Dynamics-aware optimal power flow

Abstract — The development of open electricity markets has led to a decoupling between the market clearing procedure that defines the power dispatch and the security analysis that enforces predefined stability margins. This gap results in market inefficiencies introduced by corrections to the market solution to accommodate stability requirements. In this paper we present an optimal power flow formulation that aims to close this gap. First, we show that the pseudospectral abscissa can be used as a unifying stability measure to characterize both poorly damped oscillations and voltage stability margins. This leads to two novel optimization problems that can find operation points which minimize oscillations or maximize voltage stability margins, and make apparent the implicit tradeoff between these two stability requirements. Finally, we combine these optimization problems to generate a dynamics-aware optimal power flow formulation that provides voltage as well as small signal stability guarantees. I

Using Distributed Energy Resources to Improve Power System Stability and Voltage Unbalance

The increasing penetration of renewables has driven power systems to operate closer to their stability boundaries and makes maintaining power quality more difficult. The goals of this dissertation are to develop methods to control distributed energy resources to improve power system stability and voltage unbalance. Specifically, demand response (DR) is used to realize the former goal, and solar photovoltaic (PV) systems are used to achieve the latter. We present a new DR strategy to change the consumption of flexible loads while keeping the total load constant, improving voltage or small-signal stability without affecting frequency stability. The new loading pattern is only maintained temporarily until the generators can be re-dispatched. Additionally, an energy payback period maintains the total energy consumption of each load at its nominal value. Multiple optimization problems are proposed for determining the optimal loading pattern to improve different voltage or small-signal stability margins. The impact of different system models on the optimal solution is also investigated. To quantify voltage stability, we choose the smallest singular value (SSV) of the power flow Jacobian matrix and the distance to the closest saddle-node bifurcation (SNB) of the power flow as the stability margins. We develop an iterative linear programming (ILP) algorithm using singular value sensitivities to obtain the loading pattern with the maximum SSV. We also compare our algorithm's performance to that of an iterative nonlinear programming algorithm from the literature. Results show that our ILP algorithm is more computationally scalable. We formulate another problem to maximize the distance to the closest SNB, derive the Karush–Kuhn–Tucker conditions, and solve them using the Newton-Raphson method. We also explore the possibility of using DR to improve small-signal stability. The results indicate that DR actions can improve small-signal characteristics and sometimes achieve better performance than generation actions. Renewables can also cause power quality problems in distribution systems. To address this issue, we develop a reactive power compensation strategy that uses distributed PV systems to mitigate voltage unbalance. The proposed strategy takes advantage of Steinmetz design and is implemented via both decentralized and distributed control. We demonstrate the performance of the controllers on the IEEE 13-node feeder and a much larger feeder, considering different connections of loads and PV systems. Simulation results demonstrate the trade-offs between the controllers. It is observed that the distributed controller achieves greater voltage unbalance reduction than the decentralized controller, but requires communication infrastructure. Furthermore, we extend our distributed controller to handle inverter reactive power limits, noisy/erroneous measurements, and delayed inputs. We find that the Steinmetz controller can sometimes have adverse impacts on feeder voltages and unbalance at noncritical nodes. A centralized controller from the literature can explicitly account for these factors, but requires significantly more information from the system and longer computational times. We compare the performance of the Steinmetz controller to that of the centralized controller and propose a new controller that integrates centralized controller results into the Steinmetz controller. Results show that the integrated controller achieves better unbalance improvement compared with that of the centralized controller running infrequently. In summary, this dissertation presents two demand-side strategies to deal with the issues caused by the renewables and contributes to the growing body of literature that shows that distributed energy resources have the potential to play a key role in improving the operation of the future power system.PHDElectrical and Computer EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162969/1/mqyao_1.pd

Modeling, Control and Identification of a Smart Grid

We are in front of an epochal change in the power distribution and generation scenario. The increasing request of energy, the energy dependency of several countries from few foreign nations endowed with oilfield or gas field, and, on the other hand, the climate change and environmental issues are the main explanation of the recent development and spread of renewable distributed energy generation technologies. Examples of them are photovoltaic panels, wind turbines or geothermal, biomass, or hydroelectric. They are called small-size generators, or micro-generator, since the amount of power they can produce is significantly lower than the one produced by the huge, classical power plants. These distributed energy resources (DERs) are located close to where electricity is used, in the distribution network. Furthermore, they are connected to the electrical grid via electronic interfaces, the inverters, that could allow us to control the power injected into the grid. This thesis is focused on the study of some crucial aspects of this new energetic scenario: 1. Modeling: we recall the classical models and a recent linearized one of the power systems, that will be very useful for the design and the analysis of our algorithms. 2. Optimal Reactive Power Flow (OPRF) problem: in this part we recall classical and recent algorithms that deal with the reactive power regulation. In particular, we focus on the ones that solve the OPRF problem, i.e. the problem of the amount of reactive power to be injected by each micro-generators, in order to achieve “optimal” performance. We choose, as an optimality achievement, the minimization of the line losses. Finally we derive and propose our OPRF algorithm, providing formal proves of its convergence to the optimal solution. 3. Optimal Power Flow (OPF) problem: the OPF problem’s aim is to find an operating point of the power system that optimize a cost function (tipically the generation cost) satisfying the power demand and some operative constraints. After recalling the most popular algorithms that solve the OPF problem, we propose two of them. In this framework there are mainly two possible scenarios. The first is related to the “utility point of view”, where the total cost accounts for the production cost of the energy (that comes from big generation plants such as nuclear or hydro-electrical plants) and for the remuneration to be paid to the owners of DERs. In this framework, the utility imposes a behavior procedure to be followed by the producers to compute the amount of energy they have to inject into the grid to minimize the total cost. The first algorithm deal with this scenario. The second one is related to the “producer point of view”. Since the owners of the DERs are paid proportionally to the energy that they inject, they would like to maximize the power they inject, while keeping satisfied some operative constraints. The result is a game among the agents. A first treatment on this scenario is given by the second algorithm. 4. Switches monitoring for topology identification: in this part, after a literature review, we propose a algorithm for the identification of switches actions. They modify the topology of the electrical grid, whose knowledge is fundamental for monitoring, control and estimation. This algorithm works analyzing how the phasorial voltage profile vary and recognize a kind of signature left by the switches status change

Distributed Network Synchronization: The Internet And Electric Power Grids

Synchronization is a fundamental requirement of most networked engineering applications. It enables the necessary coordination among agents required to implement several communication systems as well as network protocols. Despite the great recent advances in understanding synchronization, a complete synchronization theory is yet to be developed. This thesis presents a systematic study of synchronization on distributed systems that covers theoretical guarantees for synchronization, performance analysis and optimization, as well as design and implementation of algorithms. We first present several theoretical results that deepen the understanding of how coupling, delay and topology affect the behavior of a system of coupled oscillators. We obtain a sufficient condition that can be used to check limit cycle stability, and use it to characterize a family of coupling functions guaranteeing convergence to in-phase synchronization (phase consensus). The effect of heterogeneous delay is then investigated by developing a new framework that unveils the dependence of the orbit's stability on the delay distribution. Finally, we consider the effect of frequency heterogeneity. While coupled oscillators with heterogeneous frequency cannot achieve phase consensus, we show that a second order version of the system can achieve synchronization for arbitrary natural frequencies and we relate the limiting frequency of the system to the harmonic mean of the natural frequencies. Based on the insight provided by our theoretical results, we then focus on more practical aspects of synchronization in two particular areas: information networks and power networks. Within information networks, we examine the synchronization of computer clocks connected via a data network and propose a discrete algorithm to synchronize them. Unlike current solutions, which either estimate and compensate the frequency difference (skew) among clocks or introduce offset corrections that can generate jitter and possibly even backward jumps, this algorithm achieves synchronization without any of these problems. We present a detailed convergence analysis together with a characterization of the parameter values that guarantee convergence. We then study and optimize the effect of noisy measurements and clock wander on the system performance using a parameter dependent H2 norm. In particular, we show that the frequency of the system drifts away from its theoretical value in the absence of a leader. We implement the algorithm on a cluster of IBM BladeCenter servers running Linux and we experimentally verify that our algorithm outperforms the well-established solution. We also show that the optimal parameter values depend on the network conditions and topology. Finally, we study synchronization on power networks. By relating the dynamics of power networks to the dynamics of coupled oscillators, we can gain insight into how different network parameters affect performance. We show that the rate of convergence of networks is related to the algebraic connectivity of a state dependent Laplacian which varies with the network power scheduling and line impedances. This provides a novel method to change the voltage stability margins by updating the power scheduling or line impedances. Unfortunately, there exists a decoupling between the market clearing procedure used to dispatch power and the security analysis of the network, that prevents the direct use of this solution. Furthermore, focusing on voltage stability may generate other types of instabilities such as larger transient oscillations. This motivates the use of a unifying stability measure that can minimize oscillations or maximize voltage stability margins, and can be readily combined with current dispatch mechanisms generating a dynamics-aware optimal power flow formulation