Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure

The environments of Markarian galaxies

The extensively studied Markarian sample of 1500 ultraviolet excess galaxies contains many Seyfert, starburst, and peculiar galaxies. Using the 20 minute V plates obtained for the construction of the Hubble Space Telescope Guide Star Catalog, the authors investigated the morphologies of the Markarian galaxies and the environments in which they are located. The relationship between the types of nuclear activity and the morphologies and environments of the Markarian galaxies is discussed. The authors conclude that the type of nuclear activity present in the galaxies of the Markarian sample is not dependent on either the morphology or the local environment of the galaxy. This is not to imply that nuclear activity per se is not influenced by the environment in which the nucleus is located. Rather the type of nuclear activity (at least in the Markarian population) does not appear to be determined by the environment

Restitution - Purchaser\u27s Remedies Where Real Estate Broker Falsely Purports to be Owner\u27s Agent and Misrepresents Owner\u27s Minimum Price

Defendant, a licensed real estate broker, represented that he was exclusive agent for the sale of 72 acres of property. Plaintiff made him an offer to purchase at $4,000 per acre, but was later informed by defendant that the owner had rejected the offer, insisting on at least$5,000 per acre. Plaintiff then submitted an offer of $5,000 per acre, which defendant subsequently indicated that the owner had accepted. The deal was consummated with most of the papers handled through a third party employee of defendant. Plaintiff subsequently learned that defendant had never been the agent of the owner, had never presented plaintiff\u27s offers to the owner, had misrepresented the minimum price of the property, and instead had purchased the property himself and resold it to plaintiff at a profit of$1,000 per acre. Plaintiff brought an action for damages in the superior court against defendant broker and the third party employee for violation of a fiduciary obligation. The superior court rendered judgment against both defendants for $72,049 compensatory damages, and awarded exemplary damages of$36,000 against defendant broker individually. The district court of appeal held that although the allegation of fiduciary relationship was not sustained by the evidence, plaintiff could still recover in quasi-contract due to defendant\u27s unjust enrichment. The court accordingly struck out the award of exemplary damages, reversed the judgment as against the third party, and affirmed the judgment against defendant on the reduced amount. On rehearing, held, the cause should be reversed generally, one judge dissenting. No fiduciary relationship is created when a broker makes false representations to a buyer. But at the election of the defrauded party, a constructive trust may be imposed upon the wrongdoer based on unjust enrichment rather than tort. Since the plaintiff disavowed the theory of unjust enrichment, however, an affirmance of the judgment for the plaintiff upon that theory is not proper, though plaintiff will be given leave to amend his complaint. Ward v. Taggart, (Cal. App. 1958) 329 P. (2d) 320

Bankruptcy - Priorities - Status of Employer Contributions to Union Welfare Fund

Under a collective bargaining agreement an employer was required to contribute eight dollars monthly to a union welfare fund for each of its employees who were union members. A trust agreement authorized the trustees of this fund to file claims of priority in any proceeding involving the employer\u27s insolvency. In a bankruptcy proceeding the trustees of the fund sought priority as wage claimants for the employer\u27s unpaid contributions to the fund which had accrued during the three months prior to bankruptcy. In the same proceeding the United States sought priority for unpaid taxes. The referee ruled that the unpaid employer contributions were not wages within section 64a(2) of the Bankruptcy Act, and relegated the trustee\u27s claim to the status of payments due unsecured creditors. The district court vacated the referee\u27s order and granted wage priority to the employer contributions. On appeal, held, affirmed. Since employer contributions to union welfare funds are in a realistic sense part of the agreed compensation for services rendered, and are also bargained for as an integral part of the wage package, they must be considered as wages under section 64a(2) of the Bankruptcy Act. Matter of Embassy Restaurant, (3d Cir. 1958) 254 F. (2d) 475, cert. granted 79 S. Ct. 42 (1958)