The MMC control system has a hierarchical control structure, including modulation control layer, converter control layer, and system control layer. Fig. 1 is the entire control system of an MMC-HVDC system.
Fig. 1 Control system of an MMC-HVDC system[1]
•System control layer
•System control is the highest-level control layer, aiming to control and coordinate power-sharing among poles and stations.[1]
•Converter control layer
•Converter control is used to control the active and reactive power injected into the connected AC system, which is required to keep the converter output voltage synchronized with the connected AC system. [1]
•Modulation control layer
•Modulation control is the most fundamental control layer of MMC control, aiming to generate fire pulses for each IGBT.[1]
This article will focus more on the converter control. There are three types of converter control: 1. power angle control, 2. vector current control, and 3. power synchronization control. This part mainly talks about the power-angle control and the vector current control under balancing grid conditions.
Power angle control is the most straightforward controller for grid-connected VSCs. The principle of power-angle control is based on the following well-known equations:
(1)
where P and Q are the active and reactive powers between two electrical nodes in ac systems with voltage magnitudes U1 and U2. The quantities θ and X are the phase-angle difference and line reactance between the two nodes. From (1), it follows that the active power is mainly related to the phase angle θ, while the reactive power is more related to the voltage-magnitude difference. These mathematical relationships are the foundation of power-angle control, i.e., the active power is controlled by the phase angle of the VSC voltage, while the reactive power or filter-bus voltage is controlled by the magnitude of the VSC voltage.
To produce three-phase alternating voltages, the VSC needs three variables: magnitude, phase angle, and frequency. With power-angle control, these three variables are given by three different controllers, i.e., the reactive-power controller (RPC) or the alternating voltage controller (AVC), the active-power controller (APC), and the phase-locked loop(PLL)[2].
(1) Reactive power controller:
(2)
(2) Alternating voltage control:
(3)
(3) Active power controller:
(4)
(4) Phase-locked loop:
Fig. 2 PLL for power angle control[2]
As we can see, the design and implementation of power angle control is simple and straightforward. However, power-angle control practically has never been applied to any real VSC-HVDC system, since it suffers from two fundamental problems: 1) The control system has no general means to damp the various resonances in the ac system; 2) the control system does not have the capability to limit the valve current of the converter.
2. Vector Current control[3]
Basic principles: the output current (difference-mode current) is mainly related to the difference-mode voltage, while the circular current (common-mode current) is more related to the common-mode voltage.
Vector current control can be conducted in dq synchronous rotating, αβ stational, abc original reference frame combined with their corresponding control methods (PI, PR, Dead Beat/Hysteresis). This article focuses more on the control based on the dq reference frame.
Fig. 3 Circuit diagram of an MMC
According to KVL, the mathematical model can be expressed as:
(5)
Assuming:
(6)
udiffj is the difference-mode voltage, ucomj is the common-mode voltage. icirj is the circular current of the common-mode current. (from the energy balancing aspect, this current is more like a common-mode current than a circular current). The output current can be expressed by the upper- and lower-arm currents as follows:
(7)
Substituting (6)(7) into (5), (5) can be expressed as:
(8)
From (8), we can see that the output current (difference-mode current) is mainly related to the difference-mode voltage, while the circular current (common-mode current) is more related to the common-mode voltage. As long as the differential voltage udiff and common voltage ucom are regulated, the output current and circular current can be controlled, and further power transmission can be controlled.
The next step will be to transform these quantities from abc reference frame to dq reference frame. Since there will be a steady-state error when tracing alternating quantities using PI controller, PI controller has to be realized in dq reference frame. The following is abc-dq transformation matrix:
(9)
The relations between the output current and difference-mode voltage can be expressed as (10) via abc-dq reference frame:
(10)
Using Laplace transform, (10) can be expressed as:
(11)
From (11) we can see that the ac output current only depends on the grid-side voltage and difference-mode voltage. According to (11), the control diagram can be obtained as shown in Fig. 4.
Fig. 4 Control diagram of the output current
From Fig. 4 we can see that there is a coupling effect between the d and q components. udiffp/q are the control variables, usp/q are the disturbing variables, and ivp/q are the outputs. According to the control theory, a negative feedback control system should be built to make the output current track the reference current.
Assuming:
(12)
Substituting (12) into (11):
(13)
The relationship between the output variable (ivd/q) and the built control variable (Vd/q) can be drawn as shown in Fig. 5.
Fig. 5 Relationship between the output variable (ivd/q) and the built control variable (Vd/q)
As mentioned before, the goal of the controller is to make the output current (ivd, ivq) track the reference current (ivd*, ivq*). Therefore, a negative feedback control system should be designed as shown in Fig. 6.
Fig. 6 Simplified diagram of the closed-loop control system
As long as we get Vd/q, we can obtain udiffd/q according to (12). Then, the output current can be obtained based on Fig. 4. Here comes the question: how to get Vd/q? A normal way is to apply PI controller as described in (14):
(14)
Finally, the control system of the output current can be obtained as shown in Fig. 7.
Fig. 7 Control system for the output current
The second step is to suppress the circulating current. The generation of circulating current is because the modulation type we applied in MMC is direct modulation, in which the nominal value of capacitor voltage is assumed to calculate the insert number of submodules. However, the capacitor voltage is floating in fact, so there will be unbalancing among the phase arms, which produces the circulating current[4]. (If we apply indirect modulation, in which the capacitor voltages measured or estimated are used when calculating the required inserted submodules, circulating current will not be generated because they have been considered during the modulation process. But additional horizontal and vertical energy balancing control should be applied[5].) The circulating current can be expressed as follows:
(15)
Ignoring the higher harmonics, circulation currents of the three-phase arms can be written as:
(16)
As we can see in (16), the circulating currents contain negative sequence components with frequencies twice the fundamental one, which needs to be suppressed. (The derivation process is complicated, and I haven't fully understood it yet, maybe I will share it in future articles.) The circulating currents do not have any impact on the AC-side voltages and currents, but they increase the power losses as well as the ripple magnitude of the SM capacitor voltage. Therefore, the circulation currents should be suppressed to zero. According to (8), the circulating current can be controlled through the common-mode voltage. Since the components we want to control are the negative sequence components with frequencies twice the fundamental one, we need to transform the circulating current in ABC reference frame to dq-2 reference frame. The transformation matrix can be written as below:
(17)
The relations between the circulating current and common-mode voltage can be expressed as (18):
(18)
Using Laplace transform, (18) can be written as:
(19)
From (19) we can see that the circulating current only depends on the common-mode voltage. According to (19), the control diagram can be obtained as shown in Fig. 8.
Fig. 8 Control diagram of the circulating current
Using the same method to build the control variable as shown from (12)-(14), the control system of circulating current can be seen in Fig. 9.
Fig. 9 Control system for the circulating current
Figs.7 and 9 show the inner-loop current controller. We can see that the reference value of the circulating current is set as 0. The reference value of the output current will be obtained according to the outer-loop power controller. The control objectives of the outer-loop controller contain 1) active power or DC voltage; (2) reactive power or AC-side voltage. Fig. 10 shows different control loops when different references are provided.
Fig. 10 Outer-loop power controller
According to the outer-loop and inner-loop controller, udiff* and ucom* can be obtained. Then the reference value of upper- and lower-arm voltages (upj* and unj*) can be obtained via (6). Then upj* and unj* will be sent to the modulation control layer to calculate the required number of the inserted submodule.
The above is mainly the control method when the AC side is in a balanced state. If there is a disturbance or unbalancing faults occurring on the AC side, the above control method will not be applicable due to two problems: 1) bad performance of PLL, 2)alternating components will generate in ivd and ivq. PI controller tracing alternating current will produce steady-state errors. I will share the control method under unbalancing AC grid in the next article.
[Reference]
Xiaoxiao Liu
Ph.D. researcher at KU Leuven/Energyville & University of Edinburgh
KU Leuven • Electrical Energy Systems and Applications (ELECTA) Department of electrical engineering(ESAT)
KasteelparkArenberg 10, bus 2445 | 3001 Leuven | Belgium
xiaoxiao.liu@kuleuven.be
EnergyVille • Electrical Networks
EnergyVille 1 | Thor Park 8310 | 3600 Genk | Belgium
xiaoxiao.liu@energyville.be
University of Edinburgh• Power Electronics and Smart Grids
Institute for Energy Systems
X.Liu-196@sms.ed.ac.uk