Comprehensive Optimization of PV Inverter Reactive and Real Power Flows in Unbalanced Four Wire LV Distribution Network Operations Xiangjing Su, Student Member, IEEE Mohammad A. S. Masoum, Senior Member, IEEE
Peter Wolfs, Senior Member, IEEE Power and Energy Centre Central Queensland University Rockhampton, Australia
[email protected]
Department of Electrical and Computer Engineering Curtin University Perth, Australia
[email protected] Abstract— Roof top PV installations are normally not controlled by the network operator but driven by consumer actions. Some power quality issues have been caused or aggravated, such as voltage rise and unbalance which restricts further PV connections. However, the latent reactive power capability of PV inverters may be utilized to provide voltage/VAR support and increase the renewable power fraction. This paper proposes a novel three-step PV control strategy based on the reactive power control of inverters and real power curtailment. The optimization model is solved by a Sequential Quadratic Programming (SQP) based global approach and the validity is tested on a real 3-phase 4-wire unbalanced distribution network model developed during the Perth Solar City trial in Western Australia. Index Terms--photovoltaic, reactive power control, real power curtailment, optimization, and Sequential Quadratic Programming.
I.
INTRODUCTION
The secure, stable and economic operation of distribution networks is expected and required by both the utilities and consumers. Voltage regulation, which has significant impacts on the normal operating regime of electrical appliances, is always one of the foremost concerns in network operation. The increasing connections of PV units in the distribution network may lead to unacceptable reverse power flow and voltage rise [1]-[3]. Voltage unbalance is another growing power quality concern [4]. With the increasing installations of PV units in the distribution network, such as single-phase roof top PV systems which are located and rated randomly, this issue is becoming more serious [5]. Many studies have been devoted to improving distribution network operation by PVs control. Among them, a considerable part is limited to the planning stage [6]-[8], that is, better network performance is achieved by optimal sitting and sizing of PVs. Despite PV allocation having a significant impact, in many circumstances the utilities cannot control PV connections to the distribution network, which is normally driven by consumer actions. With the increasing PV penetration and advances in power electronics, more attention has been called to provide more functionality by controlling reactive power injections of PVs. In [9], based on the combination of Genetic Algorithm (GA) and linearization of constraints, the optimal reactive power outputs for all PVs are found for a better voltage profile. To achieve maximum voltage improvement in the distribution network, [10] proposes to determine the operating points of DGs based on voltage sensitivities of lines. Reference [11] aims to minimize grid loss by optimally controlling reactive power outputs of PVs at low voltage levels. To ensure the global optima, a commercial global solver is used. Reference [12] presents a convex
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relaxation approach to solve the problem of optimal reactive power dispatch of PV inverters with objectives of network loss and consumption minimization. Most of the existing studies are based on a balanced network model, but the distribution network is naturally unbalanced and it will result an incorrect prediction and conclusion [5]. In addition, the optimal PV control is usually treated as a complex nonlinear optimization problem and selecting a solution algorithm with reasonable speed and accuracy is a significant challenge [11]. In this study, based on the inverter’s reactive power capability and real power curtailment, a novel and comprehensive three-step control strategy is proposed to find the optimal operating points of PV inverters in the LV distribution network. The search for optimal PVs generation is determined by the network loss, inverter loss, real power curtailment and voltage magnitude/balance profile. An optimal power flow (OPF) based optimization model of a real unbalanced distribution network is built to study the viability of the proposed PV control strategy. II.
PV CONTROL STRATEGY
A. PV Inverter’s reactive power capability
Qlower
S
P
Qupper
Figure 1. Inverter Reactive Power Limits
Figure 2. PV Control Strategy
Many PV inverters have the capability of providing reactive power to the grid in addition to the real power [13]-[14]. As shown in Figure 1, the inverter’s capacity is represented by a vector with magnitudeܵ. The semicircle with radiusܵ denotes the boundary of the inverter’s feasible operating range in PQ space. Assuming that the real power generated by PV isܲ, the boundary constraints on the PV reactive power can be given as:െξܵ ଶ െ ܲଶ ܳ ξܵ ଶ െ ܲଶ . B. Proposed Three-Step PV Control Strategy Based on the reactive power capability of inverters and real power curtailment [15], a novel three-step control strategy,
shown in Figure 2, is proposed to find the optimal operating points of PV inverters with a better network performance. Step 1: A residential system is studied where the inverters are initially sized according to the PV array real power requirement. When the PV generation is less than the inverter rating, the inverters will have a capability to supply reactive power, at a cost of incremental inverter loss. As the control is only based on reactive power and single inverter capacity, this control case is named as ‘OPTQ1S’. Step 2: A second system is then proposed where PV inverters are installed with an additional capacity factor to allow more reactive power for the active control of the distribution network performance. In this study the ratings of the PV inverters are doubled and accordingly the control case is called ‘OPTQ2S’. Step 3: As optimization effects by only reactive power management is limited because of high R/X ratio of distribution network, a final system is presented where real power curtailment is available to each inverter to allow both real and reactive power control. This control case is named as ‘OPTPQ2S’. III.
OPTIMIZATION MODEL AND ALGORITHM
A. Optimization Model To reduce the losses and improve the voltage magnitude/balance profile in the unbalanced LV network, an Optimal Power Flow (OPF) based comprehensive optimization model is formulated as follows: 4 n −1 n p 2 p ½ °¦¦ ¦ I ij Rij ° ° p =1 i =1 j =i +1 ° 2 3 °° °° 2 2 p p min ®+¦ ªki + (Viopt + − Vi + ) + ki −Vi − º + ¦¦ (ViN − Vi ) ¾ « » ¼ p =1 i∈γ ° i∈ω ¬ ° ° 3 ° p p 2 p p p p p p °+¦¦ ª¬( ki1 S PVi + ki 2 SPVi + ki 3 ) + ki ( PPVi 0 − PPVi ) º¼ ° ¯° p =1 i∈δ ¿°
Subject to:
(1)
To optimize the voltage profile, symmetrical components are used. Network unbalance is quantified by voltage unbalance factor, which has been defined separately by IEC, IEEE [16]-[17] and National Equipment Manufacturer’s Association (NEMA) [16]-[18]. In this study, the negative-sequence Voltage Unbalance Factor (VUF) is chosen as the measure of voltage unbalance with expression ofΨܸܷ ܨൌ ܸି Τܸା . In equation (1), ୮ weighting coefficients݇ା and ୧ି are used for the different sequence voltage deviations from their optimal values. Simultaneously a nodal phase voltage deviation from the rated valueܸே is applied. Thus, the objective function in (1) is defined as the sum of losses caused by the distribution lines and PV inverters, real power curtailment cost and voltage deviations at both three-phase nodes and single-phase nodes. Equality constraints in (2) are the power balance equations. Of theseܲ ሺܳ ሻ, ܲ ሺܳ ሻ and ܲ ሺܳ ሻ are the PV, load and network real (reactive) power, respectively. Inequality constraints described by (3) demonstrate the limits on inverter output. In line with IEC 60038 for nominal voltages and associated permissible tolerances for voltage derivation within LV networks, the boundary constraints on voltage magnitude and phase angle are also given in (4). B. Optimization Algorithm The optimization problem in last section is generally referred as a constrained nonlinear programming (CNLP) problem. To ensure global optima, this paper proposes to use the Matlab global optimization solver ‘GlobalSearch’ which is based on Sequential Quadratic Programming (SQP) method with multiple starting points [19]. IV.
RESULTS AND DISCUSSION
ܲ െ ܲ െ ܲ ൌ ͲǢܳ െ ܳ െ ܳ ൌ ͲǢ
(2)
A. Test Network
ܸ௪
(3) (4)
The test network is contained within Perth Solar City, a research program funded by the Australian Government Department of Climate Change and Energy Efficiency.
ଶ ଶ ଶ ܲ ܳ ܵ ܸ ܸ௨ Ǣߠ௪
ߠ
ߠ௨
Where i,j=1,2,...n, is the bus number and p=1,2,3,4 represents the phase designations a, b, c and n, respectively. In this study, as the network is unbalanced, both the bus number ݅and the phase designation are needed to identify a node ݅ .
Accordingly, ܫ andܴ are the current through and resistance
of the branch between nodes ݅ and ݆ while ܸ , ܲ ,
initialܲ to lowerܲ , customers will suffer the loss of foregone energy sales. revenue from
ଶ
ଶ
ܵ ൌ ටܲ ܳ andܵ
are the voltage magnitude, PV inverter
real power, apparent power and capacity at node݅ , respectively. ɘand ߛ are defined as the sets of three phase buses and single phase buses separately while ߜ is the set of buses where PVs are connected. In this study, optimization is based on PV real and reactive power control. Loss costs will rise with an increase in inverter current output, which is modeled as the quadratic polynomial of the apparent power ܵ with coefficients ݇ଵ , ݇ଶ and ݇ଷ . Furthermore, when curtailing the PV real power from
As shown in Figure 3, the 400/230V network is supplied from a 200kVA 22kV/400V distribution transformer and includes 101 buses and 77 consumers. Of these, 34 consumers have roof top PV systems which have typical ratings of 1.88kW. Total rated PV installation capacity is 63.8kW representing a branch penetration of 32%. The network under study is an aerial, three-phase four-wire, construction with four equally sized conductors on a mixture of 0.9m and 1.2m cross arms. The consumer mains are 6mm2 copper with R=3.7Ω/km and X=0.369Ω/km. The aerial mains are constructed with two seven strand, all aluminum conductor types: • 7/4.50 AAC – R=0.316Ω/km; X=0.292Ω/km; • 7/3.75 AAC – R=0.452Ω/km; X=0.304Ω/km. As the consumers have a mixture of single- and three-phase house connections the loading is inherently unbalanced. To better verify the validity of the proposed three-step PV control strategy and optimization model, two operational extremes are considered corresponding to different levels of PV penetration and loads. One scenario is the total PV generation is
much less than the network loads, that is, high load low generation. In this case, significant voltage drops occur. The other scenario is the PV generation is more than the network loads, namely high generation low load, which causes the reverse power flow and voltage rise. For each above-mentioned scenario, the three control cases, corresponding to the proposed three-step control strategy (‘OPTQ1S’,’OPTQ2S’ and ’OPTPQ2S’) will be applied. A reference is formed based on the original network state ‘ORIGINAL’. For the different control cases, the objective function, network losses, real power curtailment cost, voltage magnitude and unbalance factor are calculated and compared respectively in Figures 4 -19.
Phase A PV Real Power(Watts)
50
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
0
-50
6
7
9 19 36 39 43 49 51 73 PV Location Phase A PV Reactive Power(Vars)
92
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
4000 2000 0 6
7
9
19
36 39 43 PV Location
49
51
73
92
Figure 5. Phase A PV Generation by Node Phase B PV Real Power(Watts)
50
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
0
-50
3
4000
8 66 69 70 83 PV Location Phase B PV Reactive Power(Vars)
85
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
2000 0
3
8
66 69 70 PV Location
83
85
Figure 6. Phase B PV Generation by Node Phase C PV Real Power(Watts)
100 50 0
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
-50 -100
4 24 27 30 32 35 40 44 52 56 64 78 81 84 87 91 PV Location Phase C PV Reactive Power(Vars)
4000
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
2000 0
Figure 3. Pavetta 1 LV Network Diagram
4 24 27 30 32 35 40 44 52 56 64 78 81 84 87 91 PV Location
Figure 7. Phase C PV Generation by Node
B. High Load Low Generation
240
x 10
225 220 ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
210 0
100
200 300 Distance (m) →
400
Figure 8. Phase A Voltage by Node
4
Objective Function Network Loss (W) Inverter Loss Voltage Deviation P Curtailment Cost
3 2.5 2 1.5 1
240 235 230 225 220 ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
215
0.5 0
230
215
Phase B Voltage (V)
3.5
235 Phase A Voltage (V)
As indicated in Figures 4-11, initially the network was suffering from serious voltage drop, unbalance and losses. As more PV reactive power can be provided in the three control cases from ‘OPTQ1S’ to ‘OPTPQ2S’, a better network operation is achieved. Figure 4 demonstrates that both the objective function and network loss decline steadily from 3.4e4 and 13.7kW for ‘ORIGINAL’ to 2.7e4 and 13.2kW for ‘OPTQ1S’ and to 2.4e4 and 12.9kW for both ‘OPTQ2S’ and ‘OPTPQ2S’ separately. Figures 8-11 show a better balanced system with a higher voltage levels. As phase C had the worst initial voltage quality, more reactive power injection and the most significant voltage improvement occur at this phase.
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
PV Control Cases
Figure 4. Objective Function and Optimization objectives
210 0
100
200 300 Distance (m) →
400
Figure 9. Phase B Voltage by Node
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
235 Phase C Voltage (V)
Phase A PV Real Power(Watts)
2000
240
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
1500 1000 500
230
0
225
6
200
9 19 36 39 43 49 51 73 PV Location Phase A PV Reactive Power(Vars)
-200
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
-400
215
-600
100
200 300 Distance (m) →
6
7
9
400
19
36 39 43 PV Location
49
51
73
Phase B PV Real Power(Watts) 2000
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
1500
2
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
1.5
92
Figure 13. Phase A PV Generation by Node
Figure 10. Phase C Voltage by Node 1000 500 0
3
8 66 69 70 83 PV Location Phase B PV Reactive Power(Vars)
85
100
1
0 -100
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
-200
0.5
-300
3
8
66 69 70 PV Location
83
85
0
Figure 14. Phase B PV Generation by Node -0.5 0
100
200 300 Distance (m) →
400
Figure 11. Voltage Unbalance Factor by Node
C. High Generation Low Load
The impact of PV reactive power control with a high R/X ratio is quite limited. For example, the loss reduction from ‘ORIGINAL’ to ‘OPTQ1S’ is only 49W and there is no improvement from ‘OPTQ1S’ to ‘OPTPQ2S’. Figures 12-19 indicate that operation quality can be significantly enhanced by real power curtailment in the case of ‘OPTPQ2S’ with improved objective function and network loss of 1.79e3 and 35W, respectively. Objective Function Network Loss (W) Inverter Loss Voltage Deviation P Curtailment Cost
2000
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
1500 1000 500
As shown in Figures 12-19, reverse power and voltage rise occur in the network. In the initial case ‘ORIGINAL’, the operating quality of the network is quite poor with the biggest objective function and loss at 2.34e4 and 360W, respectively. To reduce the network loss and mitigate the voltage rise, PV inverters are controlled to generate inductive reactive power. In Figures 12 and 15-19, the objective function and network loss show a downward trend with 2.18e4 and 311W for both ‘OPTQ1S’ and ‘OPTQ2S’. Moreover, the voltage magnitude and balance profiles are simultaneously improved.
2500
Phase C PV Real Power(Watts) 2000
1500
0
200
4 24 27 30 32 35 40 44 52 56 64 78 81 84 87 91 PV Location Phase C PV Reactive Power(Vars)
0 -200
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
-400
4 24 27 30 32 35 40 44 52 56 64 78 81 84 87 91 PV Location
Figure 15. Phase C PV Generation by Node 245
P hase A Voltage (V)
Voltage Unbalance Factor (%)
92
0
220
210 0
7
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
240
235 0
100
200 300 Distance (m) →
400
Figure 16. Phase A Voltage by Node 1000
500
0
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
PV Control Cases
Figure 12. Objective Function and Optimization objectives
ACKNOWLEDGMENT
P hase B Voltage (V)
245
The authors acknowledge the supply of consumption data collected under the Perth Solar City trial which is a part of the Australian Government’s $94 million Solar Cities Program. The authors also acknowledge the support of Western Power in supplying additional network data, models and technical reports.
240
RERFERENCES
235 0
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
[1]
400
[2]
Figure 17. Phase B Voltage by Node
[3]
100
200 300 Distance (m) →
245
Phase C Voltage (V)
[4]
[5] 240
[6]
235 0
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
100
200 300 Distance (m) →
[7]
400
[8] Figure 18. Phase C Voltage by Node
V o lta g e U n b a la n c e F a c to r (% )
2
ORIGINAL OPTQ1S OPTQ2S OPTPQ2S
1.5
[9]
[10]
1
[11] 0.5 0 -0.5 0
[12]
100
200 300 Distance (m) →
400
[13]
Figure 19. Voltage Unbalance Factor by Node
V.
CONCLUSION
This paper has made a comprehensive study on the performance improvement of a real 3-phase 4-wire distribution network with high PV penetration. A three-step PV control strategy was proposed based on the reactive power capability of inverters and real power curtailment. An optimal PV control model with weighted network loss, positive and negative sequence voltages was proposed and implemented using a sequential quadratic programming (SQP) based global solver. The viability of the control strategy and optimization model was verified on two operational extremes of a real LV distribution network. The results demonstrate that controlling both PV real power and reactive power is a feasible and effective method to improve the operational quality of distribution network, which in turn increases the network load capacity and the capacity to increase higher fractions of renewable energy.
[14]
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