# Category Modeling and Control of Sustainable Power Systems

## CGNR and CGNR + Jacobi Pre-conditioner

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 over-determined (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 matrix-matrix multiplication of the measurement Jacobian A with its transpose, which is hidden by CGNR.

The CGNR with Jacobi pre-conditioning...

## Optimal Allocation of Wind Turbines in Active Distribution Networks by Using Multi-Period Optimal Power Flow and Genetic Algorithms

P. 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 re-evaluation 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...

## Stacked Multicell (SM) Converter

An 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 [31-33]. A 2x n – cell SM converter, as shown in Fig. 6, is com­posed of 4n switches forming 2n-commutation 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 .  Fig...

## Constraints

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 t-th hour, we will have:

Z Pit = PDt + PLt for t = T (2)

i =1

where, Pu shows the transmission network loss at the t-th hour. For a given sys­tem load demand, the transmission network loss is a function of power generation at each generating unit...

## Case Study

The hybrid optimization algorithm was applied on the above-described 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 multi-period OPF has been applied for evaluating its annual maximum wind energy exploitation considering the following acti...

## Resonant Control

Resonant controller is a stationary frame equivalent of the synchronous PI control­ler. Resonant controller has been developed for inner voltage and current loops of VSIs -. 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 low-order 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...

## Testing the System with VSI and Controllers

As 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...