~~~voltage sensitivities for decentralised opt

8/15/2019 ~~~Voltage Sensitivities for Decentralised Opt

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Control and Coordination of a Distribution Network

via Decentralised Decision Making

Mark E. Collins Richard W. Silversides Timothy C. Green

Student Member IEEE Senior Member IEEE Senior Member IEEE

Imperial College Imperial College Imperial College

[email protected] [email protected] [email protected]

Abstract—Active Network Management is the use of IT,automation and control to manage voltage and power flowconstraints in distribution networks. A multi-agent system (MAS)is proposed to perform distributed decision making on thedispatch of distributed energy resources to control networkvoltages within prescribed limits. Agents at each node estimatethe effect of their local actions on their node voltage andchoose the best solution according to a cost function. Threevoltage change approximations were implemented, one used onlylocal information whilst the other two had varying degreesof knowledge about the network. Agents apply the algorithmsiteratively so the approximate solutions are refined over time.The voltage control algorithms were tested on a Java based MAScontrolling a distribution network simulation. The results showthat approximations based on strictly local data require hysteresisto avoid hunting. Approximations with upstream network dataachieve a stable solution at all nodes.

Index Terms—MAS, Multi-Agent, Control and Coordination,ANM, Voltage Control

I. INTRODUCTION

PENETRATION of distributed energy resources (DERs),which can be described as a combination of highly vari-

able small scale generation (such as PV) and large new loads

(such as EV), are increasing within distribution networks.

This increase is causing many more cases of feeder voltages

infringing on statutory determined voltage tolerances within

distribution networks. In the case of the UK, distribution

network operators (DNOs) are legally required to adhere to

ESQCR standards of voltage tolerance [1] delivered to the

customers at the point of supply. An excursion outside of these

tolerances at the feeder is highly undesirable. At present DNOs

use a SCADA based system to monitor the network only. On-

load tap changers (OLTC) are the only form of voltage control

and are usually controlled with only local measurements asin [2]. MAS schemes have been proposed to maintain volt-

ages within constraints using state estimation [3] and off-line

optimal power flow (OPF) to centrally determine transformer

tap positions and other options such as DG constraints [4].

These proposed systems will communicate to a central point

in order to undertake their tasks, which might introduce

problems such as single point failures. Therefore a distributed

control and coordination solution may be a more desirable

option. In this paper Active Network Management (ANM) is

investigated, specifically in the area of maintaining voltage

constraints within a distribution network, in order to provide a

solution to these problems. A distributed Multi-Agent System

is presented to control and coordinate the network’s DERs’

real and reactive power dispatch via decentralized decision

making, in order to maintain the network’s feeder voltages

within ESQCR defined operating limits.

I I . DEFINING T HE D ISTRIBUTED M ULTI-AGENT S YSTEMIn this paper, the distribution network is taken to be a

network of generators, loads and feeders in a radial network.

It can be described, from a graphical point of view as tree-

like in structure; this definition is currently used in agent

systems [5]. The root node is the origin of the network with

an approximately stiff voltage, it is the point where the extra

high voltage (EHV) network connects to the high voltage

(HV) network. A node connected to the root node, via a line

impedance, is a branch node. This assignment continues to the

end of the network where the last node connects only to one

branch, in which case this node is renamed a leaf node, shown

in Fig.(1).

The control and coordination of this network will be un-dertaken by a distributed Multi-Agent System making decen-

tralized decisions. The system is built up by assigning an

agent to each electrical node; the agent is able to measure

voltage at the node and measure power flow into the node and

control the dispatch of the DERs connected to this node. The

agents can communicate with one another via a foundation for

intelligent physical agents (FIPA) communication protocol [6].

The agents are able to send messages to any agent that shares

a physical electrical connection. Using the information it

receives from its own node and from its electrically connected

adjacent nodes the agent seeks to maintain its voltage within

constraints by making decentralized decisions. The methodol-

ogy for this will be shown in later sections. The main focus

of this work is to investigate the area of distributed control

and decision making and how the approach presented in this

paper can be beneficial to distributed networks.

A. System’s advantages over centralised methods

There is a growing body of work in using a centralised agent

system to undertake control and coordination of decentralised

networks as mentioned in section I. Information is required

to travel to a central location, which causes a communication

overhead. There is currently a debate on the difficulties that


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occur in both centralised and decentralised communication

methods and which one can be considered preferable. Re-

gardless of this, since there is no formal hierarchy, if there

are problems with the communication network the agents can

continue to coordinate their actions that they take indepen-

dently. This makes the system less vunerable to single point

failures.

B. System’s advantages over distributed control and coordi-

nation

This work offers an extension to the work undertaken in

the field of Dynamic Programming Decentralized Optimal

Dispatch (DYDOP) [5] by introducing calculations based on

the electrical effects of altering power flows in a distributed

network.

III. DEFINING T HE D ISTRIBUTION N ETWORK

The MAS will control and coordinate a distribution network

using UKGDS [7] information. The system that is assessed in

this paper is shown in Fig.1. When discussing the network

the node that is being considered is labeled node n and

has defined references in terms of voltages, power flows and

impedances. Nodes connected to it are labeled n-1(upstream)

or n+1 (downstream).

Node 1 (Root)

PnQn

VnVn-2

RnXn

PnQn

‘Pn-1Q

n-1

Vn-1

Rn-1Xn-1

P ‘n-1Q‘

Pn+1Qn+1

Vn+1

Rn+1Xn+1

Pn-2Qn-2

PGn

PDnP P

P

+ + + + Dn-1

PGn-1 Gn+1

Dn+1

+ + + +

Node 2 (Branch)

Distribution

Feeder

n-1

Node 3 (Branch) Node 4 (Branch)

‘

Vn-1LD VnLD Vn+1LD

Figure 1. A distribution feeder showing terminology

Key characteristics of the system are represented as follows:

• P n :This signifies the power flowing into the node from

upstream

• P(G/L)n: This signifies a generator (G) or a load (L)• Vn: This signifies the voltage at the node• Xn − Rn :This signifies the line resistance (R) or the

reactance (X) connected between the node n and the

upstream node n-1.

• VnLD :This signifies the voltage line drop across theupstream impedance.

A. Voltage drop in two node system

Now that the terminology has been defined the electrical

characteristics can be described. The agents in the system

will base their decisions on predictions of the nodal voltages.

The voltage at the node can be calculated using a known

approximation technique [8] where we consider the voltage

in a two node network, which can be approximated to

Vn = Vn−1 − VnLD, (1)

where

VnLD = Rn ∗ Pn + Xn ∗ Qn

Vn. (2)

We can rearrange (1) to get

V n = +Vn−1 ± (V

2n−1 − 4(RnP n + QnX n))

1

2

2 . (3)

If Vn in (3) is partially differentiated with respect to Pn wecan determine the change in voltage at the node in terms of

change of power flow into the node:

∂V n

∂P n= ±

12(V

2n−1 − 4(RnP n)

−1

2 ∗ 4Rn

2 (4)

∂V n

∂P n=

Rn V 2o − 4RnP n

(5)

An agent can calculate changes in its nodal voltage due to

changes in power flow,

Vn(new) = Vn + Vn, (6)

where

Vn = −( Rn V2o − 4RnPn

) ∗ Pn, (7)

and a new approximation of the nodal voltage can be

calculated

Vn(new) = Vn − (( Rn V2o − 4RnPn

) ∗ Pn). (8)

The approximation in (8) was derived for a two-node

system. If we expand this and apply superposition, we can

approximate the voltage sensitivity at each node in a radial

network.

B. Applying the Superposition Principle

Each node in the network needs to establish local node

voltage changes for changes in power. If the system is linear, or

approximately linear, the resultant voltage at a node could be

calculated using the superposition principle, since the resultant

sensitivity to power flow (∂ Vn/ ∂ Pn ) would be the sum of the

sensitivities at its own node and all upstream nodes. However

when we analytically describe the system expansion from a

two node to multiple nodes and derive the sensitivity (9), it

is clear the inter dependence of the system effects is very

complicated.

∂ Vn∂ Pn

= ∂ (Vn − Vn−1)

∂ Pn+ ∂ (Vn−1 − Vn−2)

∂ Pn−1· ∂ Pn−1∂ Pn

+ ...

(9)

∂ (Vn−2 − Vn−3)

∂ Pn−2· ∂ Pn−2∂ Pn

...∂ (V0 − V1)

∂ P1· ∂ P1∂ Pn

Therefore it cannot be said that superposition strictly ap-

plies. In order to correctly calculate the effects of power

changes in the network all these sensitivities would need

to be calculated by each agent. However, since the agent


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system is an iterative solution, sensible approximations of the

components in (9), could allow for a solution to arise, albeit

with a sub optimal outcome in terms of an optimal power flow

solution.

C. Sensitivity Approximations Implemented

Three sensitivity approximations were implemented on theagent system;

∂ Vn∂ Pn

= Rn

V2n−1 − 4RnPn(10)

∂ Vn∂ Pn

=

Rn

V2o − 4(

Rn)Pn(11)

∂ Vn∂ Pn

=

(RiVi

) + RnVn(old)

(12)

The first approximation (10) assumes that the node con-

nected immediately upstream has a constant voltage and the

node voltage sensitivity can be calculated using the imme-

diate upstream impedance. The second approximation (11)

acknowledges that there will be changes in the voltage drops

in all branches up to the root node but approximates the

denominator in each term by the root voltage. The third

approximation acknowledges that each branch voltage drop

should be calculated using the local node voltage and that

these node voltage can be communicated from one node to the

next. With these assumptions applied at each node, the change

in voltage at each node due to change in power flow can be

calculated. This calculation can be used in the decentralizeddecision making process and will be discussed in the following

section.

IV. MAINTAINING VOLTAGE C ONSTRAINTS V IA

DECENTRALISED D ECISION M AKING

The system proposed in this paper controls and coordinates

the network by allowing the agent assigned to a node to

maintain its voltage within tolerances. It does this by making

local decisions using information about its own power dispatch

services and services it receives from electrically connected

nodes. It then applies a cost to these services based upon the

actual cost of generation and an artificial voltage operating

cost (which will be explained in greater detail later in this

section). The agent also helps to maintain the nodal voltage

tolerances at other nodes in the network by offering services.

The nodal agent algorithm is presented in the flow chart in

Fig.2.

A. Information Measured From the System

The first task of each agent is to acquire the relevant

measurements from its node as shown in Fig.1.

Start

Initial System Measurements

Intialise Variables

Receive Voltage Information

From N Minus One

Receive Power Information

From N Plus One

Set Constraints

Calculate States

Calculate Voltage

Add To Voltage Array

Calculate Cost

Add To Cost Array

If=Pn-1 Target Received Update Cost Array

If=Vn+1 Target Received Update Cost Array

If=Cycled through

All States

Select Minimum Cost State

Receive Power Demand

From N Minus One

Receive Voltage Demand

From N Plus One

Send Voltage Demand

to N Minus One

Send Power Demand

to N Plus One

Update Gen/Load Set Points

Start

End

Calculate Min Voltage

Cost State

A. B.

Send Voltage Information

to N Minus One

Send Power Information

to N Plus One

Figure 2. Nodal Agent Algorithm

B. Receive Voltage Information n-1 and Power Information

n+1

At this stage node n receives a Voltage Cost Array from

node n-1 and a Power Cost Array from node n+1. The

Voltage Cost Array (13) contains an array of voltages and

the corresponding cost of operating at that voltage. The Power

Cost Array (not shown) contains an array of changes in power

operating point and the corresponding cost.

VoltageCostArray[i] = (13)

This information provides more states for node n to operate

in and the associated costs for these new states.

C. Receive Voltage and Power Demands

Node n will receive a Voltage Demand Array from node

n-1 and a Power Demand Array from node n+1. The Voltage

Demand Array (14) contains a single element which contains

the requested voltage operating point along with the cost. The

Power Demand Array (15) also contains a single element

containing the requested change in power operating pointalong with the cost. In both cases, the cost is included as

a cross check against the original offer.

VoltageDemandArray[0] = (14)

PowerDemandArray[0] = (15)

This information provides incentive for node n to operate

in voltage or power states it otherwise might have found

unnecessary to maintain its own nodal voltage constraints.


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D. Calculate Min Voltage Cost State

This is the decision making part of the algorithm. By using

the information received, node n selects its minimum operating

cost state that maintains voltage constraints. This part of the

algorithm can be seen in Fig.2B.

1) Set Power Constraints and Calculate States: The agent’s

power constraints, or its ability to increase or decrease its nodal

power, is defined by how much extra power is available orcurtailment of power is available. It combines its own power

constraints with the constraints received from node n-1 and

node n+1 and calculates the total number of states available.

Once it has done this the agent constructs the Nodal Voltage

Array.

2) Calculate Voltage and Add to Voltage Array: The Nodal

Voltage Array is an array of all possible voltage states node

n can operate in, it is based on three options: its own

DER dispatch, the voltage operating states of node n-1 and

the power operating states of node n+1. When considering

upstream voltage changes (16) is used to generate these states.

It is derived from (1) where Vn-1 is an array of upstream

voltage states.

Vn[i] = Vn−1[i] −VnLD (16)

The algorithm will then use (17) to cycle

through,P ng,P nlstates and P n+1states as well as its

reactive counterparts, Qng,Qnlstates and Q to achieve

an array of Nodal Voltage states.

Vn(new)[i] = Vn[i] − (∂ Vn∂ Pn

) ∗ (Pn + Pn+1[i]) (17)

This is the main equation used in the algorithm. Once the

Nodal Voltage Array has been calculated each voltage state can

be assigned an associated Nodal Cost set by a cost function.

3) Calculate Cost and Add to Cost Array: The cost function

consists of two parts, the cost of generation/load change at

the node and the artificial cost of the nodal operating voltage.

The generation cost is based on a standard linear current cost

system used to cost for increments in power generation shown

in Fig.3.

0 1 2 3 4 50

100

200

300400

500

600

700

800

900

1000

Power (P.U)

C o s t ( £ )

Generation Costs

Generator Real Power

Load Real Power

0.95 1 1.050

1000

2000

30004000

5000

6000

7000

8000

9000

10000

Voltage (P.U)

Voltage Costs

C o s t ( £ )

Nodal Voltage Costs 1

Nodal Voltage Costs 2

1.020.98

aa-b a+b

Figure 3. Illustration of Linear Generation Costs and Voltage Costs

The artificial voltage cost has been developed to allow a cost

to be placed on the voltage so that it is approximately zero

when within defined operating constraints, but becomes much

larger when moving towards the constraint and exceptionally

large when outside the constraints. The artificial voltage cost

(given in GBP for compatibility) is based around a function

(18) with width parameter k=40, and the curve parameter t=12.

This is graphically represented as a bath tub curve shown in

Fig.3.

f(x) = (k ∗ (x − 1) ∗ (a + b))t (18)

The nodal cost function assigns a cost to the Nodal Voltage

states within the Nodal Voltage Array and also cycles throughall the nodal costs updating the states that nodes n+1 and n-1

have provided. The Nodal Cost Array is then calculated using

(19).

NC[i] = f(Vcalc[i]) + g(Pn[i]) − h(V n−1[i]) − y(P n+1[i])(19)

4) Send Voltage and Power Information: The nodal agent

uses the Nodal Cost Array to construct a Power Cost Array

to send to node n-1 and a Voltage Cost Array to send to node

n+1 so that those nodes can benefit for its services, it also

sends on the voltage and power information it receives from

the n+1 and the n-1 nodes, acting as a broker between itself and the nodes upstream and the nodes downstream and vice

versa.

5) Select Minimum Cost State: Once all the Nodal Cost

states have been calculated the minimum cost state is selected

using (20).

argmin(NC [i]) (20)

This equation calculates the operational voltage state which

is the cheapest for the node to operate in, to maintain its own

voltage constraints and also for the benefit of the network.

It will then alter its own power state and, if necessary, send

a Voltage Demand Array to node n-1 and a Power Demand

Array to node n+1.

At this point the agent will begin the procedure again,

implementing changes when desired or maintaining the status

quo when not. The next section will look at the system in

action.

V. EMPIRICAL E VALUATION

In order to empirically evaluate the system a selection of

tests were carried out, the first set of which (A-C) focuses

upon the sensitivity approximation devised in section C. Test

A uses approximation (10), test B approximation (11), and test

C approximation (12).

Each test was conducted on a 4 bus system initially lightlyloaded, shown in Fig.1, then a large load upstream was

switched into the network. One of the nodal agents in the

network had cheap generation available while the other two

were relatively expensive. Fig.5A shows the result of the

first test. The sensitivity used in the algorithm implemented

was unaware of the full network and this resulted in a poor

calculation of the resultant voltages caused by the actions of

the nodal agents. Once the initial dip was corrected and the

voltage constraints met, a hunting pattern occurred. Since the

nodal agents were unaware of the effect they would have on the

other nodes, node 4 assumed it could produce less power (at


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5 10 15 20 25 30 35 40 45 500.95

0.96

0.97

0.98

0.99

1

1.01

1 unit = 5 seconds

V o l t a g e ( P . U

)Nodal Voltage Change

5 10 15 20 25 30 35 40 45 500.95

0.96

0.97

0.98

0.99

1

1.01

V o l t a g e

( P . U

)

Nodal Voltage Change

1 unit = 5 seconds5 10 15 20 25 30 35 40 45 500.95

0.96

0.97

0.98

0.99

1

1.01


)


1 unit = 5 seconds

10 20 30 40 50 60 70 80 901000.950.960.970.980.99

11.011.021.03

1.041.05 Nodal Voltage Change

1 unit = 5 seconds10 20 30 40 50 60 70 80 90 100

0.950.960.970.980.99

11.011.021.03

1.041.05

V o l t a g e ( P .

U )



)

1 unit = 5 seconds10 20 30 40 50 60 70 80 90 100

0.950.960.970.980.99

11.011.021.03

1.041.05


)


1 unit = 5 seconds

AAA B C

D E F

Figure 4. System Results: (A) Approximations Test One (B) ApproximationsTest Two (C) Approximations Test Three (D) System Test One (E) SystemTest Two (F) System Test Three. In all cases V1 (Dark Blue) V2(Green)V3(Red) V4(Light Blue)

less cost) and still be able to maintain constraints, and although

this was true for its own node, the actions of this agent causedthe voltage at node 3 to move close to its constraint boundary.

The agent at node 3 then requested node 4 to go back to

its previous state and the whole thing would cycle through.

Hysteresis can be added to the behavior of the agents to correct

for hunting, but this is not ideal.

Fig.5B shows the result of the second test. The sensitivity

was calculated with full knowledge of the network impedance

to the root node. This result is much improved compared to

the first test, showing less of a dip under constraints and also

no hunting occurs. This is because of the agent’s heightened

understanding of the network, it could make more sensible

calculations on the resulting voltage from its actions. However

there was a small over shoot. This over shoot can be removed

by improving the algorithm further by introducing a sensitivity

based on adaptation.

When the upstream nodal voltage changes are added to the

solution (Fig.4C) it becomes even more finely tuned removing

the overshoot. What can be concluded is that the agent

needs to know some information about the network topology

and its previous actions, if the network is unchanging then

approximation (11) is probably just as viable as approximation

(12), however an unchanging network is hardly ever the case.

Therefore if approximation (12) is used in the future it will be

made to adapt to changes in the network. Also the information

it receives from upstream nodes will be tuned over time to addeven more accuracy to the prediction of resultant voltages. For

completeness the third approximation was tested against other

scenarios (tests D-E).

Fig.5D shows a scenario where the generator at the end

of the line is the cheapest. At t=20s there is an increase in

load at node 2, which is solved by the cheapest generator. At

t=40s there is a decrease in load and the system thus returns

to its previous state. At t=60s load increase at node 3, node

4 solves this problem. At t=80s the load decreases and the

system returns to normal.

Fig.5E shows a scenario where the generator at node 2 is

the cheapest. At t=20s there is an increase in load at node 4,

which is solved by the cheapest generator. At t=40s there is a

decrease in load the system thus returns to its previous state.

At t=60s load increase at node 3, node 4 solves this problem.

At t=80s the load decreases and the system returns to normal.

Fig.5F shows a scenario where all generation costs the same.

At t=20s there is an increase in load 2, which is solved by

the generator load 3. At t=40s there is a decrease in load the

system thus returns to it previous state. At t=60 load 4 increase

at node 4 solves this problem. At t=80s the load decreases and

the system returns to normal.

VI . CONCLUSIONS

The paper described a distributed control algorithm for

distribution network voltage using a multi-agent system. Each

agent calculates, in approximate form, how changes of power

at its node affect the node voltage and at regular time intervals

makes choices on control actions using a cost-function to

determine the best action. By decentralizing the control, single

point failures may be eliminated. The approximations inherent

in estimating the voltage change are corrected over time asfurther decisions are made. A test system using a real-time

network simulation and Java implementation of the agents

was used to test the effectiveness of the proposal on a simple

test network. Three different approximations for node voltage

sensitivity were tested in which more accurate approximations

could be formed but at the expense of requiring more infor-

mation to propagate from node to node. The results show that

two out of the three approximations can achieve stable results

for changes in load and generation in the network.

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