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In many parts of the world, electric power systems have seen a significant shift towards generation from renewable energy and natural gas. Because of their ability to flexibly adjust power generation in real time, gas-fired power plants are frequently seen as the perfect partner for variable renewable generation. However, this reliance on gas generation increases interdependence and propagates uncertainty between power grids and gas pipelines, and brings coordination and uncertainty management challenges. To address these issues, we propose an uncertainty management framework for uncertain, but bounded gas consumption by gas-fired power plants. The admissible ranges are computed based on a joint optimization problem for the combined gas and electricity networks, which involves chance-constrained scheduling for the electric grid and a novel robust optimization formulation for the natural gas network. This formulation ensures feasibility of the integrated system with a high probability, while providing a tractable numerical formulation. A key advance with respect to existing methods is that our method is based on a physically accurate, validated model for transient gas pipeline flows. Our case study benchmarks our proposed formulation against methods that ignore how reserve activation impacts the fuel use of gas power plants, and only consider predetermined gas consumption. The results demonstrate the importance of considering uncertainty to avoid operating constraint violations and curtailment of gas to the generators.

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained AC optimal power flow problem, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then propose an accurate, yet tractable analytical reformulation of the chance constraints. The reformulation maintains the full, non-linear AC power flow equations for the forecasted operating point, and models the impact of uncertainty through a linearization around this point. We discuss different solution algorithms, including one-shot optimization with and without recourse, and an iterative algorithm which enables scalable implementations. We further discuss how more general chance constraint reformulations can be incorporated within the iterative solution algorithm. In a case study based on four different IEEE systems, we compare the performance of the solution algorithms, and demonstrate scalability of the iterative scheme. We further show that the analytical reformulation accurately and efficiently enforces chance constraints in both in- and out-of-sample tests, and that the analytical approach outperforms two alternative, sample based chance constraint reformulations.

This paper presents a novel method to describe battery degradation. We use the concept of degradation maps to model the incremental charge capacity loss as a function of discrete battery control actions and state of charge. The maps can be scaled to represent any battery system in size and power. Their convex piece-wise affine representations allow for tractable optimal control formulations and can be used in power system simulations to incorporate battery degradation. The map parameters for different battery technologies are published making them an useful basis to benchmark different battery technologies in case studies.

Due to increasing shares of renewable energy sources, more frequency reserves are required to maintain power system stability. In this paper, we present a decentralized control scheme that allows a large aggregation of refrigerators to provide Primary Frequency Control (PFC) reserves to the grid based on local frequency measurements and without communication. The control is based on stochastic switching of refrigerators depending on the frequency deviation. We develop methods to account for typical lockout constraints of compressors and increased power consumption during the startup phase. In addition, we propose a procedure to dynamically reset the thermostat temperature limits in order to provide reliable PFC reserves, as well as a corrective temperature feedback loop to build robustness to biased frequency deviations. Furthermore, we introduce an additional randomization layer in the controller to account for thermostat resolution limitations, and finally, we modify the control design to account for refrigerator door openings. Extensive simulations with actual frequency signal data and with different aggregation sizes, load characteristics, and control parameters, demonstrate that the proposed controller outperforms a relevant state-of-the-art controller., Comment: 44 pages, 17 figures, 9 Tables, submitted to IEEE Transactions on Power Systems

In this paper we present a novel methodology for leveraging Receding Horizon Control (RHC), also known as Model Predictive Control (MPC) strategies for distributed battery storage in a planning problem using a Benders decomposition technique. Longer prediction horizons lead to better storage placement strategies but also higher computational complexity that can quickly become computationally prohibitive. The here proposed MPC strategy in conjunction with a Benders decomposition technique effectively reduces the computational complexity to a manageable level. We use the CIGRE low voltage (LV) benchmark grid as a case study for solving an optimal placement and sizing problem for different control strategies with different MPC prediction horizons. The objective of the MPC strategy is to maximize the photovoltaic (PV) utilization and minimize battery degradation in a local residential area, while satisfying all grid constraints. For this case study we show that the economic value of battery storage is higher when using MPC based storage control strategies than when using heuristic storage control strategies, because MPC strategies explicitly exploit the value of forecast information. The economic merit of this approach can be further increased by explicitly incorporating a battery degradation model in the MPC strategy.

This paper is the first part of a two-part series in which we present results from an experimental demonstration of frequency regulation in a commercial building test facility. In Part I, we introduce the test facility and develop relevant building models. Furthermore, we design a hierarchical controller that consists of three levels: a reserve scheduler, a building climate controller, and a fan speed controller for frequency regulation. We formulate the reserve scheduler as a robust optimization problem and introduce several approximations to reduce its complexity. The building climate controller is comprised of a robust model predictive controller and a Kalman filter. The frequency regulation controller consists of a feedback and a feedforward loop, provides fast responses, and is stable. Part I presents building model identification and controller tuning results, whereas Part II reports results from the operation of the hierarchical controller under frequency regulation., Comment: 24 pages

This paper is the second part of a two-part series presenting the results from an experimental demonstration of frequency regulation in a commercial building test facility. In Part I, we developed relevant building models and designed a hierarchical controller for reserve scheduling, building climate control and frequency regulation. In Part II, we introduce the communication architecture and experiment settings, and present extensive experimental results under frequency regulation. More specifically, we compute the day-ahead reserve capacity of the test facility under different assumptions and conditions. Furthermore, we demonstrate the ability of model predictive control to satisfy comfort constraints under frequency regulation, and show that fan speed control can track the fast-moving RegD signal of the Pennsylvania, Jersey, and Maryland Power Market (PJM) very accurately. In addition, we report the observed effects of frequency regulation on building control and provide suggestions for realworld implementation projects. Our results show that hierarchical control is appropriate for frequency regulation from commercial buildings., Comment: 22 pages

Due to high power in-feed from photovoltaics, it can be expected that more battery systems will be installed in the distribution grid in near future to mitigate voltage violations and thermal line and transformer overloading. In this paper, we present a two-stage centralized model predictive control scheme for distributed battery storage that consists of a scheduling entity and a real-time control entity. To guarantee secure grid operation, we solve a robust multi-period optimal power flow (OPF) for the scheduling stage that minimizes battery degradation and maximizes photovoltaic utilization subject to grid constraints. The real-time controller solves a real-time OPF taking into account storage allocation profiles from the scheduler, a detailed battery model, and real-time measurements. To reduce the computational complexity of the controllers, we present a linearized OPF that approximates the nonlinear AC-OPF into a linear programming problem. Through a case study, we show, for two different battery technologies, that we can substantially reduce battery degradation when we incorporate a battery degradation model. A further finding is that we can reduce battery losses by 30% by using the detailed battery model in the real-time control stage.

Over the past years, the share of electricity production from wind power plants has increased to significant levels in several power systems across Europe and the United States. In order to cope with the fluctuating and partially unpredictable nature of renewable energy sources, transmission system operators (TSOs) have responded by increasing their reserve capacity requirements and by requiring wind power plants to be capable of providing reserves or following active power set-point signals. This paper addresses the issue of efficiently incorporating these new types of wind power control in the day-ahead operational planning. We review the technical requirements the wind power plants must fulfill, and propose a mathematical framework for modeling wind power control. The framework is based on an optimal power flow formulation with weighted chance constraints, which accounts for the uncertainty of wind power forecasts and allows us to limit the risk of constraint violations. In a case study based on the IEEE 118 bus system, we use the developed method to assess the effectiveness of different types of wind power control in terms of operational cost, system security and wind power curtailment., Comment: 7 Pages

This paper proposes a novel algorithm to optimally size and place storage in low voltage (LV) networks based on a linearized multiperiod optimal power flow method which we call forward backward sweep optimal power flow (FBS-OPF). We show that this method has good convergence properties, its solution deviates slightly from the optimum and makes the storage sizing and placement problem tractable for longer investment horizons. We demonstrate the usefulness of our method by assessing the economic viability of distributed and centralized storage in LV grids with a high photovoltaic penetration (PV). As a main result, we quantify that for the CIGRE LV test grid distributed storage configurations are preferable, since they allow for less PV curtailment due to grid constraints., Comment: accepted for 19th Power Systems Computation Conference 2016, Genoa, Italy

This paper proposes a new methodology to maximize the feasible set of power injections and cross-border power transfers in meshed multi-area power systems. The approach used polyhedral computation schemes and is an extension to the classic procedure for cross-border transfer capacity assessment in the European power network, including the computation of bilateral cross-border transfer capacities as well as multilateral flow-based approaches. The focus is the characterization of inter-area exchange limits required for secure power system operation in the presence of physical transmission constraints, while maximizing the utilization factors of the transmission lines. The numerical examples include a case study of the ENTSO-E transmission system.

The growing amount of fluctuating renewable infeeds and market liberalization increases uncertainty in power system operation. To capture the influence of fluctuations in operational planning, we model the forecast errors of the uncertain in-feeds as random variables and formulate a security constrained optimal power flow using chance constraints. The chance constraints limit the probability of violations of technical constraints, such as generation and transmission limits, but require a tractable reformulation. In this paper, we discuss different analytical reformulations of the chance constraints, based on a given set of assumptions concerning the forecast error distributions. In particular, we discuss reformulations that do not assume a normal distribution, and admit an analytical reformulation given only a mean vector and covariance matrix. We illustrate our method with a case study of the IEEE 118 bus system, based on real data from the European system. The different reformulations are compared in terms of both achieved empirical violation probability and operational cost, which allows us to provide a suggestion for the most appropriate reformulation in an optimal power flow setting. For a large number of uncertainty sources, it is observed that the distributions of the line flows and generator outputs can be close to normal, even though the power injections are not normally distributed.

In this paper we propose distributed dynamic controllers for sharing both frequency containment and restoration reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. The communication structure of the controller is distributed in the sense that only local and neighboring state information is needed, rather than the complete state. We derive sufficient stability conditions, which guarantee that the AC frequencies converge to the nominal frequency. Simultaneously, a global quadratic power generation cost function is minimized. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal DC voltages. The results are valid for distributed cable models of the HVDC grid (e.g. $\pi$-links), as well as AC systems of arbitrary number of synchronous machines, each modeled by the swing equation. We also propose a decentralized, communication-free version of the controller. The proposed controllers are tested on a high-order dynamic model of a power system consisting of asynchronous AC grids, modelled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation., Comment: arXiv admin note: text overlap with arXiv:1505.07402

This paper puts forward the vision of fully decoupling market operations from security considerations through controllable power flows. In "A Fully Controllable Power System", power system security is no longer dependent on the location of the power injection points. In the ideal case, this leads to the elimination of redispatching costs, which amount to several million dollars per year in large systems. This paper determines the upper and lower bounds for the number of controllable lines and number of controllers to achieve this decoupling in any system. It further introduces the notion of the controllability vector CV, which expresses the effect of any controller on the AC line flows. Based on two alternative definitions for controllability, two controller placement algorithms to maximize controllability are presented and their results are compared.

It has been shown that the heating, ventilation, and air conditioning (HVAC) systems of commercial buildings can offer ancillary services to power systems without loss of comfort. In this paper, we propose a new control framework for reliable scheduling and provision of frequency reserves by aggregations of commercial buildings. The framework incorporates energy-constrained frequency signals, which are adopted by several transmission system operators for loads and storage devices. We use a hierarchical approach with three levels: (i) reserve capacities are allocated among buildings (e.g., on a daily basis) using techniques from robust optimization, (ii) a robust model predictive controller optimizes the HVAC system consumption typically every 30 minutes, and (iii) a feedback controller adjusts the consumption to provide reserves in real time. We demonstrate how the framework can be used to estimate the reserve capacities in simulations with typical Swiss office buildings and different reserve product characteristics. Our results show that an aggregation of approximately 100 buildings suffices to meet the 5 MW minimum bid size of the Swiss reserve market., Comment: 29 pages, 8 figures, 3 tables, submitted to the IEEE Transactions on Power Systems

In this paper we propose a distributed dynamic controller for sharing frequency control reserves of asynchronous AC systems connected through a multi-terminal HVDC (MTDC) grid. We derive sufficient stability conditions, which guarantee that the frequencies of the AC systems converge to the nominal frequency. Simultaneously, the global quadratic cost of power generation is minimized, resulting in an optimal distribution of generation control reserves. The proposed controller also regulates the voltages of the MTDC grid, asymptotically minimizing a quadratic cost function of the deviations from the nominal voltages. The proposed controller is tested on a high-order dynamic model of a power system consisting of asynchronous AC grids, modelled as IEEE 14 bus networks, connected through a six-terminal HVDC grid. The performance of the controller is successfully evaluated through simulation., Comment: arXiv admin note: text overlap with arXiv:1503.07358, arXiv:1409.8013

Due to the increasing amount of electricity generated from renewable sources, uncertainty in power system operation will grow. This has implications for tools such as Optimal Power Flow (OPF), an optimization problem widely used in power system operations and planning, which should be adjusted to account for this uncertainty. One way to handle the uncertainty is to formulate a Chance Constrained OPF (CC-OPF) which limits the probability of constraint violation to a predefined value. However, existing CC-OPF formulations and solutions are not immune to drawbacks. On one hand, they only consider affine policies for generation control, which are not always realistic and may be sub-optimal. On the other hand, the standard CC-OPF formulations do not distinguish between large and small violations, although those might carry significantly different risk. In this paper, we introduce the Weighted CC-OPF (WCC-OPF) that can handle general control policies while preserving convexity and allowing for efficient computation. The weighted chance constraints account for the size of violations through a weighting function, which assigns a higher risk to a higher overloads. We prove that the problem remains convex for any convex weighting function, and for very general generation control policies. In a case study, we compare the performance of the new WCC-OPF and the standard CC-OPF and demonstrate that WCC-OPF effectively reduces the number of severe overloads. Furthermore, we compare an affine generation control policy with a more general policy, and show that the additional flexibility allow for a lower cost while maintaining the same level of risk., Comment: 7 pages, 3 figures

In this paper, we present distributed controllers for sharing primary and secondary frequency control reserves for asynchronous AC transmission systems, which are connected through a multi-terminal HVDC grid. By using Lyapunov arguments, the equilibria of the closed-loop system are shown to be globally asymptotically stable. We quantify the static errors of the voltages and frequencies, and give upper bounds for these errors. It is also shown that the controllers have the property of power sharing, i.e., primary and secondary frequency control reserves are shared fairly amongst the AC systems. The proposed controllers are applied to a high-order dynamic model of of a power system consisting of asynchronous AC grids connected through a six-terminal HVDC grid., Comment: arXiv admin note: text overlap with arXiv:1409.8013

Network topology in distribution networks is often unknown, because most switches are not equipped with measurement devices and communication links. However, knowledge about the actual topology is critical for safe and reliable grid operation. This paper proposes a voting-based topology detection method based on micro-synchrophasor measurements. The minimal difference between measured and calculated voltage angle or voltage magnitude, respectively, indicates the actual topology. Micro-synchrophasors or micro-Phasor Measurement Units ({\mu}PMU) are high-precision devices that can measure voltage angle differences on the order of ten millidegrees. This accuracy is important for distribution networks due to the smaller angle differences as compared to transmission networks. For this paper, a microgrid test bed is implemented in MATLAB with simulated measurements from {\mu}PMUs as well as SCADA measurement devices. The results show that topologies can be detected with high accuracy. Additionally, topology detection by voltage angle shows better results than detection by voltage magnitude., Comment: 5 Pages, PESGM2015, Denver, CO

Dynamic Thermal Line Rating (DLR) is deemed to be an effective way to increase transmission capacities and therefore enabling additional operational flexibility. The transmission capacities are dynamically determined based on current or expected weather conditions. First pilot projects have proven its efficiency. In this paper we present two approaches to determine the location and amount of ramping capabilities for corrective control measures in the case of errors in the forecast of the line rating. Both approaches result in robust optimization problems, where the first approach guarantees that there is a suitable remedial action for every realization of uncertainty in a given uncertainty set. The corrective control action is calculated once the forecast error is known. The second approach relies on affine policies which directly relate the current line rating to corrective control measures, if needed, which enables a decentralized operation. In case studies, the two approaches are compared and the reduction of overall operational costs is demonstrated exemplarily for different parameters.

This paper presents a decentralized controller for sharing primary AC frequency control reserves through a multi-terminal HVDC grid. By using Lyapunov arguments, the proposed controller is shown to stabilize the equilibrium of the closed-loop system consisting of the interconnected AC and HVDC grids, given any positive controller gains. The static control errors resulting from the proportional controller are quantified and bounded by analyzing the equilibrium of the closed-loop system. The proposed controller is applied to a test grid consisting of three asynchronous AC areas interconnected by an HVDC grid, and its effectiveness is validated through simulation.

In this paper we present a framework to efficiently characterize the available operational flexibility in a multi-area power system. We focus on the available reserves and the tie-line flows. The proposed approach is an alternative to the current calculation of the Available Transfer Capacity (ATC), as it considers location and availability of reserves, transmission constraints, and interdependencies of tie-line flows between different areas, while it takes into account the N-1 security criterion. The method is based on computational geometry using polytopic projections. It requires only a limited amount of information exchange and does not need central coordination. The method has two versions: a passive and an active approach, where neighboring areas can share reserves. In that respect we also introduce the term "exported flexibility", which could form the basis for a new trading product in electricity markets. Case studies demonstrate the improved tie-line utilization, especially if reserves are shared, and the visualization benefits., Comment: submitted to IEEE Transactions on Power Systems

Increased distributed Photo-Voltaic (PV) generation leads to an increase in voltages and unwarranted backflows into the grid. This paper investigates Demand Response (DR) with Electric Water Heaters (EWHs) as a way to increase the PV hosting capacity of a low-voltage feeder. A control strategy relying only on power measurements at the transformer is proposed. Flexible loads are optimally dispatched considering energy acquisition costs, a PV shedding penalty, and power and energy constraints. Furthermore, grouping of loads and PV plants is investigated, and switching penalties are used to reduce the unnecessary switching of loads. It is shown that this strategy can substantially increase the PV hosting capacity of a Low-Voltage (LV) feeder, even when only basic controllability is available., Comment: Working Paper, to be submitted at PowerTech 2015

The grid integration of intermittent Renewable Energy Sources (RES) causes costs for grid operators due to forecast uncertainty and the resulting production schedule mismatches. These so-called profile service costs are marginal cost components and can be understood as an insurance fee against RES production schedule uncertainty that the system operator incurs due to the obligation to always provide sufficient control reserve capacity for power imbalance mitigation. This paper studies the situation for the German power system and the existing German RES support schemes. The profile service costs incurred by German Transmission System Operators (TSOs) are quantified and means for cost reduction are discussed. In general, profile service costs are dependent on the RES prediction error and the specific workings of the power markets via which the prediction error is balanced. This paper shows both how the prediction error can be reduced in daily operation as well as how profile service costs can be reduced via optimization against power markets and/or active curtailment of RES generation., Comment: Accepted for SUSTECH 2014, Portland, Oregon, USA, July 2014

In this article a model predictive control (MPC) based frequency control scheme for energy storage units was derived, focusing on the incorporation of stability constraints based on Lyapunov theory and the concept of passivity. The proposed control schemes, guaranteeing closed-loop stability, are applied on a one-area and two-area power system. For the two-area power system, a coordinated (centralized) control and an uncoordinated (decentralized) control approach is conducted. The stability properties of the different MPC setups were derived, implemented and simulated. Furthermore the corresponding control performance was analyzed.

This paper presents a medium-term self-scheduling optimization of pumped hydro storage power plants with detailed consideration of short-term flexibility. A decomposition of the problem into inter- and intrastage subproblems, where the intrastage problems themselves are formulated as multi-stage stochastic programs, allows the detailed consideration of short- term flexibility. The method is presented together with three alter- native approaches, where the short-term flexibility is considered differently: (1) with aggregated peak and off-peak prices, (2) with price duration curves and (3) with deterministic intrastage subproblems. The methods are compared and evaluated in a Monte Carlo operation simulation study. The study is performed on a realistic hydro power plant with consideration of revenue from ancillary services., Comment: submitted to PSCC 2014 conference

Operational flexibility is an important property of electric power systems and plays a crucial role for the transition of today's power systems, many of them based on fossil fuels, towards power systems that can efficiently accommodate high shares of variable Renewable Energy Sources (RES). The availability of sufficient operational flexibility in a given power system is a necessary prerequisite for the effective grid integration of large shares of fluctuating power in-feed from variable RES, especially wind power and Photovoltaics (PV). This paper establishes the necessary framework for quantifying and visualizing the technically available operational flexibility of individual power system units and ensembles thereof. Necessary metrics for defining power system operational flexibility, namely the power ramp-rate, power and energy capability of generators, loads and storage devices, are presented. The flexibility properties of different power system unit types, e.g. load, generation and storage units that are non-controllable, curtailable or fully controllable are qualitatively analyzed and compared to each other. Quantitative results and flexibility visualizations are presented for intuitive power system examples., Comment: Accepted for PSCC 2014, Wroclaw, Poland, August 2014

Large-scale deployment of RES has led to significant generation shares of variable RES in power systems worldwide. RES units, notably inverter-connected wind turbines and PV that as such do not provide rotational inertia, are effectively displacing conventional generators and their rotating machinery. The traditional assumption that grid inertia is sufficiently high with only small variations over time is thus not valid for power systems with high RES shares. This has implications for frequency dynamics and power system stability and operation. Frequency dynamics are faster in power systems with low rotational inertia, making frequency control and power system operation more challenging. This paper investigates the impact of low rotational inertia on power system stability and operation, contributes new analysis insights and offers mitigation options for low inertia impacts., Comment: Presented at IFAC World Congress 2014, Capetown, South Africa (Flaws in Table I corrected.)

Frequency control reserves are an essential ancillary service in any electric power system, guaranteeing that generation and demand of active power are balanced at all times. Traditionally, conventional power plants are used for frequency reserves. There are economical and technical benefits of instead using energy constrained units such as storage systems and demand response, but so far they have not been widely adopted as their energy constraints prevent them from following traditional regulation signals, which sometimes are biased over long time-spans. This paper proposes a frequency control framework that splits the control signals according to the frequency spectrum. This guarantees that all control signals are zero-mean over well-defined time-periods, which is a crucial requirement for the usage of energy-constraint units such as batteries. A case-study presents a possible implementation, and shows how different technologies with widely varying characteristics can all participate in frequency control reserve provision, while guaranteeing that their respective energy constraints are always fulfilled., Comment: working paper, submitted to PSCC 2014

An on-going debate in the energy economics and power market community has raised the question if energy-only power markets are increasingly failing due to growing feed-in shares from subsidized renewable energy sources (RES). The short answer to this is: No, they are not failing. Energy-based power markets are, however, facing several market distortions, namely from the gap between the electricity volume traded at day-ahead markets versus the overall electricity consumption as well as the (wrong) regulatory assumption that variable RES generation, i.e., wind and photovoltaic (PV), truly have zero marginal operation costs. In this paper we show that both effects over-amplify the well-known merit-order effect of RES power feed-in beyond a level that is explainable by underlying physical realities, i.e., thermal power plants being willing to accept negative electricity prices to be able to stay online due to considerations of wear & tear and start-stop constraints. We analyze the impacts of wind and PV power feed-in on the day-ahead market for a region that is already today experiencing significant feed-in tariff (FIT)-subsidized RES power feed-in, the EPEX German-Austrian market zone ($\approx\,$20% FIT share). Our analysis shows that, if the necessary regulatory adaptations are taken, i.e., increasing the day-ahead market's share of overall load demand and using the true marginal costs of RES units in the merit-order, energy-based power markets can remain functional despite high RES power feed-in., Comment: Working Paper (9 pages, 11 figures, 5 tables) - Some revisions since last version (10 February 2014). (Under 2nd review for IEEE Transactions on Power Systems)