This section describes the input-output variables, parameters and functions associated with a state estimator. Fig. 3. 1 shows how DSSE fits in DMS as a part of distribution Supervisory Control And Data Acquisition (SCADA) system [1] [2].
Fig. 3. 1: DMS and DSSE
SCADA is defined as a control system for real time monitoring of the network and setting the control functions required for DMS. The data acquisition is performed by instrumentation and communication facilities into the control room. The collected data from all over the network are passed through SE tools before they are monitored. Corrective and preventive actions are taken based on information obtained from SE tools, by various enabling control functions, e.g. Volt and VAr control, network reconfiguration,
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economic dispatch and load control [26]. The data is also preserved for future use, e.g. load modelling and condition monitoring.
As can be seen in Fig. 3. 1, the SE tool requires to be fed with dynamic data transmitted by sensor devices, along with static data that comprises network parameters. The SE tool usually involves an optimization model, which solves non-linear power flow equations with the input data, to filter out the erroneous information. Detailed discussions of the input-output variables, parameters and network components, comprising the SE building blocks, are provided in the following sections.
3.1.1 Input and Output Data
State Variables: The network state variables are phasor voltages, current flows, real and reactive power injections and flows.
The voltage magnitude and phase angle of connection points are referred to as 'primary states'. State values are often accompanied by a subscript to denote the associated node index. and refers to voltage and phase angle of node index And
present phase angle and voltage differences between node and node All other
state variables can be expressed as functions of the primary state values, provided network parameters are known.
Other state variables (current, power injection and power flow) are termed 'secondary states'. These are dependent on and related to the primary variables by injection and flow balance equations associated with the observed network model. The current, real and reactive power injection and real and relative power flow are generally presented by respectively, where the subscripts present associated node indices. The order of the subscripts indicates the direction of flow.
Measurement Data: The measurements are classified into three types: The real, pseudo and the virtual measurements.
Real measurements are actual telemeter data collected from sensors in real or near real time. The confidence in real measurement is calculated based on the sensor precision. The pseudo-measurements are load modelled data which are not real time
measurements. As pseudo-measurements are assumption-based data, the degree of trust in these is very low.
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The virtual measurements are also not actually measured, but their values are known with greater confidence. These are zero injection zero load nodes, open circuit breaker flow measurements, etc.
Each measurement is associated with a weighting factor that is calculated from the inverse of measurement variance, . is the standard deviation dependent on the precision of the corresponding measurement, which will be explained further in section 3.4.2. As measurement variances are smallest for virtual measurements and largest for pseudo-measurements, the weighting factor is highest for virtual and lowest for pseudo- measurements. The measurement values are also referred to as observed values in the statistical literature.
Static and Dynamic Data: The input data to the estimation tools are classified as static and dynamic data.
Static data normally remains unchanged over time, e.g. network topology, transformer impedance, line parameters (resistance, reactance, admittance and susceptance), location and types of sensors and measurement weights.
The dynamic data are measurement data that change over time. This includes voltage phasor values, current and power flows, power injections and transformer tap positions.
True and Estimated Values: Performances of an estimation tool can be verified by comparing true and estimated values.
The actual value of the state variable is termed the true value. However, the real time true value is not generally known in practice. The simulated information obtained from load flow analysis for a known condition of the system is considered as the true values. True values are also termed as 'real values' and 'load flow values'.
Estimated values are the information generated by the SE tool after rigorous data processing. These include both primary and secondary estimated state variables (as well as network parameters in case of generalized state estimation). In most cases, the SE tool executes an optimization process to estimate the primary state variables, and calculates the secondary state values using the most updated and estimates after achieving convergence within some criteria. The estimated values are afterwards provided to DMS functionalities.
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Nodes and Branches: In distribution systems, connection points are generally termed as nodes and power distribution lines as branches. One of the nodes is considered as a reference node and is referred to as the 'slack' node. The equivalent π model of a transmission/distribution line is generally considered in power system state estimation problems. A π model of a branch connecting node and is shown in Fig. 3. 2 [1].
Fig. 3. 2: The equivalent π model of transmission/distribution line
The main components of the π model are: series impedance , shunt admittance ,
. The suffices indicate the bus/node index being connected by the branch. When series
resistance and reactance are represented by and respectively, the following expressions are achieved for a branch connecting node and
The shunt conductance, and shunt susceptance are defined as follows
Transformers: A transformer equivalent model is required for modelling network equations. The transformers are also treated as an equivalent branch/line while considering tap position. The equivalent model with turns ratio 1:a and series impedance is
Vk ,ϴk Ikm k Imk Vm ,ϴm m zkm= rkm + j xkm ymmsh ykksh
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presented in Fig. 3. 3. Where represents transformer copper losses and is leakage reactance [1].
Fig. 3. 3: Transformer approximate equivalent model
Nodal Equations: The nodal formulation is obtained incorporating Kirchhoff's current law that introduces the admittance matrix, . The real and imaginary parts of are presented by and therefore . is defined as below for a node network,
Where
It is assumed that and . For a tap changing transformer,
the components of admittance matrix change as shown below:
Where is the transformation ratio from the receiving end side and as shown in Fig. 3. 3. For branches other than transformers, the value of is set to one in the admittance matrix.
Generators and Loads: Load and power generation are considered as power consumption and injection respectively. Therefore, their presence does not have any effect on the
Imk m Vm, ϴm k Ikm 1:a Vk, ϴk zt = rt + j xt
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network model and they are treated in the load balance equations. The sign convention for power injection is and for power consumption is . In all cases, the aggregated power of a node is taken into consideration.