Planeamento
Aulas Teóricas
Course Content -- Lesson by Lesson
COSE -- Course Content
Introduction
Quantities to control
Sensors and actuators
Control mechanisms
Computer-based modern control
Simplest control problems in EPS
Simplest control problems in EPS
Single generator under no load
Voltage control
Frequency control
AVR Automatic Voltage Regulator
Physical system
Block diagrams
Automatic Voltage Regulator
Stability
Root locus
Series compensation
Parallel compensation
Nonlinearities and linearizations
AVR -- continuation
Review
Block diagram for AVR
Issues of input/output in frequency and time
Input: step, ramp
Output: oscillatory or not, critically dampened, unstable
Rise time, overshoot, settling time, etc
Multiple frequencies
Frequency of oscillation and root location
Compensation schemes and linearization process
Compensation: series compensation and shunt compensation
Historical devices for compensation
Introduction of zeros and derivative control
PID as a universal electronic control
Understanding derivative control as anticipated information
Use of V versus deltaV
Successive linearization
Nonlinearities and control action
Sources of nonlinearity: magnetization curve for iron, saturation, limits and bounds
Generator loading: effects on model, KG and TECHNOLOGIES
Where to introduce disturbances or perturbations in the model
Generator as a PV bus
Rotor dynamics: voltage and power; electrical and mechanical
Imbalance of turbine output and electric demand
Spinning masses as energy storage
Power regulation, frequency regulation
Review
Power imbalance for the couple turbine and demand
Storage: mechanical or kinetic of spinning masses
Amount of kinetic energy: ½Iw²
Inertia moment: dI=r²dM
Energy measured in s? Meaning of the inertia constant H
Development of the corresponding TF
Node model for the power equilibrium
Turbine TF: a simple TF with a single time constant
More of the physical model: a hydraulic regulator
Reason to include a time constant for that
Order of magnitude
The control system
Negative feedback -- review of why negative
PID and proportional control
R parameter: effects of its value
Pref, a reference entry for extra control
Frequency regulation
Load elasticity
Regulation energy
Steady state analysis
Interpretation of frequency deviations
Secondary control or integral control
Secondary control
Need for and role of secondary control
Integral control
Effect of gain of integral feedback
New characteristic eq
Stability issues
More than one generator in one plant
Voltage control
Frequency control or power control
Primary control is proportional
Secondary control is integral
Tertiary control is set point control by the Dispatch
More than one generator in one plant
Presentation of the problem of interconnecting plants
The problem of interconnection
Why interconnection has no dynamics
How to model interconnection
Minimal realization
Simplest model for two-area interconnection
Analysis of a two equal areas interconnected
Application of superposition principle
Characteristic equation
Roots and solution types
Root locus
Oscillatory responses of increasingly higher frequencies
Need for a new model
Analysis of a two equal areas interconnected
Analysis of a two equal areas interconnected
Revisions
Problem 3
Analysis in time domain
An introduction to time-domain analysis
Standard form
Symbolic block diagram
Concepts and notation
Transfer matrix
Characteristic polynomial
Poles are eigenvalues
State space representation
Modal matrix
Normal form
J is a diagonal of eigenvalues
Illustration for mode decoupling
Controllability
Linear, constant matrix feedback
New controlled system
(A,B) controllable
Plant matrix with feedback
Where are the other controls?
Solution and exp(At)
x(t) as a convolution integral
Controllable canonical form
Controllability canonical form and optimal control
Controllability canonical form
Its dual: observability canonical form
Importance of coefficients a’s
Role of b’s
Trace(A)
Concepts of Optimal control
Linear quadratic regulator
Ricatti eq
The engineering problem: choosing Q’s and R’s
Limitations to the use of Optimal Control
Systems in triangle: two generators and one load
Load as a unit step at a load bus
"Complete model" for the generator
Control problem vs transient response
Linear analysis vs nonlinear analysis
Voltage regulator and frequency regulator together
"Complete model" for the generator
Control problem vs transient response
Linear analysis vs nonlinear analysis
Revision of triangle systems
Linearization formulas
AVR+AGC coupling
Possible instabilities
Stabilization by coupling: PSS
Input Output and TF for PSS
Voltage regulator and frequency regulator together
Nodal demand is an electric quantity
Role of delta and emf
Integration of the models
Simulation of the slow oscillations in interconnection power
The role PSS Power System Stabilizer
Models for PSS
The role of tertiary control
Economic Dispatch
The role of tertiary control
Non-automatic control
Costs curves: total, marginal, efficiency, average
Key aspects of the curves
Lossless dispatch
Problem Mathematical formulation
Two ways to solve the problem:
Using a Lagrangean approach and
Using variable substitution
The results: equal incremental costs
How this can be carried out by bisection
ED with losses and bounds
Why introduce losses into the problem
The need for penalty factors
Losses as a function of decision variables
Math formulation and results
How the problem can now be solved using the same techique
The need for ityeraions dure to PF’s
How to compute losses and PFs:
Bs methods and power flow methods
Fundamentals of those methods
Mathematical derivations
Handling inequality constraints and OPF
Handling inequality constraints and OPF
Examples of inequality constraints in ED problems
Understanding why constraints must enter the active set and why they must leave
Kuhn Tucker conditions
The interpretation of the new added Lagrange multipliers and why the constraints must be relaxed
Introducing the OPF problem
Optimal Power Flow
Objective of the OPF problem
Variables: what are they? (decision, dependent, auxiliary variables)
Constraints: equality and power flow equations
Inequality and transmission limitations
Simple bounds on the variables: powers, taps, ...
A first approach: reduced gradient
How to set it up and how to solve it
What is the reduced gradient an how to use it to update the decision vector
OPF by Newton and by LP
Newton for OPF
Approach, difficulties and results
Advantages and disadvantages
LP for OPF
Successive linearization
OPF for planning and operations
The issue of system securityEvaluation of security costs
OPF leads to the UC problem
Dynamics, state, state equations and the UC problem
Concepts of dynamics and state
State equations, state transitions, decision space
Combinatorial nature of UC problem
Examples of unit dynamics
Grid for Dynamic Programming
Nodal costs and arc costs
Bellman optimality principle
Backward DP and forward DP
Thermal units and hydro resources
State of a thermal unit
States for operation, maintenance, ...
The importance of operation costs and operation constraints for state definition
Examples of a state transition diagram for a unit with variable startup costs, minimum up time, MUT, and minimum down time, MDT
Hydro resources
Cascade systems
Operation curves: head, flow, power
Reservoir dynamics, river dynamics, time constraints
Spill models
Minimal cost network flow problems
Nodal equations
Arc quantities: generation, pump, storage, spill
MCNF as a special LP
Basic, nonbasic, marginal true values
How to obtain these values for a given tree
Dynamic Programming applied to UC
State transition diagram
Multiple states, multiple transitions
Problem formulation
Solution approach by Dynamic Programming
Creation of a DP grid
Node costs (or profits) and arc costs
Criterion for operations
Optimal solution and computational efficiency
Hydrothermal coordination and scheduling of a complex dynamic resource
Hydrothermal coordination
Empiric principles for coordination
Hydro and load peak-shaving
Example of hydrothermal coordination
Marginal value of water and total value of water
Relationship between gamma and lambda
Resource coordination and revisions
Review of primal problem and dual problem in the context of resource scheduling
Economic interpretation
Review of concepts of reserve and capacity: sources and requirements
Costs for reserve and capacity
Problem 12
Water value -- marginal costs and non-marginal
Water value as a function of reservoir location and reservoir volume
Water value for a weekly scheduling: constant value, non-constant, zero value -- interpretation in view of water constraints
Water value interaction between short-term scheduling and medium-term scheduling
Qualitative differences with respect to investment planning