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Optimal Voltage Control in Distribution Networks with Dispersed Generation P. Kacejko, Member, IEEE, S. Adamek, and M. Wydra
Abstract-- The article presents a new method for voltage control in medium voltage distribution networks with dispersed generation. A linear mathematical model of a distribution network has been proposed. The model makes possible to optimally select feeding voltage of a medium –voltage network as well as reactive power in dispersed power sources according to the actual load and active power generation.
the mentioned dispersed generation source. It can be more complicated when there are more than one generator connected to the main feeder via a number of lines (Fig. 1).
Index Terms--dispersed storage and generation, voltage control, optimal control.
B
I. INTRODUCTION
ASED on theoretical considerations and experiments [1] it can be seen that interconnection of dispersed generation, generation of active and reactive power to a medium voltage (MV) distribution network significantly influences voltage in buses located in the vicinity of the interconnection point. Voltage value at the point of interconnection to a MV network is determined by a number of parameters, such as amount of generation (generated active and reactive power), voltage drops caused by customer loads and feeder bus voltage. Maximum voltage increase resulting from a particular generator operation can occur at customer minimum load conditions. The highest possible voltage values are calculated at the assumption that only one analyzed generator is connected to the main MV feeder. The voltage can be obtained from:
U G = U GPZ +
PG Q ⋅ RG −GPZ + G ⋅ X G −GPZ Un Un
(1)
where: Un – nominal network voltage, UG – voltage in the interconnection point, UGPZ – feeder bus voltage, PG , QG – active and reactive powers generated at the point of interconnection, RG-GPZ , XG-GPZ – line resistance and reactance between generator and the main feeder. In practice, it is possible that active power supplied to the network can bring about voltage increase exceeding allowable values, which in turn induces energy production limitations in P. Kacejko is with Department of Electrical Engineering and Computer Science, Lublin University of Technology, Lublin, 20-618 Poland (e-mail:
[email protected]). S. Adamek is with Department of Electrical Engineering and Computer Science, Lublin University of Technology, Lublin, 20-618 Poland (e-mail:
[email protected]). M. Wydra is with Department of Electrical Engineering and Computer Science, Lublin University of Technology, Lublin, 20-618 Poland (e-mail:
[email protected]).
Fig. 1. Distribution network with dispersed generation, 1 – main feeder, 2 – network split point, 3 – MV power line, 4 – transformer station MV/LV, 5 – independent power producer.
Research performed in [2] has shown that adequate coordination of voltage control at the feeding node with the reactive power generated in dispersed sources can limit the mentioned overvoltage and can enhance voltage quality in all network nodes. II. VOLTAGE QUALITY IN A DISTRIBUTION NETWORK Power supply quality assessment is mainly based on making voltage value the closest possible to the nominal voltage. The simplest way to evaluate the parameter is to determine differences between actual nodal voltages and the nominal voltage. The obtained value is referred to as voltage deviation. For n nodes in a network n voltage deviations can be obtained which are usually calculated in nodes with customer loads connected. In general, it is possible to obtain different voltage deviations for every node. The basic assessment task is to check whether the measured voltage is confined within the limits shown in (2): U i ≥ 0.9 ⋅U n (2) U i ≤ 1.1⋅U n where: Un – nominal network voltage, Ui – i-th node voltage [4].
2
Meeting of the condition (2) does not mean that voltage conditions in the network are optimal. Loads operate the most efficient when they are fed with voltage approaching the nominal voltage value. Other voltage values can impair efficiency and operational reliability of the loads. Thus, it seems reasonable to elaborate a voltage quality indicator for all nodes in the network Results of many-year investigations indicate that customer loses caused by voltage deviations are directly proportional to the square of those deviations. In [3] whose the author dealt with the optimization of tap-changer position in transformers in order to obtain optimal customer supply conditions, a the following voltage quality factor has been defined: 2 n ⎛ U −Un ⎞ (3) wskU = ∑ ⎜ i ⎟ Un ⎠ i =1 ⎝ where: wskU – voltage quality factor, Ui – i-th node voltage, Un – nominal network voltage, n –number of nodes. Disadvantage of the factor described in (3) is that it does not allow to compare quality of different voltage levels (e.g. LV and MV) and even quality between single buses because it is dependent on number of nodes n. In order to generalize and normalize the network voltage quality factor its given-below new form has been proposed: wskU %
1 n ⎛ Ui −Uo ⎞ = 100 ⋅ ⋅∑⎜ ⎟ n i =1 ⎝ U n ⎠
2
remaining ones are load nodes and in one of them a dispersed generation source operates.
Fig. 2. Simplified distribution network with dispersed generation, 0,1,2,3 – network node, Uz – feeding voltage, U1, U2, U3 – node voltage, (R01, X01), (R12, X12), (R23, X23) – main line resistance and reactance between nodes, (P1, Q1), (P2, Q2), (P3, Q3) – active and reactive load power at network nodes, (Pg, Qg) – active and reactive generated power.
In this particular case, voltage values in successive nodes, can be obtained from the following expressions (symbols correspond to the ones of Fig. 2): U1 = U Z − ΔU 01 = = UZ −
III. DISTRIBUTION NETWORK MODEL Analytical determination of voltage values at customer load connection points is practically impossible, because of no precise data on load flow in LV and MV distribution networks. Assuming that LV networks have been designed, built and operate without exceeding allowable voltage drops it can be expected that if voltage at LV bars of a MV/LV station does not exceed allowable limits then LV network loads also are fed with voltage of adequate level (within nominal limits). In such a case the only question to be solved is to estimate voltage values in a MV network. A simplified network shown in Fig. 2 has been considered for the investigation purposes. It consists of 4 nodes, where node 1 is a feeding node and three
Un
Q1 + Q2 + Q3 − Qg
⋅ R01 −
Un
⋅ X 01
(5)
U 2 = U Z − ΔU 01 − ΔU12 = = UZ −
(4)
where: wskU% – percentage quality factor, Uo – set point voltage at substations MV/LV. The factor (4) corresponds to the percent value of a standard deviation given by (3) where Uo is an expected voltage value to be obtained at a substation/node MV/LV. In a general case this value can depend on specific network conditions and its load level (e.g. winter peak, summer off peak). Taking into consideration voltage drops in LV networks it is advantageous to maintain voltage value exceeding the nominal voltage in order to compensate the mentioned voltage drops (e.g. 420 V in LV network). Usefulness of quality voltage factor described in (4) has been experimentally acknowledged [2]. The presented voltage quality factor (4) does not include any relevant information as in how many nodes voltage exceeds the allowable voltage and in how many nodes voltage is too low. Thus, in quality considerations it is the condition (2) that should primarily be checked.
P1 + P2 + P3 − Pg
−
P1 + P2 + P3 − Pg Un
P2 + P3 − Pg Un
⋅ R12 −
⋅ R01 −
Q1 + Q2 + Q3 − Qg Un
Q2 + Q3 − Qg Un
⋅ X 01 +
(6)
⋅ X 12
U 3 = U Z − ΔU 01 − ΔU12 − ΔU 23 = = UZ − −
P1 + P2 + P3 − Pg
P2 + P3 − Pg Un
Un ⋅ R12 −
⋅ R01 −
Q1 + Q2 + Q3 − Qg
Q2 + Q3 − Qg Un
Un
⋅ X 01 +
(7)
P Q ⋅ X 12 − 3 ⋅ R23 + 3 ⋅ X 23 Un Un
Equations (5),(6),(7) can be rewritten in a matrix form shown below: ⎡ R01 ⎢ ⎢ Un ⎡U1 ⎤ ⎡1⎤ ⎢U ⎥ = ⎢1⎥ ⋅ U + ⎢ R01 + R12 ⎢ 2⎥ ⎢ ⎥ Z ⎢ U n ⎢ ⎢⎣U 3 ⎥⎦ ⎢⎣1⎥⎦ ⎢ R01 + R12 ⎢ ⎣ Un ⎡ R01 ⎢ ⎢ Un ⎢R − ⎢ 01 ⎢ Un ⎢ R01 ⎢ ⎣ Un ⎡ X 01 ⎢ ⎢ Un ⎢X − ⎢ 01 ⎢ Un ⎢ X 01 ⎢ ⎣ Un
R01 Un R01 + R12 Un R01 + R12 Un X 01 Un X 01 + X 12 Un X 01 + X 12 Un
⎤ ⎥ ⎥ X 01 + X 12 ⎥ ⎡ Pg ⎤ ⎥⎢ ⎥+ Un ⎥ ⎣Qg ⎦ X 01 + X 12 ⎥ ⎥ Un ⎦ ⎤ R01 ⎥ Un ⎥ ⎡P ⎤ 1 R01 + R12 ⎥ ⎢ ⎥ ⎥ ⋅ ⎢ P2 ⎥ + Un ⎥ ⎢P ⎥ ⎣ 3⎦ R01 + R12 + R23 ⎥ ⎥ Un ⎦ X 01 Un
(8)
⎤ ⎥ ⎥ ⎡Q ⎤ 1 X 01 + X 12 ⎥ ⎢ ⎥ ⎥ ⋅ ⎢Q2 ⎥ Un ⎥ ⎢Q ⎥ ⎣ 3⎦ X 01 + X 12 + X 23 ⎥ ⎥ Un ⎦ X 01 Un
By introducing to the above equation factors dependent on resistance, reactance and node voltage, respectively the following expression has been obtained:
3
⎡ r1g x1g ⎤ ⎡U1 ⎤ ⎡1⎤ ⎥ ⎡ Pg ⎤ ⎢U ⎥ = ⎢1⎥ ⋅ U + ⎢ r ⎢ 2 ⎥ ⎢ ⎥ Z ⎢ 2 g x2 g ⎥ ⎢Qg ⎥ + ⎢ r3 g x3 g ⎥ ⎣ ⎦ ⎢⎣U 3 ⎥⎦ ⎢⎣1⎥⎦ ⎣ ⎦ ⎡ r11 r12 r13 ⎤ ⎡ P1 ⎤ ⎡ x11 x12 x13 ⎤ ⎡ Q1 ⎤ − ⎢⎢ r21 r22 r23 ⎥⎥ ⋅ ⎢⎢ P2 ⎥⎥ − ⎢⎢ x21 x22 x23 ⎥⎥ ⋅ ⎢⎢Q2 ⎥⎥ ⎢⎣ r31 r32 r33 ⎥⎦ ⎢⎣ P3 ⎥⎦ ⎢⎣ x31 x32 x33 ⎥⎦ ⎢⎣ Q3 ⎥⎦
IV. OPTIMIZATION OF VOLTAGE CONTROL IN A TEST NETWORK (9)
In order to generalize the above considerations into a multisection line with dispersed generation (Fig. 3) the expression (9) can be rewritten into the matrix form (10).
Fig. 3. Main distribution line with dispersed generation
⎡ r1g1 r1g 2 ⎡U1 ⎤ ⎡1⎤ ⎢r ⎢U ⎥ ⎢1⎥ ⎢ 2 g1 r2 g 2 ⎢ 1⎥ ⎢ ⎥ ⎢ # # ⎢ # ⎥ ⎢# ⎥ ⎢ ⎥ = ⎢ ⎥UZ + ⎢ r r U 1 ⎢ ig1 ig 2 ⎢ i⎥ ⎢ ⎥ ⎢ # ⎢ # ⎥ ⎢# ⎥ # ⎢ ⎢ ⎥ ⎢ ⎥ ⎣⎢U n ⎦⎥ ⎣1⎦ ⎣⎢ rng1 rng 2 " x x1gj " x ⎡ 1g 1 1g 2 ⎢x ⎢ 2 g1 x2 g 2 " x2 gj " ⎢ # # # # # +⎢ " " x x x ig 2 igj ⎢ ig1 ⎢ # # # # # ⎢ ⎣⎢ xng1 xng 2 " xngj " ⎡ r11 r12 ⎢r ⎢ 21 r22 ⎢# # −⎢ r r ⎢ i1 i 2 ⎢# # ⎢ ⎣⎢ rn1 rn 2 ⎡ x11 ⎢x ⎢ 21 ⎢ # −⎢ ⎢ xi1 ⎢ # ⎢ ⎣⎢ xn1
" r1i " r2i # # " rii # # " rni
" r1gj " r2 gj # # " rigj # # " rngj
" r1gm ⎤ ⎡ Pg1 ⎤ " r2 gm ⎥⎥ ⎢⎢ Pg 2 ⎥⎥ # # ⎥ ⎢ # ⎥ ⎥⋅⎢ ⎥ + " rigm ⎥ ⎢ Pgj ⎥ # # ⎥ ⎢ # ⎥ ⎥ ⎢ ⎥ " rngm ⎦⎥ ⎣⎢ Pgm ⎦⎥
x1gm ⎤ ⎡ Qg1 ⎤ x2 gm ⎥⎥ ⎢⎢ Qg 2 ⎥⎥ # ⎥ ⎢ # ⎥ ⎥⋅⎢ ⎥+ xigm ⎥ ⎢ Qgj ⎥ # ⎥ ⎢ # ⎥ ⎥ ⎢ ⎥ xngm ⎦⎥ ⎣⎢Qgm ⎦⎥
" r1n ⎤ ⎡ P1 ⎤ " r2 n ⎥⎥ ⎢⎢ P2 ⎥⎥ # # ⎥ ⎢#⎥ ⎥⋅⎢ ⎥ + " rin ⎥ ⎢ Pi ⎥ # # ⎥ ⎢#⎥ ⎥ ⎢ ⎥ " rnn ⎦⎥ ⎣⎢ Pn ⎦⎥
(10)
x12 " x1i " x1n ⎤ ⎡ Q1 ⎤ x22 " x2i " x2 n ⎥⎥ ⎢⎢Q2 ⎥⎥ # # # # # ⎥ ⎢# ⎥ ⎥⋅⎢ ⎥ xi 2 " xii " xin ⎥ ⎢ Qi ⎥ # # # # # ⎥ ⎢# ⎥ ⎥ ⎢ ⎥ xn 2 " xni " xnn ⎦⎥ ⎣⎢Qn ⎦⎥
where: U – network node voltage vector, Uz – feeding voltage, Pg, Qg – active and reactive power generation vector, PL, QL – active an reactive load powers, R, X, Rg, Xg – matrixes of coefficients. Equation (10) acquires following form: (11) U = 1 ⋅ U Z + R g Pg + X g Q g - RPL - XQ L
The above formulated expressions can be used for the optimization of voltage control in distribution networks with dispersed generation. Voltage quality factor (4) has been used as an objective function to be minimized. This can be written as following expression (12). wskU ( U ) → min
According to (12) the forcing data set is an active generator power vector Pg and load powers PL, QL. Control data set will be the main feeder voltage Uz and reactive generator power vector Qg. The model of a test network is based on a real MV distribution network presented in [2], with dispersed generation added. The Test Grid base model without dispersed generation can be found at [5] in PTI format. For the analysis and calculation sake maximum load value has been assumed. PowerWorld software has been used for load-flow calculations and the obtained results have been imported to a MS Excel sheet. The quality voltage factor defined in (4) has been calculated (without optimization), next a test network model described by (11) has been optimized according to (12) with the classical Newton’s method applied in a Analysis ToolPack module. In the course of the optimization process the objective function (12) gets minimized within limits described by (2). Technical constraints such as step change of tap voltage control in transformers and reactive power limits in generators have been taken into account. It has been assumed that generators can operate with reactive power varying in the range ±0,4 of their active power. The procedure has yielded values of the main feeder voltage Uz and reactive generator power vector Qg. The main feeder voltage Uz should correspond to the set voltage value at tap changing controller of a HV/MV (110/15 kV/kV) transformer, while reactive generator power vector Qg should be send to generators via SCADA systems. Optimization results together with enhanced voltage quality in a distribution network are presented in Table I. TABLE I OPTIMIZATION CASES Description without dispersed generation with dispersed generation, without reactive power control Qg = 0 after optimization, only new vector of set point reactive powers for generators Qg after optimization, only new feeding voltage assigned Uz after optimization, new feeding voltage assigned Uz, new vector of set point reactive powers for generators Qg
Case 1 2 3 4 5
Case
It has been assumed that a test network consists of overhead MV lines of relatively small capacitance that can be neglected without yielding any significant evaluation errors.
(12)
1 2 3 4 5
TABLE II ACTIVE POWER GENERATION PG1 PG2 PG3 PG4 [MW] [MW] [MW] [MW] 0 0 0 0 0,5 0,5 0,5 0,3 0,5 0,5 0,5 0,3 0,5 0,5 0,5 0,3 0,5 0,5 0,5 0,3
PG5 [MW] 0 1,0 1,0 1,0 1,0
4 TABLE III REACTIVE POWER SETPOINTS OBTAINED IN OPTIMIZATION PROCESS QG4 QG5 QG3 QG1 QG2 UZ Case [Mvar] [Mvar] [Mvar] [kV] [Mvar] [Mvar] 1 2 3 4 5
1)
15,75 15,75 15,75 16,2 16,2
0 0 0,2 0 -0,2
0 0 0,2 0 0,2
0 0 0,2 0 0,2
0 0 0,12 0 0,12
0 0 0,4 0 -0,4
TABLE IV RESULTS OF VOLTAGE OPTIMIZATION IN MV NETWORK WITH DISPERSED GENERATION Case wskU%1) wskU%2) LWP3) 1 4,96% 5,06% 19 2 4,05% 4,14% 6 3 4,01% 3,93% 6 4 2,59% 2,50% 0 5 2,52% 2,37% 0
voltage quality factor obtained with the optimization process based on a simplified test grid model (10) 2) voltage quality factor calculated for a test grid by power flow software (PowerWorld Simulator) with the use of the obtained optimal vectors based on a simplified test grid model 3) LWP – number of nodes with exceeded voltage limits Table II presents set points of active power generated in dispersed sources. Optimization results obtained for various cases given in Table I are presented in Table III and Table IV. It can be seen that the discussed simplified method can be used to enhance voltage quality factor (4). The best results have been obtained for the case 5 where the optimization method simultaneously changes feeding voltage Uz and reactive power Qg of dispersed generation. Slightly less satisfactory results of node voltage regulation can be obtained by changing only feeding voltage Uz and when it is only reactive power Qg of dispersed sources that is used for voltage regulation then the method becomes ineffective. V. CONCLUSIONS Voltage control in distribution networks is now realized based on a daily load curve (winter peak, summer valley). As there is no simple method to be applied for voltage value estimation in load nodes it is difficult to find whether the accepted voltage control rules are optimal for customer loads. This paper presents a simplified mathematical model that can be used for voltage estimation in load nodes, which in turn can be useful for calculating factors of voltage quality and its objective evaluation. Owing to its simplicity the method can be implemented in various SCADA systems or local voltage controllers installed in power substations. The presented method makes possible to significantly reduce negative effect of voltage increase caused by active power generation in dispersed sources. VI. REFERENCES [1] [2]
W. Rojewski and M. Sobierajski, "Voltage problems in MV network with interconnected with local heat and power plant" presented at the 9th Int. Conf. Actual Power Systems Problems, Jurata, Poland, 2003. P. Kacejko, S. Adamek and P. Pijarski, "Influence assessment of dispersed generation on static voltage quality factors " presented at the 14th Int. Conf. Actual Power Systems Problems, Jurata, Poland, 2009.
[3] [4] [5]
D. Kot, "Optimal voltage control in medium voltage distribution networks with dispersed generation," Ph.D. dissertation, Power Systems Dept., Cracow, 2005. Standard EN 50160: Voltage Characteristics in Public Distribution Systems. Test Grid model in PTI format http://elektron.pol.lublin.pl/users/ksiz/TestGrid/model_PTI_v30.raw
VII. BIOGRAPHIES Piotr Kacejko has graduated (MSc) from the Lublin University of Technology, Poland, Faculty of Electrical Engineering. For 25 years he has been a member of the university teaching staff. He has received PhD and DSc degrees from the Lublin University of Technology and Warsaw University of Technology, respectively. He was also employed as a Consultant Engineer in the Power Distribution Company Lubzel Ltd. and Polish National Grid Company (PSE). He spent a couple of months as a research fellow in the Faculty of Engineering, University of Glasgow, UK. Since 2006 he’s been, as a full professor, the head of Power Systems Department, TU Lublin. He is the co-author of over 100 papers and 4 books on power system analysis, protection problems and reliability enhancement. Prof. Kacejko is also a co-author of commercial software used for short circuit analysis (SCC). He works as an expert and a consultant for companies planning connection of power sources (plants, and wind farms) to the grid. He is a member of IEEE. Sylwester Adamek has received his MSc. degree in electrical engineering from the Lublin University of Technology in 2001. Since then he is he has been employed in the Faculty of Electrical Engineering and Computer Science, Department of Power Systems. His research interest is focused on dispersed generation, power networks control and protection.
Michal Wydra has graduated from the Lublin University of Technology in 2002 (M Sc in electrical engineering. His Ph. D he has received in 2008. He is currently employed as an assistant professor in the Power Systems Department, Faculty of Electrical Engineering and Computer Science. His special fields of interest include power system stability, wind power generation, control, integration and dynamic interaction with electrical grid.
