3.2. Model Validation
In order to evaluate the accuracy of the three-phase unbalanced power flow and the network parameters, voltage values obtained from the unbalanced three-phase power flow were compared to the actual voltage values supplied by the DSO and measured from the network, for four representative days of the four seasons of the year. In
Figure 6 is shown the total active power consumption for the four representative days. In
Figure 7,
Figure 8,
Figure 9 and
Figure 10 are shown the comparisons between the historical voltage profiles and voltage profiles obtained through the three-phase unbalanced PF for the node electrically more distant from the distribution transformer for the four representative days.
The accuracy of the three-phase unbalanced power flow was evaluated through two different metrics, the Mean Absolute Percentage Error (MAPE) and the Root-Mean-Square Error (RMSE). The MAPE and RMSE are respectively given by:
where
n is the number of instants, and
and
are respectively the actual and forecasted values for the instant
t. The MAPE and RMSE values obtained per phase for the node electrically furthest to the MV/LV transformer, for the four representative days, are listed in
Table 4. As it is possible to see from
Figure 7,
Figure 8,
Figure 9 and
Figure 10, and
Table 4, the voltage values obtained are very close to the historical voltage values. The day where the voltage values present the highest error is the Winter day, with an average MAPE of 1.70%. The errors also have the tendency to decrease over time. The higher errors obtained for the Winter days may be explained by some configuration and synchronization errors in the acquisition of the data from the AMI. As these issues were solved, the voltage error values decreased significantly. The results obtained validate not only the accuracy of the unbalanced three-phase power flow implementation, but also the network’s electrical characteristics.
3.3. Simulation Results
The LVC algorithm was run in preventive control mode, for a planning horizon of 24 h and a frequency of 4 plans per hour (i.e., every 15 min). All of the consumers with HEMS were considered to be available to participate in grid operation, as well as the DSO-owned storage device located at node 117. The simulation was run for the Autumn day (
Figure 10), the most recent data available. The voltage magnitude limits considered were
of the distribution transformer nominal voltage,
. It is important to note that although the voltage magnitude limits are considered to be
, the LVC algorithm establishes stricter limits in order to compensate for the errors associated with the forecasts and state estimation, as well as the uncertainty associated with the behaviour of the flexibility-providing consumers. By doing this, fewer corrections are required in real-time operation, at the expense of a higher flexibility usage, but the grid is operated in a safer manner. In
Figure 11 a detail of the section of the network’s single-line diagram is shown where the voltage constraints are forecasted to occur. As it can be seen, the voltage violations are forecasted to occur towards the end of the feeder, that is, the nodes electrically more distant from the MV/LV distribution transformer.
In
Figure 12 and
Figure 13 the forecasted voltage profiles are shown for every customer in the LV network for a 24-h control horizon, before and after the application of the LVC tool, respectively.
As shown in
Figure 12, the voltage profiles, without the application of the LVC preventive control algorithm, surpass the predefined voltage magnitude upper limit during the solar peak production period of the day. Furthermore, it can also be seen that the voltage magnitude profiles tend to follow a curve similar to the solar PV production curve. This can be explained from the analysis of
Figure 6. Since the consumption is low during the peak solar production period of the day, the excessive microgeneration leads to reverse power flows, thus resulting in a voltage rise.
Figure 14 shows in greater detail the voltage rise effect for the feeder and time instant where the worst voltage violation is registered, with and without the application of the LVC algorithm.
In
Figure 15 the control action established to the DSO-owned storage device is shown. In
Figure 16,
Figure 17,
Figure 18,
Figure 19,
Figure 20 and
Figure 21 the control actions established to the consumers with HEMS are presented. In
Table 5 a summary of the total flexibility provided by the HEMS is provided, together with the flexibility that is effectively requested by the LVC algorithm to the private consumers with HEMS.
As can be seen from
Figure 16,
Figure 17,
Figure 18,
Figure 19,
Figure 20 and
Figure 21 and
Table 5, the algorithm uses only a small amount of the total flexibility provided by the HEMS in order to perform the active management of the LV network. Simulation results for one year, based on the four representative days, estimate that the total flexibility required from domestic consumers is 1821.50 kWh, 3.47% of the total flexibility available. From the analysis of
Figure 15, it can be seen that the LVC algorithm uses the energy storage device, once the overvoltage is registered at around 11:45, respecting the pre-established merit order. However, since the DSO-owned device is electrically far from the violation node (see
Figure A1), it is unable to fully solve the voltage constraint. Once this resource is exhausted, the LVC selects the next DER, in this case the HEMS that is electrically closer to the voltage violation. The process continues until the voltage constraint is solved. From
Figure 15 it can also be seen that the LVC algorithm tries to regularize the SoC of the storage device, in order not to jeopardize the availability of the resource for future time instants. To counteract the consumption peak registered at the peak solar production period of the day, the storage device slowly discharges during periods where it does not disturb the normal operation of the network, thus maintaining the SoC level at a safe point for the next control period. For comparison purposes, in
Figure 22,
Figure 23 and
Figure 24 the control actions required to maintain the voltage magnitude within the limits are presented, if only generation curtailment was considered instead of using available flexibility.
As it can be seen from
Figure 22,
Figure 23 and
Figure 24, a total of three generators would need to be curtailed, in order to maintain the voltage magnitude within the limits. The total amount of energy curtailment required to securely operate the network is 2.42 kWh. With the proposed method, no curtailment is required.
In
Table 6 the active power losses are presented, with and without the application of the LVC tool, as well as the percentage of reduction that was obtained for the simulation day, and the annual estimation. As can be seen, a total reduction of 3.50% was achieved with the LVC tool for this scenario. For comparison purposes, if the curtailment strategy was adopted (
Figure 22,
Figure 23 and
Figure 24), the total amount of losses would be 20.47 kWh, a reduction of 1.71%. With the proposed method, it is expected an annual loss reduction of 2.44%. This is an interesting result, since the reduction of the power losses is not an objective of the LVC algorithm. This result can be explained by the fact that the LVC algorithm tries to find the resource that is electrically closer to the node where the voltage constraint occurs, in practice reducing the power flows in the feeder.
The presented results show the potential of the proposed tool to be applied to highly stressed networks, allowing for their secure operation in scenarios of high DG penetration. Furthermore, from the DSO point-of-view, the LVC tool would allow to defer (or even avoid) large investments in network reinforcement and/or DSO-owned DER, such as ES devices, to maintain the secure and efficient operation of the network. Taking into account the current deployment state of AMI, it is reasonable to assume that the proposed solution could be deployed to real networks in the near future. The tool will be demonstrated on a smart grid pilot in Portugal, where the proposed functionalities will be tested in a real testbed to assess the robustness and efficiency of the proposed framework.