For the validation of the proposed adaptive control, the power system shown in

Figure 4 was selected and implemented in Matlab/Simulink/SimScape Power. This system is based on the CIGRE Medium Voltage (MV) reference grid presented in [

22]. For our analysis, we assumed that the specific power system consists of four cells interconnected in the configuration shown in

Figure 4. The number of cells was selected to obtain a sufficient meshed topology in the system with a sufficient number of cells (above two) which leads to a better assessment of the controller. During the tests, two adaptive controllers were used, one in cell 1 and one in cell 2. Cell 3 was not assumed to have DGs and, therefore, FCC whatsoever. However, imbalances happening in cell 3 were implemented to investigate the effect on the controllers of cells 1 and 2. Last, but not least, none of the three MV cells were equipped with control to restore frequency, which for these tests was assumed to be the task of the HV cell only. It should be pointed out here that, in connection with the parameters of

Figure 2, the main system parameters for cells 1–3, such as inertia constant H, load damping factor D, time delays T

_{G} and T

_{T}, as well as integrators’ gains K

_{I} were all set zero. This assumption does not affect the test results since the presence of these parameters is not a prerequisite for the proposed controller to operate. Also, the nature of the resources in the three cells, all of which are assumed as inverter-based units, makes the absence of inertia and time delays a reasonable assumption. The latter entails that in terms of dynamics, the frequency of all three MV cells is the same and it depends on the parameters of the HV cell. The parameters that were fixed throughout the tests for this cell are shown in

Table 3. Other important parameters such as the droop slope of each area were changed based on each scenario. It is noteworthy that the selection of these parameters was not based on a systematic approach but it was done based indicative literature values.

#### 4.1. Scenario A: Short-Term Analysis

This scenario includes the investigation of the adaptive controller’s qualitative behaviour for short-term imbalance incidents without the presence of frequency restoration control. The latter was omitted for the sake of clarity of results in order to have a clear view of the fuzzy controller’s response to input signals. As a consequence, due to the absence of any frequency restoration, all test results in this scenario present a steady-state frequency and imbalance deviation. In order to assess the ability of the controller to discern the location of the imbalance, three different imbalances were implemented in each of the three MV cells. Each imbalance was a load change of 3 MW located at nodes 2, 9 and 12, respectively.

Also, each imbalance takes place at

t = 100 s and the controller gains

g_{1} and

g_{2} were set to 5 and −50 respectively. The results in

Figure 5 show the response of the frequency and tie-line errors in conjunction with the CPFC curtailment for two of the three investigated imbalances. In this case, it is self-evident that the two controllers successfully pinpoint the imbalance location resulting in CPFC reduction only in cell 2 when the imbalance takes place in cell 1, or in both, cells 1 and 2, when the imbalance takes places in cell 3. Furthermore, for the case that the imbalance happens in cell 2 the results are similar to the ones shown in

Figure 5a. That means that the CPFC ratio of cell 2 remains unchanged, whereas the CPFC value of cell 1 is curtailed. It is also noteworthy that the variation of CPFC in all these tests does not go below 50%. This is due to the limited imbalance deviation for the specific incident compared to the base power of 50 MVA. With the selection of a gain value equal to −50 for the imbalance error, the latter is amplified enough to see a significant reduction of CPFC to about 50%. By further increasing the gain, or by changing the membership functions and/or the rule table, it is possible to increase the output range of the CPFC curtailment to even lower values. Since it is not easy to predict the exact values of the input errors in a power system model like the one used, the controller has been tested and validated in its full input/output range in a stand-alone set of tests with fully controllable inputs.

#### 4.2. Scenario B: Long-Term Analysis

This scenario is used to investigate the behaviour of the control scheme in a 24 h operation of the above-described network. To this end, the power profiles shown in

Figure 6 were used. These profiles have a sampling rate of 15 min. The input data shown in this diagram were scaled down and used as input signals to variable loads/generators in the model. In order to do this, the original data were divided by the maximum power of each profile in order to calculate the values in pu.

Once the pu values of load were obtained, the minimum load value was used as base-load in the system (fixed load at each bus) and the variable load was introduced as dynamic loads at each bus. In order to have differentiation among the buses, the dynamic load profile of each bus was modified using a random number generator. Finally, to get the actual power at the buses, each pu load profile was scaled-up by a factor based on the nominal load of each bus given by the CIGRE model. The same scaling-down and -up strategy was also used for the PVs and WG profiles, ignoring, however, the differentiation among PVs (all PVs produced the same profile of power). Furthermore, of the four cells making up the specific test grid, only two were equipped with the adaptive control. In order to highlight the impact of these controllers on the overall stability as well as to better assess the impact on the energy usage, the HV cell in this model was assumed to incorporate a relatively small droop slope corresponding to 1 MW/Hz. The contribution of the DER units in the droop slope was selected so that it would reflect their capability of varying their output power within specific margins. Thus, RES such as PVs and WG were assumed to be able only to reduce their output power (curtailment of generation) in case of production surplus. Also, other DER units such as batteries were considered to have capability of both increasing/decreasing their power, responding to any frequency variation. Due to this asymmetric contribution of DER, the scheduled droop slope of each unit should be selected such that a symmetric overall CPFC can be achieved. In our case, however, in order to investigate the impact that an asymmetric CPFC could have on the overall stability, the aggregated maximum droop slope or CPFC of each cell was selected −233 kW/Hz (negative delta f) and −300 kW/Hz (positive delta f) for cell 1 and −314 kW/Hz (negative delta f) and −610 kW/Hz (positive delta f) for cell 2.

Apart from the significant asymmetry in the aggregated CPFC, the part of the characteristic concerned with the positive frequency deviations provided by cells 1 and 2 is approximately equal to the HV droop slope which is fixed. Also, since this part of the CPFC is delivered by RES and since one of the main objectives of the test is to show the curtailment reduction caused on such kind of useful energy, the disturbance scenarios included stepwise reductions in the scheduled load profile of

Figure 6. Specifically, each timeframe (15 min) one-step change in the power consumption of each bus is implemented. Each change is selected to −10% of the actual power at the moment of reduction. This way, the resulting frequency disturbances lead to increase of frequency and activation of the controller part mainly related to the PVs and WG of the power system. For the quantification of the resulting reserves reduction, two types of mathematical formulation were used. The first one corresponds to the absolute energy usage expressed by the formula:

The second formulation is an expression of the cost of the usage of these reserves expressed as:

Last, but not least, the other HV area parameters used in this scenario were

K_{p} = 100 Hz/pu and

H = 5 s. Based on the afore-mentioned assumptions, the 24 h simulation test with and without the use of adaptive FCC control shows that a significant reduction in the use of FCC reserves can be achieved in total, but also for the individual types or RES reserves as well. The results obtained for this scenario are summarized in

Table 4 and

Table 5, respectively.

Table 4 illustrates the energy/cost saving for all DER when the proposed control is used (left column) in contrast with the classic fixed droop (right column). The results in this table show a significant overall reduction in both the energy (19.7%) and the cost (26.7%) by means of the adaptive modification of CPFC in the system. Similarly, a more specific table (

Table 5) shows the impact on the adaptive control on the RES of the system. It is evident that with the use of the proposed controller a significant reduction in RES energy loss is achieved. It is worth noting that the significant reduction in the use of reserves does not compromise the overall stability since the maximum frequency deviation for a fixed-droop FCC is 52.50 Hz, whereas the implementation of the adaptive control increases only slightly the deviation to 52.54 Hz. Likewise, the minimum frequency deviations with and without the use of adaptive control are 49.42 Hz and 49.51 Hz, respectively. The relatively high frequency deviation in both versions of the controller is due to the low overall droop slope of the system. Last, but not least, the system remains stable despite the asymmetric droop due to the type of reserves.

Figure 7 shows the frequency response of the two cells over time for the case of adaptive FCC control. It is worth noting that by implementing a slightly modified controller version with an increase of the CPFC ratio above 1 when the incident takes places inside the corresponding cell, it would be possible to maintain the frequency deviation equal to the fixed-droop version of the controller. In such a case, the local character of the reserves activation remains the same, with all the related benefits of this approach.

The drawback of such a variation, however, is the requirement of a higher amount of reserved power. Thus, in our study we only investigated the curtailment of CPFC with the concession that a slight increase of frequency deviation is acceptable. An operator, however, could select the alternative method if the availability of extra reserves is not an issue.