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Understanding the uncertainty associated with operating variable generation systems helps manage the level of risk associated with delivering services. Moreover, appropriate selection of the rating and charge/discharge characteristics of an energy storage device, coupled with appropriate operational management, can improve the ability of a variable generation system to participate in certain markets. For example, energy storage may be used to help provide firm power over certain periods of time, which can improve the ability of the variable generation system to participate in a frequency response market.

This article explores the use of simulation and optimization techniques for investigating the characteristics that a variable generation system with energy storage should have for given operational profiles. Two examples are considered in this article:

In the first, optimization techniques are used to determine the rating and charge/discharge characteristics of a variable generation system to maximize revenue on the spot market. A study of this type is based on historical data of power output and market price and does not require detailed consideration of technology selection.

In the second example, simulations are used to explore controlling the operational characteristics of a system that combines variable generation with energy storage, and to evaluate the effect that different energy storage interface configurations will have on grid response. Initially, a high-level representation of the energy storage device is used in this type of study. As the study progresses, more detailed representations of different technologies are included in the simulation framework.

Using optimization to manage risk
Historical data of power output and market prices may be used to determine whether an energy storage device would improve the ability of a variable energy producer to participate in certain markets. In this article, spot market participation is considered, although the techniques discussed are applicable to ancillary markets.


Figure 1 shows a schematic of energy flow considered in the optimization framework. Energy from the variable energy source is distributed between the grid and the energy storage device. The energy storage device may be charged from both the variable energy source and the grid. The optimization problem is then not only to determine the charge/discharge profile of the energy storage device over a period of time, but also to determine the most appropriate energy mix at any given time for charging the energy storage device and supplying energy to the grid. The optimization aims to maximize revenue while ensuring that physical constraints associated with operating the energy storage device are not violated.


Figure 2 shows an example of results from an optimization for a two-day period. The energy storage device is charged during periods of lower market price and discharged during periods of higher market price. Note that compared to a real-world scenario, this example is relatively simplistic for illustrative purposes.


Figure 3 shows the operation of the energy storage device. In this example, storage capacity was limited to 1,200 kWh, and the charge/discharge rate was limited to 200 kW.

As the amount of historic data used in the optimization formulation increases, the risk associated with the optimization outcome decreases. The optimization may be formulated using linear programming, which is beneficial for reducing the computational time of larger-scale problems.

Using simulation to inform engineering decisions

Once the rating of the energy storage device has been determined, a simulation study may be conducted to inform technology selection and the development of appropriate feedback control and supervisory control subsystems for the combined energy storage/variable energy system.

Development of the feedback control and supervisory control systems may proceed on a lower fidelity model of the energy storage device. Lower fidelity models execute faster because they omit detailed representations of power electronic devices, enabling faster simulations and faster iterations during design. This approach works well because the bandwidth of the feedback control and supervisory control systems will be sufficiently lower than that of the power-electronic switching algorithms, meaning that inclusion of power electronics will have little effect on the RMS operation in the system simulation.


Figure 4 shows the response of a system designed to provide firm power at the grid point of connection (POC). The system was simulated using a lower fidelity model of an energy storage device connected to a wind farm model. The test uses a simple supervisory control system that monitors the amount of energy stored. If the energy stored is greater than 10% of capacity, then the feedback control system regulates active power at the grid POC to 0.6 per unit. Once the energy stored drops below 10% of capacity, then the energy storage system is charged to capacity at a fixed rate, before the POC regulation is re-engaged. Figure 4 shows a short-term cycling effect caused by insufficient wind power to provide the required level of grid power, demonstrating that regulation to 0.6 per unit involves a higher level of operational risk for lower wind speeds with the chosen energy storage capacity.

After the feedback and supervisory control systems have been developed, the simulation model is typically enhanced to include detailed representations of various technologies. The main difference on the grid response between the lower fidelity model and detailed model will be harmonics generated from the power-electronic converter that interfaces the energy storage system with the grid.


Figure 5 shows active and reactive power output for a simulation study that compares a standard six-device insulated-gate bipolar transistor (IGBT) bridge with a six-cell and 24-cell (per phase) IGBT modal multilevel converter (MMC) as an interface to an energy storage system. The system is commanded to move from 0.3 per-unit active power to 1.0 per-unit active power at 0.4 seconds, while regulating reactive power to 0. From the simulation results in Figure 5, it is clear that the reference tracking capability of the feedback system is not impaired by the inclusion of different power-electronic architectures.


Figure 6 shows the voltage waveforms at the output of the converters for each architecture. Also shown in Figure 6 is the total harmonic distortion (THD) of the voltage waveform. As expected, the THD decreases as the number of power electronic devices in the bridge architecture increases. Detailed studies help determine the power-electronic architecture, filtering architecture, or combination of the two that is required to meet harmonic distortion requirements.

In conclusion, optimization, modeling and simulation can help reduce risk by informing the development of variable energy/energy storage systems. Optimization techniques may be applied to historical data to determine the energy capacity and charge/discharge characteristics of an energy storage system for a specific purpose, such as improving the operators’ position in the spot market or providing ancillary services, including frequency regulation. Modeling and simulation are invaluable in the development of appropriate feedback and supervisory control systems, as well as in the assessment of technology choices that will streamline the integration of the system into the grid.

Graham Dudgeon, Ph.D., is an energy industry manager at MathWorks, a Natick, Mass.-based developer of technical computing software.

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