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Frequency Containment Reserves might be insufficient to provide an appropriate response in the presence of large disturbances and low inertia scenarios. As a solution, this work assesses the supplementary droop frequency-based Emergency Power Control (EPC) from HVDC interconnections, applied in the detailed Nordic Power System model. EPC distribution and factors that determine the EPC performance of an HVDC link are the focus of interest. The main criteria are the maximum Instantaneous Frequency Deviation and used EPC power. The presented methodology is motivated based on the theoretical observation concerning linearized system representation. However, the assessed and proposed properties of interest, such as provided EPC active and reactive power, their ratio, and energy of total loads and losses in the system due to the EPC, concern highly nonlinear system behavior. Finally, based on the obtained study, remarks on the pragmatical importance of the EPC distribution to the frequency nadir limitation are provided., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

With increasing penetration of variable renewable energy sources (vRES) and a higher rate of electrification in the society, there will be future challenges in maintaining a continuous balance between electricity supply and demand. To investigate the possibility of different technologies to provide balancing services, to dimension future balancing services and design technical requirements for future balancing services, the future need of balancing power must first be known. Future power systems are often analysed by performing simulations capturing the energy produced, consumed or transmitted for different power system components with resolution of one trading period (TP), here called TP energy simulations. However, these simulations do not fully capture the continuous intra-TP power balance that must be kept at every time instance. In this paper, we propose a model to perform high-resolution intra-TP simulations to estimate the need of balancing power based on TP energy simulations. The model is applied to the Swedish system operator (SO) Svenska kraftn\"at's TP energy simulations of a scenario with high vRES penetration and a highly electrified society in year 2045. The results show that a considerable need of balancing power will occur frequently, where faster ramping of components tend to increase the need of balancing power while assuming that the transmission reliability margin (TRM) is used to net imbalances clearly decreases the need of balancing power., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

Deep reinforcement learning (DRL) is a machine learning-based method suited for complex and high-dimensional control problems. In this study, a real-time control system based on DRL is developed for long-term voltage stability events. The possibility of using system services from demand response (DR) and energy storage systems (ESS) as control measures to stabilize the system is investigated. The performance of the DRL control is evaluated on a modified Nordic32 test system. The results show that the DRL control quickly learns an effective control policy that can handle the uncertainty involved when using DR and ESS. The DRL control is compared to a rule-based load shedding scheme and the DRL control is shown to stabilize the system both significantly faster and with lesser load curtailment. Finally, when testing and evaluating the performance on load and disturbance scenarios that were not included in the training data, the robustness and generalization capability of the control were shown to be effective., Comment: In proceedings of the 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022), July 25-30, 2022, Banff, Canada

The post-contingency loadability limit (PCLL) and the secure operating limit (SOL) are the two main approaches used in computing the security margins of an electric power system. While the SOL is significantly more computationally demanding than the PCLL, it can account for the dynamic response after a disturbance and generally provides a better measure of the security margin. In this study, the difference between these two methods is compared and analyzed for a range of different contingency and load model scenarios. A methodology to allow a fair comparison between the two security margins is developed and tested on a modified version of the Nordic32 test system. The study shows that the SOL can differ significantly from the PCLL, especially when the system has a high penetration of loads with constant power characteristics, or a large share of induction motor loads with fast load restoration. The difference between the methods is also tested for different contingencies, where longer fault clearing times are shown to significantly increase the difference between the two margins., Comment: 8 pages

In the Nordic region, many interconnectors are formed by HVDC links, as Scandinavia, Continental Europe and the Baltic region are non-synchronous AC systems. This paper presents two cost benefit analyses on the utilization of HVDC interconnectors in the Nordic countries: in the first we investigate the utilization of HVDC interconnectors for reserve procurement and, in the second, we assess the implementation of implicit grid losses on HVDC interconnectors in the day-ahead market. The first analysis is motivated by real events in 2018 where the inertia of the Nordic system dropped below a critical level and the most critical generating unit, a nuclear power plant in Sweden, was redispatched to guarantee the security of the system. In order to guarantee system security while reducing the costs of preventive actions, in summer 2020 new frequency products were introduced in the Nordic system: the Fast Frequency Reserves (FFR). HVDC lines, however, can perform similar tasks at lower costs. In our analysis, we are, thus, investigating the cost savings of using HVDC lines for frequency support using their Emergency Power Control (EPC) functionality, instead of redispatching or FFR. The second analysis is based on the proposition of Nordic Transmission System Operators (TSOs) to introduce linear HVDC loss factors in the market clearing. With our analysis, we show that linear loss factors can unfairly penalize one HVDC line over the other, and this can reduce social benefits and jeopardize revenues of merchant HVDC lines. In this regard, we propose piecewise-linear loss factors: a simple-to-implement but highly-effective solution. Moreover, we demonstrate how the introduction of HVDC loss factors is a partial solution, since it disproportionally increases the AC losses. Our results show that the additional inclusion of AC loss factors can eliminate this problem., Comment: Submitted to "CIGRE Centennial Exhibition 2021" on December 15, 2020. arXiv admin note: text overlap with arXiv:1910.05607, arXiv:2001.00664

During summer 2018, the Nordic system's kinetic energy dropped below a critical level. As a consequence, Svenska kraftn\"{a}t, the Swedish transmission system operator (TSO), requested the largest production unit to reduce its power output to guarantee system's security. This action resulted in a deviation from the generation dispatch determined by the market and in high costs for the Nordic TSOs. In this regard, this paper presents a tool for comparing mitigation strategies from an economic point of view and evaluates potential economic benefits of utilizing the Emergency Power Control (EPC) functionality of HVDC lines for the provision of fast reserves as a compliment to Frequency Containment Reserves (FCR). Moreover, the analysis is extended to the years 2020 and 2025 using inertia estimations from the Nordic TSOs. The findings of the paper suggest that the frequency of redispatching actions will increase in the future and that the cost of security for Nordic TSOs could be reduced by 70\% if HVDC links are used for frequency support., Comment: Submitted to "IET Generation, Transmission & Distribution" on June 12, 2020 - Revised on September 6, 2020 - Accepted on September 16, 2020

This paper develops a new method for voltage instability prediction using a recurrent neural network with long short-term memory. The method is aimed to be used as a supplementary warning system for system operators, capable of assessing whether the current state will cause voltage instability issues several minutes into the future. The proposed method use a long sequence-based network, where both real-time and historic data are used to enhance the classification accuracy. The network is trained and tested on the Nordic32 test system, wherecombinations of different operating conditions and contingency scenarios are generated using time-domain simulations. The method shows that almost all N-1 contingency test cases were predicted correctly, and N-1-1 contingency test cases were predicted with over 93 % accuracy only seconds after a disturbance. Further, the impact of sequence length is examined, showing that the proposed long sequenced-based method provides significantly better classification accuracy than both a feedforward neural network and a network using a shorter sequence., Comment: 8 pages

Power system security assessment methods require large datasets of operating points to train or test their performance. As historical data often contain limited number of abnormal situations, simulation data are necessary to accurately determine the security boundary. Generating such a database is an extremely demanding task, which becomes intractable even for small system sizes. This paper proposes a modular and highly scalable algorithm for computationally efficient database generation. Using convex relaxation techniques and complex network theory, we discard large infeasible regions and drastically reduce the search space. We explore the remaining space by a highly parallelizable algorithm and substantially decrease computation time. Our method accommodates numerous definitions of power system security. Here we focus on the combination of N-k security and small-signal stability. Demonstrating our algorithm on IEEE 14-bus and NESTA 162-bus systems, we show how it outperforms existing approaches requiring less than 10% of the time other methods require., Comment: Database publicly available at: https://github.com/johnnyDEDK/OPs_Nesta162Bus - Paper accepted for publication at IEEE Transactions on Power Systems

Considering that the existing setup of the European electricity markets promotes the spatial coordination of neighbouring power systems only on the day-ahead market stage, regional system operators have to rely mainly on their internal balancing resources in order to guarantee system security. However, as power systems are forced to operate closer to their technical limits, where flexible generation becomes scarce, the conventional market paradigm may not be able to respond effectively on the wide range of uncertainty. The operational flexibility of the power system depends both on the technical parameters of its components, i.e., generators and transmission infrastructure, as well as on the operational practices that make optimal use of the available assets. This work focuses on alternative market designs that enable sharing of cross-border balancing resources between adjacent power systems through High Voltage Direct Current (HVDC) interconnections which provide increased controllability. In this context, we formulate a stochastic market-clearing algorithm that attains full spatio-temporal integration of reserve capacity, day-ahead and balancing markets. Against this benchmark we compare two deterministic market designs with varying degrees of coordination between the reserve capacity and energy services, both followed by a real-time mechanism. Our study reveals the inefficiency of deterministic approaches as the shares of wind power increase. Nevertheless, enforcing a tighter coordination between the reserves and energy trading floors may improve considerably the expected system cost compared to a sequential market design. Aiming to provide some insights for improvement of the sequential market-clearing, we analyse the effect of explicit transmission allocation between energy and reserves for different HVDC capacities and identify the market dynamics that dictate the optimal ratio.