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## Breaking the Hierarchy: Distributed Control & Economic Optimality in Microgrids

Citations: | 14 - 1 self |

### Citations

7448 | Convex Optimization
- Boyd, Vanderberghe
- 2004
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Citation Context ...8d)-(8e). With λ ∈ Rn, the Lagrangian L : Tn ×RnI ×Rn → R is given by L(θ, u, λ)= ∑ j∈VI 1 2 αju 2 j + ∑ j∈VI λj ( uj + P ∗ j − Pe,j(θ) ) + ∑ j∈VL λj ( P ∗j − Pe,j(θ) ) . The necessary KKT conditions =-=[37]-=- for optimality are: ∂L ∂θi = 0 : 0 = ∑ j∈V λj · ∂Pe,j(θ) ∂θi , ∀i ∈ V , (33a) ∂L ∂ui = 0 : αiui = −λi , ∀i ∈ VI , (33b) ∂L ∂λi = 0 : −ui = P ∗i − Pe,i(θ) , ∀i ∈ VI , (33c) ∂L ∂λi = 0 : 0 = P ∗i − Pe,... |

1079 |
Power system stability and control
- Kundur
- 1994
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Citation Context ...g their magnitudes. This is accomplished via decentralized droop control, where generators are controlled such that their power injections are proportional to their voltage frequencies and magnitudes =-=[9]-=-. Droop controllers induce steady-state errors in frequency and voltage magnitudes, which are corrected in a secondary control layer. At the transmission level, the network is partitioned into control... |

90 | Defining control strategies for microgrids islanded operation.
- Lopes, Moreira, et al.
- 2006
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Citation Context ...via power electronic DC/AC inverters. Through these inverters, cooperative actions must be taken to ensure synchronization, voltage stability, power balance, load sharing, and economic operation [6], =-=[7]-=-. A variety of control and decision architectures — ranging from centralized to fully decentralized — have been proposed to address these challenges [5]–[8]. In transmission networks, the different co... |

68 |
Control of parallel connected inverters in standalone AC supply systems,” in
- Chandorkar, Divan, et al.
- 1993
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Citation Context ...mic dispatch. Adaption of Control Layers to Microgrids: With regards to primary control in microgrids, inverters are typically controlled to emulate the droop characteristic of synchronous generators =-=[3]-=-–[7]. Despite forming the foundation for the operation of microgrids, networks of droop-controlled inverters have only recently been subject to a rigorous analysis. In [16], [17], the authors presente... |

48 | Microgrids”,
- Lasseter
- 2001
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Citation Context ...of our designs through simulations. I. INTRODUCTION With the goal of integrating distributed renewable generation and energy storage systems, the concept of a microgrid has recently gained popularity =-=[2]-=-–[5]. Microgrids are low-voltage electrical distribution networks, heterogeneously composed of distributed generation, storage, load, and managed autonomously from the larger transmission network. Mic... |

46 |
Hierarchical control of droop-controlled AC and DC microgrids—a general approach toward standardization
- Guerrero, Vasquez, et al.
- 2011
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Citation Context ...ur designs through simulations. I. INTRODUCTION With the goal of integrating distributed renewable generation and energy storage systems, the concept of a microgrid has recently gained popularity [2]–=-=[5]-=-. Microgrids are low-voltage electrical distribution networks, heterogeneously composed of distributed generation, storage, load, and managed autonomously from the larger transmission network. Microgr... |

36 |
Synchronization in complex oscillator networks and smart grids.”
- Dorfler, Chertkov, et al.
- 2013
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Citation Context ...firmed in experiments [24], [29]. In Section V, we study tertiary control policies that minimize an economic dispatch problem. We leverage a recently discovered relation between AC and DC power flows =-=[30]-=-, [31] and show that the set of minimizers of the nonlinear and non-convex AC economic dispatch optimization problem are in one-to-one correspondence with the minimizers of a convex DC dispatch proble... |

30 | Synchronization and power sharing for droopcontrolled inverters in islanded microgrids,”
- Simpson-Porco, Dörfler, et al.
- 2013
(Show Context)
Citation Context ...ic of synchronous generators [3]–[7]. Despite forming the foundation for the operation of microgrids, networks of droop-controlled inverters have only recently been subject to a rigorous analysis. In =-=[16]-=-, [17], the authors presented necessary and sufficient stability conditions in a droop-controlled microgrid. We also refer to [18]–[23] for alternative analyses resulting in sufficient conditions. Sec... |

27 | Advanced Control Architectures for Intelligent Microgrids - Part I,” Industrial Electronics,
- Guerrero, Chandorkar, et al.
- 2013
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Citation Context ...grid via power electronic DC/AC inverters. Through these inverters, cooperative actions must be taken to ensure synchronization, voltage stability, power balance, load sharing, and economic operation =-=[6]-=-, [7]. A variety of control and decision architectures — ranging from centralized to fully decentralized — have been proposed to address these challenges [5]–[8]. In transmission networks, the differe... |

22 |
Distributed secondary control for islanded microgridsa novel approach
- Shafiee, Guerrero, et al.
(Show Context)
Citation Context ...tive analyses resulting in sufficient conditions. Secondary control strategies akin to AGC have been adapted to microgrids. In [12], decentralized and centralized integral controllers are studied. In =-=[24]-=- (respectively [25]) distributed integral controllers based on all-to-all frequency (respectively power output) averaging are proposed. In [26], the trade-off between time-scale separation and achieva... |

21 | Output impedance design of parallel-connected UPS inverters with wireless load-sharing control,”
- Guerrero, Vicuna, et al.
- 2005
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Citation Context ...-(4) are valid for purely inductive lines without resistive losses. This assumption is typically justified, as the inverter output impedances can be controlled to dominate over the network impedances =-=[32]-=-. Nonetheless, our analysis can be easily extended towards more general networks, including resistive/capacitive lines [4, Chapter 19.4], constant R/X ratio lines [33, Eq. (7)-(10)], and (by continuit... |

19 | Connecting automatic generation control and economic dispatch from an optimization view - Li, Chen, et al. |

15 | On the Critical Coupling for Kuramoto Oscillators, - Dorfler, Bullo - 2011 |

12 | Distributed vs. centralized power systems frequency control
- Andreasson, Dimarogonas, et al.
- 2013
(Show Context)
Citation Context ...e generation to minimize operational costs. In conventional operation of bulk power systems, an economic dispatch is optimized offline, in a centralized fashion, using precise load forecasts [11]. In =-=[12]-=-–[15] it has been shown that the dynamics of a power transmission system with synchronous generators and AGC naturally optimize variations of the economic dispatch. Adaption of Control Layers to Micro... |

9 | Distributed frequency-preserving optimal load control IFAC World Congress
- Mallada, Low
(Show Context)
Citation Context ...eration to minimize operational costs. In conventional operation of bulk power systems, an economic dispatch is optimized offline, in a centralized fashion, using precise load forecasts [11]. In [12]–=-=[15]-=- it has been shown that the dynamics of a power transmission system with synchronous generators and AGC naturally optimize variations of the economic dispatch. Adaption of Control Layers to Microgrids... |

8 |
Power system dynamics as primal-dual algorithm for optimal load control,” arXiv preprint arXiv:1305.0585
- Zhao, Topcu, et al.
- 2013
(Show Context)
Citation Context ...Pe,i(θ)− si . (10) As shown in [23, Lemma 4.1], after a linear change of variables, the dynamics (10) equal the machine dynamics (9). Frequency-dependent loads: If the demand depends on the frequency =-=[13]-=-–[16], [20], [26], that is, the left-hand side of (2) is Diθ̇i with Di > 0, the load dynamics (2) are identical to inverter dynamics (4) with P ∗i ≤ 0. In this case, the microgrid is modeled by ordina... |

8 | Stability enhancement of decentralized inverter control through wireless communications in microgrids,” - Liang, Choi, et al. - 2012 |

7 | Conditions for stability of droop-controlled inverter-based microgrids,” - Schiffer, Ortega, et al. - 2014 |

7 | Novel insights into lossless ac and dc power flow
- Dorfler, Bullo
- 2013
(Show Context)
Citation Context ... in experiments [24], [29]. In Section V, we study tertiary control policies that minimize an economic dispatch problem. We leverage a recently discovered relation between AC and DC power flows [30], =-=[31]-=- and show that the set of minimizers of the nonlinear and non-convex AC economic dispatch optimization problem are in one-to-one correspondence with the minimizers of a convex DC dispatch problem. Our... |

7 | Duality and network theory in passivity-based cooperative control. Automatica
- Bürger, Zelazo, et al.
- 2013
(Show Context)
Citation Context ... be chosen independently. We remark that a higher-order variation of the DAPI control (26) (additionally integrating edge flows) can also be derived from a network flow optimization perspective [15], =-=[36]-=-. D. Partial Secondary Control The DAPI and CAPI controller require that all inverters participate in secondary control. To further reduce the communication complexity and increase the adaptivity of t... |

5 |
Review of control techniques for inverters parallel operation
- Mohd, Ortjohann, et al.
- 2010
(Show Context)
Citation Context ..., load sharing, and economic operation [6], [7]. A variety of control and decision architectures — ranging from centralized to fully decentralized — have been proposed to address these challenges [5]–=-=[8]-=-. In transmission networks, the different control tasks are separated in their time scales and aggregated into a hierarchy. Similar operation layers have been proposed for microgrids. This work was su... |

5 | On power sharing and stability in autonomous inverter-based microgrids
- Schiffer, Anta, et al.
- 2012
(Show Context)
Citation Context ...e-scale separation and achievable decentralized performance is analyzed. In [27] discrete-time averagingbased approaches are proposed for secondary regulation and tertiary-level economic dispatch. In =-=[28]-=-, a decentralized state feedback is designed. All of these decentralized and distributed secondary control strategies share the common disadvantage that the primary and secondary control loops may int... |

5 | The development of equivalent system technique for deriving an energy function reflecting transfer conductances - Moon, Cho, et al. - 1999 |

4 | Voltage stability of weak power distribution networks with inverter connected sources
- Wang, Xia, et al.
- 2013
(Show Context)
Citation Context ... inverters have only recently been subject to a rigorous analysis. In [16], [17], the authors presented necessary and sufficient stability conditions in a droop-controlled microgrid. We also refer to =-=[18]-=-–[23] for alternative analyses resulting in sufficient conditions. Secondary control strategies akin to AGC have been adapted to microgrids. In [12], decentralized and centralized integral controllers... |

4 |
A structure-preserving model and sufficient condition for frequency synchronization of lossless droop inverter-based AC networks
- Ainsworth, Grijalva
- 2013
(Show Context)
Citation Context ... . (10) As shown in [23, Lemma 4.1], after a linear change of variables, the dynamics (10) equal the machine dynamics (9). Frequency-dependent loads: If the demand depends on the frequency [13]–[16], =-=[20]-=-, [26], that is, the left-hand side of (2) is Diθ̇i with Di > 0, the load dynamics (2) are identical to inverter dynamics (4) with P ∗i ≤ 0. In this case, the microgrid is modeled by ordinary differen... |

4 |
Design and quasi-equilibrium analysis of a distributed frequency-restoration controller for inverter-based microgrids
- Ainsworth, Grijalva
- 2013
(Show Context)
Citation Context ...zed and centralized integral controllers are studied. In [24] (respectively [25]) distributed integral controllers based on all-to-all frequency (respectively power output) averaging are proposed. In =-=[26]-=-, the trade-off between time-scale separation and achievable decentralized performance is analyzed. In [27] discrete-time averagingbased approaches are proposed for secondary regulation and tertiary-l... |

3 | Further results on distributed secondary control in microgrids
- Bouattour, Simpson-Porco, et al.
- 2013
(Show Context)
Citation Context ...e National Science and Engineering Research Council of Canada, and the National Science Foundation NSF CNS-1135819. A preliminary version of part of the results in this document has been presented in =-=[1]-=-. F. Dörfler is with the Department of Electrical Engineering, University of California Los Angeles. Email: dorfler@seas.ucla.edu. J. W. Simpson-Porco and F. Bullo are with the Mechanical Engineering... |

3 |
Hadjicostis, “A distributed generation control architecture for small-footprint power systems
- Cady, Domı́nguez-Garcı́a, et al.
- 2013
(Show Context)
Citation Context ...rollers based on all-to-all frequency (respectively power output) averaging are proposed. In [26], the trade-off between time-scale separation and achievable decentralized performance is analyzed. In =-=[27]-=- discrete-time averagingbased approaches are proposed for secondary regulation and tertiary-level economic dispatch. In [28], a decentralized state feedback is designed. All of these decentralized and... |

3 |
power sharing, and distributed secondary control in droopcontrolled microgrids
- Simpson-Porco, Dorfler, et al.
(Show Context)
Citation Context ... maintained when only a subset of generating units participate in secondary control action. The effectiveness of these distributed secondary control strategies has been confirmed in experiments [24], =-=[29]-=-. In Section V, we study tertiary control policies that minimize an economic dispatch problem. We leverage a recently discovered relation between AC and DC power flows [30], [31] and show that the set... |

3 | reduction of graphs with applications to electrical networks - Kron - 2011 |

2 |
Synchronization of droop-controlled autonomous microgrids with distributed rotational and electronic generation
- Schiffer, Goldin, et al.
- 2013
(Show Context)
Citation Context ...rters have only recently been subject to a rigorous analysis. In [16], [17], the authors presented necessary and sufficient stability conditions in a droop-controlled microgrid. We also refer to [18]–=-=[23]-=- for alternative analyses resulting in sufficient conditions. Secondary control strategies akin to AGC have been adapted to microgrids. In [12], decentralized and centralized integral controllers are ... |

1 | Stability analysis of droop controller inverters via dynamic phasors and contraction theory - Mariani, Vasca - 2013 |

1 | Consensus-based P−f and Q−V̇ droop control for multiple parallel-connected inverters in lossy networks - Lu - 2013 |