with a sampling interval
h of 10 s, which amounts to a total of 2000 s. The minimum cycle elapsed time,
, is given a value of 60 s. No disturbance has been considered, i.e.,
. The initial status of each TCL has also been conveniently randomised using a binary probability distribution. The estimated ambient temperature
is fixed at 20
C in case of refrigerators and electric water heaters. For the remaining TCLs,
is a variable.
The results are shown in
Figure 3 and
Table 4 and are summarised as follows. The system deviation
accurately tracks the system operator power signal,
r, most of the time. The exception is the time interval between 510 and 750 s, where the maximum
stays at the value given by
, the maximum available charging power. The reason is that the grid operator established a value of
r that the VB is not capable of producing as it is outside the range previously defined by
and
. This situation should be avoided by taking into account the capability, SOC, and power information of the VB. When the signal
r changes, several TCLs change their status, which means that they become unavailable for 1 min. This explains the peaks and valleys in
and
when
r is modified. The absolute error is lower than 6 kW in absolute value whenever
r is between
and
. Otherwise, the VB cannot follow the system operator signal and the absolute error is either
or
. The charging/discharging capacities
/
and the maximum charging/discharging powers
/
appear to be constant in
Figure 3a,d,e. In fact, they evolve with time but the changes are very small because the simulation time is not large enough to notice great changes in the ambient temperatures. The greatest values of these variables are given in
Table 4. The charging capacity
is about 6.5 times greater than the discharging capacity
at every time instant. The reason is the lack of symmetry in the charging and discharging process, as the TCL takes more time to change its temperature
when it is not forced to by electromechanical components, i.e., when it is switched off (
). Regarding the maximum charging/discharging power,
is about twice as large as
, since the sum of the nameplate powers
doubles the sum of the average powers
for every TCL
.
The improvement achieved by the new controller proposed in this paper is depicted in
Figure 3f. In this figure,
is compared to
between the seconds 270 and 510, which is the system deviation signal when the anticipation to the variations imposed by TCLs constraints is not included in the controller. As mentioned above,
follows
r with an absolute error not greater than an individual TCL nameplate power, while
is several times greater, as it depends on how many TCLs have to change their status forced by any of their inner constraints, which is almost random. Specifically, in this case, the maximum absolute error
becomes around 15 times higher than the maximum absolute error
, in absolute value.
Besides performing short-duration regulation, the VB is able to maintain a system deviation of −300 kW for more than 15 min, as can be seen from time 1010 to 2000 s. This means that this VB can provide ancillary services to the grid similar to the usual primary and secondary regulation, according to the current definition given by the Spanish normative [
40], which is followed by the grid operator of the country, Red Eléctrica de España. Using European Network of Transmission System Operators (ENTSO-E) terminology [
41], this VB could supply regulation similar to Frequency Containment Reserves (FCR) and Frequency Restoration Reserves (FRR) services. The main difference between the regulation provided by the VB and the primary and secondary regulation is that the first acts on the demand side, whereas the others act on the generation side. As a general rule, the VB will fail to follow signal
r earlier if the amount of power requested is larger.
4.2. Case Study: VB Potential in Spain
The results of the study of the VB potential in Spain are reported here. Every existing TCL at each of the three climate areas of this country are assumed to be part of the corresponding VB. The charging capacity, discharging capacity, maximum charging power, and maximum discharging power of each climate area of Spain throughout a natural year are shown in
Figure 4 and
Figure 5. The ratios of greatest capacity and maximum power per home are shown in
Table 5. Information about the contribution of each residential type of TCL to the VB potential of each climate region is collected in
Table 6,
Table 7,
Table 8 and
Table 9. The average values from
Table 3 for the parameters of each type of TCL have been used in the study, along with the ambient temperature of each climate area, obtained from the hourly temperature model [
42] of the most populated cities at each climate area during 2019: Bilbao (North Atlantic), Madrid (Continental), and Barcelona (Mediterranean). In the case of refrigerators and electric water heaters, the ambient temperature is assumed to be constant and equal to 20
C.
Some interesting results should be highlighted. The Mediterranean is the climate area with the highest VB potential, while the North Atlantic has the lowest. Electric water heaters and refrigerators have the highest contribution to the charging and discharging capacity in three climate areas. Moreover, this contribution is constant during the year, as it can be checked in
Figure 4 and
Figure 5. The reason is that the home ambient temperature is considered constant and equal to 20
C. Refrigerators have more charging capacity in every climate area, while water heaters have more discharging capacity, see
Figure 4. These constant capacities can be used for demand management at any time of the year. The remaining devices have a variable capacity contribution, as can be easily seen by the numerous peaks and valleys appearing in
Figure 4 and
Figure 5. This is a consequence of the variability of the temperature along different days and seasons. The capacity and maximum power of heat and cold pumps depend on the weather. In general, heat pumps can only be used on cold days and most of them are in winter. In contrast, cold pumps are mostly used on hot days, typically during summer. Reversible heat pumps and cold pumps have a greater contribution in Continental and Mediterranean areas than in the North Atlantic area. The reason is the greater number of them in these areas, see
Table 2. Consequently, the variability in capacity and maximum power potential is more important in those climatic areas, see
Figure 4 and
Figure 5. Some summer days, the contribution of pumps to maximum charging and discharging power exceeds 50%, as can be easily checked by visual inspection in
Figure 5. During these days, most of the cold pumps are working. Thus, VBs with efficient controllers could exploit this variability to improve national electric systems. Finally, the lack of symmetry in the charging and discharging process, explained in
Section 4.1, clearly manifests here as a greater discharging capacity than charging capacity, as well as a greater maximum charging power than maximum discharging power, both for every climate area.
4.3. Discussion
A huge amount of energy and power flexibility of TCLs can be efficiently managed at real-time in a cost-effective way using a virtual battery. The control method proposed in this article to perform power regulation, control, and communication between TCLs and the aggregator improves the accuracy in tracking the system operator command power signal and does not require great investments in hardware or electronics because most of them are already installed, including the TCLs, thermal sensors, and Internet connection. This is an efficient and cost-effective alternative to conventional batteries or fossil fuel solutions that require complete new installations. Furthermore, VB potential is expected to increase in the next few years due to the progressive electrification of heating devices.
Another important benefit that VBs provide is the decentralisation and empowerment of consumers in the goal of balancing the grid. They become potential participants in balancing markets. Although these markets are not currently completely developed in Europe, the European Union has launched Regulation 2019/943 [
43] and Directive 2019/944 [
44], where balancing markets are considered. As mentioned in [
43], these markets can either be individually accessed or be part of an aggregation, ensuring non-discriminatory access to all participants and respecting the need to adapt to the increasing share of variable generation and increased demand responsiveness. VBs fit properly with these requirements.
In the case of Spain, net balancing energy amounted to approximately 1209 GWh in 2019 [
45]. This means an average power of 138 MW. However, positive and negative hourly peaks of more than 4000 MW are produced [
46]. The study performed in this paper shows that taking advantage of FM trough VBs clearly helps to achieve power regulation goals in Spain, especially in extreme situations. The remuneration for participating in balancing markets must be important to encourage TCL owners to become contributors. Although the Mediterranean climate area has the highest residential power and capacity potential in Spain, VBs management should be profitable in any climate region if the economic profit is sufficient.