#### Sensitivity-based damping recovery scheme for handling stability contingencies

Ph.D. Student: Gurupraanesh Raman | Advisor: Jimmy C. -H. Peng | Collaborator: Hatem Zeineldin, Khalifa University, UAE | Project Duration: 2017-2019

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Droop control and its variants is among the most popular decentralized power sharing methods. It has the advantages of plug-and-play operation, control scalability and independence on high-bandwidth communication. However, it presents an important technical challenge -- maintaining small-signal stability under real-time operation.

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The principle of droop control is shown in Figure 1. The small-signal stability of systems with droop-connected distributed generators depends on the droop gains, network impedances as well as the number of interconnected sources. The damping of the critical system modes can change frequently in real-time and the supervisory control system is tasked to maintain the grid stability through supervisory control.

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Figure 1. Output frequency and voltage characteristic under P-f/Q-V droop control.

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Stability is a global phenomenon, in that the location of the system poles depends on all the droop gains and network impedances. Therefore, some level of centralization is needed for supervisory control response. Accordingly, we propose the control framework shown in Figure 2, where a central damping recovery controller issues droop updates (specifically, reduction of the frequency droop coefficients) to the local droop controllers. Droop updates are triggered in response to "damping low events" that can be generated by any local controller if the local power outputs become poorly damped or undamped.

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Figure 2. Supervisory control framework for damping recovery.

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A novel sensitivity measure

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The communication links for droop update between the supervisory controller and the various sources in the network are vital, with some nodes more critical than others from the perspective of small-signal stability. This work describes a method to grade the impact of supervisory control inputs to the various nodes using a novel sensitivity measure. The central idea of the damping recovery scheme is that, once the sensitivity is known, the droop gain kf of the nodes are decreased by fixed increments, in the decreasing order of node sensitivity. In other words, the most critical node (node broadly includes an inverter and its associated droop controller) is first commanded to reduce its kf value, to determine if the "damping low event" then comes to an end. Otherwise, the droop update progresses through the remaining nodes in decreasing order of sensitivity. Such a process ends up causing the minimum changes to the droop coefficients, which in turn minimizes the deviations from the initial power sharing proportions. Such a sensitivity-based method is especially advantageous in case there are sources whose droop gains can't be changed (e.g., synchronous generators or inverters with no/loss of communication).

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An important issue to address here is the computational complexity of the sensitivity calculation process. Conventional sensitivity analysis entails the calculation of the left and right eigenvalues; this process has a cubic complexity to the number of nodes (inverters). In this work, we derive an alternative damping sensitivity formula (DSF), which can enable the sensitivity calculation with linear complexity as shown in Figure 3.

The proposed DSF is obtained by assuming that the interconnectedness of an node is a direct indicator of the sensitivity of that node. Using relevant assumptions, we reduce the multi-inverter system to a single-inverter approximation from the perspective of each node, which is shown to yield the same sensitivity order as the multi-inverter system. Note that such an approach yields the correct sensitivity order, not the actual sensitivity magnitude.

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On implementing the proposed damping recovery method, we find that it is more advantageous with respect to conventional methods such as single-point frequency compensation. Single point correction represents a class of methods where a single node provides the ancillary service of frequency recovery in a bid to improve the system damping. While this can yield quick recovery, the power sharing is significantly disrupted form the designed proportions.

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The proposed method depends on low bandwidth supervisory control links, which are not necessary for the normal operation. The event-based implementation ensures that minimum data flow occurs under normal conditions. When communication failure occurs during the damping recovery, the proposed method still remains the optimal scheme that minimizes the power sharing disparity. However, the final disparity will be obviously higher as compared to the same case without communication failure.

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Figure 3. Comparison of execution time (averaged over 10 runs) in MATLAB for calculating the node sensitivities from conventional sensitivity analysis and the proposed damping sensitivity formula.

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Figure 4. Performance comparison of the proposed damping recovery scheme and single-point correction.

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Remarks

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Formal optimization must be carried out in an “offline” manner to determine the best droop gains in the planning stage, taking into consideration line losses, economic dispatch, and other operational objectives. However, when stability contingencies occur in real-time, i.e., during "online" operation, this work proposes a sensitivity-based droop adjustment that ensures that damping recovery occurs with the minimum change in the droop gains, and thereby, the minimum disruption in the power sharing proportions.

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