1. Introduction
In recent years, the economic development and the fast speed of the urbanization process causes the power consumption to grow rapidly. Therefore, the traditional distribution systems are facing a series of challenges, e.g. increasing operation efficiency, enhancing service reliability, improving power quality and safe-interconnecting distributed generation [
1,
2,
3,
4]. The VSC-HVDC [
5,
6,
7,
8] technology based voltage source converter shows advantages because of the rapidly growing applications of power electronics technology in the electricity distribution field: (1) distributed generation (DG) and energy storage (ES) devices interfaced to the AC distribution network require DC/AC or AC/DC conversion while a complete DC network can save lots of converter links and reduce costs and power losses but improve operational flexibility [
9,
10,
11]; (2) AC distribution networks require AC/DC conversion which supplies a growing number of DC loads—a DC distribution network can eliminate the links which will greatly reduce energy conservation [
12,
13]; (3) urbanization and the extensive use of power-electronic devices cause voltage fluctuations, voltage dips, harmonic pollution and other power quality problems in AC distribution networks [
2,
3,
4]. Studies also show that DC distribution networks have lots of other advantages: environmentally friendly, high capacity of power supply, low-cost of distribution cables and lines, reduced transmission utilization and losses, improved power quality, and needing no reactive power compensation [
1,
12,
13].
Considering the comprehensive advantages of the DC distribution network, considering the huge investment into development of independent DC distribution networks, the use of a hybrid AC/DC distribution scheme then gradually transiting to a complete DC distribution system is more feasible in practice. Therefore, an AC/DC power distribution system based on VSC-MTDC cannot only realize independent control of active and reactive power, but also improve the power quality and power supply capacity of the distribution network, facilitate the DG connection, and reduce losses and costs. The study of the power flow calculation method of the AC/DC distribution system with VSC-MTDC will be an important basis to analyze the steady-state and transient characteristics, control and protection technologies of VSC-MTDC. Therefore, it will be the main focus of this paper.
At present, the research on the modeling and control algorithms already has made some achievements for the AC/DC transmission system with VSC-HVDC, but the study of the AC/DC distribution system with VSC-MTDC is still in its infancy. Alternating iterative algorithms or unified iterative algorithms are commonly applied to the problem of power flow calculation for the VSC-MTDC system [
14,
15,
16]. Among reported works, in [
17], based on a steady-state model of VSC-HVDC, a mathematical model based on Newton method power flow calculation was developed and then a power flow algorithm was proposed which calculate AC and DC alternately. In [
18], considering different control modes of VSC, correction equations were derived. On the basis of these correction equations, a uniform iterative power flow calculation algorithm for systems equipped with VSC-HVDC was proposed. In [
19], under fixed control parameters and fixed power flow control objectives, respectively, a novel algorithm for power flow calculation based on equivalent injection power was proposed. In [
20,
21], a VSC model for VSC-MTDC power flow calculation was derived. According to the combinations for control variables
M (modulation degree) and
δ (PWM phase angle), four kinds of control schemes were brought forward; and corresponding interface functions for AC/DC alternant calculation are provided. In all the above research, converter losses are treated as equivalent to a resistance or simply ignored. To assume that the active flow through the converter is equal to the DC power flow means that the calculation under this assumption is not accurate enough. In [
22], a generalized alternating iterative power flow algorithm for AC/DC networks suitable to different converter control modes is proposed. In [
23], the converter losses model is studied in detail prior to proposing an alternating iterative power flow algorithm for AC/DC network incorporating VSC-MTDC which is compatible with other existing commercial AC power flow calculation software.
In this paper, considering the losses of reactor, the filter and the converter, a mathematical model of VSC-HVDC is derived. After building AC/DC distribution network architecture, the differences in the modified equations of the VSC-MTDC-based network under different control patterns are analyzed. In addition, corresponding interface functions under five control patterns are provided, and a back/forward iterative algorithm is proposed. Finally, by calculating the power flow of a modified IEEE14 AC/DC distribution network, the efficiency and validity of the model and algorithm are evaluated. With different distributed generations connected to the network at different yet appropriate locations, power flow results show that network losses and power absorption from transmission networks are reduced.
3. Modeled Case
The modified IEEE14 bus AC/DC distribution system shown in
Figure 4 is used to verify the effectiveness of the proposed algorithm. The voltage base value is 23 kV and the power base value is 100 MVA. The IEEE14 bus AC/DC distribution system consists of two DC networks, four AC networks (one first AC network and three branch AC networks) and five VSC inverters whose high-voltage sides are connected with AC bus 3, 5, 2, 7 and 11, respectively.
Figure 4.
Modified IEEE14 bus AC/DC distribution system based on VSC-MTDC.
Figure 4.
Modified IEEE14 bus AC/DC distribution system based on VSC-MTDC.
The data of voltage and power is shown in per unit (p.u.). The parameters of inverters are the same. Impedance of converter transformer is 0.0015 + j0.1121 p.u., usage ratio μ of converter transformer DC voltage is , filter susceptance is j0.045 p.u., reactor impedance is 0.0001 + j0.1643 p.u. AC bus 1 is the balance bus of the first AC network, and the AC amplitude is 1.06 p.u. AC bus 5, 7 and 11 are balance buses of branch AC network 2, 3, 4, and their voltage amplitudes are 1.04, 1.03 and 1.02 p.u., respectively. Voltage amplitudes of the rest PQ buses are 1 p.u., angles are 0°.
Distributed generations (DGs) are connected at different buses in the IEEE14 bus AC/DC distribution system. Then three schemes are proposed and shown in
Table 1. VSC control data of DC network is shown in
Table 2, control modes are mentioned in 1.2. Control pattern 5 is constant AC voltage mode, and control pattern 3 is constant DC voltage and reactive power mode.
The power flow calculation result of the AC system is shown in
Table 3, while the DC system result is shown in
Table 4.
All the schemes converge after three iterations. Additionally, the results meet the control requirement of each VSC. For Scheme 1 in
Table 4, voltage phase angle of VSC II, VSC III lags behind the corresponding AC bus voltage phase angle, so VSC absorbs active power from AC network. Voltage phase angle of VSC I, VSC IV, VSC V leads ahead of the AC-side voltage phase angle, so VSC injects active power to AC network. The result is same as the calculation value of
Ps. For scheme 2, voltage phase angle of VSC I, VSC III lags behind the corresponding AC bus voltage phase angle, so VSC absorbs active power from AC network. Voltage phase angle of VSC II, VSC IV, VSC V leads ahead of the AC side voltage phase angle, so VSC injects active power to AC network. The result is the same as the calculation value of
Ps. For Scheme 3, voltage phase angle of VSC III lags behind AC bus voltage phase angle, so VSC absorbs active power from the AC network. Other VSC voltage phase angle leads ahead, so VSC injects active power to AC network. It is indicated that DGs can supply active power to AC network through DC network, and achieve bidirectional power flow.
Table 1.
Summary of Schemes.
Table 1.
Summary of Schemes.
Scheme | Photovoltaic Power Generation | Wind Power Generation | Fuel Cells | Gas Turbine Power Generation |
---|
Scheme 1 | Bus | AC 3 | AC 5 | AC 8 | AC 12 |
Flow | 0.04 | 0.02 | 0.03 | 0.02 |
Scheme 2 | Bus | AC 3 | AC 8 | DC II | DC IV |
Flow | 0.04 | 0.02 | 0.03 | 0.02 |
Scheme 3 | Bus | DC I | DC II | DC IV | DC V |
Flow | 0.04 | 0.02 | 0.03 | 0.02 |
Table 2.
Control parameters of VSC.
Table 2.
Control parameters of VSC.
VSC | I | II | III | IV | V |
---|
Control pattern | 3 | 5 | 3 | 5 | 5 |
| 2.004 | 2.000 | 2.006 | 2.000 | 2.000 |
| 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| −0.022 | 0.000 | −0.022 | 0.000 | 0.000 |
Table 3.
Results of power flows of AC system.
Table 3.
Results of power flows of AC system.
Bus | Scheme 1 | Scheme 2 | Scheme 3 |
---|
Voltage Amplitude | Voltage Phase | Voltage Amplitude | Voltage Phase | Voltage Amplitude | Voltage Phase |
---|
1 | 1.0600 | 0.0000 | 1.0600 | 0.0000 | 1.0600 | 0.0000 |
2 | 1.0386 | −1.1888 | 1.0393 | −1.1383 | 1.0385 | −1.1948 |
3 | 1.0567 | 0.2496 | 1.0556 | 0.1930 | 1.0567 | 0.2493 |
4 | 1.0550 | 0.2203 | 1.0540 | 0.1636 | 1.0550 | 0.2200 |
5 | 1.0400 | 0.0000 | 1.0400 | 0.0000 | 1.0400 | 0.0000 |
6 | 1.0392 | −0.0424 | 1.0392 | −0.0424 | 1.0392 | −0.0424 |
7 | 1.0200 | 0.0000 | 1.0200 | 0.0000 | 1.0200 | 0.0000 |
8 | 1.0160 | 0.0497 | 1.0169 | 0.1491 | 1.0133 | −0.2495 |
9 | 1.0149 | 0.0430 | 1.0158 | 0.1424 | 1.0123 | −0.2562 |
10 | 1.0160 | −0.1161 | 1.0160 | −0.1161 | 1.0160 | −0.1161 |
11 | 1.0400 | 0.0000 | 1.0400 | 0.0000 | 1.0400 | 0.0000 |
12 | 1.0228 | −0.5417 | 1.0212 | −0.6613 | 1.0212 | −0.6613 |
13 | 1.0158 | −0.6934 | 1.0142 | −0.8134 | 1.0142 | −0.8134 |
14 | 1.0170 | −0.8612 | 1.0154 | −0.9818 | 1.0155 | −0.9818 |
Table 4.
Results of power flows of DC system.
Table 4.
Results of power flows of DC system.
VSC | I | II | III | IV | V |
---|
Scheme 1 | | 2.0040 | 2.0041 | 2.0060 | 2.0044 | 2.0040 |
| 0.0039 | −0.0039 | −0.1181 | 0.0281 | 0.0900 |
| 0.0932 | −0.1324 | −3.5780 | 0.8273 | 2.5423 |
| 0.8500 | 0.8433 | 0.8358 | 0.8363 | 0.8604 |
| 0.0064 | −0.0090 | −0.2417 | 0.0551 | 0.1772 |
| −0.0220 | 0.0100 | −0.0220 | 0.0512 | 0.0840 |
Scheme 2 | | 2.0040 | 2.0040 | 2.0060 | 2.0046 | 2.0040 |
| −0.0011 | 0.0011 | −0.1135 | 0.0131 | 0.1003 |
| −0.0561 | 0.4543 | −3.4322 | 0.6765 | 2.8354 |
| 0.8492 | 0.8434 | 0.8363 | 0.8361 | 0.8608 |
| −0.0037 | 0.0310 | −0.2321 | 0.0451 | 0.1977 |
| −0.0220 | 0.0100 | −0.0220 | 0.0512 | 0.0846 |
Scheme 3 | | 2.0040 | 2.0041 | 2.0060 | 2.0044 | 2.0040 |
| 0.0039 | −0.0039 | −0.1187 | 0.0283 | 0.0904 |
| 0.3787 | 0.4543 | −3.5953 | 1.2810 | 2.8354 |
| 0.8501 | 0.8434 | 0.8358 | 0.8365 | 0.8607 |
| 0.0263 | 0.0310 | −0.2428 | 0.0852 | 0.1977 |
| −0.0220 | 0.0100 | −0.0220 | 0.0514 | 0.0846 |
In
Table 5, the absorption power from the AC/DC distribution system and network loss are not identical according to the comparison of the three schemes if the DGs are connected at different buses in the AC/DC distribution network. It is obvious that DC network loss is larger than AC network loss because the inverter loss cannot be neglected, which validates considering inverter loss in this paper. All DGs are connected with AC network in Scheme 1 while all of them are connected with the DC network in Scheme 3. It is shown in
Table 5 that the absorbed power and active power loss are minimal in Scheme 1 while maximal in Scheme 3. This occurs because the potential DC/AC conversion,
i.e., loss of inverters when DGs connect into AC network, is not taken into consideration.
Table 5.
Comparison of the absorbed power and losses in the AC/DC distribution network.
Table 5.
Comparison of the absorbed power and losses in the AC/DC distribution network.
Scheme | Scheme 1 | Scheme 2 | Scheme 3 |
---|
Sin | 0.2499 + j0.0751 | 0.2502 + j0.0747 | 0.2512 + j0.0752 |
Sacloss | 0.0070 + j0.0093 | 0.0071 + j0.0095 | 0.0076 + j0.0102 |
Pconvloss | 0.0115 | 0.0116 | 0.0121 |
Stranloss | 0.0001 + j0.0108 | 0.0001 + j0.0111 | 0.0002 + j0.0123 |
Sreacloss | 0.0000 + j0.0160 | 0.0000 + j0.0164 | 0.0000 + j0.0181 |
Pdclloss | 0.0002 | 0.0002 | 0.0002 |
Sdcloss | 0.0118 + j0.0268 | 0.0119 + j0.0275 | 0.0125 + j0.0304 |
As shown in
Table 6, the loss of network increases significantly due to the growing converter loss of DGs in Scheme 1 if the converter loss is taken into account. In addition, the loss of network decreases in Scheme 3 because of the reduced convert loss caused by fewer converters if the DGs are connected to the DC network directly. It is indicated that more converters lead to higher loss if DGs which generate AC power are connected to the AC network instead of the DC network. Besides, the loss of network increases if DGs which generate DC power are connected to the AC network by converters. Hence, it is important to place the DGs properly to reduce the power consumption and losses in the DC/AC distribution network.
Table 6.
Comparison of the absored power and losses considering converter losses of distribution generation.
Table 6.
Comparison of the absored power and losses considering converter losses of distribution generation.
Scheme | Scheme 1 | Scheme 2 | Scheme 3 |
---|
Sin | 0.2546 + j0.0860 | 0.2541 + j0.0829 | 0.2535 + j0.0778 |
Sacloss | 0.0082 + j0.0112 | 0.0080 + j0.0107 | 0.0079 + j0.0105 |
Sdcloss | 0.0153 + j0.0358 | 0.0149 + j0.0345 | 0.0145 + j0.0327 |
The comparison of the absorbed power and losses with different power generation at the same location (same location in Scheme 3) in the DC/AC distribution network is shown in
Figure 5. With increasing output of DGs, AC active power loss and the absorbed power both decrease. It is shown that proper DG allocation can help to reduce losses and the absorbed power from transmission networks.
Figure 5.
Comparison of the absorbed power and losses with different power generation.
Figure 5.
Comparison of the absorbed power and losses with different power generation.
These cases indicate that converter loss cannot be neglected. It is beneficial to minimize losses and absorbed power for the optimal power flow of AC/DC distribution systems by properly allocating DG ratings at the right locations.