Study on Multi-objective Optimal Power Flow of Power System Considering Static Voltage Stability (I) Chapter 5 Multi-objective Optimal Power Flow of Power System Considering Static Voltage Stability 5. 1 Introduction Although voltage stability is a dynamic problem in essence, most power system blackouts in the world are caused by the destruction of static power flow operating conditions. However, the subsequent dynamic process aggravated the collapse of the system. In reactive power planning, the weak buses sensitive to stability are first identified by singular value decomposition method, and then reactive power compensation devices are installed on these buses, which not only takes into account voltage stability and reduces system loss, but also reduces running time. In this chapter, firstly, the weak nodes in the system are identified by characteristic structure analysis, and the installation position of reactive power compensation device is determined. Then, the static voltage stability index is added to the objective function of the optimal power flow problem, and three optimization objective functions, namely, minimizing the power generation cost, minimizing the reactive power compensation capacity and maximizing the static voltage stability margin, are determined to construct a multi-objective optimal power flow model, and the new model is solved by combining fuzzy set theory with tabu search algorithm. The feasibility of this method is verified by the calculation of IEEE 14 bus system. The biggest advantage of this method is that it can give consideration to the voltage stability and economy of the system at the same time. 5.2 Multi-objective optimal power flow model The traditional multi-objective power flow problem can be described in a concise mathematical form as follows: [] 1.2 min = (), () ... () 0 () 0tnff x f x f x f x f x x x x x x x x x x x x x t h XG x = ≤ (5.1), where x includes () If X is the objective function, i = 1, 2, n, n is the number of objective functions; H (x)=0 is an equality constraint, that is, the basic power flow equation; G (x)≤0 is an inequality constraint. 5.2. 1 objective function The objective function can be any meaningful function. At the same time, considering the safety and economy of power system, this paper will adopt the following three objective functions: (1) Minimum generation cost 21min () () GII GII GII NF X ABP CP ∑ = ∑. Ia, ib and ic are the power generation characteristic coefficients of node I; GiP is the active output of the generator node I (2) Minimize the reactive power compensation capacity to 2min()Ci Cii Nf x s Q∑=∑(5.3) where CiQ is the capacity of the reactive power compensation device installed at the node I; Is is a decision variable of 0- 1. If the reactive power compensation device is installed at node I, it is 1is=, otherwise it is 0is=, and the value of is is determined by the characteristic structure analysis method. CN is the set of all nodes equipped with reactive power compensation devices. (3) Maximize the static voltage stability margin by 3 0max()cof x=λ? λ(5.4), where coλ and 0λ are the load levels of voltage collapse and the current operating state of the system, respectively. 5.2.2 Equality Constraints Equality constraints are the active and reactive power flow equations of nodes, which can be expressed as: (0) (0)10 (1) (Cossin) ngigili jiji jjjpλ k pλ u gδ =+? +? ∑+(5.5)(0)(0)(0) 10(tan)(sin cos)nGi Li I I j ij ij ij ijjQ QλP？ U U G δBδ==？ +? ∑? (5.6) where: GiK is the multiplier of the change rate of generator active output,1max (0)+0max (0)1max (0)1() () gngi gigli nigj gjjppppp = =? =? ∑∑, GimaxP and GjmaxP are the maximum active outputs of generator nodes I and J respectively; Gj(0)P is the initial active output of generator node J when the load level is 0λ=λ (λ is the load parameter and represents the load level); 1N and GN are the total number of load nodes and generator nodes; Gi(0)P and Gi(0)Q are the initial active output and initial reactive output of generator node I when the load level is 0λ=λ, respectively; Li(0)P and Li(0)Q are the initial active power and initial reactive power of the load node I, respectively; Me? Is the power factor angle of I bus load change. 5.2.3 Inequality constraints Inequality constraints can be specifically expressed as: 38 gimin gima XP ≤ p (5.7) gimin gima max q ≤ q (5.8) cimin cimax q ≤ q ≤ q (5.9) kimin kimax t ≤ t ≤ t (5.10). I imaxu ≤ u ≤ u (5.11), where Max min and gi gi GIPP are generator node I and its active output, and max min and gi gi gi q q are the reactive output and its upper and lower limits, respectively; Max min, Ci CiQ Q are the input capacity of reactive power compensation equipment and its upper and lower limits respectively. Max min, ki ki kiT T T are the transformation ratio of on-load voltage regulating transformer and its upper and lower limits respectively; Max min and ii ii iu u u are the upper and lower limits of the voltage amplitude of node I, respectively.