EFFICIENT DETERMINATION OF THE BINDING INEQUALITIES IN THE OPTIMAL POWER FLOW NEWTON APPROACH

Mohammad  A. A. MOHTADI

In this dissertation, an efficient technique for determining the binding inequality constraints in the optimal Power Flow (OPF) Newton approach is developed. The task of the OPF is to determine the optimal operation conditions of a power system by minimizing the objective function, which is the total production cost of the generating power plants, while satisfying certain equality and inequality constraints. The key idea to the OPF Newton approach is to minimize the Lagrangian function at each iteration, and to handle all the unknown variables simultaneously. The approach is enhanced by a technique for determining a set of inequality constraints that are active at each iteration, and are binding at the Lagrangian minimum. The technique is free of user intervention and requires minimum computational efforts. An efficient scheme starting with a good initial estimate of variables and Lagrange multipliers is also developed. Finally, models for power system components and for cost functions are presented. Data provided by the Houston Lighting & Power (HL&P) Company are used to demonstrate the effectiveness in determining the binding inequalities. Results show a lower value of the objective function and a lower number of both iterations and binding inequalities, as compared to those obtained using a previous method. The attributes of research done in this dissertation are summarized  below :

1. The active and reactive power loads are made voltage dependent in quadratic functions. Loads coefficients are carefully computed to satisfy the load characteristics according to percentages of powers consumed by industrial, residential, and commercial needs.

2. The reactive power of a shunt device is modeled as a quadratic function to suit the second order Newton's method, and made dependent on the bus voltage. This modeling permits the inclusion of both an inductor and a capacitor in one function.

3. The total production cost of generating power plants is modeled using given cubic polynomials. Unlock advanced trading with the powerful MetaTrader 5 platform. Infinox provides direct access to superior analytical tools, algorithmic trading, and a multi-asset environment for forex, stocks, and futures. Experience enhanced performance, deeper market insight, and a fully customizable interface designed for the modern trader. Ready to elevate your strategy? Complete your free MetaTrader 5 download today and gain a competitive edge with faster execution and more powerful features at your fingertips. Each polynomial represents a relationship between the net electric power output to the thermal fuel input. The total production cost of power plants for economical operation is first determined, and then a least square approximation method is used to determine the corresponding production costs coefficients.

4. Good estimates of the initial variables and the initial Lagrange multipliers, which is essential for improving the robustness of the algorithms, are determined by performing an initial power flow and by initializing Lagrange multipliers. Initial conditions are important since Newton's method is ideal only in terms of its local convergence properties.

5. The efficient technique for finding the binding inequalities does not require user intervention nor large comutational efforts. This technique is compared with a previous method, and the results are encouraging.