The focus of this paper is to present performance indices for unbalance radial feeder having different characteristic and composition of time varying static ZIP load models. These provide a framework for benchmarking of distribution automation projects. 15 minutes characteristics time interval for load flow and load modeling are considered to meet smart grid implementation criterion. A forward-backward sweep method is employed for load flow solution. Developed performance indices were illustrated on modified IEEE 37 node test feeder. Performance indices are useful for analysis, operational, planning and integration of stochastic renewable sources.
In a deregulated environment for making the correct investment decisions, a power flow computation is very important for operational, design and planning point of view. For adequate analysis and maximum benefit from the emerging smart grid technologies, an efficient load flow solution and detailed modeling of distribution feeder required. An efficient power flow analysis power-flow solution must be able to model the special features of distribution systems in sufficient detail. The distribution system has following distinctive properties:
High resistance to reactance ratio,
Radial structure,
Extremely large number of branches/nodes, and
Unbalanced and multi-phase (usually three phases).
More recent methods are based on the concept of doing backward and/or forward sweep, and take into account the radial structure of distribution systems. G. W. Chang, S. Y. Chu, and H. L. Wang [
Consideration of voltage-dependency characteristics and composition in load modeling provides the actual behavior of the loads in response to voltage variations.
15 minutes characteristics time interval load curve for the industrial, commercial and residential loads are developed to meet smart meter measurement criterion.
Unbalance charactertics are accounted in load and feeder component modeling.
This algorithm gives node voltages as well as their angle and can handle the effect of charging capacitances of the network. So this method can be used for reactive power compensation studies.
Developed performance indices computed for whole day. These performance indices are substation reserve capacity, voltage unbalance factor, feeder power loss to load ratio, branch loading, voltage deviation, and power factor.
If detailed load data are not available to a utility, at least a rough approximation is believed as a better option rather than none, since it brings attention to the critical characteristics of loads and their relative compositions, diversity, etc. Load modeling aims to characterize the form of daily use of electricity by various types of consumers connected to each load point. For this one has to specify type of consumer, correspondent load model and daily load curve. Aggregated load at each load point are a summation of consumption values of each type of consumer (residential, commercial, industrial, or other). This paper has considered that each load point has a mix of time varying load for industrial, residential and commercial consumers in a random proportion. Consumers are generally grouped into three major classes: residential, commercial and industrial. In this paper IEEE 37 node test feeder assumed to be supplying power to a delta connected load at each node having a mix of industrial, residential, and commercial type consumers.
The spot load at each node k shared among industrial, residential and commercial consumers and participation of each category load is characterized by relevant factors. The specific value of aforesaid relevant factor is generated by normalization of normally distributed pseudorandom numbers at each 15 minutes characteristics time interval h such that following condition must be satisfied for all load buses.
Critical load characteristics for each type of consumers may express by means of the sum of constant impedance (Z), constant current (I) and constant power (P) load models. In this paper voltage dependency of active and reactive power consumption are modelled by three components: constant impedance (Z), a constant current (I) and a constant power (P) injections. Each category consumers have consumer constant Impedance [Z], constant current [I], and constant power [P] components [
The calculation of load current is carried out as mentioned in W. H. Kersting [
ZIP active and reactive load compositions for each node k at each 15 minutes characteristics time interval h are characterized by following relevant factors.
As measurements of individual consumers load are taken by electronic equipment that accumulates them in programmed intervals by the utilities (1, 5 or 15 min) and this accumulation is called average power (demand) for these intervals. In this paper, the load curves defined at intervals of 15 minutes were developed, resulting therefore in 96 intervals in daily curve. Modeling load patterns of residential, commercial and industrial customer are carried out by using daily load profiles reported in [
Load Class | Constant Power | Constant Impedance | Constant Current |
---|---|---|---|
Residential | 80% | 19% | 1% |
Commercial | 60% | 40% | 0% |
Industrial | 80% | 20% | 0% |
In this section all components of a power distribution system are modeled as two-port network elements. For accurate modeling, distribution system can be broken into “series” components and “shunt “components. Series component of feeder is shown in
Series components of a distribution system are line segments, switches, transformers and voltage regulators, while shunt components of comprise of spot loads, distributed loads and capacitor banks. Both series and shunt components are modeled using ABCD parameters [
Characterization of each component of feeder is fairly standardized for all components without having to actually check the type of the device.
The feeder line modelling and the line parameters can be obtained by the method developed by Carson and Lewis [
The impact of the numerous transformers in a distribution system is significant. Transformers affect system loss, zero sequence current, grounding method, and protection strategy. Distribution transformer model as shown in
A three-phase transformer is presented by two blocks as shown in
where
It must be noted that above coefficients are machine dependent constants. For this paper, core losses are represented by the functions and typical constants shown above. Per unit leakage admittance matrix are used for two port model [
where
Voltage regulator and shunt capacitor banks are commonly used in distribution systems to help in voltage regulation and to provide reactive power support. In this paper, the voltage regulator and capacitor are not modelled.
Connectivity matrix establishes a relationship between two buses connecting through a line segment. A simple distribution system as shown in
First Column of the connectivity matrix denotes number of an outgoing line segment from each sending bus. Second, fourth and sixth column of the connectivity matrix represent receiving end bus from each sending bus, while third, fifth and seventh column of the connectivity matrix represents line segment connect above to receive bus to each sending bus. If any connectivity failed to present, the corresponding element in above matrix will contain null-entries.
The forward/backward sweep (FBS) method is highly related to the physical models and includes following steps.
a) Initialization of Node Current: Firstly, all the buses are initialized to the voltage specified at the source bus of the network which is usually 1Ð00 p.u.
b) Backward sweep: This compute branch current from end nodes and update nodal currents and voltages from end node to the source node, passing through the series feeder components
c) Forward sweep: This compute node voltage from source nodes to end node and update nodal voltages from source node to end node, passing through the series feeder components.
d) Compute Error: The difference between calculated and specified complex bus voltages for source node is referred as the error value in per unit.
e) Convergence Criterion: For load flow convergence, process adopted here is a distributed radial backward/forward sweep with convergence criterion as seen below.
If above the relationship does not satisfied them, change in apparent power at last nodes of main feeder, laterals and sub laterals are calculated using below Equations.
Update each last node k voltage using Equation (33) for the next iteration.
This Forward sweep (FS) and Backward sweeps (BS) process is continued till load flow convergence. The following constraints are considered in the formulation of the problem.
All service zones are connected and served by the feeder.
Radial network configuration must be maintained for distribution feeders.
Propose algorithm is based on the forward-backward sweep method and implemented through the following steps.
Step 1: Read input data regarding the unbalanced radial distribution feeder and generate connectivity matrix
Step 2: Generate a daily load profile for various categories of consumers connected each node for each 15 mintues characteristics time interval.
Step 3: Normalization of randomly generated load relevant factor for various categories consumers at each node and decompose each load category connected to each node into three different load models for each 15 minutes characteristics time interval.
Step 4: Set characteristics time interval = 1 and tolerance.
Step 5: Initialize the variables and voltage at each node; correspondingly calculate total load current at each bus.
Step 6: Initialize iteration. Assign initial voltages = 1 PU for each bus.
Step 7: Compute backward sweep method and update/compute all bus currents from bus load from the last node to the first node), passing through the series feeder components
Step 8: Compute forward sweep method by assigning bus voltage = 1 pu for substation and update/compute all bus voltage from bus load from the first node to the last node.
Step 9: Compute error using Equation (31).
Step 10: Check convergence criterion for two consecutive iteration Equations (32). If criterion is not satisfied go to the next step, otherwise go to step 12.
Step 11: Update each last node voltage using Equations (33) and (34) and go to step 7.
Step 12: Compute all performance indices. Check whether the characteristics time interval is less than 96. If yes increase characteristics time interval by 1 and go to step 5, otherwise go to the next step.
Step 13: Store results.
Development of indices is beneficial to evaluate feeder performance over an each 15 minute time interval. Formulation of performance indices is described below.
Apparent Power unbalance Indice [
Unbalanced three-phase loads or no uniformly spread single-phase loads, time-varying operations will lead to voltage variation and unbalance at three-phase equipment terminals. The effect of voltage unbalance is quite severe and voltage unbalance factor (VUF) [
Measurement indice can be developed to assess the distribution feeder performance in terms of substation reserve capacity [
Ratio of feeder losses to the total loads [
Voltage deviation Indice [
This Indice [
The power factor has been increasingly recognized as one of the principal measures of efficiency and improves the voltage profile. Residential, commercial loads have a low power factor and reactive power for these loads is delivered from the source. Industrial consumers are compelled to compensate the reactive power otherwise are penalized (power factor surcharge penalty).To minimize the negative effects of low power factor on feeder power distribution on the feeder lines, it is imperative to record what time of the day the node has lower power factor.
In order to illustrate the validity and effectiveness of the proposed method, modified IEEE 37 node test feeder [
Twenty-four hourly random load scenarios at each node is a combination residential, commercial and industrial consumer having ZIP load models. Voltage regulator is also removed.
As mentioned in
Increased feeder loading also increases feeder loss as shown in
A general trend of deviation of voltage magnitude and voltage unbalance from their nominal values was observed along the feeders, especially with feeders supplying greater distances, loads, PV generation, and their unequal connection between phases. As mentioned in
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An efficient load flow algorithm for the unbalance radial distribution feeder with voltage sensitive and time varying load is developed. Proposed algorithm is tested on highly unbalance IEEE 37 node test feeder and found good convergence property makes it’s suitability for large-scale distribution systems. Characteristics and composition of residential, industrial and commercial consumers are accounted through voltage dependent and time varying load models, which plays an important role in the planning and operation of distribution networks. Low
computational time, storage of all data in vector form and connectivity matrixes has great potential to be used in on-line operation. Performance indices and 15 minutes characteristics time interval load modeling finds suitability for benchmarking of distribution automation projects. The proposed algorithm can also be an efficient tool for evaluating the impact of integration of stochastic renewable energy resources and loads with large variance in the smart distribution networks.