Optimal Allocation of Reactive Power Compensators ... - Science Direct

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ScienceDirect Energy Procedia 103 (2016) 165 – 170

Applied Energy Symposium and Forum, REM2016: Renewable Energy Integration with Mini/Microgrid, 19-21 April 2016, Maldives

Optimal Allocation of Reactive Power Compensators and Energy Storages in Microgrids Considering Uncertainty of Photovoltaics Shiyu Liua, Fan Liua, Tao Dinga, Zhaohong Biea* a

State Key Laboratory of Electrical Insulation and Power Equipment, Smart Grid Key Laboratory of Shaanxi Province, Xi’an Jiaotong University, Xi’an, 710049, China

Abstract The intermittence of DGs which challenges the voltage and power quality manifests the need for new planning and operation strategies for microgrids. Considering the uncertainty of PV output, the advantages of both reactive power compensators (RPC) and energy storages (ES) are investigated in this paper. With the objective to minimize the power loss of microgrids, the optimal allocations of RPCs and ESs are solved as an optimal power flow problem. Monte Carlo method is utilized to simulate the different scenarios of PV output with its probability. IEEE-33 system is implemented to investigate the effect of RPCs and ESs on the voltage mitigation and power loss reduction. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-reviewofunder responsibility of of REM2016 Peer-review under responsibility the scientific committee the Applied Energy Symposium and Forum, REM2016: Renewable Energy Integration with Mini/Microgrid. Keywords: Reactive power compensators; Energy storages; Uncertainty of PV; Optimal powe flow; Monte Carlo simulations

1. Introduction Nowadays the environmental deterioration and scarce source caused by the general use of fossil fuels have motivated utilities for local connection of renewable energy resources at the distribution level. Power engineers are facing new challenges for planning and operation of power systems due to the recent changes in the power structure [1-2]. It leads to transform conventional distribution systems into multiple modern interconnected distribution systems, namely, micro-grids. Microgrids are constructed from a set of distributed generators (DGs), storage units and loads, which are connected to a low-voltage system and can operate in either grid-connected or islanded mode [3].

* Corresponding author. Tel.: +86-29-8266-8655; fax: +86-29-8266-5489. E-mail address: [email protected].

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the Applied Energy Symposium and Forum, REM2016: Renewable Energy Integration with Mini/Microgrid. doi:10.1016/j.egypro.2016.11.267

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Either optimal reactive power (i.e. capacitor placement) or active power (i.e. energy storages) planning has been regularly performed by distribution engineers with several objectives such as power losses and cost reduction. As the number and capacity of DGs increase, new challenges bring on the overvoltage and power losses. Reactive power compensators (RPC) such as shunt capacitors are utilized to guarantee the specific physical and operating constraints to be satisfied [4-5]. In addition, the energy storage (ES), characterized by its fast response, real-time control, non-carbon emission, is able to defer the output fluctuation of DGs, improving the voltage profile and power quality [6-7]. However, the investigation on the allocation of both RPC and ES has gained less attention. Changing the structure of the distribution system itself by introducing the microgrids, the stochastic nature of newly added DGs manifests the need for new planning and operation strategies for current distribution systems. During last five decades, several efforts have been made to solve the optimal probabilistic power flow with uncertainty of DGs, which can be summarized as point estimate method[8], chance-constraints[9], Monte Carlo simulation[10] and so on. [8] presented an application of two-point estimate method (2PEM) to account for uncertainties in the optimal power flow (OPF) problem. The twopoint estimate method, 2m scheme, does not provide generally good results if the number of input random variables is high , and the accuracy is not guaranteed with fewer runs. [9] employed the basic probability constraints of network operation to allocate shunt capacitors while the annual power fluctuating cumulative probability curve based chance constraint was added to determine the reactive power allocation of SVG. The proposed model was solved with LHS based PSO algorithm, which increased the computation time. Although it needs time for computation, the Monte Carlo method is able to simulate the uncertainty of PV according to its probability to get a good result. In this paper, considering the effect of the uncertainty of PV, the optimal allocation and sizing of both RPCs and ESs are investigated, with the objective to minimize the power loss in the grid-connected mode. Monte Carlo method is employed to simulate different scenarios in PV output based on the Beta probability density functions. The paper is organized as follows. Section 2 presents the models used for optimal power flow considering uncertainty of PVs. In Section 3 explains the solution algorithms. Section 4 describes the test case IEEE-33 system, where the voltage profile and power loss are discussed. Finally, the conclusions are drawn in Section 5. 2. Optimal Power Flow Model Considering Uncertainty of PV Integration 2.1. Probabilistic Modeling of PV The nature of PV resources is probabilistic. In practical, the PV power output is characterized by randomness and volatility while the output power of PV array changes rapidly with change of solar radiation intensity. The solar irradiance is modeled by Beta probability density function, which is related to the output of PV. Therefore, the probability density function of PV output Pv [11] is D 1

f ( Pv )

1 *(D  E ) § Pv · ˜ ¨ ¸ AK *(D )*( E ) © Pmax ¹

§ Pv · ¨1  ¸ © Pmax ¹

E 1

(1)

In the formula, Pmax rmax AK is the maximum active power output of PV system; rmax is the maximum radiation; A is the total area of PV array; ¨ is the total photoelectric conversion effiency. Hence, probability density function of active power output of PV is related to maximum solar radiation and the shape parameters of Beta distribution Į and ȕ. 2.2. Optimal Power Flow Model Integrated with PV In general, the microgrids operate as a radial network in grid-connected mode. It was usually formulated as a set of recursive equations, namely branch flow formulations in literature [12-13]. Given the positive direction of branch power flow is from bus ‘i’ to bus ‘j’ and the power flow equations can be

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Shiyu Liu et al. / Energy Procedia 103 (2016) 165 – 170

expressed by





­ PV , j  PL , j ¦ Ajk  ¦ Aij  rij Iij2 , j  B ° kG  j iS  j ° ° QL , j ¦ W jk  ¦ Wij  xij Iij2 +bs,jU 2j , j  B °° kG  j iS  j ® 2 2 °U j U i  2 rij Aij  xijWij  rij2  xij2 I ij2 ,   i, j  E ° ° Aij2  Wij2 2 =I ij ,   i, j  E ° U i2 °¯









(2)



where B is the set of buses; E is the set of branches; PL,j and QL,j are active and reactive load demand of bus j; PV,j is the injected PV power of bus j; Aij and Wij are the active and reactive power flow from bus j to k; rij and xij are resistance and equivalent reactance of branch ij; bs,j refers to shunt susceptance from j to ground; Uj is the voltage magnitude of bus j; S(j) is the set of all parents of bus j and G(j) is the set of all children of bus j; Iij is the current of branch ij. Power flow equations are supposed to be modified in order to consider the reactive power generated by the RPCs and the real power charged or discharged by the distributed ESs if they exist in the system. In this paper, considering PV based generation, sizing and allocation of both RPC and ES are investigated to maintain the voltage within a desirable range, while minimizing the power loss. The specific optimization model with physical constraints can be formulated as min (3) ¦ rij I ij 2  i , j E

s.t. PV , j  PL, j r PES , j

¦

Ajk 

kG  j

¦  Aij  rij Iij 2 ,

j  B

(4)

iS  j

j  B

(5)

U 2j Ui2  2 rij Aij  xijWij  rij2  xij2 Iij 2 ,  i, j  E

(6)

¦ Wjk  ¦ Wij  xij Iij2 +bs,jU 2j ,

QRPC, j  QL, j

kG  j

iS  j





I ij 2

Aij2

 Wij2 U i2



0 d I ij 2 d I ijmax

,   i, j  E ,



2

,

  i, j  E ,

U imin d U i d U imax , i  B , min QRPC



max d QRPC, j d QRPC ,

j :

(7) (8) (9) (10)

(11) QRPC , j y j s j , j  : where ȍ is the set of buses for shunt capacitors/reactors; Iij,max is current capacity limit of branch ij; Uimin and Uimax are lower and upper bound of voltage magnitude at bus j; QRPC,j is the reactive power capacity installed at bus j; QRPCmin and QRPCmax are lower and upper bound of shunt capacitors/reactors capacity at bus j; yj is the discrete size of RPC units; sj is the number of RPC units installed at bus j. PES,j is the active power capacity installed at bus j. The power of EPS units is positive in the discharging period and negative in the charging period. 3. Solution Algorithms In Monte Carlo based techniques, samples from input random variables are generated and then the deterministic problem is solved for each sample. In this paper, the outputs of PV, that is, the random variables are sampled based on the Beta pdf in each sample, running for Nt times as the total samples.

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The optimal solutions are two vectors with the length of candidate buses for installing RPCs and ESs, as shown in the following: QRPC [QRPC _1  QRPC _ k  QRPC _ N ] (12) C

PES

(13)

[ PES _1  PES _ k  PES _ N P ]

where QRPC represents the capacity of RPCs, which is installed on bus k, and Nc is the number of candidate buses; PES is the capacity of ESs, which is installed on bus k, and NP is the number of candidate buses. Branch and bound, which is an effective mathematical programming algorithm for solving optimization problem is used in this paper for optimal allocation of RPCs and ESs. Utilizing branch and bound method in each run based on the Monte Carlo simulations, the procedure will be as follows: 1) Choose the candidate buses to install the EPCs and ESs. 2) Sample the outputs of PVs according to the Beta probability density function; 3) The power loss is calculated for the microgrids in grid-connected mode. For this purpose, the optimal power flow is run with respect to the sampled PV output at each run. The optimal solutions of QRPC and PES are calculated to store the allocation in the microgrid. 4) Once the (3)-(11) are solved for all Nt samples, the statistical information of the output variables are calculated. 4. Numerical Results Widely recognized standard network IEEE-33 bus system was utilized for implementation of the algorithm and sensitivity studies. The modified system’s load is 5.084+j2.547 MVA. During the normal operation of the system, without adding any distributed energy resources to the system, the power loss is 0.203+j0.14MVA. PVs are integrated to the system with the total capacity of 0.78 MW, with each bus installed 0.06MW. The topology of IEEE-33 bus system is described in Fig.1(a). Based on the actual rule 13 p.m. at noon, the shape parametersĮ and ȕ of Beta distribution which PV output follows is selected to be 65, 3, respectively. The probability of PV output is described in Fig.1(b). The number of Monte Carlo samples is selected as 1000 times. The computational tasks were performed on a 2.0 GHz personal computer with 4GB RAM with CPLEX commercial solver.

(a)

IEEE-33 bus network (PV marked as red square)

(b) Probabilistic distribution of PV output

Fig. 1 Topology of IEEE-33bus system considering the uncertainty of PV

Reactive power compensators can reduce power losses, improving voltage profile or increase system capacity. In this case, the reactive power can be generated by capacitor banks. Firstly, only the reactive power compensators are considered to minimize the power loss. Sensitivity studies are performed to see the effect the total capacity of the allocated RPC on the power loss. The locations and sizes of RPCs vary for different total rated capacities of RPCs are shown in Table.1. The last column is the expected value of power losses calculated in 1000 simulations. It is shown that by inserting the RPCs into the system, the power loss is decreased. The locations of RPCs are gathered near the bus 32 while the sizes of RPCs vary

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for different total capacity of RPCs. Table 1 Optimal RPCs allocations in IEEE-33 system Total capacity of RPCs

Results

Expectation of power

(kVar)

loss(kW)

100 200 300

Buses installed

32

QRPC(kVar)

100

Buses installed

30,31,32

QRPC(kVar)

100,50,50

Buses installed

29,30,31,32

QRPC(kVar)

100,50,100,50

167.0 158.6 151.0

The energy storages in the microgrids can reduce the negative impact of the intermittent nature of renewable resources, which is beneficial to save the amount of energy generated by PV modules. Secondly, only these ESs are considered to improve the system. The optimally allocated ESs and the expectation power loss in the microgrids for the case that the total rated capacities of ESs are shown in Table.2. It is seen that ESs have an positive effect on the power reduction. Table 2 Optimal ESs allocations in IEEE-33 system Total capacity of ESs (kW)

Results

100 200 300

Expectation of Power loss(kW)

Buses installed

17,31,32

PES(kW)

25,25,50

Buses installed

16,30,31,32

PES(kW)

50,50,50,50

165.1 154.9

Buses installed

14,16,17,29,30,31,32

PES(kW)

25,50,50,25,50,50,50

145.6

In this part both the RPCs and ESs are added to the system simultaneously to minimize the power loss. Given RPC with 200 kVar and ESs with 200 kW, the power loss is compared in Table 3 . The voltage profile before and after compensation is described in Fig.2. The optimal locations of RPCs are at bus #30,#31,#32 while ESs are at buses #16,#17,#30,#31,#32 .Table.3 confirms that by adding both RPCs and ESs into the system, the power loss is significantly reduced and the voltage profile is well improved. Table 3 Comparison of power loss reduction among RPCs only, ESs only and both RPCs and ESs installation Without RPCs or ESs

RPCs only

ESs only

Power loss (kW)

174.9

158.6

154.9

137.2

Power loss reduction

-

9.32%

11.44%

21.55%

Before Compensation After Compensation

1.00

Voltage/p.u.

0.98

0.96

0.94

0.92

0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32

Bus Number

Fig. 2 Comparison of voltages before and after compensation

Both RPCs and ESs

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Shiyu Liu et al. / Energy Procedia 103 (2016) 165 – 170

5. Conclusions This paper presents optimized strategies for planning grid-connected microgrids in distribution systems. The optimal allocation of both RPCs and ESs are explored based on the optimal power flow model considering the uncertainty of PVs. The effect of capacity of RPCs and ESs are investigated respectively, showing that an increase in capacity contributes to the power loss reduction and voltage improvement. What’s more, the results from IEEE-33 bus system indicate that the combination of RPCs and ESs installation can improve the voltage profile and reduce power loss. Further work will focus on the probability of load, and investigate on the isolated mode in microgrids. 6. Acknowledgments This work was supported in part by the National Natural Science Foundation of China under Grant 51577147 and the Independence research project of State Key Laboratory of Electrical Insulation and Power Equipment in Xi’an Jiao Tong University (EIPE14106) References: [1] Heydt GT. The next generation of power distribution systems. J IEEE Trans. Smart Grid. 2010; 1(3): 225-235. [2]. Carrasco JM, Bialasiewicz JT, Guisado RC, et al. Power-electronic systems for the grid integration of renewable energy sources: a survey. J IEEE Trans. Ind. Electron. 2006; 53(4): 1002-1016. [3] Kumar NHS, Doolla SV. Multiagent-based distributed-energy-resource management for intelligent microgrids. J IEEE Trans. Ind. Electron. 2013; 60(4): 1678-1687. [4] Dixit S, Srivastava L, Agnihotri G. Optimal placement of SVC for minimizing power loss and improving voltage profile using GA. C 2014 International Conf. Issues and Challenges in Intelligent Computing Techniques (ICICT). 2014; p. 123-129. [5] Jafari M, Afrakhte H, Effect of optimal placement and regulation of SSVR in microgrid island operation. C 2014 19th Conf. Electrical Power Distribution Networks (EPDC). 2014; p.116-122. [6] Atwa YM, Saadany EF. Optimal allocation of ESS in distribution systems with a high penetration of wind energy. J IEEE Trans Power Syst. 2010; 25(4): 1815-1822. [7] Chacra FA, Bastard P, Fleury G, et al., Impact of energy storage costs on economical performance in a distribution substation. J IEEE Trans Power Syst. 2005; 20(2): 684-691. [8] Verbic G, Canizares. Probabilistic optimal power flow in electricity markets based on a two-point estimate method. J IEEE Trans Power Syst. 2006; 21(4): 1883-1893. [9] Liu Y, Gao S. Reactive power planning with large-scale PV generation systems considering power fluctuation. C 2015 IEEE in Power & Energy Society General Meeting. 2015; p.123-129. [10] Hajian M, Rosehart WD, Zareipour H. Probabilistic power flow by Monte Carlo simulation with Latin Supercube Sampling. J IEEE Trans Power Syst. 2013; 28(2): 1550-1559. [11] Yang SY, Li H. Research on the voltage distribution of interconnected distributed network - distributed generation. C 2011 Asia-Pacific in Power and Energy Engineering Conference (APPEEC). 2011; p.1-4 [12] Ding T, Liu S, et al., A two-stage robust reactive power optimization considering uncertain wind power integration in active distribution networks. J IEEE Trans. Sustainable Energy. 2015; p.1-11. [13] Farivar M, Low SH. Branch flow model: relaxations and convexification-part I. J IEEE Trans Power Syst. 2013; 28(3): 25542564.