POWER NETWORKS

Power Networks



Power Networks

1. Introduction

Power is often a scarce resource in wireless ad hoc networks. The primary performance objectives of wireless ad hoc networks are power conservation and utility maximization. Power control is to minimize the overall transmitted power given a constant signal-to-interference-and-noise ratio (SINR) requirement for each user. To solve this problem, many pieces of work have been done in the literature, which mainly concentrate on optimizing power and rate allocation with cross layer design. In addition to these results, several distributed cross-layer optimization frameworks were proposed to jointly allocate spectral bands, power and data rate for lifetime or utility maximization in wireless ad hoc networks. These joint data rate and power allocation strategies are based on nonlinear programming and the dual subgradient Method. The optimal solutions by means of the dual method depend on the convexity of the investigated optimization problem. However, in wireless ad hoc networks, because of multi-path routing and time-varying channel states, the optimization problem may not be convex. This implies that it cannot be guaranteed to obtain the optimal power scheduling and rate allocation since there might be a duality gap between the problem and its dual. Therefore, it is needed to introduce some new variables and transform a non-convex optimization problem into a convex one (Lin and Shroff, 2006). Obviously, this leads to the increase of computational complexity. It is also difficult to choose the appropriate dual Lagrangian Multipliers (penalty factors) and iteration step sizes, and a numerical solution obtained by the dual approach requires overwhelming computational effort, which increases exponentially as the size of the problem increases.

Bus Pmin(p.u) Pmax(p.u) a(S/hr) b(S/MW.hr) c (S/MW2.hr)1 0.30 1.8 105.0 2.45 0.0.12 0.15 0.9 44.1 3.51 0.013 0.40 1.9 40.6 3.89 0.01

Pg1 Code Pg2 Code Pg3 Code0.3 0000 0.15 0000 0.4 00000.4 0001 0.20 0001 0.5 00010.5 0010 0.30 0010 0.6 00100.6 0011 0.30 0011 0.7 00110.7 0100 0.35 0100 0.8 01000.8 0101 0.40 0101 0.9 01010.9 0110 0.45. 0110 1.0 01101.0 0111 0.50 0111 1.1 01111.1 1000 0.55 1000 1.2 10001.2 1001 0.60 1001 1.3 10011.3 1010 0.65 1010 1.4 10101.4 1011 0.70 1011 1.5 10111.5 1100 0.75 1100 1.6 11001.6 1101 0.80 1101 1.7 11011.7 1110 0.85 1110 1.8 11101.8 1111 0.90 1111 1.9 1111

Chrom Initial population Pg1(p.u) Pg2(p.u) Pg3(p.u) Fcost(s/kwh)1 000111111100 0.4 0.90 1.60 2102.02532 000100101011 0.4 0.30 1.50 2104.70703 101010011011 103 0.65 1.50 2101.25494 111001010111 107 0.45 1.10 2102.5335Sum 8409.7502Average 2102.4376Max 2104.7070Bus Pmin Pmax Qmin Qmax Vmin Vmax a b c.10-21 0.50 2.00 0.20 2.00 0.95 1.10 0 200 037.52 0.20 0.80 0.20 1.00 0.95 1.10 0 175 175.05 0.15 0.50 0.15 0.80 0.95 1.10 0 100 625.08 0.10 0.35 0.15 0.60 0.95 1.10 0 325 083.011 0.10 0.30 0.10 0.50 0.95 1.10 0 300 250.013 0.12 0.40 0.15 0.60 0.95 1.10 0 300 250.0

Variable Lower Upper Initial state Classical OPF GAOPFP1(MW) 50 200 99.211 170.237 179.367P2(MW) 20 80 80.00 44.947 44.24P5(MW) 15 50 50.00 28.903 24.61P9(MW) 10 35 20.00 17.474 19.90P11(MW) 10 30 20.00 12.174 10.71P13(MW) 12 40 20.00 18.468 14.09Q1(MVAR) -20 200 5.335 -4.886 -30156Q2(MVAR) -20 100 27.687 34.333 42.543Q5(MVAR) -15 50 ...