7296 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 6, NOVEMBER 2018
A General Decentralized Control Scheme forMedium-/High-Voltage Cascaded STATCOM
Xiaochao Hou , Student Member, IEEE, Yao Sun , Member, IEEE, Hua Han, Zhangjie Liu , Mei Su,Benfei Wang , and Xin Zhang , Member, IEEE
Abstract—This study presents a general decentralized controlscheme for cascaded H-bridge inverter-based static compensatorsin medium-/high-voltage power network. The H-bridge modulesare controlled in a decentralized manner without a central con-troller and each module makes decisions based on individual localcontroller. The local controller includes two parts: first, a Q-ωboost control is introduced to share reactive power equally; andsecond, a scalable P-V control is established for balancing dc-linkvoltage of inverters. The proposed scheme can achieve frequencysynchronization autonomously, and thus has advantages of im-proved reliability, scalability, and decreased costs. Moreover, animproved decentralized control is also proposed to adapt the grid-side dynamics when contingencies will occur. The system stabilityconditions are derived, and the feasibility of the proposed methodis verified by simulation results.
Index Terms—Cascaded STATCOM, decentralized control,medium/high voltage power network, power quality.
I. INTRODUCTION
THE cascaded H-bridge inverter is a promising family ofhigh-voltage converters due to its salient features of modu-
larity, transformer-less, and favorable voltage quality. This cas-caded structure has been widely studied and applied to motordrives, grid-tied distributed generation, battery balance man-agement, and flexible AC transmission systems (FACTS) [1].Among FACTS, the cascaded STATCOM has been a typicallypopular occasion for the enhancement of the power transmissioncapability, voltage stability and power quality [2].
For medium/high voltage applications, the coordinate con-trol of the cascaded STATCOM is essential. In the middleof the 1990s, Lai and Peng [2] firstly proposed a cascaded
Manuscript received November 14, 2017; revised March 6, 2018 and May 15,2018; accepted July 9, 2018. Date of publication August 13, 2018; date of currentversion October 18, 2018. This work was supported in part by the NationalNatural Science Foundation of China under Grants 61622311 and 61573384, inpart by the Joint Research Fund of Chinese Ministry of Education under Grant6141A02033514, and in part by the Hunan Provincial Innovation Foundation forPostgraduate. Paper no. PESL-00226-2017. (Corresponding author: ZhangjieLiu.)
B. Wang and X. Zhang are with the School of Electrical and ElectronicEngineering, Nanyang Technological University, Singapore 639798 (e-mail:,[email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPWRS.2018.2865127
multilevel STATCOM, which solves the size-and-weightproblems of transformer-based multipulse inverters and thecomponent-counts problems of multilevel diode-clamp andflying-capacitor inverters. Then, many improved variants [1],[3]–[5] are presented to maintain reactive power sharing andDC-link voltage balancing. In [1]–[5], they mainly rely on thecentralized control, in which a powerful central control unit isnecessary to gather the global information and generate ref-erence signals for all modules. Especially, numerous modulesin a HV system will lead to a complex communication net-work. The network would adversely affect the system flex-ibility and reliability, and is vulnerable to a single point offailure [4], [5].
Recently, the advanced distributed control has provided analternative to cascaded STATCOM system [6]–[8]. In [6], a dis-tributed control using standard serial communication protocolwith less-communication is early implemented. In [7], [8], amaster controller in cooperation with multiple distributed slavecontrollers has been implemented. The master controller takescharge of the system-level control functions, while distributedslave controllers are responsible for their individual control pur-poses. Since the computation pressure is distributed to the in-dividual processors, this distributed control scheme allows fora relatively slow-speed communication network compared withthe centralized control [8].
In this study, we propose a simple and reliable decentral-ized control scheme for cascaded STATCOM. Compared withthe centralized [1]–[5] and distributed control frames [6]–[8],the proposed scheme has two obvious features: 1) each mod-ule is controlled in a decentralized manner without a complexcommunication network; 2) the grid impedance is shaped as amainly resistive line to facilitate the Q-ω control and P-V control[9]. Although there is not a central control unit, the proposedscheme can also achieve the same functions of reactive powercompensation, AC grid synchronization and DC-link voltagebalance with respect to existed methods [2]–[8]. Thus, the char-acteristics of low cost and flexible scalability are attained forlarge-scale cascaded STATCOM.
II. DECENTRALIZED CONTROL FOR CASCADED STATCOM
A. Models of Cascaded STATCOM
Fig. 1 illustrates the diagram of cascaded STATCOM, whichconsists of N H-bridge modules.
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 6, NOVEMBER 2018 7297
Fig. 1. Schematic diagram of MV/HV cascaded STATCOM modules.
From Fig. 1, the output active power Pi and reactive powerQi of i-th module are expressed by
Pi + jQi = Viejδi · ((Vpe
jδp − Vgejδg )/(|Zline | ejθl i n e )
)∗
(1)where Vi and δi represent the output voltage amplitude andphase angle of i-th module. Vg and δg are the voltage amplitudeand phase angle of utility grid. |Zline | and θline are the gridimpedance amplitude and angle. Note that the grid impedanceis shaped as a mainly resistive line (θline ≈ 0) to facilitate theQ-ω boost control [9]. The voltage Vpe
jδp at the point of com-mon coupling (PCC) is the sum of all module voltages.
Vpejδp =
N∑
j=1
Vjejδj (2)
From (1)–(2), the power transmission characteristic is given
Pi =Vi
|Zline |
⎛
⎝N∑
j=1
Vj cos (δi − δj ) − Vg cos (δi − δg )
⎞
⎠
(3)
Qi =Vi
|Zline |
⎛
⎝N∑
j=1
Vj sin (δi − δj ) − Vg sin (δi − δg )
⎞
⎠ (4)
B. Proposed Decentralized Control in Normal-Grid Condition
To synchronize each module with the grid and regulate thegrid-injected reactive power, a decentralized Q-ω boost controlscheme is proposed as
ωi = ω∗ + kq (Qi − Q∗) (5)
where ωi is the angular frequency reference of i-th module. ω∗
represents the nominal value of the grid angular frequency. kq is
a positive gain of the Q-ω boost control. Q∗ denotes the nominalreactive power capacity of each module.
In order to balance the DC capacitor voltage Vdci of eachmodule, a decentralized P-V control (6) is constructed as
Vi = V0 + kp(Vdci − V ∗dc) (6)
where Vi is the voltage amplitude reference of i-th module. V ∗dc
is the capacitor voltage reference of each module. V0 representsthe initial voltage. kp is a gain of P-V control, which will bedesigned in the following part.
C. Steady-State Analysis
In steady state of normal-grid condition, reactive power shar-ing among modules is obtained due to the identical grid fre-quency (ω1 = · · · = ωN = ω∗) from (5)
Q1 = Q2 = · · · = QN = Q∗ (7)
Meanwhile, because each module shares the same grid cur-rent, the active power losses of all modules are approximatelyequal in nominal state [8], [11]. Namely,
P1 = P2 = · · · = PN = −P ∗ (8)
where P∗ denotes a nominal power loss of a module.From (7) and (8), the voltage amplitudes and phase angles of
the modules are equal in steady state.
V1 = V2 · · · = VN = V ∗; δ1 = δ2 · · · = δN (9)
where V∗ denotes the steady-state voltage amplitude. Thus, thevoltage amplitude and phase angle of PCC is derived from (2)
Vp = NV ∗; δp = δ1 = δ2 · · · = δN (10)
Then, the steady-state power of each module is obtained bycombing (3)–(4) and (7)–(10)
Pi =−P ∗ = SC
(NV ∗/Vg − cos δ
); Qi =Q∗ = −SC sin δ
(11)where SC = V ∗Vg/|Zline | represents the power transfer ca-pacity of a single module. δ = δp − δg refers to the steadypower angle, which is equal to δ = −arcsin( Q ∗
SC) in steady-state
from (11).
D. Stability Analysis
From (11), the delivered reactive power depends mostly onthe power angle, and active power is predominately dependenton voltage amplitude difference. Thus, stability analysis of Q-ωand P-V can be decoupled to facilitate their individual designs[10]. In this section, to verify the stability of proposed methods,small signal analysis is carried out.
1) Power Angle Stability: Since δi = ωi , combining (4), (5),(9), (10) and linearizing them around the steady state points yield
˙δi = k
⎛
⎝N∑
j=1,j �=i
(δi − δj
)−M(cos δ)
(δi − δg
)⎞
⎠ (12)
where k = kqV∗2/|Zline | and M = Vg/V ∗. δi , δg , δj denote
small perturbations around the equilibrium point.
7298 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 6, NOVEMBER 2018
From (12), the system matrix is given by
˙δ = −k · L · δ (13)
where we have the equations shown at the bottom of this page.The eigenvalues of the system matrix A = −kL are given by
λ1 (A) = −kM cos δ; λ2 (A) = · · · = λN (A)
= −k(M cos δ − N). (14)
Thus, the necessary and sufficient condition of power anglestability is obtained as follow
M cos δ − N > 0 (15)
That is, the power angle stability condition is concluded bysubstituting M = Vg/V ∗ into (15)
Vgcos δ − NV ∗ > 0 (16)
From (16), cos δ must be greater than zero, and the powerangle δ should lie in (−π/2, π/2) under the stability constraint.According to above steady-state analysis, δ = −arcsin( Q ∗
SC) is
a stable equilibrium point. From (14), a fast convergence rate ofthe power angle dynamic can be obtained by flexibly regulatingthe Q-ω control coefficient kq , but a too large kq would causeunacceptable impulse frequency responses during the transientprocess. Thus, a proper kq could be designed by making a com-promise between settling time and overshoot.
2) DC-Link Voltage Stability: The dc-link voltage stability isessential for the normal operation of the cascaded STATCOM. Itis guaranteed by P-V control (6). To analyze the voltage stability,the mathematical model of the fore-end DC-link capacitor is setup firstly.
CdVdci
dt= − Vdci
Rloss− Pi
Vdci(17)
where C is the value of DC capacitor. Rloss implies an equiva-lent resistor of power losses, connected in parallel with the DCcapacitor in the model [11].
Combining (3), (6), (8)–(10), (17) and linearizing themaround the steady state points yield⎧⎨
⎩
Pi = V ∗|Zl i n e |
[(N − M cos δ)Vi +
∑Nj=1 Vj
]
Vi = kp Vdci ;˙V dci =− 1
Rl o s s C Vdci − P ∗V ∗2
d c CVdci− 1
V ∗d c C Pi
(18)
From (18), the system matrix of voltage stability is given by
˙Vdc = Av Vdc (19)
where Vdc = [ Vdc1 Vdc2 · · · VdcN ]T ; Av = −[bI + kpA1 ];{
A1 = a[−dIN×N + 1N 1T
N
]
a = V ∗|Zl i n e |V ∗
d c C ; b = 1Rl o s s C + P ∗
V ∗2d c C
; d = M cos δ − N
(20)The voltage stability can be analyzed by inspecting the eigen-
From (20)–(21), as a, b, and d are greater than zero, the nec-essary and sufficient condition of voltage stability is concludedas follow
− b
a(N − d)< kp <
b
ad(22)
E. Improved Decentralized Control forAbnormal-Grid Condition
When contingencies occur in power grid, an improved decen-tralized control is proposed by adding a feed-forward compen-sation to (6).
Vi = V0 + kp(Vdci − V ∗dc) +
Vg − V ∗g
Nf ew(23)
where Vg and V ∗g are real-time voltage amplitude and nominal
voltage amplitude of grid. Note that the voltage compensationdoes not require all modules to take part in. That is, as long asNf ew modules (Nf ew ≈ 10% N∼ 20% N ) need to acquire thegrid information, the adverse effect of the contingencies can becompensated.
For these Nf ew modules, their reactive power referencesshould be regulated according to their individual voltageamplitude.
ωi = ω∗ + kq
(Qi − Vi
V ∗Q∗)
(24)
III. SIMULATION RESULTS
The simulations are carried out to verify the proposed ideas ofQ-ω control (5) and P-V control (6). The local control diagramof i-th module is presented in Fig. 2. The system parameters ofthe medium voltage STATCOM are listed in Table I. Typically,the physical parameters of each H-bridge module are firstlyassumed: the rated capacity 100 kVA, rated AC voltage 600 V/50 Hz, dc-link voltage 900 V, and conversion efficiency 95%.Then, the detailed designs of control parameters are presentedas follows:
δ = [ δ1 δ2 · · · δN ]T
L =
⎡
⎢⎢⎢⎣
M cos δ − N + 1 1 · · · 11 M cos δ − N + 1 · · · 1...
.... . .
...1 1 · · · M cos δ − N + 1
⎤
⎥⎥⎥⎦
= (M cos δ − N)IN×N + 1N 1TN
IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 6, NOVEMBER 2018 7299
Fig. 2. The local control diagram of i-th STATCOM module.
TABLE ISIMULATION PARAMETERS
Fig. 3. Results in normal-grid condition. (a) Reactive power. (b) Active power.(c) Frequency. (d) Voltage amplitude. (e) DC-link voltage. (f) Power angle.
1) According to the grid voltage class V ∗g = 6kV, we choose
the number of cascaded modules N = 10.2) The nominal reactive power capacity of each STATCOM
module Q∗ = 100 kVar is set. Normally, the active powerloss of each module is about five percent of the reac-tive power capacity (P ∗≈ 5 kW). As the dc-link volt-age V ∗
dc= 900 V, an equivalent resistor of power lossesRloss = 162 Ω is calculated.
3) The Q-ω control gain kq is chosen according to (14)–(16).4) The P-V control gain kp is chosen according to (22).5) The initial voltage V0 should reach the steady-state voltage
V ∗ as close as possible, which is derived from (11).
A. Simulation Results in Normal-Grid Condition
To illustrate the effectiveness, the simulation in normal-gridcondition (Vg = V ∗
g ) is firstly carried out. The different initialphase angles of modules are set. Fig. 3 shows the simulation
Fig. 4. Results in abnormal-grid condition. (a) Grid voltage amplitude.(b) Voltage amplitude of ten modules. (c) Reactive power. (d) Frequency.
TABLE IIHIL TEST PARAMETERS
results of the proposed decentralized control. As seen fromFig. 3(a), the function of nominal reactive-power compensa-tion (Q1 = · · · = Q10 = 100 kVar) is realized. From Fig. 3(b),the absorbed active power is about 5 kW, which is equal tothe power losses of each module. Fig. 3(c) indicates that theautonomous frequency synchronization with the utility grid isobtained. Fig. 3(d) shows the output voltage amplitudes of tenmodules. Fig. 3(e) reveals that the DC capacitor voltage bal-ance among modules is achieved. Moreover, Fig. 3(f) showsthat the steady-state power angle between PCC and utility gridis close to 0, which is in accordance with stability analysis whereδ ∈ (−π/2, π/2).
B. Simulation Results in Abnormal-Grid Condition
The simulation in abnormal-grid condition is conducted toverify the validity of the improved decentralized control (23)–(24). In this case, mudule#1 and mudule#2 are chosen as thevoltage compensation modules (Nf ew = 2). Fig. 4(a) showsthe real-time grid voltage amplitude. Initially, grid voltage isnormal, and all modules work normally during t = 0 s − 2 s.Then 400 V grid voltage sag and 400 V grid overvoltage occurat t = 2 s and t = 6 s, respectively. From Fig. 4(b), V1 and V2decrease by 200 V at t = 2 s and increase by 200 V at t =6 s to adapt the grid dynamics, while V3 ∼ V10 are identicaland unchanged. Accordingly, Q1 and Q2 decrease at t = 2 sand increase at t = 6 s according to (24) in Fig. 4(c), whileQ3 ∼ Q10 are equal and remain unchanged. Fig. 4(d) revealsthat the autonomous frequency synchronization with the grid insteady state is also achieved under grid dynamics.
IV. HARDWARE-IN-THE-LOOP (HIL) RESULTS
To verify the feasibility of the proposed control scheme, alow-voltage system comprised of four cascaded modules is alsoimplemented by real-time HIL tests based on OPAL-RT plat-
7300 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 33, NO. 6, NOVEMBER 2018
Fig. 5. Steady-state results of HIL test. (a) Voltage and current waveforms of output AC voltage of four modules v1 ∼ v4 , grid voltage vg , and grid current ig .(b) Operation frequency f1 ∼ f4 , and DC-link capacitor voltage V dc1 ∼ V dc4 . (c) Output active power P 1 ∼ P 4 , and output reactive power Q1 ∼ Q4 .
form. The system parameters are listed in Table II. The nominalreactive power capacity of each STATCOM module is 20 kVar,and the active power loss of each module is about 1 kW. Thedesign guidelines of control parameters are similar to that of theabove Simulation Section III.
The HIL test results are shown in Fig. 5. The waveforms fromtop to bottom in Fig. 5(a) are output AC voltages of four modulesv1 ∼ v4 , grid voltage vg , and grid current ig . As seen, thefour cascaded modules have the same output voltage amplitude,phase angle, and frequency in steady-state.
Fig. 5(b) shows the operation frequency and DC-link capac-itor voltages of four modules in startup and steady state. Theautonomous frequency synchronization with the utility grid andthe voltage balance of DC-link capacitors are realized.
Fig. 5(c) illustrate the power response. Clearly, nom-inal reactive-power compensation (Q1 = · · · = Q4 = Q∗ =20 kVar) is realized, and the balance between the absorbed ac-tive power and the power losses is obtained (P1 = · · · = P4 =P ∗ = 1 kW).
V. CONCLUSION
This study exploits a new control concept for cascadedSTATCOM in medium/high voltage power system. It realizesautonomous frequency synchronization, reactive-power com-pensation, and DC capacitor voltage balance without a complexcommunication network. Thus, the reliability and expandabilityof the cascaded STATCOM are significantly improved, whichis very suitable for a large-scale high voltage system. In futurework, some hierarchical control schemes will be constructed forpractical cascaded STATCOM, where the decentralized controltakes a role of primary control, and secondary supervisory con-trol takes charge of the ancillary services, such as, system startupand power monitoring.
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