State-matrix-independent dynamic process estimation method in real-time for weakly observable measurement nodes without PMU

A method for estimating a dynamic process of nodes without Phasor Measurement Unit (PMU) in real time in a power grid using only dynamic measurements of nodes with PMU and Supervisory Control And Data Acquisition (SCADA) measurement data or state estimation data, which is independent of grid parameters and renewal of state matrix, without relying on the estimated nodes to be observable when the estimated nodes and the nodes with PMU are in a same electric island,

• wherein the method uses recursive least square for locating a linear combination relationship between variances of measurement nodes without PMU and variances of measurement nodes with PMU from quasi-stable state data sequence during a period of time, including SCADA measurement data or state estimation data at a number of consecutive time points, and subsequently estimating the dynamic process of the node without PMU in real time based on the linear combination relationship,
• the method comprising steps:
• Step 1:
• selecting, by at least one processor of a wide area measurement system (WAMS) server in a control center for the power grid, nodes i without PMU and their physical quantities Xi of which dynamic process to be estimated, wherein the physical quantity is one selected from a set comprising voltage magnitude, voltage phase angle, current magnitude, current phase angle, active power, reactive power, frequency, and rotating speed of generator;
• Step 2:
• for each node i without PMU, selecting, by the at least one processor, a set of nodes with PMUs Spmu-i for estimating the dynamic process, the set of nodes comprising a number of nodes with PMU from which the electric distances to the node i without PMU are nearer than others, while ensuring nodes with PMU are in a same electric island with the node i to be estimated, the nodes in the set Spmu-i are selected according to node impedance matrix calculated offline in typical operation mode, or designated by operator, or determined by online automatic search according to minimum number of line segments that connect the node with PMU to the node without PMU, the measurements of the nodes in the set Spmu-i which have the same measurement type as that to be estimated will be selected and used in the dynamic process estimation;
• Step 3:
• initializing, by the at least one processor, linear combination coefficients bij between the variance ΔXi of Xi of node i without PMU and the variances ΔXj of the corresponding measurements Xj of the relevant nodes with PMU, where Xi being quantity to be estimated and jεSpmu-i,and initializing the parameters for recursive least square method;
• Step 4:
• for each measurement Xi, according to the measurement values at sampling time Tk of SCADA or the calculation values at the time Tk of state estimation, and to corresponding historical values, obtaining, by the at least one processor, the linear combination coefficient bij(Tk) between the variance ΔXi(Tk) of the quantity to be estimated of the node without PMU and the variance ΔXj (Tk) of the corresponding measurements of the nodes with PMU at the time Tk, where jεSpmu-i, and index k is a integer starting from 0, and denotes the number of SCADA sampling or state estimation calculation;
• Step 5:
• according to the linear combination coefficient bij(Tk) at the time Tk obtained in step 4 based on data from SCADA measurement or state estimation, calculating, by the at least one processor, the variance of Xi(t) at each time of PMU sampling relative to Xi(Tk) by the following formula:
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• where Xj(t) is the measurement value from the node j with PMU at PMU sampling time t, and subsequently obtaining the estimated value of quantity Xi of the node i without PMU at time t by the following formula:
• Xi(t)=ΔXi(t)+Xi(Tk),
• with
• Tk<t<Tk+1;
• and
• Step 6:
• when a new SCADA measurement data or state estimation data for time Tk+1 arises, processing returns back to the step 4 and the linear combination coefficient is updated.