Coordinated Reactive Power Control of OLTC and ...

Coordinated Reactive Power Control of OLTC and WTGs for Improved Steady State Voltage Profile Gao, Hong Chao Department of Electrical Engineering Chonnam National University [email protected]

Ahn, Seon-Ju Department of Electrical Engineering Chonnam National University [email protected]

Abstract With the penetration of the renewable energy of wind farm increasing rapidly in the past decades, reactive power control of wind farms has become a crucial issue. This paper proposes a quadratic programming based optimization method of reactive power distribution between wind turbines to improve the steady state voltage profile while meet the point of common coupling (PCC) reactive power demand. In addition, a comprehensive modelling of wind farm and power flow analysis is presented. Comparison between the conventional average distribution principle and optimal distribution is analyzed. With the simulation, it is shown that with optimum of reactive power distribution between wind turbine generators (WTGs), voltage profile can be improved meanwhile the number of on load tap changes (OLTC) can be decreased.

Keywords Wind farm, power flow, reactive power control, OLTC, quadratic programming

1.

INTRODUCTION

Due to the deterioration of the global climate, new renewable energy in the energy market is gradually showing advantage. The global wind energy market was worth $130 billion in 2013 and $165.5 billion in 2014. Therefore, many related to wind farm grid issues become the focus of the study. However, the issue of reactive power control of wind farm is observed and proposed by many researchers. With the increasing integration of wind power plants, grid utilities require extended reactive power supply capability, not only during voltage dips, but also in steady state operation [Hoan V. Pham et al, 2014]. The transmission system operators (TSOs) in different countries commonly define the grid code control requirements for WF. The reactive power requirements can formulated in terms of power factor or reactive power reference at the PCC. Grid code compliance for distribution and transmission connection is an important consideration in wind

Choi, Joon-Ho Department of Electrical Engineering Chonnam National University [email protected]

farm construction and voltage/reactive power control is a necessary element in achieving such compliance. When it comes to the reactive power control of wind farm, many relevant issues worth being taken into consideration, such as, power factor requirement, dynamic voltage support requirement, low/high voltage ride through and reactive power compensation devices. In addition, according to the different research topic, the model of wind farm adopted is also different. For example, wind farm generators are often modeled as one equivalent generator driven by a single equivalent wind turbine, when the effect of wind farm transmission system is studied: 1) wind farm to damp the sub-synchronous oscillation of a power system; 2) secondary voltage control combined with wind farms and synchronous generators. And wind farm is often represented by an exact number of wind turbine generators, when the topic of wind farm controller design is studied: 1) the coordination of wind farm and static VAR compensator (STATCOM); 2) allocation of reactive power of wind farm generators to satisfy the PCC requirements. There are a lot of distribution principles of the allocation of reactive power between WTGs, such as even distribution, proportional distribution and so on. However, because of the wind distribution, wake effect and other effects, the wind turbines in the same wind farm does not own same operating state at the same time. So simply adopting the even distribution principle or the proportional sharing principles is not the optimal use of reactive power supplied by the wind generators. Based on this consideration, reactive power optimal allocation will be presented in detail in this paper. The problem of reactive power allocation between WTGs is formulated as an optimization problem subject to restrictions. The principal objective function is in order to make the terminal voltage of each WTG most effectively close to the wind farm average voltage value through the allocation and control of reactive power between each WTG. In recent years, an ever-increasing research attention has been paid to the solution of the optimal reactive power dispatch problem (ORPDP) based on the application of a variety of heuristic optimization

algorithms such as genetic algorithm [I. J. Fang et al, 2011], particle swarm optimization [V. S. Pappala, 2010], evolutionary programming [Q. H. Wu et al, 1995] and differential evolution [M. Varadarajan et al, 2008]. However, these technologies easily suffer from the partial stagnation or premature convergence and genetic operators have to be carefully selected or developed. The objective of this paper is to introduce a quadratic programming-based controller for optimal control of reactive power allocation between WTGs, which the voltage profile is improved and the number of onload tap changes of tap-changing transformer is effectively decreased. This paper is organized as follows. A detailed wind farm model is presented in section 2. In section 3, the proposed optimization method of allocation of reactive power between WTGs and its formulation is introduced. Simulation results and analysis are demonstrated in section 4. And the conclusion is given in Section 5.

2.

WIND FARM MODEL

2.1 Wind farm configuration To avoid wake effects, the wind farm can be made longer and more stretched out. Choice of wind configuration should depend on wind data and meteorological environment. However, this is not taken into consideration in this paper. Therefore, the configuration is selected based on the radial layout as shown in Figure 1. Recommended spacing is 5-9 rotor diameters separating towers within a row and 35 diameters between rows [Gilbert M. Masters, 2004]. Six diameters are used here. A higher number of turbines mean longer cables and higher loss, therefore, each radial connects eight wind turbines which has the rated power of 3.6 MW and rotor diameter 104m. Besides that, an offshore platform is necessary for the transformer to step up the voltage for high voltage transmission. 33 kV XPLE 240

33 kV XPLE 120

33 kV XPLE120

33kV XPLE 95

33 kV XPLE 95

33 kV XPLE 95

33 kV XPLE 240

33 kV XPLE 120

33 kV XPLE120

33kV XPLE 95

33 kV XPLE 95

33 kV XPLE 95

33 kV XPLE 240

33 kV XPLE 120

33 kV XPLE120

33kV XPLE 95

33 kV XPLE95

33 kV XPLE 95

Bus 9

33 kV XPLE 240

Bus 17

Bus 10

33kV XPLE 400

Bus 1

Bus 42

33 kV XPLE 240

Bus 2

Row1~row5

33kV XPLE 400

Column1~column8

33 kV XPLE 240 33kV XPLE 400

Bus 25

Bus 18

PLATFORM

Onshore Bus 43

Grid Bus 44 Slack bus

TRANSFORMER 33/150

XLPE 150 kV

2.26 km 33kV

XPLE 40

0 33 kV XPLE 240

33 kV XPLE 240

33 kV XPLE 120

33 kV XPLE120

33kV XPLE 95

33 kV XPLE 95

33 kV XPLE 95

20 km Bus 33

.56

33kV XPLE 400

12

Bus 26

7.41 km

km

33 kV XPLE 240

33 kV XPLE 240

33 kV XPLE 120

33 kV XPLE120

33kV XPLE 95

33 kV XPLE 95

33 kV XPLE 95

Bus 41

Bus 34

0.8427 km

Fig. 1 Wind Farm Configuration

2.2 Size of cables Larger conductor cross-section gives less losses and the power rating is higher. In this study, the maximum generated by each radial is 28.8 MW and WTGs absorb or produce maximum 13.92 MVar. Therefore, 33 kV XPLE submarine cables [Randi Aardal Flo, 2009] delivered by ABB are adopted here. Three different sizes of cables are divided in each radial based on different power rating. The 400 𝑚𝑚2 cable are connected between the platform and the first wind turbine. The following two cables from the first WT must have a cross section of 240 𝑚𝑚2 and 120 𝑚𝑚2 cables are adopted for the wind turbines from the third one to sixth one. The last three cables adopt the 95 𝑚𝑚2 cables. The cable data for the cables between WTs in each radial and the cables between the offshore platform and the radials are given as shown in Table 1 and Table 2. Cross- Power R L C section rating [ohm] [ohm] [μF] [𝑚𝑚2 ] [MW] 95 15.0 0.20225 0.11643 0.13483 120 18.6 0.16854 0.10857 0.15169 240 29.3 0.08427 0.09796 0.19383 Table 1 Cable data between the wind turbines Bus number

Cable R L C length [ohm] [ohm] [μF] [km] 1-2/1- 34 12.56 0.7536 1.38104 3.5168 1-10/1-26 7.41 0.4460 0.81477 2.0748 1-18 2.26 0.1356 0.24845 0.6328 Table 2 Cable data between the platform and radial 2.3 Transmission system and transformer Between 2002 and 2009, many famous offshore wind power projects advanced to commissioning, such as Horns Rev of Denmark, North Hoyle of the UK, according to the different wind farm sizes and offshore distances, 20 km submarine high voltage alternative current (HVAC) transmission cable is decided in this study. The cable parameters of 150 kV XPLE submarine is given in appendix. The size of wind farm we proposed is 144 MW, therefore, a 160 MVA tap-changing transformer (150/33 ± 10% kV with 33 taps ) is installed at offshore platform to set up the voltage for transmission and regulate voltage. Besides that, the high capacitance of submarine cable results in the need of reactive compensation. An estimate of the reactive power produced by the 150 kV HVAC can be taken into consideration according to equation (1) [M. J. da R. B. Marques, 2010]. Compensation only at the onshore end is possible, but

adding compensation both end can greatly improve the transmission distance as well as the current profile along the HVAC link, and as a result, transmission loss can be reduced. Thus, approximately 60% of reactive power is compensated at both the onshore and offshore. Q = ω × C × L × 𝑉2 (1) 2.4 grid impedance The estimation of grid impedance has an effect on the stability of the system. The grid impedance can be calculated as equation (2) and (3) [Stefan Lundberg, 2006]. Rg = 𝐿𝑔 =

V2 gl−l

(2)

√K2 xr +1Ksc Prated 𝐾𝑥𝑟𝑅𝑔

(3)

2𝜋𝑓𝑔

Where, 𝑉𝑔𝑙−𝑙 is the line-to-line voltage of the grid; 𝐾𝑥𝑟 is the XR-ratio of the grid and K sc is the short circuit ratio (the short circuit power of the grid divide by the rated power of the wind farm).

3.

The purpose of the reactive power control is to adjust the reactive power generated to meet the reactive reference at the PCC, as shown in Figure 2. As the previous presentation, there are many distribution principles of reactive power between WTGs, such as even distribution, proportional distribution. However, because of the wind distribution, wake effect and other effects, the WTs in the same wind farm may have different operating state. Voltage profile of WTG buses is mainly dependent on the P and Q of each WTG, thus steady state voltage profile of WTGs can be improved by optimal reactive allocation which can reduce the number of switching operations of OLTC and/or shunt capacitor/reactors. Power loss can be reduced by optimizing the reactive power distribution between WTs, but the effect of reactive power allocation is small. Qgiref Qgiref Qgiref

PCC

Grid Bus 44 Slack bus

V

PI controller

Distribution principle

* PCC

Fig. 1 The proposed reactive power control

(5)

𝑉𝑚𝑖𝑛 ≤ 𝑉𝑖 ≤ 𝑉𝑚𝑎𝑥

(6)

𝑄𝑗𝑚𝑖𝑛

(7)

≤ 𝑄𝑗 ≤

𝑄𝑗𝑚𝑎𝑥

Where, 𝑉𝑖 is the voltage of bus 𝑖, 𝑉𝑎𝑣𝑔 is the average ∗ value of the voltages of all the WTG bus, and 𝑄𝑊𝐹 is the reactive power reference value of WF. 3.2 Quadratic programming and formulation The general format of quadratic programming is as equation (8). 1 min 2 𝑥 𝑇 𝐻𝑥 + 𝑓 𝑇 𝑥 (8) (9)

𝐴𝑒𝑞 ∙ 𝑥 = 𝑏𝑒𝑞

3.1 Proposed optimization method

Onshore bus 43

Subject to: 𝑊𝑇 ∗ ∑𝑁 𝑖=1 𝑄𝑗 = 𝑄𝑊𝐹

Which subject to: A∙𝑥 ≤𝑏

PROPOSED CONTROL STRATEGY

VPCC

With the purpose of improving the voltage profile, the optimization problem is formulated as equation (4), which is used to make the terminal voltage of each WTG most effectively closed to the wind farm average voltage value through the allocation and control of reactive power between each WTG. Equations (5)-(7) are constrains. 2 𝑁𝑊𝑇 (𝑉𝑖 − 𝑉𝑎𝑣𝑔 ) min ∑𝑖=1 (4)



Qgiref Qgiref

(10)

𝑙𝑏 ≤ 𝑥 ≤ 𝑢𝑏 (11) A , 𝑏 is the matrix and vector in linear inequality constraints respectively; 𝐴𝑒𝑞 , 𝑏𝑒𝑞 is the matrix and vector in linear equality constraints severally; and 𝑙𝑏 , 𝑢𝑏 is used to present lower bounds and upper bounds of variable. Then words about algorithm choosing are that ‘trust-region reflective’ handles problems with only bounds or only linear equality constraints, however, ‘interior-point-convex’ handles only convex problems. Thus, ‘active-set’ algorithm is chosen here. Therefore, the previous problem is solved by formulation of parameters which is necessary. The effort is presented as shown in equations (12) - (17). 𝑁

𝐵𝑈𝑆 H(m, n) = ∑𝐾=1 𝐾(𝑘, 𝑚) ∗ 𝐾(𝑘, 𝑛)

f(m) =

𝐵𝑈𝑆 ∑𝑁 𝑘=1 𝐾(𝑘, 𝑚) ∗

𝐾𝑖𝑗 = 𝑍𝑖𝑗 − 𝑁

1 𝑊𝑇

(𝑉𝑘,0 − 𝑉𝑎𝑣𝑔,0 )

𝑊𝑇 ∑𝑁 𝑖=1 𝑍𝑖𝑗

(12) (13) (14)

Where 𝑍𝑖𝑗 is the sensitivity between bus voltage 𝑖 and reactive power 𝑗 which can be obtained through the inverse Jacobian of power flow. And the inequality constrains: 𝑍𝑖,𝑗 1 ≤ 𝑖 ≤ 𝑁𝑊𝑇 A(i, j) = { (15) −𝑍(𝑖−𝑁𝑊𝑇 ),𝑗) 𝑁𝑊𝑇 + 1 ≤ 𝑖 ≤ 2𝑁𝑊𝑇

b(i) =

𝑉𝑖,𝑚𝑎𝑥 − 𝑉𝑖,0 1 ≤ 𝑖 ≤ 𝑁𝑊𝑇 { (16) 𝑉(𝑖−𝑁𝑊𝑇 ),0 − 𝑉(𝑖−𝑁𝑊𝑇 ),𝑚𝑖𝑛 𝑁𝑊𝑇 + 1 ≤ 𝑖 ≤ 2𝑁𝑊𝑇 Finally, the equality constraints: 𝐴𝑒𝑞 = [1,1, ⋯ ,1] (17) ∗ 𝑏𝑒𝑞 = ∆𝑄𝑊𝐹 (18) Besides that, the flow chart of control strategy based on the optimal reactive power allocation principle is shown in Fig. 3. Fig. 4 The reactive power reference at the PCC Initialization

voltage profile

voltage per unit

Update active power Pg_input, reactive power Qg_input and reactive power reference Q_ref At the PCC.

Update busdata and linedata.

Power flow calculation

Solve the problem of reactive power allocation with optimization method

1.06 1.05 1.04 1.03 1.02 1.01 1 0

Update busdata with the optimal reactive power allocation

5 wind turbine number

10

Fig. 5 Voltage profile with even distribution principle voltage profile

Solution is best?

Reset tap position

0.95