Volt/VAR Control and Optimal Power Flow Jie Mei Georgia Institute of Technology
The Definition of Power • Define P as real power, which reflects the energy consumption in the network. • Define Q as reactive power, it reflects the energy exchange between generators and loads, while it does not really consume any energy. • Imagine a simple capacitor circuit • Appliances have capacitor or inductor will need Q • Define S as complex power. S = P + jQ
Why is Q so important? • Although Q does not really consume any energy, P will be affected a lot as Q flows in the network • Imagine a transmission line segment AB with resistance R • Line loss will be , but I is determined by both P and Q through
Buses Classification • Four quantities of interest associated with each bus • Real Power, P • Reactive Power, Q • Voltage Magnitude, V • Voltage Angle • At every bus, two of these four quantities will be specified and the remaining two will be unknowns. • Type1. Slack Bus-voltage magnitude and angle are known. Must have a source of both real and reactive power, thus usually choose the root bus as slack bus • Type2. PQ Bus-P and Q are specified, usually called load bus. • Type3. PV Bus-P and V are specified. Must have a variable source of reactive power such as a generator or capacitors to maintain the voltage
Goal of Voltage Control • Maintain acceptable at the service entrance of all customers served by the feeder under all possible operating conditions, as appliances can achieve best performance at rated voltage.
Voltage Depends on Reactive Power • Imagine a transmission line (not distribution line), with a utility at node 2, we have
Voltage Control by Reactive Power • Why not use active power P? • P can only be generated from generator(if we do not consider PV here), which will be adjusted in five-minute scale based on the cost and the load prediction, so you can never change the generator frequently • While Q can be generated without too much cost in much shorter time scale, so we want to achieve voltage control through Q management.
Voltage Control by Reactive Power • Ways of Reactive Power Compensation • Fixed and Switched Capacitor Banks and inductors • Static VAR compensator (SVC) and other FACT devices • ...... • Thus we achieve voltage control though placement of VAR capacitor sources • Voltage could also be changed through load tap changer(LTC)……
How to Set VAR Control Devices? -Optimal Power Flow • We treat the voltage control as an optimization problem. • Objective Function: Minimum system network losses • Subject to Constraints: Capacitor Limits Line Limits Tap Limits Voltage Limits
How to Set VAR Control Devices? -Optimal Power Flow • We treat the voltage control as an optimization problem. • Objective Function: Minimum system network losses • Subject to Constraints: Change Discrete to Continuous? Capacitor Limits Line Limits Tap Limits Voltage Limits
How to calculate the network loss? • Get the equivalent circuit with the initial power information and system admittance matrix • Apply newton’s method to solve the power flow matrix and get all the information at all the nodes. • Calculate the loss at each lines and add them up to get the total network loss. • Power flow solution algorithm-PF_Calculation_JieMei • Input: • i) System Admittance Matrix • ii) Initial Power Matrix • Output: • P,Q,V, and angle at all buses.
Power Flow Algorithm-Newton Admittance Matrix Power Matrix
Power Flow Algorithm-Newton Initial Voltage Matrix
Power Flow Algorithm-Newton Formula Sequence A
Power Flow Algorithm-Newton Formula Sequence B
Power Flow Algorithm-Newton Formula Sequence C
Power Flow Algorithm-Newton Update the initial voltage matrix
A Simple 4-bus Distribution System • Admittance Matrix
A Simple 4-bus Distribution System • Outputs Voltage: • Line loss can be calculated by • Improve this algorithm to OPF solution?
Challenges for Newton Method • 1) Traditional Newton’s method may not converge, it is highly depends the initial values. In another word, you may not get a optimal power flow solution. • 2) Traditional Newton’ method needs big space, because it needs to calculate the Jacobian matrix every iteration. Thus big number of buses may not use newton method. • 3) Difficult to incorporate Solar energy and Wind power energy which are difficult to predict. • 4) Time delay to communication. The control devices may take longer time than they are required to.
Why Game Theory? • 1) Easier to incorporate unpredictable energy? • 2) Greatly shrink the computation storage? • Then maybe game theory method performs worse than newton method, it will be a good method to achieve an acceptable OPF solution for a system with a lot of buses and unpredictable energy.