LESSONS OF EASTER ISLAND
March 17th, 2016
We consider a problem, in which we seek to solve the system of linear equations Ax = b, where A is an n by m real matrix, b a known real vector of dimension n by 1 and x an unknown real vector of dimension m by 1. Here, n > m because the state estimation problem is overdetermined (more equations than unknowns). For a power system state estimation problem, matrix A is the measurement Jacobian.
In the WLS normal equations formulation of the power system state estimation problem, ATA describes the gain matrix that is symmetrical positive definite (SPD) by structure, so the conjugate gradient (CG) method is applicable. Note that the gain matrix requires matrixmatrix multiplication of the measurement Jacobian A with its transpose, which is hidden by CGNR.
The CGNR with Jacobi preconditioning...
Read MoreP. Siano, P. Chen, Z. Chen, and A. Piccolo
Abstract. In order to achieve an effective reduction of greenhouse gas emissions, the future electrical distribution networks will need to accommodate higher amount of renewable energy based distributed generation such as Wind Turbines.
This will require a reevaluation and most likely a revision of traditional methodologies, so that they can be used for the planning and management of future electrical distribution networks. Such networks evolve from the current passive systems to active networks and smart grids, managed through systems based on Information Communication Technology.
This chapter proposes a hybrid optimization method that aims at maximizing the Net Present Value related to the investment made by Wind Turbines developers in an ac...
Read MoreAn alternative topology based on the FCM converter is the SM converter which stacks two FCM converters together; the upper stack is switched only when a positive output is required and the lower stack is switched only when a negative output is required [3133]. A 2x n – cell SM converter, as shown in Fig. 6, is composed of 4n switches forming 2ncommutation cells controlled with equal duty cycles, 2n – 2 flying capacitors with the same capacitance and different dc rating voltages equal to E/2n, 2E/2n, …, (n 1)E/2n. As a result, the electrical stress on each switch is reduced and more equally distributed, so that each switch must support E / 2n volts [27].

In this problem, constraints are divided into three groups of operational constraints, environmental constraints, and battery constraints. These constraints are respectively defined in the following sections.
1.1.1 Operational Constraints
In minimizing the fuel cost of the ED, the total generating power of the units should be equal to the system load demand plus the transmission losses. The storage effect on the load of the system was described before. Regarding this effect, if PDt is the total demand of the system at the tth hour, we will have:
Z Pit = PDt + PLt for t = T (2)
i =1
where, Pu shows the transmission network loss at the tth hour. For a given system load demand, the transmission network loss is a function of power generation at each generating unit...
Read MoreThe hybrid optimization algorithm was applied on the abovedescribed distribution system.
It is assumed that WTs of three different capacities are chosen by the WT developers. These capacities are 225 kW, 660 kW and 900 kW.
Maximum three WTs of each type are allowed at a given location. This requirement may be set by the available land for building WTs. For another distribution network with a different load level, WTs with different capacities may be considered.
Consequently, GA is used to search for the optimal number of WTs of each type at the candidate locations. It is also assumed that the power factor is the same for all WTs connected to the same bus.
The multiperiod OPF has been applied for evaluating its annual maximum wind energy exploitation considering the following acti...
Read MoreResonant controller is a stationary frame equivalent of the synchronous PI controller. Resonant controller has been developed for inner voltage and current loops of VSIs [27][28]. This controller acts on a very narrow band around its resonant frequency CO. Usually, this method has been applied to the voltage control loop. As voltage controller, the implementation of harmonic compensator for loworder harmonics is possible without influencing all the behaviors of the current controller. Transfer function of Proportional Resonant (PR) controller can be as follows:
(6.7)
where kh is the resonant gain for the resonant peak adjustment.
This PR controller is also called P+ multi frequency resonant controller...
Read MoreAs discussed, two controllers (feedback controller for FC and inverter controller) are constructed using the equations discussed before. These controller are constructed together because the PI feedback controller requires an AC feedback voltage from the inverter to calculate the DC feedback current. Both the inverter and fuel cell controller must then run together. In this test, the simulation will be run with a static and dynamic load demand and the performance of the FC system is discussed.
Fig. 14 Fuel Cell, DC/DC Converter, and DC/AC Inverter Simulation 
Fig. 15 Fuel Cell Controller Output Feedback Current 
Output feedback current simulation results discussed in fig...
Read More3.1 Conceptual Discussion and Background
Apart from VRT capability, another key requirement associated with the integration of wind generation technology into the transmission grid has been the need for reactive power support. As in the case of VRT capability requirements, the increasing penetration of WGRs has resulted in the regional reliability organizations and/or utilities mandating a certain level of reactive power support requirements from interconnecting wind farms. While the potential reactive power support that could be obtained from WGRs was relatively limited during low penetration levels, the same is not the case with transmission systems possessing 1012% penetration of WGRs...
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