Advances in Energy System Optimization

Important changes are currently underway in electric power systems, namely concerning the integration of distributed generation based on renewables to cope with Green-House Gas (GHG) emissions and external energy dependency. Moreover, the introduction of new loads such as electric vehicles and other storage systems, as well as local micro-generation and the possibility of using demand as a manageable resource create new challenges for the overall power system optimization. The deployment of smart metering and advanced communications capabilities will allow power systems to be managed more in accordance with generation availability, demand needs, and network conditions. A key issue for this optimal management is the existence of dynamic tariffs, according to the availability of several resources, congestion situations, generation scheduling, etc. Dynamic tariffs foreshadow a more active role for the consumer / prosumer concerning electricity usage decisions (consumption, storage, generation, and exchanges with the grid), namely in the residential sector. Demand Response (DR) can be used in this context by residential end-users to make the most of energy price information, weather forecasts, and operational requirements (e.g., comfort) to minimize the electricity bill. Nevertheless, the implementation of DR actions require the time availability of residential end-users, data processing capability, and the need to anticipate the corresponding impacts on the electricity bill and end-users satisfaction regarding the quality of energy services in use. Energy management systems (EMS) capable of offering decision support should be used to assist end-users optimizing the integrated usage of all energy resources. A multi-objective model has been developed aimed at minimizing the electricity bill and the possible dissatisfaction caused to the end-user by the implementation of DR actions. An evolutionary algorithm to cope with the multi-objective and combinatorial nature of the model has been developed, which is tailored to the physical characteristics of the problem, namely using adequate solution encoding schemes and customized operators. Simulation results show that significant savings might be achieved by optimizing load scheduling, local micro-generation, and storage systems including electric vehicles (EVs) in both grid-to-vehicle (G2V) and V2G (vehicle-to-grid) modes.

If electrical energy demand is not balanced with electricity generation the results are additional electrical power grid investments and system stability risks. An increasing energy demand caused by charging plug-in electric vehicles (PEVs) is expected to affect distribution grid levels in the future. Uncontrolled PEV charging causes additional grid stress but PEVs are also capable of balancing the demand to the present supply situation via charging control strategies. Different control strategies for PEVs have been tested to address this issue. They can be classified as indirect, direct and autonomous control strategies. However, it is still under discussion, which charging strategy is best suited to integrate PEVs into feature dependent power generation on a distribution grid level. We investigated the advantages and weaknesses of autonomous control via local voltage measurement compared to direct and indirect charging control. Here we found that autonomous control of PEVs can counteract voltage dips caused by simultaneous charging. This is of great benefit for smart grids because autonomous control realised with PEVs internal systems can reduce the investment in communication technology on the infrastructure side. Nevertheless, this research also shows the limits of autonomous control. It can be concluded that a mix of different control strategies is necessary to realise PEVs demand response opportunities. Autonomous control will play an important role supporting the control of PEVs to stabilise smart grids.

In this paper, a model predictive control approach is presented to optimize generator and storage operation in the German transmission grid over time spans of hours to several days. In each optimization, a full AC model with typical OPF constraints such as voltage or line capacity limits is used. With given RES and load profiles, inter-temporal constraints such as generator ramping and storage energy are included. Jacobian and Hessian matrices are provided to the solver to enable a fast problem formulation, but the computational bottleneck still lies in solving the linear Newton step. The deviation in storage operation when comparing the solution over the entire horizon of 96 h against the model predictive control is shown in the German transmission grid. The results show that horizons of around 24 h are sufficient with today’s storage capacity, but must be extended when increasing the latter.

To cope with a growing amount of congestion in the transmission grid, decision support systems for transmission system operation have to be developed. Thus, this paper presents a security-constrained optimization framework including post-contingency control for the application in transmission grid operation with excellent applicability to large-scale power systems and outstanding computational performance.

We present results of two model based scenario analysis focussing on the future German power sector which is characterized by a rising share of renewable energies and an associated higher demand for flexibility. Case study 1 is based on a general comparison between a decentrally and a centrally orientated electricity system. The research question of case study 2 is whether flexibility should be centrally balanced by a national market-based dispatch or dispatched in a decentralized manner within regional balancing areas. The combined results of these two case studies offer the possibility to show the differences between a decentralized and a centralized electricity system regarding the dispatch of generation, storage and flexibility options as well as resulting effects on variable costs, CO₂ emissions, grid usage and RE integration. Decentralization as control strategy leads to higher variable generation costs due to more expensive generation and less efficient flexibility options that come into the market, while the majority of demand and supply still needs a transmission grid for balancing.

We model an energy system with a storage device, a renewable energy source and with market access as a Markov decision process. We have identified four classes of pure policies (PFAs, CFAs, VFAs and lookaheads), each of which may work best depending on the characteristics of the system (volatility of prices, stationarity, accuracy of forecasts). We demonstrate that each of the four classes can work best on a particular instance of the problem. We describe the problem characteristics that bring out the best of each policy.

In remote microgrids, the integration of renewable energy sources (RES) is essential to meet the demand in conjunction with the dispatchable fuel-based generation units. The need to facilitate RES efficiently and the very high cost of fuel transportation in these areas make installing battery energy storage system (BESS) an appealing solution. However, the high cost of BESS requires optimizing the BESS technology selection and size to increase their benefits to the microgrid. In this paper, the optimal BESS installation decisions are determined from the perspective of an investor with the objective of profit maximization. The maximum size of BESS that the investor is willing to install for a certain discharge price is determined for various BESS technologies. Also, a new approach to determine the minimum acceptable discharge price at which the installation would make profit for the investor is proposed. Thereafter, the optimal microgrid and BESS operation is determined to minimize the total microgrid costs while meeting its growing demand considering the installation decisions obtained from the proposed investment model.

An original methodology is presented to perform multi-period planning of isolated microgrids in a green field context. The aim is to build an isolated radial network to supply power to a set of initially unconnected loads whose consumption is growing through the planning horizon. The planning tool’s outputs are: (1) network routing, (2) network sizing and (3) investments timing. These 3 steps are undertaken so that they minimize the total Net Present Value of the whole system. In this paper, the emphasis is put on the structure of the distribution planning problem. In particular, its optimal substructure allows to make use of a dynamic programming approach to tackle the time dimension of the optimization problem. Furthermore, several characteristics of radial networks are presented on the basis of which the main problem can be decoupled in independent subproblems. This reduces the size of the search space and consequently the computational burden. A non-linear and unbalanced tri-phase representation of the network is used to account for the effect of single-phase connected loads on the voltage profile. The effectiveness of the proposed method is illustrated through a case study.

Transmission grid extension is a central aspect of the future energy system transition. This is due to the diverging occurrence of renewable energy feed-in and consumption. The existing layout of the German grid was not designed to accommodate this divergence. To analyze the most cost-effective grid extensions, efficient methods for techno-economic analysis are required. The challenge of conducting an analysis of grid extensions involves the lumpy investment decisions and the non-linear character of several restrictions in a real-data environment. The addition of new lines makes the grid characteristic variable for approximately load flow calculations. The following paper presents an application of the Benders Decomposition, dividing the problem into an extension and a dispatch problem combined with a Karush–Kuhn–Tucker-system. This combination enables one to solve the problem within reasonable time by using the favorable conditions contained in the sub-problem. The method is applied to the analysis of the integration of renewable energy within the context of German transmission grid extension planning for the year 2030. It can be shown that curtailing feed-in peaks of renewables can significantly reduce the extent of grid extensions necessary to sustain the energy system in Germany.

The increasing electricity generated by the renewable energy generation units connected to the distribution grid can lead to the allowed level of voltage range and current rating in the lines being exceeded. One option to prevent this from happening is line extension. This article describes a method of quantifying the line extension, its costs and the impact of load shifting which can be used in electricity system models. The region considered is the state of Baden-Württemberg in Germany. The operation of the distribution grid is simulated based on region-specific electricity demand and electricity generation. In order to use the voltage range of 10% (based on DIN EN 50160) completely, the countrywide installation of regulated distribution transformers is assumed. The allowed level of voltage and current rating is mainly exceeded in regions with a high supply of photovoltaic electricity at the low voltage level. With the modelled assumptions and the extension of renewable energy under consideration, an expense of about 760–880 million Euros in Baden-Württemberg will be required by the year 2030 to ensure that the operation complies with the technical restrictions. By using load shifting, the expense can be reduced by 140–220 million Euros.

High voltage transmission networks play a crucial role in the ongoing transformation from centralized power generation in conventional power plants to decentralized generation from renewable energy sources (RES). The rapid expansion of RES requires a structural rearrangement of the entire power system to ensure the current level of supply security. Scientific approaches to the characterization and improvement of power transmission networks, however, often lack the availability of reliable and appropriate data on the networks’ structure. Using SciGRID, which was recently released open source, we generate a topological grid model for Germany using open data provided by OpenStreetMap. Starting from this particular grid model we characterize the structure of the German transmission grid by means of graph-theoretical decomposition approaches to complexity reduction. Our procedure aims to identify key features and characteristics complementing the grid’s electrotechnical properties; it is for example used to characterize the SciGRID approach and validate the resulting models against other (potentially not open source) transmission network models. In addition, it paves the way for networks with reduced complexity, which might be beneficial in optimization problems addressing system design and operation.

Feasible scientific usage of transmission grid data requires a node-edge-model with georeferenced information (location of substations or positioning of power lines) and specific electric parameters of each included element. The paper summarizes available data sets for existing and future line sections of the European transmission grid. The developed process model shows a suitable, transparent approach for integration of varying data into one coherent model. The resulting structure provides a consistent transmission grid model for scientific research in simulations.

To support decision making in the context of restructuring the power system, models are needed which allow for a regional, long-term operation and expansion planning for electricity generation and transmission. Input data for these models are needed in a high spatial and temporal granularity. In this paper, we therefore describe an approach aimed at providing regionalized input data for generation and transmission expansion planning models. We particularly focus on a dynamic assignment of renewable energy sources and electrical load to potential buses of the transmission grid. Following a bottom up approach, we model the existing and potential distributed generation and load at the lowest possible spatial resolution based on various databases and models. Besides large power plants, which are directly connected to the transmission grid, a decentralized grid connection is modeled on the distribution grid level based on Voronoi polygons around the corresponding substations. By simplifying the load flow over the distribution grid to a shortest path problem, we model the feed-in into the transmission grid as a variable, depending on the nearest available transmission grid connection. As a result, the connection to the buses at transmission grid level is kept variable in case of grid expansion measures at substation level.

Optimal Power Flow problem is considered as minimization of quadratic performance function subject to linear and quadratic equality/inequality constraints, AC power flow equations specify the feasibility domain. Similar quadratic problems arise in discrete optimization, uncertainty analysis, physical applications. In general they are nonconvex, nevertheless, demonstrate hidden convexity structure. We investigate the “image convexity” property. That is, we consider the image of the space of variables under quadratic map defined by power flow equations (the feasibility domain). If the image is convex, then original optimization problem has nice properties, for instance, it admits zero duality gap and convex optimization tools can be applied. There are several classes of quadratic maps representing the image convexity. We aim to discover similar structure and to obtain convexity or nonconvexity certificates for the individual quadratic transformation. We also provide the numerical algorithms exploiting convex relaxation of quadratic mappings for checking convexity. We address such problems as membership oracle and boundary oracle for the quadratic image. Finally the results are illustrated through some examples of 3-bus systems, namely, we detect nonconvexity of them.

This work presents a convex model to be used in the analysis and optimization of power distribution systems with distributed generation (DG). The steady-state operation point is calculated through a linearized model of the network, which makes it possible to calculate the branch currents and bus voltages through linear expressions. The optimization model proposed to optimize the operation of capacitor banks and DGs uses a linear objective function, along with linear constraints, binary and continuous variables. The model can be applied to problems related to the operation and expansion of smart grids. A study case using real distribution system data is presented, comparing the results with the solution of the nonlinear load flow.