Distributed Volt/Var Control in Unbalanced Distribution Systems with Distributed Generation Ahmad Reza Malekpour, Anil Pahwa and Balasubramaniam Natarajan Department of Electrical and Computer Engineering Kansas State University Manhattan, KS, USA e-mail:
[email protected],
[email protected],
[email protected] Abstract— Future power distribution systems are expected to have large number of scale smart measuring devices and distributed generation (DG) units which would require real-time network management. Integration of single-phase DG and advanced metering infrastructure (AMI) technologies will add further complexity to the power distribution system which is inherently unbalanced. In order to alleviate the negative impacts associated with the integration of DG, transformation from passive to active control methods is imperative. If properly regulated, DGs could provide voltage and reactive power support and mitigate the volt/var problem. This paper presents a distributed algorithm to provide voltage and reactive power support and minimize power losses in unbalanced power distribution systems. Three-phase volt/var control problem is formulated and active/reactive powers of DGs are determined in a distributed fashion by decomposing the overall power distribution system into zonal sub-systems. The performance is validated by applying the proposed method to the modified IEEE 37 node test feeder. Keywords—Power distributed generation
distribution
system;
optimization;
I. INTRODUCTION Worldwide interest in distributed generation (DG) is quickly rising, driven by increased governmental support incentives, via regulations as well as global environmental concerns [1]. DGs are installed near load centers to improve the system reliability and reduce power losses. Integration of DG in power distribution system imposes many challenges in terms of protection, power quality and voltage regulation [2][4]. Moreover, massive integration of DGs might have negative impacts on the transmission system such as transmission system line losses, reverse power flow from the distribution system, operational procedures and capacity margin [5]. One of the fundamental operating requirements of power distribution system is volt/var control where its primary purpose is to improve voltage profiles along the feeder and reduce real power losses under all loading conditions. Considering the growth of DG in the U.S. [6], a wellcoordinated control of DG will play a significant role in mitigating the issues and providing volt/var support.
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DG control schemes fall into two categories: centralized [7]–[12], and distributed [13]–[16]. The centralized approaches are based on optimal power flow (OPF) techniques [7] while distributed approaches are mostly based on local DG active and/or reactive power control. In [8], mixed integer linear programming is used to formulate the volt/var optimization including transformer load tap changers (LTC), switchable capacitors, and reactive power of DGs. In [9], the LTC and step voltage regulators (SVRs) were used to find the optimal voltage in distribution systems based on centralized control. Optimal management of the reactive power by controlling the inverters of PV units was proposed in [10]. Probabilistic volt/var control was studied in [11] considering the uncertainty associated with renewable DGs. In [12], a comprehensive centralized approach was presented for voltage constraints management in active distribution grid. In [13], a distributed automatic voltage control was introduced for voltage rise mitigation due to DG integration in distribution systems. A decentralized control of DG for voltage and thermal constraint management was presented in [14]. Combined local and remote voltage and reactive power control in the presence of induction DG machines was presented in [15]. In [16], an automatic distributed voltage control algorithm based on sensitivity approach is used to control the node voltages regulating the reactive power injected by DGs. The majority of the researchers use a balanced network model to handle the volt/var control problem [7]-[19]. However, power distribution systems are unbalanced in nature composed of unbalanced three phase and single phase feeders and laterals serving customers through unbalanced line configurations with different phase loading levels [20]. Moreover, deploying single phase DGs could worsen the imbalance in power distribution system. If DG comes to play a significant role in the future, power distribution system optimization studies fail to provide accurate solutions using the single phase network models. In this regard, [21] proposed a three phase OPF to determine the tap changer and capacitor setting in power distribution system. In [22], a three phase OPF to mitigate the voltage unbalance is developed. In [23],
three-phase OPF is introduced to solve the volt/var control problem where the goal was to minimize reactive power of DG units while satisfying operational constraints. Distributed control methods are inherently locally optimal due to the lack of full system information. Centralized approaches provide the best performance possible at the expense of significant investment in meters, communications, control systems and computations. Hence, solving centralized OPF in medium and large scale power distribution system with high proliferation of DG is computationally impractical. In this paper, a distributed three-phase OPF for loss minimization problem is proposed to reduce the computational burden by decomposing the overall power distribution system into zonal sub-systems. OPF is solved in each zone and multiple OPFs are coordinated through an iterative process by exchanging a modest amount of data between adjacent zones. The goal is to find the active/reactive power of DGs such that power loss is minimized while meeting system constraints. II. CENTRALIZED VOLT/VAR CONTROL The centralized volt/var control problem including DG units is mathematically formulated as a nonlinear optimization problem involving the minimization of predefined objective functions while regulating the voltage over feeders and scheduling the active/reactive power control of DGs as follows: •
Power losses ͳ ݂ ൌ ୧୨ୟୠୡ ୨୧ୟୠୡ ሺͳሻ ʹ
ǡஷ
subject to the following equality and inequality constraints. • ܲ
Three phase distribution power flow equations: ே
ൌ ܸ ܸ ܻ
ሺߠ െ ߜ ߜ ሻሺʹሻ ୀଵ ே
ܳ ൌ ܸ ܸ ܻ ሺߠ െ ߜ ߜ ሻሺ͵ሻ ୀଵ
• • •
•
െ ܲ ሺͶሻ ܲ ൌ ܲீ ܳ ൌ ܳீ െ ܳ ሺͷሻ Bus voltage limits: ܸ ܸ ܸ௫ ሺሻ Distribution line limits: ܲ ܲ௫ ሺሻ Active/reactive power limits of DG generators: ௫ ܲீ ܲீ ሺͺሻ ܲீ ௫ ሺͻሻ ܳீ ܳீ ܳீ Phase imbalance limits: ଶగ ɂఋ ߜ െ ߜ ሺͳͲሻ
ɂఋ ɂఋ
ଷ ଶగ
ଶగ ଷ
ଷ
ߜ െ ߜ ሺͳͳሻ
൏ ߜ െ ሺߜ
ߜ
൏
ߜ
൏
ଶగ
ሻሺͳʹሻ
ଷ ߜ ሺͳ͵ሻ
݂: The objective function ܰǣ Number of buses ܲ ǡ ܳ : Three phase active and reactive power injected at bus i ܸ : Three phase voltage magnitude at bus i ܻ : Three phase magnitude of (i, j) element of YBus admittance matrix ߠ : Three phase angle of (i, j) element of YBus admittance matrix ߜ : Three phase angle of voltage at bus i ܸ ௫ ǡ ܸ : Maximum and minimum voltage magnitude ܲ௫ : Maximum active power flow in line ij ܲ : Three phase active power flow in line ij ǡ ܳீ : Three phase active and reactive power injected at ܲீ bus i ௫ ௫ ǡ ܳீ : Minimum and minimum active and reactive ܲீ power generation of DG at bus i : Three phase active and reactive power load ܲ ǡ ܳ demand at bus i
ɂఋ : Phase imbalance tolerance ܲ ǡ ܳ and ܲீ ǡ ܳீ could be single-phase active/reactive power while line configuration and phase imbalance are reflected in ܻ ǡ ߠ , respectively.
The presented OPF formulation is a non-convex optimization problem. The branch and bound method could solve the problem and provide global solution at the expense of high computational burden which is impractical for realtime volt/var control applications. An alternative is using Taylor series expansion to transform the problem to a convex form. The detailed description of converting to convex form, solving the problem, and comparison of solutions with the branch and bound method is provided in [23]. However, the real-time volt/var control calls for faster algorithms to deal with the rapid load variations or intermittency in renewable generators. III. DISTRIBUTED VOLT/VAR CONTROL A. Zonal decomposition of power distribution system In this section, zonal decomposition method is introduced to reduce the OPF computational cost and come up with fast optimal solutions for the volt/var control problem. As shown in Fig. 1, power distribution system can be divided into two overlapping zones where border bus i connects zones 1 and 2. The vector of variables in overlapping zone is denoted by y. Vector ܠଵ represents the OPF variables in zones 1 and not included in zone 2. Similarly, vector ܠଶ denotes the OPF variables in zones 2 and not included in zone 1. In summary,
(ܠଵ , ܡଵ ) and (ܡଶ , ܠଶ ) are the set of state vectors in zones 1 and 2, respectively. For simplicity, it is assumed that no generator is installed at the border bus. However, generators at the border bus could be easily embedded into formulation. The entries in y could be the voltage magnitude and phase angles in bus i or the active/reactive powers flowing through the bus i.
(a) Before decomposition
process is initiated to coordinate the decomposed subproblems. The iterative process is repeated until specified termination criteria are met i.e. deviation between duplicated variables in border buses are less than ߝ. ȁܡଶ െ ܡଵ ȁ ߝሺͳͺሻ The following steps are performed to apply the proposed zonal decomposition technique: Step 1- Based on the geographical distribution of power distribution system, apply zonal decomposition using the model proposed in Fig. 1. Step 2- Duplicate the border buses and introduce pseudo generation concept. Step 3- For each zone, solve volt/var optimization using (1)-(13). Step 4- Exchange the calculated active/reactive power of pseudo generators at boundary buses. Step 5- Check if the deviation between duplicated variables in border buses are less than ߝ. If satisfied, stop the iteration and provide optimization results. Otherwise, go to step 3. IV. SIMULATION RESULTS
(b) After decomposition Figure 1. Zonal decomposition of power distribution system (a) Before decomposition (b) After decomposition.
B. Mathematical formulation Considering the variables defined for zones 1 and 2 and overlapping zone, the optimization problem can be written as: ݂ଵ ሺܠଵ ሻ ݂ଶ ሺ ܠଶ ሻሺͳͶሻ
A. Network description The modified IEEE 37 node test feeder [24] is used to demonstrate the performance of proposed approach. As shown in Fig. 2, the system is partitioned into three zones according to the geographical boundaries.
ሺܠǡܡሻ௭ଵǡሺܡǡܢሻ௭ଶ
where ݂ଵ and ݂ଶ are the objective functions in zones 1 and 2, respectively. The optimization problem could be divided into two optimization sub-problems by duplicating the border bus ݅ to buses ݅ଵ and ݅ଶ . The power flowing through the border bus ݅ can be interpreted by putting pseudo generators ܩభ and ܩమ on buses ݅ଵ and ݅ଶ , respectively, where the pseudo generators could either generate or absorb power. In order to model the coupling effect of sub-problems, variables ࢟ଵ and ࢟ଶ are defined as copies of ࢟ representing generated or absorbed power from pseudo generators ܩభ and ܩమ , respectively. The decomposed problem matches the original problem at the optimal point if there is no gap between ࢟ଵ and ࢟ଶ . ࢟ଵ െ ࢟ଶ ൌ Ͳሺͳͷሻ The OPF in zone 1 can be mathematically expressed as
ܠభ ǡܡభ ௭ଵ
݂ଵ ሺܠଵ ሻ ߙଵ Ǥ ሺܡଵ െ ܡଶ ሻଶ ሺͳሻ
where the first term denotes the objective function in zone ͳ and the second term represents the penalty associated with the gap between ࢟ଵ and ࢟ଶ weighted by the penalty coefficient ߙଵ . It is worth noting that ࢟ଶ is considered as a fixed parameter for optimization in zone 1. Similar expression can be extracted for zone 2. ݂ଶ ሺ ܠଶ ሻ ߙଶ Ǥ ሺܡଶ െ ܡଵ ሻଶ ሺͳሻ ܠమ ǡܡమ ௭ଶ
The proposed strategy is applicable for decomposing the power distribution system into several zones. Once the loss minimization problem is set up for all zones, an iterative
Figure 2. Modified IEEE 37 node test feeder
In the original system, approximately one third of the total system load is connected to node 2. In order to highlight the effect of DGs in loss minimization and reducing the grid effects as the major source of power, two third of the load connected to node 2 are moved to node 24. All loads are assumed to be constant power star connected spot loads and the tap changer voltage is set to 1 p.u. The minimum and maximum phase imbalance range between any phases is set to ͳͳͷι and ͳʹͷι , respectively. Eight single-phase 25 kW DGs are connected with variable power factor capability ranging from 0.9 leading to 0.9 lagging. The accepted voltage range is set to be from 0.95 to 1.05 p.u. The maximum mismatch between border variables ߝ is set to 0.001. The penalty coefficients ߙଵ and ߙଶ are set to 1. The studies were implemented in MATLAB using an Intel(R) Core(TM) i7, 3.4 GHz personal computer with 8 GB of RAM.
the proposed approach, results obtained from the proposed framework are compared with the centralized approach. Table I shows the active/reactive power dispatch of DGs from both centralized and proposed distributed approach. It can be seen that the results from distributed method are very comparable with those obtained via centralized method. In particular, the maximum errors between the two models are 1.7% and 4.6% for DG active and reactive power generation, respectively. The execution times are 79 seconds for distributed approach and 149 seconds for centralized approach. Fig. 3 shows the converged deviation between the optimal active and reactive power flowing through node 9, respectively. The optimum values are obtained after 4 iterations where the deviation between duplicated variables at bus 9 becomes less than ߝ.
B. Results Loss minimization problem is studied using the proposed zonal decomposition approach. To cross check the validity of
(a) Active power mismatch
(b) Reactive power mismatch
Figure 3. Converged deviation between active and reactive power flowing through node 9. (a) Active power mismatch (b) Reactive power mismatch TABLE I. ACTIVE (KW) AND REACTIVE (KVAR) POWER GENERATION OF DGS USING CENTRALIZED AND DECENTRALIZED APPROACHES
8 12 14 16 22 26 34 37
ୟ 22.923 0 0 0 0 0 0 0
ୠ 0 0 0 0 0 0 23.192 23.203
Centralized ୡ ୟ 0 1.5038 23.752 0 23.752 0 23.752 0 23.762 0 22.956 0 0 0 0 0
0 0 0 0 0 0 1.0119 1.1127
ୡ 0 3.3701 3.8402 4.773 5.254 1.729 0 0
ୟ 22.756 0 0 0 0 0 0 0
ୠ 0 0 0 0 0 0 23.085 23.101
Decentralized ୡ ୟ 0 1.4419 24.074 0 24.074 0 24.074 0 24.174 0 22.7455 0 0 0 0 0
0 0 0 0 0 0 0.9941 1.0727
ୡ 0 3.229 3.7596 4.5928 5.2495 1.6479 0 0
TABLE II. ACTIVE (KW) AND REACTIVE (KVAR) POWER GENERATION OF DGS USING CENTRALIZED AND DECENTRALIZED
Centralized ୪୭ୱୱ (kW) ୪୭ୱୱ (kVar) σ (kW) σ (kVar) ୱ୪ୟୡ୩ (kW) ୱ୪ୟୡ୩ (kVar)
(a) Active power mismatch
Decentralized
Phase A
Phase B
Phase C
Phase A
Phase B
Phase C
18.995
9.593
26.074
19.075
9.678
25.926
6.881
3.153
8.966
6.9473
3.236
8.8336
22.923
46.394
117.975
22.756
46.187
119.142
1.5038
2.1246
18.966
1.442
2.066
18.4792
722.77
602.197
998.142
724.31
602.48
996.679
361.74 6
313.927
520.299
363.62
314.53
520.888
The maximum errors observed are 0.8%, 2.6%, 0.9%, 4.1%, 0.21% and 0.51% for total active/reactive power losses, total active/reactive power generation from DGs and the active/reactive power drawn from substation, respectively. V. CONCLUSIONS The integration of single-phase DGs could negatively affect the safety and efficient operation of unbalanced power distribution systems. However, if active/reactive powers of DGs are properly regulated, DGs could play an important role in voltage and reactive power support for power distribution systems. This paper presents a distributed algorithm to solve the volt/var control problem aiming to minimize power losses in unbalanced power distribution system. Zonal decomposition method in introduced to reduce the computational cost and come up with fast optimal solutions for the volt/var control problem. A modified IEEE 37 node test feeder including eight single-phase DGs is employed to illustrate the performance of the developed model. The proposed algorithm is validated against centralized volt/var strategy to ensure it provides optimum solutions.
(b) Reactive power mismatch
VI. ACKNOWLEDGMENT
Figure 4. Converged deviation between active and reactive power flowing through node 28. (a) Active power mismatch (b) Reactive power mismatch
The authors would like to thank the NSF for providing support for this research through award No. CNS-1136040. The views expressed in this paper are of the authors.
Fig. 4 shows the converged deviation between the optimal active and reactive power flowing through node 28, respectively. Since in the beginning of the iteration process, active/reactive powers of pseudo generators are not known, each zone runs the OPF autonomously by setting the power of pseudo generators to zero. In the next iterations, the zones exchange the calculated power, resulting in rebalanced mismatches as shown in Figs. 3 and 4. Table II shows the total power losses, total active/reactive power generation from DGs and the active/reactive power drawn from substation (ୱ୪ୟୡ୩ and ୱ୪ୟୡ୩ ) using centralized and distributed approaches.
VII. REFERENCES [1]
[2] [3]
[4]
The Potential Benefits of Distributed Generation and the Rate-Related Issues That May Impede Its Expansion, U.S. Department of Energy, 2007 F. P. Sioshansi, Distributed Generation and its Implications for the Utility Industry Academic Press; 1 edition, 2014 M Raoofat, AR Malekpour, “Optimal allocation of distributed generations and remote controllable switches to improve the network performance considering operation strategy of distributed generations” Electric Power Components and Systems 39 (16), 1809-1827. Carvalho, P.M.S.; Correia, P.F.; Ferreira, L.A.F. “Distributed Reactive Power Generation Control for Voltage Rise Mitigation in Distribution Networks” IEEE Transactions on Power Systems, Volume: 23 , Issue: 2, 2008 , pp. 766- 772.
[5]
[6] [7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[Online].Available: http://www.cpuc.ca.gov/NR/rdonlyres/29DCF6CC45BC-4875-9C7D-F8FD93B94213/0/CPUCDGImpactReportFinal 2013_05_23.pdf. Modeling Distributed Generation in the Buildings Sectors, U.S. Department of Energy, 2013. M. Yang ; K-J. Kim, “Optimal Power Flow Calculation Structure for Energy Management System in Real-Time” in Proc 2013 IEEE Symposium on Computational Intelligence Applications In Smart Grid (CIASG) A. Borghetti, “Using mixed integer programming for the volt/var optimization in distribution feeders”, Electric Power Systems Research, vol. 98, no. 8, pp 39-50, 2013. Senjyu, T.; Miyazato, Y.; Yona, A.; Urasaki, N.; Funabashi, T. “Optimal Distribution Voltage Control and Coordination With Distributed Generation” IEEE Transactions on Power Delivery, Volume:23 , Issue: 2, 2008 , pp. 1236- 1242. Cagnano, A.; De Tuglie, E.; Liserre, M.; Mastromauro, R.A.”Online Optimal Reactive Power Control Strategy of PV Inverters” IEEE Trans. Ind. Electron., vol 58, 2011, pp. 4549- 4558. Malekpour AR, Niknam T. “A probabilistic multi-objective daily volt/var control at distribution networks including renewable energy sources” Energy 2011;36:3477–88. F. Capitanescu, I. Bilibin, E. Romero Ramos, “A Comprehensive Centralized Approach for Voltage Constraints Management in Active Distribution Grid” IEEE Trans. on Power Syst., vol. 29, no. 2, pp. 933942, 2014.. Carvalho, P.M.S.; Correia, P.F.; Ferreira, L.A.F. “Distributed Reactive Power Generation Control for Voltage Rise Mitigation in Distribution Networks” IEEE Transactions on Power Systems, Volume: 23 , Issue: 2, 2008 , pp. 766- 772. T. Sansawatt, L.F. Ochoa, and G.P. Harrison, “Smart decentralized control of DG for voltage and thermal constraint management”, IEEE Trans. on Power Syst., vol. 27, no. 3, pp. 1637-1645, 2012. F. A. Viawan and D. Karlsson, “Combined local and remote voltage and reactive power control in the presence of induction machine distributed generation,” IEEE Trans. Power Syst., vol. 22, no. 4, pp. 2003-2012, 2007. M. Brenna, E. De Berardinis, L. Delli Carpini, F. Foiadelli, P. Paulon, P. Petroni, G. Sapienza, G. Scrosati, and D. Zaninelli, “Automatic Distributed Voltage Control Algorithm in Smart Grids Applications”, IEEE Trans. Smart Grid, vol. 4, no. 2, pp. 877-885, 2013. A. Kargarian Marvasti, Y. Fu, S. DorMohammadi, M. Rais-Rohani, “Optimal Operation of Active Distribution Grids: A System of Systems Framework” IEEE Trans. Smart Grid ,vol 5, no 3, pp. 1228 – 1237, 2014. Faria, P. ; Soares, T. ; Pinto, T. ; Sousa, T.M. ; Soares, J. ; Vale, Z. ; Morais, H., “Dispatch of distributed energy resources to provide energy and reserve in smart grids using a particle swarm optimization approach” in Proc 2013 IEEE Symposium on Computational Intelligence Applications In Smart Grid (CIASG) Wu, Chenye; Akhavan-Hejazi, Hossein; Mohsenian-Rad, Hamed; Huang, Jianwei; “PEV-based P-Q Control in Line Distribution Networks with High Requirement for Reactive Power Compensation”, in Proc. of the IEEE PES Conference on Innovative Smart Grid Technologies (ISGT’14), Washington, DC, February 2014. Y. Ruifeng, T.K. Saha, “Voltage Variation Sensitivity Analysis for Unbalanced Distribution Networks Due to Photovoltaic Power Fluctuations” IEEE Trans. Power Syst., vol. 27, no. 2, pp. 1078–1089, May 2012. S. Paudyal, C. A. Canizares, K. Bhattacharya, “Optimal Operation of Distribution Feeders in Smart Grids” IEEE Trans. Ind. Electron., vol. 58, no. 10, pp. 4495–4503, Oct. 2011. Araujo, L.R. ; Penido, D.R.R. ; Carneiro, S. ; Pereira, J.L.R. “A ThreePhase Optimal Power-Flow Algorithm to Mitigate Voltage Unbalance” IEEE Trans. Power Del., vol. 28, no. 4, pp. 2394 - 2402, 2013. S. Deshmukh, B. Natarajan, A. Pahwa “Voltage/VAR Control in Distribution Networks via Reactive Power Injection Through Distributed Generators” IEEE Trans. Smart Grid, vol. 3, pp. 40–47, Sep. 2012.
[24] [Online].Available:http://ewh.ieee.org/soc/pes/dsacom/testfeeders/
