## Power Supply System Software

Programme Summary

Major: 13.04.02 Power Industry and Electrical Engineering

Specialisation: Power Supply

Degree: Master

Course units:

Unit 1. Analysis of steady state regimes of complex electric power systems.

Unit 2. Determining generalized parameters of equivalent circuits.

Unit 3. Direct solution of basic state equations.

Unit 4. Calculation methods involving transformation of input equations or the input circuit.

Unit 5. Methods of solving the sets of state equations.

Unit 6. Electric power system reduction.

Unit 7. Vector diagrams of AC machines.

Unit 8. Equivalent circuits for synchronous and induction machines.

Unit 9. AC machine control system equations.

Unit 10. Mathematical models of an electric power system.

Course contents:

Unit 1. Analysis of steady state regimes of complex electric power systems.

General description of the problem. Basic equations. Classification of calculation methods. Determining node voltages at a given current distribution. Determining power values and power losses in branches at given current distribution and node voltages. Control of static load parameters. Linear approximation when load is viewed as a constant power.

Unit 2. Determining generalized parameters of equivalent circuits.

Node inherent and mutual resistance. Adjusting the node resistance matrix upon network switching changes. Recalculation of the node resistance matrix upon a reference bus change-out. Definition of a current distribution factor matrix and a voltage distribution factor matrix. Calculation of inherent and mutual branch resistances. Definition of an inherent and mutual branch resistance matrix. Incidence matrix.

Unit 3. Direct solution of basic state equations.

Determining branch currents and node voltages based on the superposition principle. Loop opening method. Control of complex transformation ratios by adding ideal transformers and additional currents in the equivalent circuit. Allowing for excitation current and iron losses in a transformer. Determining the power capacity of generator branches. Calculation of quasi-steady state regimes of electric power systems with no isolation of a balancing bus.

Unit 4. Calculation methods involving transformation of input equations or input circuit.

Graph feedback loops exclusion method. Graph loop elimination method. Calculation of power network regimes with banded matrix. Calculation of power network regimes with nodal admittance matrix which is close to the quasi-tridiagonal matrix. Definiens method. Calculation method involving the definition of diagonal blocks. Nodal analysis method. Breaking into subcircuits by means of removing the connecting branches when replacing them with driving currents. Breaking a circuit into subcircuits by splitting the branches. Breaking a circuit into subcircuits by isolating boundary nodes. Diakoptics methods when applying loop-current equations.

Unit 5. Methods of solving the sets of state equations.

Solution of linear algebraic equation sets. Ordered elimination method; approximation method; the Gauss–Seidel method; Newton’s method; minimization methods; topological methods. Two-way minimization methods based on Newton’s plane. Quadratic descent method. Methods of diakoptics. Existence and ambiguity of solutions. Conditions for convergence of calculation methods. Diagonal relaxation method. Regularization of calculation methods.

Unit 6. Electric power system reduction.

The objective of system reduction. Equivalence criteria. Elementary equivalence transformations. Reduction on the basis of a linear equivalent circuit without the generator station EMF.  Reduction on the basis of the node exclusion method in the invariant power loss conditions. Reduction through the integration of generator branches based on the complex EMF values. Accurate and approximate reduction. Designing the steady-state operation of a power supply system comprising in-house power plants through a successive system reduction in parallel and separate operation.

Unit 7. Vector diagrams of AC machines.

Vector diagrams of synchronous generators in a synchronous operation with the power system. Vector diagrams of synchronous motors in a synchronous operation with the power system. Vector diagrams of induction motors. Vector diagrams of synchronous generators and motors in a drop-out situation.

Unit 8. Equivalent circuits for synchronous and induction machines.

Equivalent circuits for synchronous and induction machines when calculating the transients in synchronous conditions and in non-zero sliding conditions. Inductive and active resistances and time constants of synchronous machines. The impact of saturation on synchronous inductive resistance. Negative sequence inductive resistance of a synchronous machine. The impact of element parameters on the system stability.

Unit 9. AC machine control system equations.

Basic equations of synchronous machine excitation current regulators. The equation for proportional voltage control. The equation for compounding system. The equation for the regulator with compound excitation and lagging voltage correction. Automatic transfer switch parameters and their impact on stability. Gain factors. Basic equations of generator prime mover speed governors. Servomotor equations. Time constants of automatic regulators. Allowing for synchronous generator regulators when determining transient parameters. The behaviour of regulators during oscillations. The relationship between the speed governor type and stability.

Unit 10. Mathematical models of an electric power system.

Compound system and research. Lyapunov stability theory. Lyapunov method. Investigation of the roots of a characteristic equation. Algebraic and frequency criteria of static stability. Design of a complex positioning system. The full and simplified math models for calculation of transients. Equations of motion. Application of complete and simplified equations. Designing the transient of a compound system comprising a random number of generators and loads. Defining the power capacity by principle of superposition. The method of successive intervals applied for sophisticated electric power systems.

Activities:

• Teacher-led group activities in a classroom;
• Extracurricular self-study of the teacher’s assignments and tasks, including the use of educational facilities (obligatory);
• Office-hours.

Total hours – 216

Total points – 6

Classroom hours – 39

Unsupervised hours – 141

Term paper in the 2nd semester

Midterm assessment – Examination