A Simple Algorithm for Distribution System Load Flow ...

IEEE International Conference on R e c e n t A d v a n c e s a n d I n n o v a t i o n s i n E n g i n e e r i n g ( I C R A I E - 2 0 1 4 ) , May 09-11, 2014, Jaipur India

A Simple Algorithm for Distribution System Load Flow with Distributed Generation Sivkumar Mishra,Member IEEE IIIT, Bhubaneswar Odisha, India [email protected]

Debapriya Das, Member IEEE IIT, Kharagpur West Bengal, India [email protected]

Abstract—With increasing penetration of distributed generators (DG) in power distribution system, the distribution system load flow methods also need to be modified. Hence, the selection of suitable model of DG is important for the accurate load flow. In this paper, a simple algorithm for distribution system load flow with DG is proposed considering DGs as constant negative loads. The results for three test distribution systems are presented. Keywords—distributed generation, load flow, radial distribution systems, forward backward sweep

I.

INTRODUCTION

Load flow analysis is an important tool for power system planning and operation. However, conventional load flow methods such as Newton-Raphson or Fast Decoupled, which are typically designed for electrical transmission systems, are not suitable for power distribution system load flow analysis. Distribution networks are typically radial in nature and the feeders have high R/X ratio, hence are ill conditioned for such load flow. For various applications in distribution automation(DA) , several load flow methods have been developed in the last two decades [1], which are known as distribution system load flow (DSLF) methods. These methods exploit the special topological characteristics of the radial distribution networks (RDN). Among several DSLF methods, forward backward sweep (FBS) based methods are proven to be the most simple and fast method to carry out distribution system load flow [2]. The electric distribution system recently gained focus due to increasing penetration of distributed generators (DGs). Integration of DGs into the distribution systems alters the basic configuration from a passive system to an active one. This brings in certain benefits [3-4] as well as challenges [ 5-6]. The major technical benefits are [7]: •

Reduced line losses

•

Voltage profile improvement

•

Reduced emissions of pollutants

•

Increased overall energy efficiency

•

Enhanced system reliability and security

•

Improved power quality

•

Relieved T & D congestion

Subrata Paul Jadavpur University, Kolkata West Bengal, India [email protected]

Dugan [8] has enlisted fourteen challenges relevant to the analysis of DG in the distribution systems such as providing the screening applications, power flow solution, multiphase analysis, circuit model size, dynamics, harmonics, determining the value of DG, modeling sub transmission, assessing distribution reliability, loss analysis, protective device coordination, transformer connections etc. Thus, DSLF analysis with DG has attracted researchers to model DGs in the best possible way for suitable inclusion. In the light of above developments, in this paper the DG modeling issue for DSLF analysis is addressed. Considering a FBS based DSLF method with a novel bus identification scheme and constant negative power model of DGs, the results for three test distribution systems are presented. II.

LOAD FLOW FOR RADIAL DISTRIBUTION NETWORKS

Literature review [1] reveals that many methods are available to carry out load flow in a RDN. In this paper, a FBS based load flow algorithm [9] is considered. A. Modeling for a Balanced RDN Assuming balanced nature of RDN, an equivalent single phase feeder is shown in Fig.1. where a is the sending end bus, a’ is the receiving end bus, Ia is the feeder branch current and Zaa’ is the impedance of the branch feeder. The sending end voltage Va and the receiving end voltage Va’ are related as per (1).

Va' =Va - zaa.Ia

(1)

Fig.1. Equivalent single phase feeder

The loads connected to various buses of a distribution system are assumed as constant power loads. To implement the load flow the load connected at each bus is represented as equivalent current injections (ECI). Consider an arbitrary bus-i of a RDN (Fig.2) where a constant complex power load SLi=PLi+jQLi is connected. For bus i , the corresponding load current injection or equivalent current injection (ECI) ILi is computed as a function of the bus voltage Vi.

ILi = ( Pi − Qi) / Vi* ,

i = 1, 2............nb

(2)

IEEE International Conference on R e c e n t A d v a n c e s a n d I n n o v a t i o n s i n E n g i n e e r i n g ( I C R A I E - 2 0 1 4 ) , May 09-11, 2014, Jaipur India

Pi and Qi in this case are equal to the corresponding loads PLi and QLi at bus-i.

Fig.2. Equivalent current injection at bus-i

B. Bus Identification Scheme For a fast implementation of FBS based load flow, Mishra et al [10] have proposed several arrays for bus identification. These arrays are proven to be extremely useful for its reduced search time and fast implementation of load flow. For convenience, a brief review of the various arrays as proposed in [9-10] is presented here. An array of dimension double the number of branches (nbr) of a radial distribution system, namely, adb(2*nbr) is proposed, which stores all the adjacent or neighboring buses of each of the buses of the RDN. Two other arrays mf and mt of dimension ‘nb’, where nb = number of buses in a RDN, are proposed, which act as pointers of the adb array. These arrays in turn govern the reservation of allocation of memory locations for each bus, i.e mf and mt point to the starting and end addresses in the adb array respectively. Similarly, all the previous buses are identified and stored in an array pb. These arrays can be formed from the general system data of a RDN. Two more arrays, namely, nsb and sb are proposed. The array nsb stores the number of subsequent buses corresponding to various branches of a RDN and has a dimension equal to nbr. The sb array stores all the subsequent buses to each of the the branches of the system. Two pointer arrays mfs and mts are also introduced to point to the start and end memory locations in sb array. The arrays mfs, mts, nsb and sb can be formed from the input data of a RDN. MATLAB codes to form all the proposed arrays from the input data are presented in [10]. The general storage and pointer operations of these arrays are explained in Fig.3 and Fig.4 with reference to a fictious RDN of nb buses and nbr branches.

Fig.3. Storage and pointer operation of mf, mt and adb arrays

Fig.4. Storage and pointer operation of mfs, mts, sb and nsb arrays

C. FBS based DSLF FBS based DSLF is a well established method. This method exploits the various topological specialties of the RDN and is quite fast as well as simple to implement. This is an iterative method and each iteration consists of two steps. In the first step, starting from any end bus the RDN branch currents are gradually calculated till the substation bus or the root bus. This is termed as a “backward sweep”. In the second step i.e forward sweep, starting from the substation bus all subsequent buses up to the end buses are updated using (1). This equation uses the previously calculated branch currents in the backward sweep. This process continues till voltage magnitudes converge. The current in any branch of a RDN can be calculated using (3).

I i = Current of 'i ' th branch=

∑

i = all subsequent buses to j

ILi

(3)

A complete flow chart of the FBS based DSLF using the proposed bus identification scheme is presented in Fig.5. III.

MODELING OF DGS FOR DSLF

Distributed Generation (DG) is an electric active power source connected directly to the distribution network or customer side of the meter [11]. However, DG is not a new concept but it is an emerging approach for providing electric power in the heart of the power system [4]. It encompasses several technologies which can be broadly categorized as renewable or nonrenewable. Renewable DG includes small hydro plants, wind turbines, photo voltaic cells, fuel cells, geothermal power plants, biomass power plants, tidal power plants, wave power plants etc., whereas non renewable category includes conventional fossil fuel based generators, micro turbines, CHP plants etc. In this context, a broader term such as Distributed Energy Resources(DER) can be defined, which refers to the electric power generation resources that are directly connected to the medium voltage(MV) or low voltage (LV) distribution systems and it includes both generation units

IEEE International Conference on R e c e n t A d v a n c e s a n d I n n o v a t i o n s i n E n g i n e e r i n g ( I C R A I E - 2 0 1 4 ) , May 09-11, 2014, Jaipur India

(DGs) and energy storage technologies like batteries, fly wheels, super conducting magnetic energy storage etc. [12].

A. PQ Model of DGs Since DGs are normally smaller in size when compared with the conventional power sources, the constant PQ model is commonly found to be sufficient for the distribution system load flow analysis [17]. This model is adequate because DGs typically not permitted to regulate the voltage. Instead, they regulate power and power factor, hence modeled as negative loads [8]. Most of the DGs are equipped with automatic voltage regulators (AVR) and operate in constant power output mode. Therefore, voltage output level of the DGs are same as system voltage. Hence, it is preferable to handle the interconnection nodes of DGs as the PQ node model rather than the PV node model as shown in Fig.6 [18].

Fig.6. The models of load and DG as their power factor

B. FBS based Load Flow with DG Units With DGs modeled as negative loads, the equivalent loads at bus-i can be expressed as:

Pi = PLi − Pgi

(4-a)

Qi = QLi − Qgi

(4-b)

PLi and QLi are the constant power loads connected at bus -i and Pgi and Qgi are the real and reactive powers injected by the DG connected at bus-i respectively. The ECIs then can be calculated at all the buses using (2). The backward and forward sweeps are then followed as per the flow chart in Fig.5 to execute the load flow.

Fig.5. Flow chart of DSLF

One of the challenges [8] considering DG in the analysis and design of distribution systems, is the power flow solution taking into account the proper modeling of embedded DGs. Teng [13] has proposed three types of mathematical models of DGs for load flow analysis i.e a) constant power factor model for synchronous generator and power electronics based DGs b) variable reactive power model for induction generator based DGs and c) constant voltage model for large scale controllable DGs. Depending on the control, the DG may be set to output power at either constant power factor for small DG or constant voltage for large DG. Thus, two types of DG models need to be developed: constant PQ modeled as negative loads with currents injecting into the node and PV nodes [14]. The model of DGs as PV or PQ depends on its operational mode and control characteristics [15]. In reference [16], three models DGs i.e a) induction generator model b) synchronous generator model and c) power electronics interfaces, are presented.

C. Test Distribution Systems with DG Units Three test distribution systems are considered to validate the model and the method described in this paper. Fig.7 shows a 12 bus radial test system with DGs connected at bus -6 and 12 and the system data is presented in Table-I. Fig.8 shows the second test radial distribution system of 33 bus [19] and DGs are connected at bus 5 and 18. Pg and Qg of these DGs (both test systems) are considered to be 10% and 7% of total active power and reactive power load of the corresponding system respectively. The third test distribution system is a 69 bus radial system [20-21] with six DGs connected at bus-11, 22, 31, 38, 53 and 58 as shown in Fig.9.

Fig.7. 12 bus test distribution system

IEEE International Conference on R e c e n t A d v a n c e s a n d I n n o v a t i o n s i n E n g i n e e r i n g ( I C R A I E - 2 0 1 4 ) , May 09-11, 2014, Jaipur India

Fig.9. 69 bus test distribution system TABLE II. Bus no. 2 3 4 5 6 7 8 9 10 11 12

12-BUS SYSTEM LOAD FLOW RESULTS Conv. volt.. mag. (p.u) Without DG With DGs 0.9943 0.9954 0.9890 0.9913 0.9806 0.9849 0.9699 0.9773 0.9666 0.9751 0.9638 0.9729 0.9529 0.9647 0.9497 0.9625 0.9469 0.9610 0.9460 0.9608 0.9458 0.9611

Fig.8. 33 bus test distribution system

IV.

RESULT AND DISCUSSION

The proposed DSLF algorithm is implemented in MATLAB (R2010a) and simulated in a 2.4GHz Intel Core i3 system with 2GB RAM. Convergence tolerance is considered as .0001p.u. The converged voltage magnitudes for 12 bus test system is presented in Table-II. The voltage profiles for the three test distribution systems (with and without DGs) are shown in Fig. 10, 11 and 12. Number of iterations, execution times and overall real power losses for the three test distribution systems are presented in Table-III. TABLE I.

Fig.10. Voltage profiles of 12 bus test distribution system

12-BUS SYSTEM DATA Fig.11. Voltage profiles of 33 bus test distribution system

SE Bus

RE Bus

Br. No.

r (Ω)

x (Ω)

P (kW)

Q (kVAR)

1 2 3 4 5 6 7 8 9 10 11

2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11

1.0890 1.1858 2.0933 3.1823 1.0890 1.0043 5.6386

0.4598 0.4961 0.8712 1.3310 0.4598 0.4114 1.5972

2.0933 2.8919 1.5125 1.2342

0.8712 0.8228 0.4235 0.3509

60 40 55 30 20 55 45 40 35 40 15

60 30 55 30 15 55 45 40 30 30 15

Fig.12. Voltage profiles of 69 bus test distribution system

IEEE International Conference on R e c e n t A d v a n c e s a n d I n n o v a t i o n s i n E n g i n e e r i n g ( I C R A I E - 2 0 1 4 ) , May 09-11, 2014, Jaipur India TABLE III. COMPARISON OF LOAD FLOW RESULTS [4] W. El-Khattam, and M.M.A Salama, “ Distributed generation technologies, definitions and benefits,” Elect. Pow. Sys. Res., vol. 71, 12 bus RDN 33 bus RDN 69 bus RDN pp. 119-128, 2004. [5] P.Dondi, D.Bayoumi, C.Haederli, D.Julian, and M.Suter, “ Network without With without With without With integration of distributed power generation,” J. Pow. Sourc., vol. 106, DG DG DG DG DG DG no.1-2, pp. 1-9, 2002. No. [6] J. A. Pecaslopes, N. Hatziargyrious, J. Mutale, P.Djapic, and N.Jenkins, 4 3 4 4 4 4 of “Integrating distributed generation into electric power systems: a review iter.s of drivers, challenges and oppurtunities,” Elect. Pow. Sys. 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