DC Power Transmission ( ACDC 2018 ) Optimal reactive power control in a converter station during low-power operation of HVDC

When the high-voltage DC (HVDC) system is operated in low-power transmission, the overplus of reactive power provided by AC filters may still exist apart from satisfying the need of the converter station, restricted by the minimum number of filter banks. This will lead to a large number of surplus reactive power into AC system, affecting the safe and stable operation of power grid. Here, the impacts of the adjustment of on-load tap changer of converter transformer and the adjustment of control angle of the converter station on reactive power consumption are analysed. Taking effects on the adjustment of control devices and the interchange of reactive power into account, a static reactive power optimisation model based on the actual control strategy of reactive power in a converter station is set up, which provides theoretical basis for an optimal control during lowpower operation. Taking Tian-Guang HVDC project as an example, the simulation results verify its effectiveness of the proposed method.


Introduction
The reactive power compensation and voltage control in converter station are key points for the security and stability of high-voltage DC (HVDC) and ultra-HVDC (UHVDC).The DC converter will consume a large amount of reactive power in the transmission of active power, and the fluctuation of AC voltage occurs due to insufficient or excess reactive power, which might seriously affect the safety of power grid.Owing to the harmonic performance of the converter station and the limitation of AC filters, a certain number of AC filter banks, called absolute minimum filter capacity limit, must be put into the station when HVDC system operates.However, the capacity of AC filters for each group increases rapidly restricted by numerous factors, and 287 Mvar AC filters, for example, has been put into ±800 kV Bin-Jin DC transmission project.Therefore, when HVDC system runs during the period of low power, the reactive power provided by AC filters will far greater than that consumed by converter, which leads to considerable interchange of reactive power between the converter station and AC system.Meanwhile, the load is usually low in power grid, and excess reactive power exists in AC line under light load during this period.If a large amount of reactive power is injected into AC system at this time, the voltage rise of the converter station and nearby grid will aggravate the difficulty of voltage regulation in local area, which brings great impact to the stability of power grid operation, and DC system might be even forced to stop under specific way.
Domestic and foreign scholars have made great efforts on reactive power control of HVDC power transmission system in low-power operation.In [1], the solution to suppress the voltage rise caused by low-power operation based on the non-linearity of reactive power consumption in a converter station is proposed.The excrescent reactive power can be absorbed by increasing the minimal extinction angle of converter.Two kinds of low load reactive power optimisation (LLRPO) function of HVDC and UHVDC applied in China Southern Power Grid are introduced in [2], and suggestions on LLRPO function improvement in practice are proposed.Wang et al. [3] introduce a reactive power control method of 'open loop + closed loop' in a converter station, in which DC voltage is considered as control variable and exchange of reactive power of AC/DC system as feedback variable.Lei et al. [4] and Xiao et al. [5] comprehensively analyse and summarise the LLRPO function of Xing-An and Yun-Guang HVDC, separately.
In the aspect of reactive power optimisation of AC/DC system, the existing research focuses on the transmission grid, including power plants, AC substations, and DC converter stations.A multiobjective reactive power optimisation model of AC/DC system is set up considering the minimal active power loss and high-voltage quality in [6], and Li et al. [7] take further consideration on the energy-loss characteristics of the converter stations in detail.However, the actual control requirements of a converter station, AC filter requirements, for example, are not taken into account in above.Based on the FACTS device, reactive power optimisation model of AC/DC transmission and distribution network are separately established with specified parameter of a converter station in [8,9].
It is obvious that there are following problems of previous research: (i) a convincing scheme of device motion or parameter setting cannot be given in the low-power operation of HVDC power transmission system; (ii) the existing research on reactive power optimisation of AC/DC hybrid system is not suitable for a single converter station without considering the actual control requirements.The remainder of this paper is organised as follows.Section 2 analyses characteristics of reactive power and their influence factors in a converter station.Then, a reactive power optimisation model is built.Section 3 is a case study on Tian-Guang HVDC project.Section 4 summarises the paper and gives suggestion on further research.

Characteristic analysis of reactive power in converter station
With the operation of HVDC system, the interchange of reactive power between the converter station and AC system is shown in Fig. 1.Specially, adjustable low-voltage reactors or fixed highvoltage reactors are installed near the converter station in some projects, which is not suitable for this paper.
Therefore, the interchange of reactive power between the converter station and AC system is calculated by and It shows that reactive power is injected into a converter station from AC system when Q exp is positive.The feature of thyristor determines that the converter needs to absorb reactive power from AC system whether it works in rectifier or inverter state.With stable operation of the converter, some expressions are ) where Q exp stands for the exchange of reactive power; and φ represent active power, reactive power, DC voltage, ideal no-load DC voltage, DC current control angle, and power factor angle of the converter, respectively; X r , k b, and k T , located in the valve side in Fig. 1, stand for commutating reactance, the number of six-pulse converter per pole, and the ratio of converter transformer; Q acf is the reactive power provided by AC filters, Q ACFnorm and U ACFnorm are total rated capacity and rated voltage amplitude of AC filters, and U t , f ACact , and f ACnorm are the actual voltage, actual frequency, and rated frequency of AC system.
Then Q d can be achieved from (2) by introducing ( 4) and ( 5) It is assumed that the voltage U t of AC bus is constant, reactive power Q d of the converter station is only related to DC current I d , control angle θ d , and converter transformer ratio k T , when using constant power control.Owing to where k p stands for the number of poles in the converter station and I d can be calculated by ( 4), (5), and (7), which is The variation of I d with θ d and k T can be discussed by taking the derivative of the preceding equation ( 4) where Meanwhile, the ratio of converter transformer shown in Fig. 1 is where k TN is the rated ratio, p represents the tap position, and ΔU stands for the step voltage of converter transformer tap.Overall, from ( 6), ( 9) to (11), it is not difficult to find that: (i) I d is increasing with the increase in θ d , and then Q d is rising; (ii) I d is increasing with the decrease in p, and then Q d is rising.

Reactive power optimisation of converter station during low-power operation 2.2.1 Model for reactive power optimisation of converter station:
The traditional method to increase the reactive power consumption of the converter station is to raise its trigger angle with the maximum limit of 38° due to potential adverse effects referred in [1].Also, the conclusion summarised in Section 2.1 shows that a proper increase for converter transformer ratio helps to reduce these negative impacts.Hence, an optimal reactive power model for the converter station with minimum number of AC filters during low-power operation is proposed.
In addition, to take the connection of AC and DC system into account, as well as to adapt to the usual method, that per unit system is used for the analysis of AC system, reference values are chosen for a concise form of converter equations as follows: where S B and U B represent reference power and reference voltage of AC system, P dB and U dB the reference power and reference voltage of DC system, and k T represents reference ratio of converter transformer.More details can be found in [10].In addition, the following contents are discussed under per unit system in this section, and the subscript '*' will be deleted for a convenient writing.

Objective function:
The objective function of the model is where Q d and Q acf are computed by ( 2) and (3); θ d0 and k T0 represent common status of the converter station under a normal operating condition.The model reflects that a small amount of reactive power interchange with slight adjustment of control angle and converter transformer ratio is expected, and w 1 , w 2 , and w 3 are their weighting coefficients.Furthermore, |Q d − Q acf | and θ d are

Equality constraints:
(i) Nodal power balance equations For pure AC node i where P is and Q is represent the nodal injection active and reactive power for node i, and G ij and B ij the real part and imaginary part of the node admittance matrix element, respectively.U i indicates the voltage amplitude of node i, and θ ij indicates the phase angle of the two nodes between i and j.It is necessary to point out that node j can be either a pure AC node or a DC node (the converter AC bus).
For DC node i where positive and negative signs represent inverters and rectifiers, respectively.

ii) Basic equations for the converter station
where k μ is the coefficient considering the influence of commutation overlap.

Inequality constraints:
(i) Inequality constraints for state variables where (•) min and (•) max are minimum and maximum values of the variable (•).Especially, (22) shows that k T is a discrete variable with a series of values.

Algorithm for reactive power optimisation of converter station:
The hybrid algorithm in [11] is applied to the model founded in the preceding section.Similarly, discrete constraints are ignored first and the initial solution can be obtained by non-linear interior point method.Then, the original problem is decomposed into a discrete optimal subproblem and a continuous optimal subproblem.Specially, there is only one discrete variable in the model; hence, the enumeration method in a limited range is used for the discrete variable.Also, the continuous one is solved by nonlinear interior point method.Finally, the optimal solution is received by comparing the objective functions with different discrete variables.A hybrid algorithm flowchart is shown in Fig. 2. In this paper, sparse technology is applied in the interior point method and power flow calculation.

Comparison and analysis of different measures to adjust reactive power and voltage in converter station
In Section 2.1, the reactive power consumption of converter Q d is derived with the adjustment of control angle θ and transformer ratio k T .Taking the rectifier station of Tian-Guang HVDC project as an example, the adjustment of reactive power and voltage is simulated and analysed, and detailed parameters of the test system are referred in [12][13][14][15].Taking the transmission of 270 MW DC power as an example, it is assumed that the equivalent voltage of AC system U sys is 228 kV, and that DC system is operated in single Supposing that the trigger angle of the converter θ d is 15°, converter transformer tap position p is adjusted from 0 to −6, and the result of the adjustment, reactive power consumption of converter Q d , for example, is shown in Table 1.
Supposing that the converter transformer works at rated ratio, i.e. p = 0, trigger angle increases from 15° to 27°, and the adjustment result is shown in Table 2.
It can be seen from Tables 1 and 2, when 270 MW power transported and two sets of AC filters (1A + 1B) applied, converter station transfers the excess reactive power 60.399 Mvar, calculated as 80 × 2-99.601, to AC system in initial state, i.e. θ d = 15° and p = 0.As the converter transformer tap position p is adjusted from 0 to −6, the consumption of reactive power Q d increases from 99.601 to 103.294 Mvar, and its increment is limited.If the trigger angle of converter θ increases to 27°, the consumption of reactive power is raised to 160.531 Mvar, realising the purpose of zero interchange of reactive power between AC and DC system.In addition, as far as power loss of DC line is concerned, it is not difficult to find in Fig. 3 that comparing with transformer ratio, the regulation of trigger angle has little influence on DC current, that is, the increment caused by trigger angle is small.Therefore, it is clear to be seen that the adjustment of trigger angle is more propitious to increase reactive power consumption, as well as decrease the impact on energy loss, than that of the transformer tap.
However, the trigger angle of converter is restricted by the valve arrester, damper winding, and valve reactor.The ideal noload direct voltage decreases with the increase in trigger angle, but it may lead to a high step voltage of value and bring adverse effects.Thus, it is necessary for the converter station to adjust the transformer tap position in order to avoid running under the condition of excessive trigger angle.

Optimal control results of converter station during lowpower operation
Considering decision-makers' respective preference and order of magnitude for different targets, values are assigned to weighting coefficients as follows: w 1 = 1, w 2 = 10, w 3 = 100.Under the normal condition of sample system adopted in Section 3.1, the trigger angle works around 15° with the converter transformer changing in the vicinity of its rated ratio.Hence, the fixed values for parameters in the model are taken as p 0 = 0, θ d0 = 15°.As it can be seen from Fig. 4, there is little reactive power interchange between AC and DC system when the trigger angle ranges from 28° to 30° as converter transformer ratio varies.
Control variables p and θ d are optimised by the optimal reactive power model proposed in this paper.Compared with other strategies, the operating parameters of AC/DC system are analysed.The comparison scheme is designed as follows.
•    The results of different strategies are shown in Table 3. From the table, it is clear to be seen that strategies 2 and 3 can effectively decrease the interchange of reactive power compared with strategy 1 applying initial parameters.Meanwhile, DC voltage is reduced to far less than its rated value in the case of a long overvoltage operation.Considering the influence of transformer ratio, strategy 3 has an effective suppression of the ideal no-load direct voltage fluctuation.Though reactive power interchange and DC current obtained by the proposed method outweigh those by strategy 2, the limited energy loss can be accepted due to low DC resistance.
The above analysis shows its effectiveness of the proposed method.The method provides a theoretical basis for tuning parameters of the converter station during low operation.However, the choice of weighting coefficients leading to different optimal results may be affected by various factors, which can be focused on for further research.

Conclusion
An optimal reactive power control method of the converter station during low-power operation is proposed in this paper.Firstly, the effects of converter transformer ratio and control angle on reactive power and voltage in a converter station are derived theoretically, and the similarities and differences of the two measures are analysed and compared.Then, an optimal reactive power dispatch model of the converter station is established, comprehensively considering its actual strategies and requirements.The optimisation results provide reference for the parameters of the two regulation devices.Finally, the test results on Tian-Guang HVDC verify the effectiveness of the proposed method.
However, there are certain limitations in this paper.Apart from previously mentioned one that weighting coefficients will affect the result, the influence of change in DC control mode and the regulation characteristics of AC system are both not taken into account.

Fig. 1
Fig. 1 Diagram of reactive power in a converter station

Strategy 1 :
Set the same p and θ d as those under normal condition, i.e. p = p 0 , θ d = θ d0 .• Strategy 2: Set θ d for the minimum interchange of reactive power, and p = p 0 .

Fig. 3 Fig. 4 Q• Strategy 3 :
Fig. 3 I d changing trends with Q d