<PAGE>
 
                                                                     EXHIBIT 10B

PERFORMANCE SHARE PLAN
PERFORMANCE SHARE AWARD AGREEMENT

  You have been selected to be a Participant in the Providence Energy
Corporation Performance Share Plan (the "Plan"), as specified below

  PARTICIPANT:   James DeMetro

  TARGET NUMBER OF PERFORMANCE SHARES:  5,500

  END OF PERFORMANCE PERIOD: September 30, 2001

  PERFORMANCE MEASUREMENT GOALS:

     TARGET RELATIVE INCREASE IN TOTAL

     SHAREHOLDER RETURN VERSUS PEER GROUP              3rd Quintile
                                          -----------------------------------
 
     TARGET PRICE PER SHARE:              $28.00
                             ---------------------------------------------------

  THIS AGREEMENT is dated as of January 1, 1999, and, upon execution, shall be
effective as of October 1, 1998.  This Agreement represents the grant of
Performance Shares by Providence Energy Corporation, a Rhode Island corporation
(the "Company"), to the Participant named above, pursuant to the provisions of
the Plan.

  The Plan provides a complete description of the terms and conditions governing
the Performance Shares. If there is any inconsistency between the terms of this
Agreement and the terms of the Plan, the Plan's terms shall completely supersede
and replace the conflicting terms of this Agreement. All capitalized terms shall
have the meanings ascribed to them in the Plan, unless specifically set forth
otherwise herein. The parties hereto agree as follows:

   1.  PERFORMANCE PERIOD. The Performance Period commences on October 1, 1998,
and ends on September 30, 2001.

   2.  VALUE OF PERFORMANCE SHARES. Each Performance Share shall have an initial
value equal to the Fair Market Value of a Share on October 1, 1998. Each
Performance Share shall have a final value for purposes of determining the final
payment under this Agreement equal to the Fair Market Value of a Share on
September 30, 2001.

   3.  GRANT OF PERFORMANCE SHARES. Subject to the terms of the Plan, you are
hereby granted the targeted number of Performance Shares set forth above.

   4.  EARNING OF PERFORMANCE SHARES. Subject to the terms of the Plan, after
the applicable Performance Period has ended, you shall be entitled to receive
payout on the number and value of Performance Shares earned over the Performance
Period, to be determined as a function of the extent to which the Performance
Goals established in Section 6 have been achieved, subject to the threshold
performance requirement.
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  5.   PERFORMANCE MEASURES. The performance measures to be used for purposes of
determining the number of Performance Shares earned at the end of the
Performance Period shall be Relative Increase in Total Shareholder Return versus
Peer Group (using the E.D. Jones Distribution Peer Group as existing on the last
day of the Performance Period) ("Relative TSR"), and Share Price.

  6.   PERFORMANCE GOALS. At the end of the Performance Period, the number of
Performance Shares earned shall be based on both Relative TSR and Share Price,
subject to the threshold performance requirement set forth in Section 7. The
Relative TSR Performance Goals shall be as follows:

       ================================================================
          RELATIVE TSR                     PERCENT OF TARGET 
          PERFORMANCE                     AWARD SHARES EARNED
       ----------------------------------------------------------------
 
          Top Quintile                            150%
 
          2nd Quintile                            125%
 
          3rd Quintile                            100%
 
          4th Quintile                             50%
 
         Bottom Quintile                            0%
       ----------------------------------------------------------------

                                        
 The Share Price Performance Goals shall be as follows:


       ================================================================
             SHARE PRICE                     PERCENT OF TARGET 
                                            AWARD SHARES EARNED
       ----------------------------------------------------------------
 
                $28                                100%
  
                $26                                 50%
       ----------------------------------------------------------------

                                        
   7.  DETERMINATION OF PERFORMANCE SHARES EARNED. At the end of the Performance
Period, the Committee shall first determine the Company's percent of target
Performance Shares earned for the Performance Period based on each of the
Company's Relative TSR and Share Price Performance Goals set forth in Section 6.
Subject to the threshold performance requirement set forth in the following
paragraph, you shall earn the greater of (i) the percent of target Performance
Shares earned under the Relative TSR Performance Goal; or (ii) the percent of
target Performance Shares earned under the Share Price Performance Goal.

  Any payout of Performance Shares for a Performance Period shall be contingent
on the Company achieving a minimum average annual Total Shareholder Return over
the Performance 
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Period of the total annual return provided on 30-year United States Treasury
Notes over the Performance Period (the "Minimum Return"). In the event that the
Minimum Return is not achieved for the Performance Period, the percent of target
Performance Shares earned for the Performance Period shall be zero.

  8.   FORM AND TIMING OF PAYMENT OF PERFORMANCE SHARES. Subject to the terms of
the Plan, payment of earned Performance Shares shall be made fifty percent (50%)
in cash and fifty percent (50%) in Shares following the close of the applicable
Performance Period. Subject to the terms of the Plan, the Committee shall pay
out the earned Performance Shares within ninety (90) days of the close of the
applicable Performance Period.

  9.   NO ENTITLEMENT TO DIVIDENDS. This Award does not entitle you to receive
any dividend payments with respect to any dividends that may be paid on the
Shares during the Performance Period.

  10.  TERMINATION OF EMPLOYMENT DUE TO DEATH, DISABILITY, OR RETIREMENT. In the
event your employment is terminated by reason of death, Disability, or
Retirement during a Performance Period, you shall receive a payout of the
Performance Shares which is prorated, as specified by the Committee in its
discretion. Payment of earned Performance Shares, if any, shall be made at a
time at which payment would have been made had you remained in the employ of the
Company.

  11.  TERMINATION OF EMPLOYMENT FOR OTHER REASONS. In the event that your
employment terminates for any reason other than those reasons set forth in
Section 10 herein, all Performance Shares shall be forfeited.

  12.  NONTRANSFERABILITY. Performance Shares may not be sold, transferred,
pledged, assigned, or otherwise alienated or hypothecated, other than by will or
by the laws of descent and distribution.

  13.  TAX WITHHOLDING. The Company shall have the power and the right to deduct
or withhold, or require you or your beneficiary to remit to the Company, an
amount sufficient to satisfy federal, state, and local taxes, domestic or
foreign, required by law or regulation to be withheld with respect to any
taxable event arising as a result of this Agreement.

  14.  ADMINISTRATION. This Agreement and your rights hereunder are subject to
all the terms and conditions of the Plan, as the same may be amended from time
to time, as well as to such rules and regulations as the Committee may adopt for
administration of the Plan. It is expressly understood that the Committee is
authorized to administer, construe, and make all determinations necessary or
appropriate to the administration of the Plan and this Agreement, all of which
shall be binding upon you. Any inconsistency between the Agreement and the Plan
shall be resolved in favor of the Plan.
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 15.   MISCELLANEOUS.

       (a) This Agreement shall not confer upon you any right to continuation of
employment by the Company, nor shall this Agreement interfere in any way with
the Company's right to terminate your employment at any time.

       (b) With the approval of the Board, the Committee may terminate, amend,
or modify the Plan; provided, however, that no such termination, amendment, or
modification of the Plan may in any way adversely affect your rights under this
Agreement.

       (c) This Agreement shall be subject to all applicable laws, rules, and
regulations, and to such approvals by any governmental agencies or national
securities exchanges as may be required.

       (d) To the extent not preempted by federal law, this Agreement shall be
governed by, and construed in accordance with the laws of the State of Rhode
Island.

  IN WITNESS WHEREOF, the parties have caused this Agreement to be executed on,
and become effective as of, the dates set forth on page 1.

                                         Providence Energy Corporation



                                         By:  /s/ James H. Dodge
                                             -----------------------------

                                         Its:  President
                                              ----------------------------

                                          /s/ James DeMetro
                                         ---------------------------------
                                         Participant