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## Volt/VAR Control and Optimal Power Flow

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**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.