，如图2-1 所示。
图2-2 П型等值电路图2-3 T 型等值电路在П型等，T 型等值电路如图2-4所示。
图2-7简单辐射网
时，如图所示：
图2-8 三点电网
例如：只有两个节点时，
图2-9 两点电网
所示：
以及电压相角偏差。
图4-1 8节点主干馈线配电网
a
b
a
b图4-2程序运行
and absolute values of voltages of nodes 1, 2 and 3 were fixed.
Fig. 1 – The Test scheme
In Figure 2, the boundary of existence
state is presented in angular coordinates δ1-δ2
positive value of the Jacobian determinant:
J
>
det()0
As a result of the power flow calculation
optimization, the angle values have been received, these values corresponding to the given capacities in Fig.2 (generation is positive and loading is negative).
For the state points which are inside
function (2) has been reduced to zero. For
boundary of the existence domain, objective function (2) has not been reduced to
Fig. 2 – Domain of Existence for a Solution
Fig.3 - Boundary of existence domain
In Fig.3, the boundary of the existence domain is presented in coordinates of capacities P1-P2. State points occurring
domain (6) have been set by the capacities
domain. As a
result of power flow calculation by minimization
method in optimization, the iterative process converges to the nearest boundary point. It is due to the fact that surfaces of the equal level of objective function (2) in coordinates of nodal capacities are proper circles (for threemachine system) having the centre on the point defined by given values of nodal capacities The graphic interpretation of surfaces of the equal level of objective function for operating point state with 13000 MW loading bus 1 and 15000 MW generating
12
Fig.4 - Paths of pulling the operation point onto the feasibility boundary IV. COMBINATION OF METHODS
If to compare the Newton’s method in optimization for power flow calculation with newton-Raphson using a Jacobian matrix, the method computational costs on each
iteration will be several times greater
filled up by nonzero elements 2.5-3 times greater than with Jacobian one. Each row of Jacobian matrix corresponding
corresponding to all incident buses of the scheme. Each row of Hessian matrix contains nonzero elements in the
neighboring buses, but also their
和2的容量，节点1、2的电压幅值是给定的。
图1 试验网络
的容量也与给定的容量不同。
图2 一个解的存在域
图3 存在域边界
中，存在域的边界在坐标系P1-P2中表示出来。
存在域（
边界上的状态点受到存在域外容量的限制。
以优化牛顿法为基础对最小化）进行潮流计算导致了迭代过程收敛到最近的边界点上，这是因为在同一水平上的目标函数（2）的边界是一个圆（对于三节点的系统）
W
这个圆的圆心与给定节点容量的点重合。
在图3
负载的节点1和15000MW注入功率的节点2
标函数边界作了图形解释。
当存在域边界奇异时，Hessian
）的行列式是一个接近于0的正数或者是雅克比矩阵行列
图4 工作点移到到可行性边界的路径
在潮流计算中如果将优化的牛顿法和利用雅克比矩阵的牛顿
逊法进行比较，我们会发现每一种方法的计算成本都是利用
金子那个非零元素填充的方法的2.5到3倍。
雅克比矩阵的每一行都与每一个节点对应，它的每一个非零元素都和某一个节点有关系。
的每一行的非零元素不仅与邻近节点相对应，而且与邻近节点的礼金节点对应。
然而，我们可以通过综合应用牛顿——拉夫逊法和优化牛顿法来补偿这些不足。
这意味着一部分节点可以用传统的牛顿法来计算，其它的节点可以用优化牛顿法来计算。
第一组的节点包括那些节点容量一般不会改。