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Power system optimization models are large mathematical models used by researchers and policymakers that pose tractability issues when representing real-world systems. Several aggregation techniques have been proposed to address these computational challenges and it remains a relevant topic in power systems research. In this paper, we extend a recently developed Basis-Oriented time series aggregation approach used for power system optimization models that aggregates time steps within their Simplex basis. This has proven to be an exact aggregation for simple economic dispatch problems. We extend this methodology to include network and ramping constraints; for the latter (and to handle temporal linking), we develop a heuristic algorithm that finds an exact partition of the input data, which is then aggregated. Our numerical results, for a simple 3-Bus system, indicate that: with network constraints only, we can achieve a computational reduction by a factor of 1747 (measured in the number of variables of the optimization model), and of 12 with ramping constraints. Moreover, our findings indicate that with temporal linking constraints, aggregations of variable length must be employed to obtain an exact result (the same objective function value in the aggregated model) while maintaining the computational tractability, this implies that the duration of the aggregations does not necessarily correspond to commonly used lengths like days or weeks. Finally, our results support previous research concerning the importance of extreme periods on model results., Comment: 10 pages, 5 figures, journal pre-print

One of the fundamental problems of using optimization models that use different time series as data input, is the trade-off between model accuracy and computational tractability. To overcome the computational intractability of these full optimization models, the dimension of input data and model size is commonly reduced through time series aggregation (TSA) methods. However, traditional TSA methods often apply a one-size-fits-all approach based on the common belief that the clusters that best approximate the input data also lead to the aggregated model that best approximates the full model, while the metric that really matters - the resulting output error in optimization results - is not well addressed. In this paper, we plan to challenge this belief and show that output-error based TSA methods with theoretical underpinnings have unprecedented potential of computational efficiency and accuracy., Comment: time series aggregation, clustering, optimization, modeling

This paper introduces the full Low-carbon Expansion Generation Optimization (LEGO) model available on Github (https://github.com/wogrin/LEGO). LEGO is a mixed-integer quadratically constrained optimization problem and has been designed to be a multi-purpose tool, like a Swiss army knife, that can be employed to study many different aspects of the energy sector. Ranging from short-term unit commitment to long-term generation and transmission expansion planning. The underlying modeling philosophies are: modularity and flexibility. Its unique temporal structure allows LEGO to function with either chronological hourly data, or all kinds of representative periods. LEGO is also composed of thematic modules that can be added or removed from the model easily via data options depending on the scope of the study. Those modules include: unit commitment constraints; DC- or AC-OPF formulations; battery degradation; rate of change of frequency inertia constraints; demand-side management; or the hydrogen sector. LEGO also provides a plethora of model outputs (both primal and dual), which is the basis for both technical but also economic analyses. To our knowledge, there is no model that combines all of these capabilities, which we hereby make freely available to the scientific community., Comment: out of date

This paper proposes to use stochastic conic programming to address the challenge of large-scale wind power integration to the power system. Multiple wind farms are connected through the voltage source converter (VSC) based multi-terminal DC (VSC-MTDC) system to the power network supported by the Flexible AC Transmission System (FACTS). The optimal operation of the power network incorporating the VSC-MTDC system and FACTS devices is formulated in a stochastic conic programming framework accounting the uncertainties of the wind power generation. A methodology to generate representative scenarios of power generations from the wind farms is proposed using wind speed measurements and wind turbine models. The nonconvex transmission network constraints including the VSC-MTDC system and FACTS devices are convexified through the proposed second-order cone AC optimal power flow model (SOC-ACOPF) that can be solved to the global optimality using interior point method. In order to tackle the computational challenge due to the large number of wind power scenarios, a modified Benders decomposition algorithm (M-BDA) accelerated by parallel computation is proposed. The energy dispatch of conventional power generators is formulated as the master problem of M-BDA. Numerical results for up to 50000 wind power scenarios show that the proposed M-BDA approach to solve stochastic SOC-ACOPF outperforms the traditional single-stage (without decomposition) solution approach in both convergence capability and computational efficiency. The feasibility performance of the proposed stochastic SOC-ACOPF model is also demonstrated., Comment: The first draft of this paper was submitted to IEEE Transactions on Sustainable Energy in October 2016 (submission ID: TSTE-00842-2016). It was extended to 16 pages after revisions

On the path towards power systems with high renewable penetrations and ultimately carbon-neutral, more and more synchronous generation is being displaced by variable renewable generation that does not currently provide system inertia nor reactive power support. This could create serious issues of power system stability in the near future, and countries with high renewable penetrations such as Ireland are already facing these challenges. Therefore, this paper aims at answering the questions of whether and how explicitly including inertia and reactive power constraints in generation expansion planning would affect the optimal capacity mix of the power system of the future. Towards this end, we propose the novel Low-carbon Expansion Generation Optimization (LEGO) model, which explicitly accounts for: unit commitment constraints, Rate of Change of Frequency (RoCoF) inertia requirements and virtual inertia provision, and, a second-order cone programming (SOCP) approximation of the AC power flow, accounting for reactive power constraints. An illustrative case study underlines that disregarding inertia and reactive power constraints in generation expansion planning can result in additional system cost, system infeasibilities, a distortion of optimal resource allocation and inability to reach established policy goals.

Flexibility requirements are becoming more relevant in power system planning due to the integration of variable Renewable Energy Sources (vRES). In order to consider these requirements Generation Expansion Planning (GEP) models have recently incorporated Unit Commitment (UC) constraints, using traditional energy-based formulations. However, recent studies have shown that energy-based UC formulations overestimate the actual flexibility of the system. Instead, power-based UC models overcome these problems by correctly modeling ramping constraints and operating reserves. This paper proposes a power-based GEP-UC model that improves the existing models. The proposed model optimizes investment decisions on vRES, Energy Storage Systems (ESS), and thermal technologies. In addition, it includes real-time flexibility requirements, and the flexibility provided by ESS, as well as other UC constraints, e.g., minimum up/down times, startup and shutdown power trajectories, network constraints. The results show that power-based model uses the installed investments more effectively than the energy-based models because it more accurately represents flexibility capabilities and system requirements. For instance, the power-based model obtains less investment (6-12%) and yet it uses more efficiently this investment because operating cost is also lower (2-8%) in a real-time validation. We also propose a semi-relaxed power-based GEP-UC model, which is at least 10 times faster than its full-integer version and without significantly losing accuracy in the results (less than 0.2% error)., Comment: 8 pages, 2 figures, working paper

This paper analyzes different models for evaluating investments in Energy Storage Systems (ESS) in power systems with high penetration of Renewable Energy Sources (RES). First of all, two methodologies proposed in the literature are extended to consider ESS investment: a unit commitment model that uses the System States (SS) method of representing time; and another one that uses a representative periods (RP) method. Besides, this paper proposes two new models that improve the previous ones without a significant increase of computation time. The enhanced models are the System States Reduced Frequency Matrix (SS-RFM) model which addresses short-term energy storage more approximately than the SS method to reduce the number of constraints in the problem, and the Representative Periods with Transition Matrix and Cluster Indices (RP-TM&CI) model which guarantees some continuity between representative periods, e.g. days, and introduces long-term storage into a model originally designed only for the short term. All these models are compared using an hourly unit commitment model as benchmark. While both system state models provide an excellent representation of long-term storage, their representation of short-term storage is frequently unrealistic. The RP-TM&CI model, on the other hand, succeeds in approximating both short- and long-term storage, which leads to almost 10 times lower error in storage investment results in comparison to the other models analyzed.