Our data-based analysis shows a strong relation between unscheduled flows and frequency stability. To further understand this interaction, we now switch the perspective and investigate unscheduled flows on individual HVDC links as targets. For this purpose, we use our second model, the flow model, which predicts unscheduled flows on single HVDC links based on techno-economic features and the frequency indicators.
Importance of power imbalances for unscheduled flows
The flow model can explain a large share of unscheduled flows on various HVDC links (Fig. 6). As a recap, the flow model uses features from the stability model, such as the load or scheduled HVDC flows, as well as the frequency indicators from areas that are available in our data set. Based on these features, we achieve similar performances as in the stability models (\(R^2 \sim\) 0.2...0.85), which are acceptable values given the stochastic nature and our limited access to all influencing variables. Among the feature set, the role of the frequency integral is particularly interesting, as it closely relates to the control need within the hour.
The frequency integral plays a major role for some HVDC links, which can be related to load-frequency control delivered by these links. We first focus on the feature importance, which is indicated in Fig. 7 on the y-axis, and the feature rank, represented by black numbers. The Britned link is most prominent, as the British frequency integral is the most important feature in the respective model (blue color). The Nordic integral (orange color) is ranked among the ten most important features for Estlink, Kontiskan, and Storebaelt. In contrast, the Nordned link and particularly the Baltic cable show very low feature importances of the integral.
Our findings are fully consistent with operation modes of HVDC links reported by the transmission system operators and the ENTSO-E. Kontiskan, Storebaelt, and Estlink Fingrid et al. (2020, 2022) as well as Britned (ENTSO-E. 2019a) are used in load-frequency control. As the time series for physical and unscheduled flows correspond to the hourly average, the integral is the relevant feature of the frequency time series. The situation is very different for the Nordned link, which is not used in load-frequency control as reported in ref. (ENTSO-E. 2019a). Consistently, the frequency integral exhibits very low feature importance in the model.
Our studies complement and augment the sparsely available public information on HVDC operation. First, public information is entirely lacking for some of the HVDC links. For instance, we are not aware of any official report describing the operation of the Baltic cable. Our results show that this connection is likely not used for load-frequency control. Second, most available documents report only the general participation in load-frequency control without further details. Our results allow us to quantify this dependency as we will discuss in the following section.
Control-like and disturbance-like effects
Turning from feature importances to dependencies, we reveal control-like and disturbance-like interactions between unscheduled flows and frequency stability (Fig. 7). The correlation \(\tau\) between the SHAP values of the frequency integral and the unscheduled flows quantifies the direction of this dependency (similar to the correlation in Fig. 4). We note that we define the direction of the unscheduled flows such that positive values correspond to an outflow of electric energy. This holds for all connections such that a flow is counted differently for the two terminal sides. For instance, an unscheduled flow from CE to GB would be counted as positive for CE and as negative for GB. In that way, control-like dependencies appear in the right half of the plot (\(\tau >0\)), where positive frequency deviations lead to more outflows, while disturbance-like effects lie in the left half (\(\tau <0\)). We now discuss these effects for the four links exhibiting the highest feature importances of the integral, i.e., Britned, Estlink, Konstiskan, and Storebaelt.
Control-like effects are most pronounced for Britned and Estlink, which show high feature importance of the GB and the Nordic integral and a strong positive correlation. In contrast, the CE integral in the Britned model is negatively correlated thus showing a disturbance-like effect. (Note that the Baltic integral is not included in the Estlink model due to missing data). These observations are consistent with reports and TSO agreements. Britned is used only for uni-directional control, i.e., only for frequency support in GB (ENTSO-E 2019a), and Estlink is also dominantly used by the Nordic side for load-frequency control, according to the 2019 System Operator Agreement (SOA) (Fingrid et al. 2020). Thus, on the GB and Nordic sides, we only have a control effect, which introduces a positive dependency between frequency deviations and unscheduled outflows. On the other side of the link, the control actions behave like a disturbance, which explains the negative correlation of the CE integral in the Britned model.
Disturbance-like effects are most pronounced for Kontiskan and Storebaelt, which exhibit a negative correlation for the Nordic integral, but with relatively low feature importance. In contrast to Britned, the integral on both sides of the Kontiskan and Storebaelt links show a negative dependency (red and orange symbols), although the CE integral exhibits even lower feature importance. Reports and TSO agreements suggest, that both links are used bi-directionally for control, i.e., both sides can receive and supply frequency support (Fingrid et al. 2020, 2022). This might explain both the low feature importance as well as the observed dependencies. Both areas experience the control and the disturbance-like effect, which might cancel each other out. This might partly explain the lower importance of the frequency integral for both links. However, the disturbance-like effects dominate thus yielding the observed negative correlation for both the Nordic and the CE integral. One explanation can be the control delay, particularly if links are used for slow tertiary control (mFRR), which is slower than primary and secondary control. On the receiving side, a frequency deviation might trigger a delayed control action that partly falls into the next hour. On the supporting side, the disturbance-like effect of this action appears immediately and thus might introduce a stronger dependency between the hourly features and targets. However, also other effects of HVDC operation might play a role here.
Other effects of HVDC operation modes
The frequency integrals, i.e., systematic power imbalances, do not alone describe the unscheduled HVDC flows as demonstrated by their low feature importance for multiple links (Fig. 7). However, most flow models still exhibit a high performance (Fig. 6) thus pointing to other highly predictive features. These effects can relate to other properties of HVDC operation, which we discuss using the Britned and Kontiskan links as examples (Fig. 8).
The scheduled flows play a major role for both Kontiskan and Britned (green color). For Kontiskan, this feature is even the most important one, with the integral (red color) only following at rank five. Scheduled inflow on Kontiskan to the Nordic area is associated with an increase in the amount of unscheduled outflow. For Britned the impact of scheduled flows is nearly zero if the flows direct to GB, which is the dominating case for this border (cf. the physical flows in Fig. 5). A strong negative impact on the unscheduled outflows is only observed for a few data points with scheduled outflows from GB, i.e., scheduled outflows from GB systematically overestimate the physical outflow. The different effects of scheduled flows on Britned and Kontiskan might relate to different operation modes. On Britned the link overload capacity is used for frequency support (ENTSO-E. 2019a), such that frequency control can operate nearly independently of scheduled flows, which is consistent with a nearly vanishing impact of scheduled flows for the majority of time steps (Fig. 8). Only in the rare situation of strong outflows to CE, this situation changes. In contrast, no capacity is reserved for frequency control on Kontiskan (Fingrid et al. 2022). Control can only be provided if the market-based schedule leaves free capacity in the right direction, such that scheduled inflows to the Nordic area allow for increased unscheduled outflows as depicted by the dependency plot (Fig. 8).
If we look back at the stability models and Fig. 5, we can even see indications for these effects using the aggregated flow data. For the connections Nordic-Baltic and CE-GB, the scheduled flow is oriented in the same direction for most hours of the year as indicated in the color code in Fig. 5. GB mostly imports power via HVDC links, such that positive control power requires a further increase of the flows beyond the commercially scheduled values. Obviously, this is possible only if capacity is available, which is again consistent with ref. (ENTSO-E. 2019a) and our interpretation of Fig. 8. In contrast, links between the Nordic and CE areas are used for power flows in both directions.
Other important features are the actual generation of different types and forecast errors (blue color). Most of these dependencies exhibit a strong vertical dispersion, which indicates strong interactions with other features (Lundberg et al. 2020). Actual load, generation, and forecast errors directly relate to actual power imbalances, which can explain their importance for unscheduled HVDC flows. These features can indirectly also reflect market situation, e.g., intra-day prices or reserve energy prices, which are not included in the model. These market-based features can also influence unscheduled HVDC flows, as control via these links might only be applied if it is cheaper than other domestic operational reserves.
All in all, Britned is used for uni-directional control in GB, which in most cases does not depend much on the market-based schedule of the link, thus introducing a strong control-like interaction with the British grid frequency. This strong control effect on Britned most probably explains the control-like dependency, which we observed for the aggregated stability model in Fig. 5 (panel b). In contrast, Kontiskan exhibits disturbance-like interactions with the grid frequency on both sides, which probably relates to a bi-directional control setting. Control actions are further constrained by scheduled flows, thus diminishing the importance of the grid frequency for unscheduled flows. Similar observations can be made for other HVDC links between the Nordic and the CE area (Fig. 7), thus explaining the disturbance-like effect observed in our aggregated stability model in Fig. 5 (panel c).